• Conflict
• Virtuosity
• Strength
• All Is Right
• The Magical
• Being Free
• The Strange and Beautiful
• Alone and Accompanied
• To The Extent
• Fantastic and Rational
• Possibility from Impossibility
• A View on Existence
• Contradiction as Distinction
• Taking Together
• Underneath Not
• Choice, Self and the External World
• Context as Community
• Doing Yet Discovering
• Coercion
• Reality as Naming
• An Experiment in Distinction
• A Thing Can Be Multiple Things

“Not.”

A single concept that creates multiplicity.

From “Not,” through its distinguishing opposites, its introduction of duality, springs “All that is”—“Everything” in all its multiplicity.

It also introduces contradiction.  From “Everything” and “Not” comes “That which is not,” the opposing border of “Everything”.  A contradiction to be sure, for if “That which is not” is not “Everything”, it is itself a distinct thing and therefore to be counted among “Everything”.  We must accept this contradiction if we wish to conceive, distinguish, recognize, acknowledge our existence.  Contradiction is, in fact, the very stuff of all our discernment in life, for if a thing has parts their existence surely contradicts the unicity of the whole.  In fact, it may be the single most useful tool in carrying out that conception, that search for understanding.

Laozi used it to justify a Way or Path that is intended to deal with one other manifestation of contradiction: conflict.  It is a powerful idea.  By removing desire we implicitly remove the undesirable.  We become instantly powerful, inexhaustible.  The unattainable doesn't exist.

But in fact the idea does not solve all our problems as we are something, and not whatever we aren't, and therefore smack in the middle of conflict anyway.  We cannot remove our desire for nourishment, rest or love.  The ideal, like the ultimate contradiction, must realistically be defined recognizing the ideal isn't attainable.  Surely the Path cannot be spoken of, but we can look at this contradiction in the small, and see if it applies here within the multiplicity of things in our reality.

I desire to be able to travel from my house to the park instantly.  I desire this because after carrying out enriching activities at home, I wish to carry out enriching activities at the park and the activity of walking to the park isn't particularly enriching.  But I do distinguish activities at the park from activities at home, so I do desire to maintain the duality in the functions of the home and park.  So is the unobtainable nature of this desire of my own making?  In a sense I desire my own conflict in that I want a barrier between home and the park, yet I must now navigate my own barrier to appreciate it.

Can we come to terms with our own definitions and experience more proportionately degrees of dissatisfaction and enrichment, thereby removing disproportionate conflict?  Why not?  In fact this act provides understanding, while embracing the contradiction!  However, we will apply some of that proportion here, and say let's not be surprised when this path we seek will by definition have a barrier between us and it.  It is lesson one that the perfect way cannot be known.  But at least we accept it now.

If you identify yourself with the universe—become one with the universe—its actions become yours.  This inspires some degree of awe in the power thus conferred.  The power of the fifty-foot oak is mine.  The power of the hurricane is mine.  The power of the furnace of the Sun is mine.

As with the power of duality, its extent is limited by its own definition, so I cannot raise a hurricane at will as I can my right hand.  But the power can be tapped.  It is by allying yourself with the events, characteristics, effects, “Way” of the universe.  One might question how much power is received by merely allying yourself with a thing.  It can be seen to have various answers:

• All.  By being one with a thing, you are that thing.  Your power is all the power of the thing.  Your desires identical to the thing.
• Some.  As with any identifiable thing, its definition comes with some barriers that delineate what that thing is not.  So with the strength of the oak comes the limitation of immobility.
• None.  In allying yourself completely to a thing, you give up whatever nature of yourself that was once there, so you—that which is not the thing—do not possess any power at all, the thing possesses it all.

The three answers identify aspects of duality the tool.

• “All” comes from lack of distinction, thereby identifying the whole, or the mysterious, unknown source from which it comes.
• “Some” comes from distinguishing parts—identifying and naming.
• “None” is the complement of “All” and the recognition of the allied thing's characteristic of being really an effect of some other thing—being a distinction in some other context which, if at all, wields any power present.

To effect the correct proportion in the conflict in your life recognize it is all by definition.  Take your frustration over those things you have struggled fruitlessly to master only to find them master you, recognize that just as they flipped the coin from being “None” in your context to being “All” with you in their context, and apply your experience to flipping the coin on the context to which you belong.  Recognize the contradiction in it: you must yield control to be in control.  Recognize this isn't a mystery designed to woo you into complacency, but a genuine contradiction.  An impossibility.  Life is an impossibility and yet it exists.  There is no reason, choice or hope, and knowing that you have no control anyway, take that there is no answer why, stop and ask: why not?

Virtuosity.  It is the real object of any introspection.  We seek grace, comprehension and effect.

Effect and virtuosity are here taken to mean the same thing.  We want to be effective, and to have an effect, a direct operative effect on our world.  As Paganini was a virtuoso of the violin—he had great effect with his instrument—so would we like to be virtuosos of our lives.  To Laozi the virtuoso of life was the sage.  Just as “virtue” has taken on too lofty of connotations for us to use in place of “effect”, so has the word “sage”, so we will use “virtuoso”, or simply “a person with great effect”.

What are some ways we can effect our virtuosity?  Let us recap our understanding of the origin of things:

1. The unidentified mysterious whole is that in which things are part and which is, of course, unknown to any things part of it.
2. Through distinctions, that is naming or identification, multiplicity and the character of our lives is born.  The simplest of these distinctions, “Not”, or “that which is not ___”, is present in every distinction.  So it is with simple comprehension that a whole is shown to be divided.
3. It would appear much of the substance of our lives is entirely of our own conceptual creation, though there is some mysterious source from which we emerge and, while not perfectly knowable, is evidenced by those distinctions we cannot simply conceptualize away like desire for rest, nourishment and love.
4. It is our thesis that contradiction itself is the essence of distinction.  Distinction demonstrates the separateness of some thing that presumably is not separate, hence the need for demonstration.  Some might say that in this sense the distinction is not contradictory, but the thesis is that in fact contradiction itself is not contradictory.

It is important to note here that we are really talking about the most unyielding problems in our lives, and those which we can address through our understanding.  There is of course a degree of more traditional virtuosity a person can obtain to remove some conflict from his or her life—say by learning better grass caretaking techniques!  But we assume those alternatives have been exhausted before the approaches outlined here are attempted.

Resolving conflict is great.  But, while one might be tempted to think all enhancements to our effectiveness might be phrased in terms of resolution of conflict—finding solutions implies the resolution of problems, one might assume—but to all things correspond those things which they are not, and therefore, not all things are aspects of conflict.  How can we become stronger, better, faster in ways other than resolving conflict?

Simplification.

It is one thing to juggle a problem and hate doing it, it's another to suddenly realize one was contentedly, unwittingly juggling an unnecessary problem and to suddenly find the freedom of not having to.  By simplifying our lives we free ourselves to focus and be more effective in what remains.  As we look back at our four points we see immediately where the most basic and effective means of simplification is going to come from: erasing of distinction.  Going backward from a separated multiplicity to the whole source.

An obvious example of simplification is recognizing when you are digesting irrelevant information.  The information is just more distinction of a whole whose parts are never going to have any impact on what you are using it for.  When you ask for directions and the person you ask fills you in on the history of the landmarks along the way, you may be inclined to politely nod in interest, but you will do yourself a favor if, as the directions become complicated, you focus less on remembering the history and more on the landmarks.  This is hardly a surprising piece of advice.  What is interesting is that this very commonsense idea is an example of the traditionally “lofty” goal of becoming one with the universe and leaving duality behind.

A more useful example brings us back to the topic of conflict.  Not our own this time, rather the conflict of others.  Given our new proportion in handling conflict by design—that is conflict we create by our own definitions—we are now in a position to filter out irrelevancies in the machinations of those around us.  Where another person is caught up in the details of a conflict that is completely unavoidable, and therefore hardly worth protest from our point of view, we can step back an only invest as much excitement in the situation as is necessary, even while we may not be able to convince our friend of the same possibility.  And if we can help our friend out, we may just simplify our own lives even more.

A profound example of simplification is recognizing that distinction always includes the essence of “Not” or “Complement” and that an object and its complement are identical in all ways except their opposition to each other.  Sound tautological?  Perhaps paradoxical?  Let us look at this in a couple other ways.

Certainly one has to agree a thing and its opposite are equal in complexity.  That they have a predictable relationship.  When we look at the complex of reality sprawling out before us, we can be aided in recognizing where the contours in definition lie.  Where two phenomena are simply the opposing implications of a distinction in a larger whole.  So with the protection of a locked door comes the possibility of being locked out.  So with the existence of wealth comes the existence of poverty.  So with the existence of good comes bad.  So with every move of some object from one position of one advantage to another with a different advantage comes a change in the disadvantages of the that same object.  When seen as simplification, duality takes the form of a conservation principle, similar to, and perhaps a generalization of, the principle of the conservation of energy.  A certain calm can be afforded an individual who, though still accountable for strategic and tactical details, knows not so much has changed on the playing field of life as may at first appear on each passing event.

Perhaps most profound of all in the simplification of understanding accorded by duality the conservation principle, is that the world is what we are not.  You are you and the rest is what you are not.  That means the world is no more and no less complicated than you.  The world has a predictable relationship to you.  This most drastic of realizations might seem to afford the most drastic sources of virtuosity.

Perhaps.  But then with every change in our lives, including our effect, comes the complementary implications of that change, perhaps preventing as much from changing as one might expect.  But in some sense, you already are the ultimate virtuoso, since reality is defined in exact corresponding response to you.

Strength—we desire it.  It enhances our virtuosity.  It enables us to achieve other of our desires, or fend off other impositions on us.  It really isn't possible not to want it, for even if all we seek is peace and tranquility, we still seek to impose a condition on our environment.  When we seek the most humble and sharing of strengths or even seek not to seek at all, we still seek advantage in our particular goals.  Recognizing its inevitability, we unabashedly begin our quest for greater strength.

Here we explore an approach to attaining strength that takes advantage of our understanding of life as born from distinction.  First we take a moment to define strength and identify a few of its characteristics.

While there are many concrete definitions of strength, we will use the most basic and abstract definition.  This will make our investigation easier and yield the most universal and extensive of results.  Strength generally refers to a degree of effectiveness controlling the environment, and the essence of control is choice, so we will here take strength to mean access to options—to having choice.

Strength as choice, looked at through the duality lens, points us directly to several other definitions: weakness and exertion.  The opposite of choice is limitation, that which is already chosen.  So the opposite of strength, weakness, is limitation.  And if an unmade choice is a strength and an option already chosen is a limitation, then the act of choosing is exertion.  As a brief demonstration that even the more concrete examples of strength boil down to choice, take the weightlifter.  The weightlifter certainly has the option of moving large masses off the ground, while most of us have no such choice.  And exertion limits even the strongest weightlifter's choices in this same regard.

We will not be surprised that duality has imbued all choice with limitation.  As was already pointed out, making a choice clearly removes the degree of freedom held when the option was still available.  And though we hope a good choice will introduce more options, having any, let alone more options comes at a price.  Keeping options entails not exercising them, and both the maintenance of their availability, say working out to keep our biceps steely, and the restraint from exercising them, say saving our energy before the big competition, are limitations on our lifestyle.  In the case of the seeker of tranquility, it is likely that the only tranquility in store for the seeker is contingent on a bit of strife.  If tranquility could really be guaranteed to remain uncontested, its incontestability would certainly appear tyrannical from any context in which peace and tranquility was not previously at issue, and some objection would be expected.  In general, the maintenance of an option is itself a limitation.  And so we again find ourselves seeking proportion, this time in the strength we acquire.  With this understanding in mind, let us get on to the business of acquisition.

To the extent we wish to increase our strength—enhance our effect—we first recognize the only options we seek are ones we as of yet do not have.  Not having them appears as a limitation imposed on us.  In Conflict it was recommended that when confronted with lack of choice we turn the tables on that which imposes on us.  Do we have this choice?  In Virtuosity we said “we” are what we are and “the world” is everything else—that we and our reality are opposites, mirror images in one-to-one correspondence.  So, with the usual contradiction attendant, it would seem we do have the choice.  By changing ourselves the mirror image that is our world will change in correspondence.  Change us, we change it.  Change it, we may change its impositions on us, finding we have choice over our seeming lack of choice after all.

The interesting thing here is that in turning the tables on the world and its imposition on us, the fact that the world is our opposite turns out to require that we give up our strengths to remove its strength in limiting us.  In this paragraph we will detail how that happens.  We wish to transcend a contradiction.  In wishing to increase our strength we wish to end weakness.  In other words, we wish to have a choice over not having a choice.  Let's not argue over weather this is possible, but observe that to the extent we can accomplish this, i.e. do have the choice to end this imposition, the limitation must be of our own creation.  If we have any influence, the limitation must not actually be externally imposed, but rather the result of a choice of our own.  This gives us some power on a case by case basis—we may be able to identify the offending choice, and change it.  But more importantly, it tells us that the seemingly contradictory advice of gaining strength by relinquishing it actually makes sense.  The world is defined in terms of ourselves, including our choices, and when we relinquish our options we relinquish their restraint.  Now all that remains are those choices we do not have the option of relinquishing, the existence of which is in clear evidence around us.  A person caught in the midst of a natural disaster certainly cannot reach safety simply by changing his or her choices.  Some limitations certainly seem inevitable, as is exemplified in the paradox that the freedom obtained by relinquishing options and their attendant limitations must have its own set of limitations.

Every once in a while our observations are eerily contradictory.  But every now and again they make an eery amount of sense, as does this one.  Relinquishing options enhances our inexhaustibility.  We wish to maintain strength, so a good approach would be to do away with exertion, or in other words, attain inexhaustibility.  The trick here is to do this in a non-defeatist way.  Sure, if I give up all desire, I will never fail to fulfill my desires, but there are no new options presented in this situation.  We need to relinquish unnecessary desires.  We need to save our energy.  We need to put ourselves in a position where our decisions do not all require sacrifice.  We need to stop working from positions of disadvantage.  If that means giving up some strengths already achieved, so be it.  We should look for ways to give up things that are a struggle to maintain.  Not just anything of course.  If you are in the midst of a natural disaster, hang on until you can afford to give up your struggle.  The point is, a strength that is overly laden with limitations is not such a great strength, and giving it up with a reasonable plan for achieving strength in its place is actually not so tough to do.  And this is exactly what our understanding of strength has given us: the strength to trade what we previously clung to for a greater strength.

Our understanding places new value on our existing strengths and limitations as well as potential ones.  Revaluing the options in our lives opens new doors when we recognize the dual benefits of what we once considered weaknesses, and the dual weaknesses in strengths we once desired.  Working from a position of calm, of lack of conflict, of sufficient time, of sufficient authority, all have such great benefits that coming to accept what we once considered more meager circumstances will be worthwhile when our new strengths, and possibly, access to new heights of accomplishment are seen to be afforded us by being able to act and choose without conflict.  This revaluation shows us not just how struggle-laden strengths are less valuable than we thought, but shows us how much can be achieved with very little effort.

By doing the easy, and recognizing the reach of the easy is just as far as the reach of the difficult, we are really enhancing our strength.  It might not appear so because the allegedly weaker person next to us has the option of using the easy too.  But we truly are stronger because our neighbor has many more options to maintain and this cannot be done with easy maneuvers only so these easy maneuvers really aren't options of his.  He doesn't share our strength.  Unless we want to tip him off, which quite possibly could enhance our own strength too.

All is right—or all is good.  In order to see how all is good we will first see how all that is not good is not so bad after all.  Understanding this is essentially understanding that contradictions can be true.  Just parsing our second sentence we see solving the problem of all things not being good by recognizing all things are good is itself overcoming a contradiction.  Exploring this tricky territory is worth our while because seeing all things as good puts us in a place where just as we'd have it is just as it is.  Here no conflict is too great and our virtuosity in achieving good things is uncontested.  Here all is right.

By “right” we here mean “okay”, “intended”, or “acceptable”.  Since we are going to be reasoning in support of our conclusion about right and wrong with some discussion of true and false, something easily confused with right and wrong, we will also use “good” and “bad” to avoid confusion.  We work with contradiction as it is only realistic to do so.  One reason it is the realistic way is that things we take to be wrong appear as contradictions, impossibilities bringing out our ire that they are allowed to exist, or else things that contradict our own belief of what is right.  A second reason is simply that any real solution to this problem is begging to be disproved unless we leave things in a stasis in which bad still exists.  By virtue of our being something in particular, we are implicitly and unavoidably in conflict with all that is in contradiction to ourselves.  So, weather we like it or not, all is not good.  That we can experience it to be right, allowing the contradiction of simultaneous good and bad, can be motivated by the simple observation of where we already possess this talent in our lives, where we engage in desirable conflict.

Sometimes we work hard, grimacing and groaning as we struggle to complete and perfect our work, then finish to find ourselves very gratified.  We aren't just gratified that we don't have to work anymore.  Quite to the contrary, we're gratified at having accomplished what we did, and in fact would have grimaced and groaned much more strongly if we had been interrupted or prevented from finishing.  This suggests the way in which all can be good.  Here we have grimacing which we'd have no other way.  When a performer emotes strife, it is still a good experience for the performer.  This is good stress, good conflict.  This is not imposition in opposition to our own choices, it is the stress of a fully proportionate conflict.  This is recognizing the function of conflict in our lives.  To make this a more pervasive response to the bad in our lives, let us take a closer look at the basic mechanism behind “wrong”: contradiction.

The problematic kind of contradiction is the paradoxical kind that we will call actual contradiction.  An actual contradiction is one that isn't simply a hypothesis, but is present and true.  The existence of actual contradiction is itself contradictory but unavoidable as is evidenced by the famous Liar's Paradox “I am lying”—or more simply “this statement is false”.  Consideration of the phrase forces us to conclude either it or its opposite is actual.  There is a way to come to an understanding of actual contradiction looking at its nearby relatives, posited contradiction and seeming contradiction.  Posited contradiction is simply statement of impossible conditions—“the box is full and the box is empty,” is a statement that can clearly never be true, but is harmless enough because it is only posited, or considered.  Seeming contradiction is statement of counterintuitive conditions—“the fastest way to finish is to work slowly”.  A seeming contradiction can be true because there is no real contradiction in it, rather it is merely confusingly similar to the other forms of contradiction.  So for some tasks one makes fewer mistakes when working slowly, hence finishing the job more quickly.  However, can a posited contradiction ever be actual?  Only true things can be actual, and all false things can only ever be posited, so no, of course not.  But in a world where the positing of a phrase implies the actuality of an impossibility—a world containing the Liar's Paradox—the simultaneous answer, yes absolutely, should come as no surprise.

Let us just recap the inevitability of facing up to this issue.  There is a certain infinite regress in the Liar's Paradox.  Even when only positing it, it implies that some contradiction must be actual because:

1. consideration of the phrase forces us to ask if it could ever be true, something that itself can only be A) true or B) false, and
2. whichever the case, a contradiction must be actual, because if A) then a contradiction is actual because a person can make a contradictory statement truthfully, but if B) a person can never make this statement truthfully and so upon interpretation a person can only ever not be lying when making the statement, and again we have an actual contradiction.

Now to the contradictions that we do not experience as simple distinctions in our perception.  What about those things around us that are just plain wrong.  They should not be, and it is just unbelievably annoying that they are.  This annoyance is a definite liability in our lives.  While it may be a defense mechanism, it frequently persists when all our efforts fail, and it sometimes creates further annoyance of its own.  The obvious way to remove it without leaving ourselves defenseless is to remove our distinction of what is wrong—but keep it too.  We remember it is possible to feel conflict in a way that is proportionate, and in some sense, not wrong at all.

How can what is wrong be right?  Well, in the final context how can anything be wrong at all?  Everything is what it is.  If things are whatever is implied by the distinction that defines them, how can they be any more wrong than that which exists in distinction with them?  If all things are distinctions in the ultimate undistinguished thing we call (contradictorily) “Everything”, no thing can be any more wrong than “Everything” itself.  We see this idea in everyday life as “we are the products of our environment”.  This doesn't let us off the hook for navigating right and wrong—as we said, wrong is inevitably with us—but now we can see it in context.  Nothing is necessarily wrong in all contexts, or, there is always a context in which a thing is not wrong.  So the choice of perspective “All is right” is ours to be had.  Finding it in any one circumstance is a matter of identifying the way the impossibility in each wrong, each actual contradiction, is a matter of context.

Take those things we find wrong in ourselves.  There is a contradiction here to be navigated: how can something about ourselves be against our own concept of right?  It is us after all.  The really obvious contradiction is wanting to do something we wish we did not want to do.  If we examine both sides of the contradiction we will see why we want it, why we don't, and that any of the wrong we experience just by being in conflict can be completely set aside.  So we do not need to feel bad about ourselves that we have this contradiction, contradiction is completely normal.  At the same time the tendencies we see are also just natural extensions of our own state.  If we accept these wrongs as right, we can continue to feel them, while maintaining composure in searching for ways to remove them, possibly being more successful in that endeavor consequently.  If it is something about ourselves we dislike, rather than not “want” specifically—we do not like some physical attribute of ourselves—we still need to remember, what “we” want is about “us”, and that “us” is the person with those attributes.  Think of the consequences of success.  Becoming something we aren't is just going to give us a different set of contradictions.  Perhaps even considering this we still would consider other attributes better, but at minimum we still can consider our attributes and our opinion of those attributes as right, and not something to impede our other activities.

Tougher wrongs are to be found in those things outside ourselves.  Perhaps we have a task of accomplishing an impossible goal.  If we can get to the understanding where this impossible goal is in fact possible, certainly our problem is solved.  This goes directly to our example about choices where we needed to see the situation differently, at which time we didn't accomplish the impossible, but didn't have to anymore either.  In everyday life we might call this thinking outside the box.  We also have the benefit, without even transcending the situation by “thinking outside the box” that by accepting our task or opponent as possible or right we won't be looking for the impossible method or considering doing what we consider wrong.  We will only be looking for new dynamics which remove the conflict when it is viewed from the perspective in which it is contradictory—which is not all the time.  This, at minimum, lifts a weight enhancing our inexhaustibility.  Perhaps believing the objectionable tendency of another to be right itself just doesn't seem right.  Accepting that behavior is possibly not in us.  We can accept that and still see the transition of context between ourselves and the other.  Looked at practically we will be able, without conflict, to interact with the alternatives and recast the situation to one which both of us consider right—we will not be imposing something against that person's choices and yet will be obtaining a desired result.

Take even the toughest situation.  Someone or something is utterly destroying your world.  Certainly taking this lying down is not the thing to do, but if you really have no choice over this, your world is already destroyed.  Put the frustration aside on at least one level so you can continue to operate.  Do not accept the inevitable, it is right that you are in conflict with this particular person or thing—go ahead and be in conflict.  But feel it proportionately.  Let go of what you do not have and move forward with what you can create.  Will you be successful?  We can't say, but regardless of the situation, you will be composed, and you will possess virtuosity.

Is magic real?  Being defined as the supernatural, it clearly is not natural, and so no, it is not real.  But with contradictions present in so many very real distinctions in our lives, we might expect the magical to be present in a very real sense.  Reading here before this exposition is complete, we might expect several outcomes.  In one outcome we find below a claim to real magic—yes, a person can predict the future, move an object by force of will, make things disappear with just a thought.  In another outcome we find below a claim that the beauty of a sunset is magic enough.  In the former, new opportunities are open to us because what was previously impossible now comes under consideration as possible.  In the latter the familiar objects of our lives are recast in a light that qualifies them as magic.  The former is exciting until the lack of impossibility of our new powers deflates their excitement back to the ordinary.  The latter is disappointingly already ordinary until in the course of our lives we experience a sublime moment in which a very real and possible thing strikes us as undeniably magical.  In fact we will assert both and look for proportion in the ordinary and sublime.

Correspondence will provide us our answers.  As we observed in Virtuosity, we can gain virtuosity, effect in our world, by recognizing the implication that opposites are in direct and predictable correspondence to each other.  Distinction being the recognition of where one thing is not another, we can take all implication and consequence to be exactly the prediction correspondence enables.  Here we will explore the implications of our conception of the possible.  When we ask what are the implications of an ordinary or magical act and find that they coincide we may see where the magic is real.

Witnessing this is the easiest of them all, because we all do it all the time.  If we couldn't predict the future we could hardly expect to walk for lack of knowledge as to where the ground will be when our foot falls next.  The examples are endless and increasing in impressiveness: predicting the trajectory of a ball with basic physics, predicting the arrival of a train with a schedule, predicting the actions of a familiar person, predicting our own course in life.  As to the fantastic kinds of prediction—predicting the time of our greatest crisis so that we may avoid it—are they real?  Well, who is to say they aren't?  Or rather, is it really relevant?  In the short term, simply looking both ways as we cross the street can be seen to save our lives on a regular basis.  In the long term circling in of tragedy, if one did predict as a child something precarious in his or her future, certainly that foreknowledge would have changed that person's behavior turning a grave prediction in to something that ultimately turned out to be just plain wrong.  How often do we have concern about future events that never come to pass?  They may just as well have been true predictions that we made the most of.

The same sort of reasoning applies to other forms of the magical.  If I concentrate hard enough can I move the sugar jar in front of me?  Funnily enough, modern physics actually allows for the possibility of just about anything.  There is a non-zero probability of even the wildest of events.  Therefore there is a non-zero probability that every time the sugar levitates it is immediately following my concentration on doing exactly that.  But that's really not what we're talking about here.  What we are saying is certain everyday powers, available to us all to create with high probability, correspond to the magical.  Do we expect that these powers be unexplained?  No, if we could really levitate on demand we would recognize a new real force and define it as exactly that which results from our concentration on levitation.  Further, if we had control over the motion of an object with mere thought wouldn't we simply classify that as muscular impulse—that the object we move is an extension of ourselves?  Coincidentally, we do have the power of will over matter.  We move our bodies at will, lifting our arms to take the sugar.  We exercise our vocal cords at will and ask our table guests to pass the sugar.  Our understanding and manipulation of our environment is that force.

Of course we can make some things disappear.  We can make our chosen distinctions disappear.  Can we make something more substantive disappear?  In Conflict we implied that the park is really only a distinct physical thing exactly because we distinguish specific function in it as opposed to other places in our lives.  Can we make the park disappear?  Aside from the possibility we've left open in all our discussions that we do not have final say over all the distinctions in our lives, and therefore possibly not over the park, a more compelling reason for our not commonly being able to make the park disappear is that it functions for a lot more than strolling and relaxing.  If the park really did become completely irrelevant, one certainly might question whether it exists at all.  But other of our distinctions ensure its relevance, for example through its function for people directly or indirectly in our lives and therefore for us.  And along the lines of reasoning we applied on prediction, who is to say the changes in our physical lives are not in fact application of our prestidigitatorial skill?  When I move my arm, am I making it disappear from one spot and making it reappear in another?  In fact, if the world is that which I am not, when I simply move from one room to another, which party changed, the room or me?

Perhaps this example lacks the truly exciting sense of magic.  When I move my arm or the entire Earth below my feet they do not reappear in completely unrelated places.  Can we say though that the fact that they only move in such predictable ways is exactly what characterizes them as physical things?  The supposedly non-physical things such as ownership or destination certainly change in the apparently unconnected ways that the location of a rabbit does in a magician's act.  When people transfer ownership on the condition of the roll of a pair of dice, that recognizable thing, ownership, does change hands in an essentially unpredictable way.  Does choice of destination, whether a favorite place for recreation or immediate stop for supplies, qualify as a thing that I can move to disparate places?  If a physical thing such as mass is recognized by the force it exerts, when I change my choices thereby changing where my strength lies, does the disparate object of the force of my strength indicate a disparate change in a physical thing?

We can hardly expect to identify in words what it is to be beautiful or sublime, but when it feels magical some part of it is putting us face to face with impossibility.  When we see come into existence as if from nowhere something that has great meaning to us it should not come as a surprise that we experience at least a bit of shock if not an actual moment of sublimity.  When what was once an ordinary collection of clouds, sun and horizon becomes something new, a sunset containing within it its own patterns and interrelations, we see the appearance of something that wasn't there, yet was all along.  It was there in its parts but became recognizable as beautiful in some paradoxical moment.

Maybe all beauty is magical.  When a person says something beautiful, are they simply making possible for you something that was not possible before, showing you a distinction you didn't realize you were capable of drawing?  If you weren't capable before its communication to you, perhaps you are now a new person, for the same person to have and not have a capability is a contradiction.  This still does not remove the aspect of contradiction since seeing ourselves anew has the magic of impossibility all over it.  How can we be anything other than what we are, yet there we are, a new person.

It may as well be that magic is real as so much of our lives carries exactly the essence of magic.  Being defined as the impossible, it surely isn't real, but being in evidence before us, we may be forced simply to recognize in which context the magical is impossible and in which it becomes the real.  Recognizing magic as ordinary and at the same time actually present has freeing benefits of both dethroning the impossible and elevating our own capability.  So, though the question of whether we can become magicians for real may be obscured by the many contexts from which we must look at the question, just by recognizing the miracles we perform and participate in everyday we can make greater effect of the strength we already possess.

How strong are we?  How free?  Can we overcome the limitations on us?  One who has concluded that all can be seen as right and that by changing our understanding we can change our reality, would certainly be tempted to conclude that all limitations on us are of our own making.  This would secure for us triumph over all our conflicts, complete freedom.  It doesn't appear that we have exactly that conclusion at our fingers.  We see limitations around us everywhere, in the weather, the traffic, our captivity to our drives for nourishment, rest and love, and to a less inevitable extent, in certain efforts to improve our lives that never seem to come to fruition—getting the most money, getting the best of any thing.  Sometimes we don't even want the best, but just something in particular that remains elusive.  These obstacles may not be insurmountable regardless of whether these impositions are from outside or within ourselves because, even if there are impossibilities, we can see in them a paradox that provides the context freeing us of their limitation.

As was pointed out in Strength, that you can change your options is contradictory.  If we have the option to create a new option, then at least in some sense we had that new option all along.  It isn't a mere mistake of language creating this contradiction.  An option truly is not ours to choose if we don't realize we have it, though through the change of recognition we come to realize and therefore have the option.  Taking the contradiction as actual, and indicative of multiple contexts, rather than change as actual and the contradiction a mere mistaken identification of states before and after a change, we simplify our understanding of our lives.  It also shows us a way to recast our limitations as not limiting, and therefore as contradictions that point to a wider context free of those limitations.  Below we will first explain how contradiction can function without creating meaninglessness, and then look at the implications that has on our ability to achieve what we want.

Why should we take contradiction to exist, allowing language to state and us to conceive paradoxes, rather than take them as misnomers, mistaken identification of distinct things?  One compelling reason is that we can reason with contexts to disambiguate contradictions, but we can't remove contradictions from language.  As was pointed out in All Is Right, the Liar's Paradox makes contradiction unavoidable.  First, let us briefly consider why we normally cannot take contradictions to be actual.

Traditional logic and just plain common sense tells us we cannot allow contradictions to be true.  “If you are going to take something patently impossible to be true, you may as well take anything your wild imagination desires to be true, which will no doubt be great fun until the imagined facts fail to line up with reality once too often!”  In traditional logic, the discussion can be summarized as follows:

I.  If you are given two statements and told at least one of them is true,

and further told that the first statement is false,

what do you conclude?  That the second is true,

because one of the two must be and the first is not.  We can infer (c) from (a) and (b).

II.  At the same time, whenever you are given that some one statement is true,

you can take any other statement, true or not, and claim truthfully that at least one of the two is true.

We can take Statement 2 to be ‘2 + 2 = 5’, thus deducing “Statement 1 or ‘2 + 2 = 5’ is true”.  There is no problem here because we know Statement 1 is true, so yes at least one of those two statements is true even though ‘2 + 2 = 5’ clearly is not.  We can infer (e) from (d).

The problem with contradictions is that they allow us to conclude anything at all using these two methods of inference.  Suppose we have a statement, call it Paradoxical Statement, that is both true and false.  Given Paradoxical Statement is true, we first can infer “Paradoxical Statement or ‘2 + 2 = 5’ is true” following method II.  Then, given “Paradoxical Statement or ‘2 + 2 = 5’ is true”, which we just proved, and that also Paradoxical Statement is false, we can infer ‘2 + 2 = 5’ following method I.  We deduced from Paradoxical Statement that ‘2 + 2 = 5’.  So from any contradiction we can conclude two plus two equals five, or anything else for that matter, true or false.

When we suggest taking contradictions as actual we aren't denying the reasoning just given.  The above analysis depicts our world as having one state described by a division into two categories, true and false.  We need the above analysis to hold true.  It provides the correspondences in the duality of our distinctions.  Where we discover a contradiction for which there is no context we would choose to resolve it with, we must conclude the statement accurately reflects a categorization of false, and is merely posited, not actual.  But it should not surprise us that not everything can be categorized by any one system.  Conceptually we are perfectly welcome to and do try.  Where the categorization fails, we must choose new categories or systems, what we have been calling contexts, to cope with the phenomena encountered.  Making that choice can be seen as change itself.  The choosing of a new context in resolving our contradictions removes the degree of freedom held when the contradiction was still actual and the option of which resolution to choose was not exercised.  This closely mirrors our experience of time where a moment in time separates two distinct states, one which is already chosen and one that still contains options.  We can affect our future states, but not our past.  Though this principle applies not only to time, but anywhere we see change.

But how can we choose our way out of the toughest of our limitations?  Let us revisit for a moment our statement that reality is born of distinction.  Even if one feels this isn't a fair analysis, it seems hard to contest that for all effective purposes this is true.  Certainly all things that are distinguishable, which include all in our reality, contain distinctions, and where no distinction has been drawn by us, the relevance of any distinction we might have made disappears, for if a thing has a discernible impact on us, it is distinguished by us.  The only question that remains, are all the distinguishable features of our lives of our own making?

The originator of a distinction chooses that distinction.  The things born of distinction, the objects distinguished, it may be thought, do not have choice over their form.  The question then presents itself, are we the distinctions of another observer?  As we mentioned earlier, there are distinctive elements of our lives that certainly seem to admit no choice by ourselves.  But if reality, the place where we are, is exactly everything that we are not, there is not room for a second observer, except possibly that mirror image of ourselves, reality itself.  If there is only ourselves, can we change that border between ourselves and everything else?  Is it arbitrarily stuck where ever it fell?  If we have no choice over it, it seems to tell of another observer, but that would tell us of our distinguishing another in our our reality—a creation of our own making choices for us.  This is one of those situations that regresses infinitely.  We know certain of our own distinctions carry limiting implications of their own, and when we do not recognize the source of one of our own limitations it is exactly as if the limitation were externally imposed.  So us or them, it doesn't really matter.  Let us here consider impositions as externally imposed, and look for ways of discovering that they in fact are not, thereby freeing ourselves from them.  In our limitation is a contradiction that gives us hope of changing it.  Contradiction is visible in the question, how can we ever be denied a choice?  If a choice is denied, it is not ours to be had, and therefore not a choice.  Let us look at how we can see a choice and its denial as an opportunity to overcome limitation.

Let's analyze this by treating this outside source as a real individual.  Let's describe the individual as an opponent in a contest with us.  Suppose our opponent has imposed on us a limitation that defeats our efforts, setting up an illusory choice that no matter what course we take, comes to the same result.  We believe we have options X and Y, and make our plans on the results of choosing X.  We expect some advantage, some leverage in our life, to ensue from that choice.  We are invested in it.  We can end our frustration and see a way of frustrating our opponent, by recognizing that individual is invested in our attempting to acquire X.  It's not difficult.  It doesn't require great discipline.  We ask ourselves, if we do not have some particular option, do we really want it?  The only “option” there is Y.  We can recognize that our option is not desirable to us in the first place, thereby changing our desire for it.  When we wish for contradictions, it's not that we can't have them, but that they either present contexts that change what we want or change us into someone with new options.

When moving to create our new options, we can take advantage of the fact that ceasing to struggle with an imposition not only frustrates our opponent's dependence on our struggle, but gives us a reverse form of leverage.  We can use that leverage not to enslave our opponent to our desires, but to inform our use of the techniques we described in All Is Right to find a solution that detaches us from our pursuer, finding a sustainable solution.  In any case, by not accepting the illusion and not making our plans on X we will at least take away our opponent's appetite for deceiving us, just as we've lost our appetite for the illusion.

Why couch our description of overcoming limitation in the language of contradiction?  Because contradictions are inevitable.  They defeat any systematic approach we may choose to take.  The complications involved in the alternate approach of finding strategies with contingencies for every turn still leave open the possibility of the completeness of our approach being contradicted.  As we pointed out in Virtuosity, there is freedom gained in the observation that to every advantage possessed by one possible future there corresponds disadvantages.  So to make ourselves dependent on particular futures which do not offer a compelling possibility of composure is not so costly to decline as we might fear, just as failing to move on an opportunity for fear of unforeseen consequences denies that we may get what we really wanted, and to the extent we did not get what we wanted, that there may be as much opportunity anyway.  So to maintain freedom over our choices, accepting the inevitability of contradiction, rather than relying on fragile and easily manipulated plans provides a much more sustainable and composed approach.

We still have not answered the question of whether our limitations are of our own making.  We know certainly some are, and there is always a context in which we can view ourselves to be the source of all our distinctions, so whether or not there is another, it would seem sound advice to counter our opponent in a way allowing that individual as much freedom as possible.  We may turn out to be freeing ourselves.

Why this, why now, why?  Common questions when we are faced with seemingly arbitrary facts.  When circumstances seem particular yet not compelled by some organizing principle, we become wary that we do not understand all at play.  At the deepest level we ask, “why am I?”  We cannot answer why we are exactly what we are, but we can simplify the problem.  We will explore here how the world—“everything”—can appear to us in one particular configuration of circumstances yet still hold the amazing possibility we would expect from a concept of “everything”.  Our answer at essence is that everything, or all that is, is in fact all that can be, not just some arbitrary subset of it.  Everything includes all that could ever be conceived.  There are implications to this—understandings, freeing principles to this conception of reality.  Recognizing all possibilities exist, we no longer wonder why only this one exists as this one includes within it all others.  We lose our wariness, and we place new value on our conception while losing an unnecessary deference to seeming harsh facts restricting us.  We gain an understanding and a source of meaning in the loss of the arbitrary.

We discussed briefly in Being Free that whether we believe it to be true or not, life being born from distinction is effectively true.  We argued that all that has a discernible impact on us is distinguished by us, and all that we distinguish necessarily contains distinction.  And this leaves only distinction in our reality.  However, before we can treat distinction as a model of life with compelling descriptive power, a question must be answered.  Why this particular collection of distinctions?  We have observed there appear to be distinctions not chosen by ourselves—and that even our own distinctions contain implications that we do not choose.  These impositions from outside ourselves are in some way the real universe in which we move.  Why are they what they are?  What is everything?  What is reality?

When we ask, “what is reality”, we are compelled to answer, “all that is”.  This answer is generally dismissed as uninformative.  One asks, “‘all that is’ in distinction with what?”  Or, “then, what is not?”  And if we recognize alternatives to “what is”, how can those alternatives not exist if their nature is knowable?  The contradiction that alternatives should exist yet not—somehow waiting in the wings—can be set aside long enough for us to explore a new definition, “all that can be”.  For argument's sake we will say the alternatives are not actual but that the wings in which they lay in wait are.

So, “what is reality?”  It is “all that can be.”  We now have a definition that does not simply defer the problem as “all that is” did.  However, our definition has the appearance of being just plain wrong because we see around us astounding detail, seemingly arbitrary specifics in our reality, surely not all that can be, but some strange and beautiful subset of it.  How can “all that can be”—a definition so potent with possibility, encompassing all spectra of conceivable thought—be equivalent to “all that is”?

We have already answered our question.  The alternatives are lying in wait in the wings, and the wings are before us too.  There is no one set of distinctions that describe our reality, rather reality is any and all distinctions.  Alternatives including all that we can conceive, there are two conclusions we can draw from this thesis.  1) Anything we conceive is part of reality—it creates the specifics of reality.  2) Within reality we can find all that is conceivable—specific circumstances seen from one perspective are alternative circumstances from another.

It is simply up to us to see how present, particular circumstances are consequences of our own conceptions and where the alternatives to those circumstances—the absent circumstances—are present upon interpretation of given circumstances as a wing in which an alternative waits.  In demonstrating this thesis we cannot list all conceptions and the realities they would make.  We cannot list all alternatives and point them out in our reality.  Each thing we point out creates new distinction and further alternatives.  But we can look at examples and keep in mind our reasoning that what we distinguish and what we experience are equivalent, implying that anything distinguishable can be experienced as real.

First we briefly consider how we draw conclusions to see specifics and recognize alternatives.  We see in our distinctions implication, correspondence.  We do this, for example, when we draw conclusions from the fact that two are opposites—as we know that if not all roads are closed to us, so there must be some road must open to us.  We do this when we recognize one thing is an emergent feature of another—as a storm is the motion of water, or as the motion of a person organizing objects can be seen the phenomenon of counting, or as the colors on a page form words and pictures, or as words and pictures form thoughts.  We do this when we recognize a contradiction in actuality before us and take from that the existence of a larger perspective with contexts clarifying all alternate truths of that paradox—as we see a whole to be divided by distinction.

Another way to say this is that the specificity of reality is created by our conception.  When we conceive of a thing, simply draw a distinction, we create the implication of that distinction.  The specifics we observe are the conclusions we draw.

And so regardless what distinctions we make, our reality will unfold from those distinctions.

Many alternatives to specifics we observe are easily seen to be present in analogy since so much of our specific circumstance is strictly conceptual to begin with.  Emergent phenomena such as words within ink are concepts, so to see their alternatives is to simply to look at the ink as this alternative to words that is compelled to you.  More difficult to see are physical phenomena.

We travel forward though time.  Why that direction and not the other?  It may not be immediately possible to point to a human moving backward through time, one who conceives of his or her reality as unfolding in the opposite direction as ours, but the thesis here is such a thing could be discerned.  Physicists see that antimatter is exactly normal matter when time is reversed in the equations.  Antimatter has been observed, so upon its observation we've seen a wing of that alternate reality in which a piece of normal matter was moving backward through time.  Certainly this isn't proof humans exist in reverse in our reality.  Humans are not simply matter but an emergent phenomenon in matter.  But when matter can be seen to exist in alternative forms in actuality, and given that alternatives to emergent patterns can be easily found in the actual—as physical things can be counted upward so can they be counted backward, the same activity under a reversal in time—the two taken together make compelling evidence.

Seeking to become composed, assured—virtuosic—we look for understanding and meaning in our world.  Understanding and meaning are gained when we create a reflection of the world within that world, within our minds, by creating a model.  If any and all distinction is the entirety of what makes up our world, a fundamental model of life is found in distinction itself.  It is a tantalizing thought that the world is born purely from distinction.  If true, we have succeeded in finding a simple, elemental model of the world that allows us to explore it, predict it, communicate it, take understanding from it.  These are the basic instincts of science, philosophy, art and spirituality so when we take insights from this thought we make advances in each of these areas.  And this perspective gives us meaning by removing the arbitrary.  Life is not arbitrary.  If we look we can see where all alternatives exist and recognize that we can effect our own specifics by simply making our own distinctions with care.

In this series the fundamental model of life has been found in distinction itself.  We see in distinction not just a process of the mind, but the very essence of the world.  We have sought this theory with the goal of coming to terms with conflict, increasing our strength and enhancing our virtuosity in life.  This conception was seen to provide a basis of meaning by removing the arbitrary.  We have seen how it allows us to see all as good.  We have found it may just release us from the impositions of even our most invincible opponents.  Even where the very model of distinction breaks down we find it is still in full force recognizing the contradiction that exposes the flaw is itself a distinction pointing to alternate contexts in a wider reality untroubled by the same contradiction.  At our boldest, we've suggested that contradiction is the essence of distinction itself, that very symmetry resolving the ultimate contradiction that anything exists at all.

Quite an ambitious theory.  While the best it seems to offer is to experience conflict with proportion, the recasting of our reality it enables, even admitting the magical, does seem to offer a change in the conflicts which we are compelled to enter into as well as grace while in them.  But still there are questions some have that at first appearances are not answered by this theory.  Not everyone is comfortable seeing the universe as a mirror image of themselves.  This leaves only them in their universe, and what if they do not want to be the only one accountable for the state of affairs?  To them this theory doesn't resolve conflict, but creates it.  What do we say to them?  We claim all is right, after all.  We should be able to accommodate this perspective too.

This theory admits theory itself.  That distinction, the fundamental component of modeling, is the very model itself in this case brings all other models under this one.  For those that reciprocate, admitting contexts wider than distinction and modeling distinction in its generality, we have then just another perspective on the same model, their mutual description making them equivalent.  This very fact may disqualify distinction as a successful model to some since a condition of correctness to them may be that the competing model is to be considered categorical, admitting no other interpretations, certainly not an interpretation positing the world as a one-to-one inverted copy of ourselves.  To the distinction modeler, this is acceptable state of affairs, introducing a contradiction in the existence of a model that is equivalent yet not.  Our task then is to find resolutions to that contradiction that put us in harmony with our disagreeing modeling friend.  Below we will discuss those models or conceptions of reality involving an intelligent creator.  Characterizing the existence of God as a model alone might be seen as contentious.  But faith itself seems to have no meaning without accepting as certain something that is merely possible.  So, possibly proponents of these conceptions will agree with the understanding of life as born purely from distinction.  But just as distinctly possible is that they will disagree even while their conceptions give equal rise to the phenomenon of humans capable of distinction, and therefore, seemingly the model of distinction we use here.  But, just as these concepts of reality allow for our existence as distinguishing individuals, the concept of distinction as reality allows for the experience of ultimate beings.

Who is our friend?  Who is our enemy?  Who is our detractor and who is our benefactor?  The world is lonely when it is just us and our mirror.  But it is not lonely when we are with our friends.  Which is it?  Are we alone or accompanied?

When we are alone, we are at one.  When we are accompanied, we are separate.  Is it a contradiction that we can at once be alone, and at the same time accompanied?  When we are alone, when it is just us and everything that is not us, or our mirror, any individual we may perceive is only a point in that reflection of ourselves.  But that does not mean that individual is not separate, for we are surely to that individual merely a reflection in return.  And though that person's existence as separate is contingent on our distinction, we can continue to appreciate the actuality of that person, for the implications of what distinguishes that person, whether or not that person is conceptually actual, are the same.  When we distinguish them we interact with them.

When we perceive ourselves to possess things of value, it is not necessary, but certainly possible to also consider ourselves as beneficiaries of those things.  Once we have distinguished ourselves as beneficiaries we immediately find ourselves in the position of naming two other categories of actor in life, our detractors and benefactors.  One takes from us, the other gives to us.  As we look to the items of value in our life with the least obvious of benefactors, or the loss with most difficult to attribute of detractors, we approach the idea of an ultimate being.  That we might see that being as having human form is no surprise, for we cannot communicate with a thing that cannot be communicated to.  It is not necessary, but as we described, once distinguished that actor in our lives will have the same implications regardless of the agreement of our conception with that of others.  However we distinguish those acting in our life, their impact on us will correspond to the distinction that describes them.

When we see ourselves as one, we see that our greatest adversaries have weakness.  Or that we are never without hope.  How can we defeat what surely must be the most inescapable of impositions on us, the inescapable fact that to each thing exists its opposite?  We want good things in our life, not bad, not neutral or void.  How do we overcome that all things are ultimately in complete balance?  By being the asymmetry.  By taking every conflict and choosing from the contradiction in it the context that is good to us, always walking in the direction of right, of good.  Who is the benefactor of the existence of this capability of ours to create such a contradictory asymmetry in our lives?

We won't answer here.  Even with this discussion we will probably find this concept of ultimate beings to cause some to see the subject as consonant, some as irrelevant, while some others to find great conflict with the concept.  But we will observe in common with certain other conceptions of reality requiring ultimate beings a belief that may be compelled to us by distinction as reality.  To be with our benefactor more than our detractor, we may have to find good for both, for they are both ultimately us.

In The Strange and Beautiful we noted that we see our world as strangely specific, and wonder why it is exactly what it is.  That is, we are free at any time to ask “what if”, and since life can only reasonably taken to be defined as “everything”, where are the rest of those “what if” alternatives?  Aren't they things among “everything” too?  Our conclusion there was that these alternatives are here too.  This means that any “what if” we conceive can be seen to exist.  We will consider this again, but say further that alternatives aren't only hidden but, accepting contradictions, actual simultaneous to that which they are alternate to—we will say “to the extent that” they exist.  We will discuss this as well as simply list a number of observed perspectives and see how they are alternatives to our own experience.

First we look a little more closely at the relation between contradiction and distinction.  We here take a distinction to be a characterization of all things.  It is a parameterized thing, assigning to every thing some character or category, itself another thing.  A frequent choice of categories is just “true” and “false”.  The characterization shows the thing to have distinguished parts.  At one instance of the parameter it is of one category and at another instance it is of another category.  We say distinction, the existence of parts in a thing, contradicts the unicity of the whole: is it one or many?  So we have, by taking any impossibility, a parameterized thing.  This is true and This is false—“This” is parameterized and some instance of “This” is in the category of true and some false.  So, surely contradiction creates distinction—the parameterization of “This”.

Does distinction necessarily entail contradiction?  Yes.  This is not crucial to the point while tricky and mathematically notated so feel free to jump ahead a paragraph.  We describe here some reasoning in a logic that allows contradiction, and show not just the existence of a fixed point demonstrating a contradiction, but a point in every distinction that is contradictory.  Any distinction or categorization, call it C, that is not identity or constant does lead to contradiction.  Let Q and U be two different categories such that C( U ) ≠ Q and C( Q ) ≠ U.  If we take any distinction T that categorizes U as Q, T( U ) = Q, and everything not U to U, T( x ) = U for x ≠ U, then we can say T( x ) is never equal to x and C( T( x ) ) is never equal to C( x ).  If we define the distinction R by R( x ) = T( x( x ) ), then we see that R( R ) = T( R( R ) ).  Noting T( R( R ) ) ≠ R( R ), we have two different values for R( R ), or a contradiction.  But also, we see that C( T( R( R ) ) ) and C( R( R ) ) are both equal and not equal.  So, not only do we have that some distinction, for example R, is contradictory, but all distinctions C are inconsistent, or at best incomplete, having ambiguous definition at R( R ).

One may wonder, if all things are distinctions, what are the base objects upon which we draw distinctions.  We do not provide any.  Mathematically one may be inclined to admit symbols with no further definition, but there is no atom in a world born from distinction.  While we may not distinguish with choice all of our reality, all of it is distinguished and distinct and so distinction, if anything, is our undefined object.  Distinction does have more than an atomic nature but as all first principles are subject to unsubstantiated self-evidence so is this, and as first principles go, distinction entails very little vagueness, it being the very method of examining any theory at all.  So while we do not have a definition of what a distinction is, it is our very action of considering the question that is itself distinction, and we will have no need to formulate it, and arguably are unable to anyway, though mathematical formulations of some approximation of it may find use. 

Once we see that every characterization must be incomplete we must then recognize all things are imperfect implementations of their ideal.  This explains paradox in a sense because we now have the imperfection of all things, and so to say all things “are” is no longer contradictory.  Is this a perfect democracy?  No, nothing is perfect, so then this is an imperfect democracy.  Is this an anarchy?  Well, it is a very imperfect anarchy, if so.  But, the democracy was imperfect too, so we see that this is both a democracy—to the extent it is—and is an anarchy—to the extent it is.  While we say “to the extent that” we still mean to say these distinctions are correct, even while imperfect or incomplete at a glance—correctness is provided in resolving the contradictions of the “imperfections” in a wider context.

Relativity sees no quanta, and sees the speed of light as maximal.  Quantum Mechanics is quantized and breaks the barrier of the speed of light.  Which is right?  Since every system that describes some thing completely is necessarily incomplete in a larger context, we should expect our scientific theories to always admit improvement.  This does not lessen our theories.  Observing that by and large the speed of light is never exceeded, we can expect that, by and large, the implications of that, time dilation and relative mass, will be observable too.  Whether this can be explained as merely a phenomenon of a quantum mechanical underlying truth or that in reverse the quanta of Quantum Mechanics are merely side-effects of a field-like spring and hook nature to atoms and other interfaces to our observation of reality, is essentially not important.  They are both present as understandings.

Is the world broken up into three dimensions of space or do we just treat it as if it is?

Pondering a question, all answers can be seen to be true to some extent, and often your chosen future actions can be discovered to be obvious enough regardless of which answer is right.  “She loves me, she loves me not.  To the extent she loves me, she's shy, to the extent she doesn't, she doesn't know I exist.  In either case I should initiate some interaction.”

And of course, we still have alternates hiding away, seen from different perspectives.  History represents distinctions alternative to the specifics before us.  In the case of our own history, it represents the alternate descriptions of the world lacking the distinctions we made in progressing through time.  In the case of the history as seen from the perspectives of others, we have here the wings containing alternates to the present reality, and how could it be any other way since we write history exactly to learn from it—to answer our “what if” questions where we posit alternates that are not actual.  Do you identify with a friend or a fictional character, with a historical figure?  You see yourself as similar, though, obviously, not the same?  Every one you identify with, and anyone at all to the extent that you do identify with them, is an alternate to you as you experience yourself.

These are just some ways that absolutely everything exists.  The alternates to what we think are restrictions on what can exist, are in fact very real and not restricted from existence at all.

Our world and interaction with it leads inevitably to paradox.  As we've observed, just the positing of the Liar's Paradox forces us to accept contradiction as actual—an irrational thing to do.  But we are equipped to handle the very real nature of the impossible.  We have already noted this feature of life gives us multiplicity of distinction, and puts life in all its possibility in our purview.  Accepting the irrational, and making sense of it shows us more of our own position in life.  It sounds contradictory, as it must, but most of us, if not all of us, already understand this and operate within its strange rules of reason, even while we pretend we do not—as we must.

People know anything is possible.  By anything, I include that which is given to us in an already impossible state.  To believe the impossible you might think we have to be gullible.  Possibly, but then we each have our own set of gullibilities, though many of us seem much more skeptical than others.  Even the most skeptical among us will stop, hesitate, proceed fearfully and delicately, on hearing a proposition, impossible or otherwise, if it strikes at something fundamental.  We have our pride, our self worth, and if some cornerstone of that is questioned by one whose credibility follows directly from association with that very cornerstone, we have to think it through.  If the questioner is wrong, that damages our foundation by association, and if the questioner is right, then our cornerstone has been pulled.  So it doesn't really matter if that person is saying something impossible, the contradiction is present in our belief.  Our belief creates paradox by positing its own falsehood—through the associated person.

Similarly, we know that all life can be seen from whatever distinction we choose.  This can be seen optimistically or pessimistically.  Optimistically we look positively—we focus on what is good, and characterize the bad as deviation, defect that can be accommodated or repaired.  Pessimistically we impact others negatively when we trick them into behaviors they wouldn't have chosen, creating rules that are specified in relation to our own future actions—“when the king does it, it isn't illegal,” or, “this is different, because my intent is to further the cause of the rule”—because everything is right in some context, so we can always find a way to justify whatever we choose.  Consequences, in the sense of implication, of our choices are what they are though, and our webs do become tangled.

Further, more than knowing these things, we love them.  We love to be surprised.  Surprise puts us directly in contact with multiplicity of distinction.  We are tantalized by the possibility of the impossible.  We love to reassess the situation under alternate assumptions—applying multiple distinctions.  Miraculous feats, plot twists, inspirational reversals, schadenfreude, they all involve a belief that is contradicted and causes us to rewrite our understanding of the situation, redistinguish all elements under new terms.  The thing doesn't change, and yet it does.

We consider ourselves irrational, but is it baseless irrationality?  If we accept the truth of irrationality in life, we can remove unhelpful self-discipline, and move on to finding rational solutions.  When we reject something as irrational, we stop working on it.  Well, rightly to the person witnessing the irrational feature of life, the problem is still there, so to deny a solution just causes them to behave two ways at all times—under the assumptions of the incorrectness of the irrational observation, and under the very real impact of the observation.  It's an expensive way to live.  If we allow our irrational observations to come under consideration we can move forward with a singular life, that doesn't require constant calculation of optimality of choice as applied to the two or more understandings of our lives.  That is, a person operating under both “I have bad luck in this arena” and “that is irrational, do not assume unequal probabilities for equal events” is going to have to avoid situations that tempt bad luck, all the while only choosing situations that can be justified rationally.  This is a lot of work, and bound to run into further conflict.  Better to understand how bad luck can be seen to have an explanation, or how rational probability doesn't apply to the arena under consideration.

With all as distinction and with room only for all distinctions in our reality, we find a deep source of explanation for life's surprises both unpleasant and pleasant.  It is simply that the things we see around us function under more than one distinction.  When the irrational seems to enter our lives, we can make progress by accepting its possibility and working with it.  We appreciate those positive irrationalities and explore the perspectives they show us, and for those that impose on us, we recognize that if the fix is in, simply accepting it and counterlevering our desires with our new awareness of the fix frees us.  Even if we are not successful at countering the irrationalities in our lives, we are freed from living the tangled life of multiple premises while enjoying the fantastical beauty that the paradox of impossibility creates.

We consider here the thesis that the impossibility of life is what gives life possibility.

That is, contradiction, as we may have observed with frustration to be unavoidable in our lives, is in fact not a problem, but the source of possibility.  For a thing to be contradictory, true and false, is exactly that act of making many of one.  That a thing both “is” and “isn't” creates multiplicity, by making us distinguish in that thing where it is true and where it is false—it becomes parameterized.  This is the building block of life.  Applying that building block in every and any way gives rise exactly to reality.  It is the source of detail and variety in life, and can be identified clearly with our own consciousness, our own acts of distinction.

The most basic understanding of nature is that it is all, every bit of it, simply that which we distinguish, and every seeming fixed external fact we see is just the implication of one of our own distinctions.  One thinks of having choice over his or her distinctions, but really, once one distinction is made, further subdivisions are subject to the restrictions of the first, unless we choose to contradict ourselves, creating choice—choice of how to resolve the contradiction.  Impossibility is embraceable.  And how can we not embrace it, with life itself an inescapable impossibility, creating the very ambiguity of distinction?  Is a thing with distinguishable parts one thing or many things?  It might seem we can get around calling that a contradiction, and that is exactly what choosing and distinguishing is: getting around it.

Since anything goes, contradiction included, anything one can conceive is just as real as anything else.  Where our conceptions are nonsensical, that's where ambiguity, change, choice and the border from one thing to another is found.  Every last retinal cell, synapse, electron, law of physics, law of spirituality, law of conception is implicit in our present distinction.  That we can conceive at all, that we are conscious and draw a distinction between ourselves and everything else, is what draws those boundaries of our observed selves.  This is how our own distinction can appear as fixed and unchosen.   We find ourselves with a set of distinctions that we did not consciously distinguish but appear to have been dealt.  That this is a contradiction (our distinguishing something we did not personally distinguish) just reflects the contradiction of distinction in the first place: that a single thing is in fact many things.  Our discovered place, current distinguished reality, is just as much everything as any other though, as every possible distinction can be found somewhere within any other with a little search.

How many have despondently observed that asking the big question seems to have no answer that isn't directly at odds with reason—“where is the universe, where is that, where is that?”, “Who created what, and out of what, and who created them?”.  What religion doesn't call for straight out acceptance of contradiction or faith and acceptance of miracles?  Those who reject supernatural can do the same.  They do not have to relinquish reason in so doing, and seeing a reasonable way of doing so may just ease the tensions between those across opposing borders of belief.

Is accepting contradiction as actual possible.  It is not obvious.  It sounds wrong, by definition.  How could so much history pass with so much being missed?  Wouldn't differences between the real nature of life and the way we commonly conceive of it expose themselves eventually?

As we have stated before, one really cannot get around contradiction, as is made plain by paradoxes such as the Liar.  “I am lying.”  If that sentence is true, then it is a lie, which would imply it is not true, which itself implies that it is not a lie and therefore true—and we know what that then implies!  Some will say such sentences are not truly contradictory, but merely senseless.  Such an analysis allows us to go about our lives under the common conception of consistent, non-contradictory reasoning.  In fact, on top of such resolutions of paradox further contradictions can be created.  “This sentence is not true and is senseless.”  So if it is senseless then it is also not true (it is neither true nor false).  But concluding it is not true and senseless makes the sentence true, which is contradictory again.  No doubt a skeptic of contradiction will find a further resolution, and a lover of contradiction can create another on top of that.  We will leave this battle between paradox and resolution aside and take situation to be ambiguous.  Let's look how the two beliefs can coexist without our having noticed it.

When we are contradicted, some one or thing has indicated that an item we have taken to be true is, to the contrary, false.  If this item is something we hold dear, this can be damaging to us to the same degree to which it was dear.  Suppose, however, that by being contradicted we aren't being shown false, but rather having ambiguity introduced.  Suppose we are still correct, but now also see a sense in which we are not.  Certainly if this latter perspective is the more accurate than the former we would have noticed it sooner or later.  But in fact, isn't introducing an ambiguity nearly as damaging as flat out contradiction?  Perhaps sometimes it is more, sometimes it is less, but it is close enough we certainly might eschew use of the latter perspective due to the convenience of using the closer-by former understanding.  That it is near enough that we might miss or purposely pass by this perspective can be seen easily, using the same idea we used in resolving the paradox above.  That is, once contradicted, even if all we have discovered is that our item is not categorically, unambiguously, universally true, it still prevents us from treating it as categorically, unambiguously, universally true.  And, in fact, unambiguously true is what we really seek, it is what truly relieves us from labor of thought, frees us up to explore consequences without reexamining our premises upon each new conclusion.  So, in the end, we are still contradicted, to some degree, in the old sense, and that is enough to prevent us from exploring further.

But, having let this more subtle perspective languish due to its lack of utility in the majority of cases, we may have neglected a valuable resource for a minority, perhaps important minority, of cases.  This perspective hasn't been entirely neglected.  Versions of it appear in many recent and ancient writings.  People employ the possibility of contradicting reality on a frequent basis even today.  It is infrequently recognized as such because recognizing it removes the leverage in it.  Ultimately, taking a truth to be a falsehood appears as a lie.  So when we recognize that we are fooling ourselves, we are no longer fooling ourselves.  Of course, in the case of fooling oneself, the leverage is arguably not used to a good end.  But recognizing the wider view of a spectrum of truths, a distinction of a multiplicity, we are no longer lying to ourselves and have given up a questionable leverage for a valuable clarifying tool.

The thesis in this series has been that we have benefited from this latter perspective, it being a view on our very existence.  So in a sense we've used it without being aware of it.  The embrace of contradiction and reality as born from our own acts of distinction has been observed many times, notably in the Dao De Jing via its exploration of acting without action and naming as source of the many things of reality.  This conception isn't advocated, but its analogy is visible even in Genesis where God names the things created, night and day, separating the waters to name the resultant space sky, and bringing the creatures to Adam to be named.  It has been used without explanation at times, sometimes deceptively.  We frequently deride a practice as slippery, implying no fixed truth.  The awareness of the technique of using ambiguity without our knowledge, again arguably necessarily without our knowlege (our recognition), can be seen certainly as early as Plato in his allegory of the cave, where the extra degree of freedom of those in the light allowed them to create arbitrary realities for those fixed in the cave.  What is two different cardboard cutouts to those in the light can appear, when overlapped, as one and then two to those in the cave.

So, in a sense, we've been using this perspective all along.  And isn't it something of a relief that all these contradictions haunting our daily lives are not so intractable after all?  Perhaps life is no clearer under this more accepting conception, but possibly that is what is called for by many modern problems.

How do we make sense of the paradoxes of philosophical logic in the larger picture of philosophy as a whole?  In particular, we will consider here how to make sense of incompleteness theorems in the context of the philosophical perspective presented in this series.  In this series we take contradiction to be the very essence of all discernment, philosophical or otherwise.  To see where issues of completeness and consistency in philosophical logic support and are supported by this understanding we will look at these issues with an eye to the instincts that gave rise to them.  It might fairly be said that as it stands they do not require support—all the surprising and counterintuitive results here can be phrased in a form that is perfectly sensible—but still the objections of our initial instincts have not been fully satisfied.  We identify here our acts of distinction with our process of reason to see where distinction as understood in this series is related to the reason of philosophical logic and where contradiction relates the two.  The entry finds us briefly stepping into the mathematical world of philosophical logic.

Often drawn is the conclusion that all reality cannot be reasoned about without contradiction—that things are not all either true or false.  We say the use of the word ‘all’ ranging over the universe of all objects of reason will inevitably lead to contradiction, as per Russell's vicious circle.  We say this because certain paradoxes arise in any systematized logic that aims to represent all reason.  To characterize in modern terms what can be safely reasoned about we ask for collections of formulae Γ and individual formulae φ appropriate to a given consistent logical system L whether Γ ⊢_L φ ≡ Γ ⊢_Model φ; that is whether our criterion of truth for L is complete.  Now the results in this area are uncontroversial under the standard interpretation of consequence and biconditional, but the study arises from a more primordial question.  We not only want our theory to be consistent and definitive for every formula in it, but we want the full collection of formulae to encompass all reason as fully as possible.  We want our left hand system to be substitutable for the right hand one and the right hand one to itself be all reason.

The standard reference of completeness is our semantical system, above called Model.  Standard semantics may or may not encompass all that can be reasoned about, but we will leave the specific nature of Model aside and refer to a third system C that is assumed to be consistent and capable of interpreting at least every formula Model is and also all Model falls short of.  That there may be more than one such C will be left aside as more detailed a point than inspection of our instinct requires, and we will pick one, all results following equally for any such one.  So, our instinct is to find the largest systems of logic L such that for all Γ and φ in not just L but C, Γ ⊢_L φ ≡ Γ ⊢_C φ.  The observation here is that this system can only meet our instinctual conditions of consistency and completeness if this is a fully tautological statement—that is, without any content or sense.  If L is really capable of definitively expressing all C can express, the statement is no more than C = C.  If there is some difference between L and C then the primordial instinct is contradictory—they are not substitutable.  It is only once we create that contradiction that L is somehow distinct from C yet substitutable with C that we give sense to our systems of reason L.  And without contradiction, we have only a contentless tautology that tells us nothing.  The nature of this concept of nonequivalence corresponds well with Wittgenstein in his picture concept, and with his Tractatus statement 6.3751 demonstrating the that a thing cannot be two different colors, “... a particle cannot have two velocities at the same time; that is to say, it cannot be in two places at the same time; that is to say, particles that are in different places at the same time cannot be identical.”  Though he might stop investigating our line of reasoning at this point of impossibility, we can still continue on since we do not restrict ourselves to seeing only facts that are the case as part of the world.  We in fact want L ≠ C but still ∀Γ, φ Γ ⊢_L φ ≡ Γ ⊢_C φ.  This is contradictory, but the resolution of this instinctual overstep is where the subtlety of our systems of logic come from.

That it is only when our concept of reason falls short of all reason that it makes a useful definition of reason is well supported with evidence from both first order logic and higher order logic.  No system of reason can be complete and consistent yet first order logic is.  Γ ⊢_FOL φ ≡ Γ ⊢_C φ.  The resolution of apparent impossibility of the completeness of first order logic is that it is not complete, certainly not of all reason.  We have this from cardinality arguments and the Löwenheim-Skolem theorems.  It is even easier to resolve than that because clearly the first order formulae do not have sufficient richness to encompass all predicates of thought until we add enough axioms to create a higher order system such as set theory.  That is, we weaken our quantification for which the equivalence holds to a class of formulae significantly lacking in expressiveness.  Higher order logic is explicitly incomplete without the pretense of full exhaustiveness of its class of formulae.  Gödel showed there are Γ and φ such that Γ ⊢_HOL φ ≡ Γ ⊢_HOL ¬φ.  So even if higher order logic did admit arbitrary formulae, some of them cannot be given meaning so that we have ¬( ∀Γ, φ Γ ⊢_HOL φ ≡ Γ ⊢_C φ ).  If it were complete it would induce inconsistency or incompleteness on C.  But again, we really don't want it complete because that fact would become contentless at that time.

One might wonder if these contradictions, Gödel's incompleteness theorems and our instinctual conflicts, are really related.  Could we have Gödel's result without identifying HOL with C?  No.  Without a reference to be incomplete against HOL isn't incomplete.  That is, if we're going to restrict the formulae over which its judgments are quantified, we aren't going include those it doesn't assign a value.  To put it unabashedly informally, it appears it is exactly our insistence that we can discuss objects of reason with reason that leads to Tarski's universality of language and the feature of contradiction in our larger contentless picture that allows us to create a smaller much richer picture characterized by vast tracts of consistency.

It can be said that a philosopher is in conflict with reality.  The philosopher goes to great pains to show us how the world really is—in distinction with what it appears to be.  It isn't just the philosopher of course, and it isn't just correcting our view.  We all do it, and various roles we take—philosopher, scientist, artist, teacher, individual making his way—all share this character.  And we don't just correct mistaken views but clarify confused ones, create new ones, and validate existing ones, seeing them in a new light.  The principal philosophical problem addressed in this series is conflict with, up to now, a focus on contradiction as distinction.  Contradiction is an issue of truth and falsity.  Paradox is a contradiction showing the limitation, or mere boundary as we would have it here, of the logical, rational point of view.  As rational investigators it would seem we have one guiding principle that should hold true in our search for new views.  Whatever new description of reality we find, as different as it may be from our common conception, we really cannot expect it to be rational—correct—unless it describes exactly our common conception.  That is, whatever new truths we conclude, a full description of reality should describe exactly what we see now, including the error-prone, confusing common conception we started with.  It is exactly this feature—that we should express a new view that is nothing other than the old view—that leads the rational investigator to face contradiction.  In this entry we will see where our view that explains our reality with contradiction can describe a view not requiring truth and falsity.  We continue to accept distinction as the source of our reality, but recognize in distinction not just contradiction, but naming.

As we stated, all our existing phenomena should remain in our new view, so truth and falsity will remain.  We alluded to this resolution in To The Extent, where we recognized truth and falsity as just two categories in a model of distinction as a function over yet other distinctions, a category just being another thing, a thing just being another distinction.  In Being Free we pointed out that our rational, non-contradictory view is a division of our world into two categories, true and false.  From this perspective any distinction, or function, over so many things can be modeled with another distinction that rewrites our function as a collection of true and false statements—as a function is seen as a relation in mathematics.

We will focus here on the coupling of distinct things, which we may call laying against or taking together.  In the rational view of language, statements, or sentences, denote truth.  Other components of sentences just denote other things—nouns, adjectives, etc.  We can remove truth and falsity easily from many of our sentences.  So if we say “I am happy”, or “I am happy” = “truth” in a rational view, we can also say “My feeling” = “happiness”.  Choosing the form of equation may lead us to view even this latter phrase as a statement of truth.  When we do, the relation to contradiction is clear, particularly if we transcribe our first phrase more directly and say, “I” = “happy”.  The ideas “I” and “happy” cearly are not the same, so the statement is a contradiction.  But in fact what it denotes is not what is under consideration.  The thing under consideration is the taking of the two together.  The denotation, even as a rational view would have it, can be many things—truth, as in a statement, falsity, as in sarcasm, hogwash, as in “what do you really mean and who are you really referring to in the indexical ‘I’?”  The point is, that all these denotations are part of separate further distinctions.  In all of them the sense is the same, and that is that clearly “I” and “happy” aren't the same thing, but there is a “feeling” to resolve this taking together of distinct things, and that that feeling is elaborated by the distinctive nature of the name “happy”.  The fact that we are discussing language shows that the experience of this statement takes place within a larger distinction where the graphical forms, the words “happy” and “I”, are given meaning.  We can say, to the extent “I” and “happy” are the same thing, other of my distinctions then convey yet more sense.

We've discussed sense in Contradiction as Distinction where we observed, it is only when we identify two different things that sense exists.  The sense discussed by Frege is revealed by the identification of two things that clearly are not identical—they denote the same thing but aren't the same thing because identification of two identical expressions communicates nothing.  So reexamining sense, we can see it as the very parameterizations of a thing that allow us to resolve contradiction in any identification of it with another thing.

Naming is then seen as just another identification of expressions such as “the object in the middle of the table” = “the crunchy red piece of fruit in this room”.  One doesn't consider it desirable, let alone feasible, to bring the actual object into our thought, so we name it.  We take something distinct from it and call that the thing's representation.  That representation has the appearance of approximating the object named.  We can picture a partial order of sense where taking the actual object conveys the most sense—all of it.  Then expressions or images we take to refer to the object contain successively less of that sense in that they convey less information about the object.  So “the sweet, red, crunchy piece of fruit in the center of our table” is a closer approximation of the actual apple than “the red object before us”.  The least informative reference, and least approximate description, is the proper name.  So if we've named the apple Plato we are explicitly recognizing “Plato” is completely independent of the nature of the thing, as is evident from the fact that the same name can be used as easily to refer to an ancient philosopher as to a piece of fruit.  In a reality as distinction light, each of these representations is as much a name as the last as they are all expressions and as expressions they are distinct from the thing and require parameterization to be seen as identical with the thing. 

We took simultaneous truth equivalences and generalized them to simultaneous thing equivalences.  This principle in generality is just the single identification.  Taking this form of equation, A = B, and the natural language form, A is B, as distinction itself redraws our operation of naming as just as another of these identification of things.  The question of what is sense of names has a specific answer from this perspective.  A name is not outside the domain of discussion, but is just another thing within the domain of discussion having just another sense like any other thing.  Essentially we are saying there is no atomic senseless name.

We have now a new view of life.  To look at all as naming—something recommended to us by the text quoted in our first entry.  To some extent we have united views as distant in time as those of Frege and Laozi.  This view has much to offer in the way of further clarification of various of the phenomena we experience.  The connection between negation, or A is not B, and how it can be simple, as it is in the rational view, or difficult, as it is in resolution of intuitionism with classical logic, or a subtle creative principle, as it is in a world born from distinction, is a topic for another entry.  But many topics for discussion arising from this view can only be carried out as we live our lives and pay closer attention to the power of naming over the very real exigencies and spectacles of our lives.

All in our reality is distinguishable, and all we distinguish is in our reality.  Reality may be understood in many ways, but clearly reality as distinction presents itself as a comprehensive way.  At the same time, this description of reality, distinction, is vague.  But it can be nothing else, for any particularity we give it will clearly make it but one thing, undescriptive of all things.  We can only expect all reality to be perfectly descriptive of all reality, so our unsubstantiated first principle in describing it must be the entirety of the description.  And it seems fitting that the very act of distinction of the author or reader of this document be the first principle, entire theory and entirety of reality, the reality of the author and reader consisting of the distinction of this document.

Truth is everywhere in our consideration of reality.  Indeed, the sentences in this document are almost all statements.  Statements are about truth.  And yet, we see an air of particularity in truth.  Not all sentences are about truth.  Questions of what and where are not statements of truth.  With our very mechanism of considering reality relying so heavily on truth, how can we keep as meaningful our statements, yet see truth as merely a phenomenon in reality?

In the last entry we suggested doing so by viewing distinction as taking together, or laying against.  This is exemplified by naming, where the identification of two things—one or each a name for the other—is seen in the basic form of A is B, or A = B.  The replacement of truth by naming may be perfectly clear in some statements we would normally take to be about truth, such as “I am Happy”, where we carry out an act of disambiguation quite similar to that in the naming statement “That man is Socrates”.  But if naming and distinction do not rely fundamentally on truth and falsity, what are we to make of statements like “I am not happy”?  “Not” is closely related to distinction, for what is distinction except the experience of things as not being the same?  With the intimacy of negation and distinction, and the apparent intimacy of “not” with truth and falsity, how can we maintain truth and falsity as merely among the discerned?

We mentioned in A View on Existence that being contradicted, as when we are told what we took to be true is in fact false, that rather than being shown false, we have simply introduced ambiguity.  Now, rather than the strict distinction we carried out, we also lay against that a new beast, not-true.  And taking “not” as elemental in our understanding, “not-true” is just some name that carries no specific sense or denotation at all—just as in Taking Together, “Plato” carried none of the sense of the apple “Plato” named.  “Not-true” as just another name is free to be filled in in as many ways as we can distinguish in whatever we take together with it.  And this is telling of the lack of primacy of truth, for “not” applies not just to truth and falsity but anything at all, as in “I am not happy”.  And what is “not-happy”?  There are many things distinct from “happy”.  There may be close relation between “I am not happy” and “‘I am happy’ is not true”, but this appearance of “not-true” argues for a strict true-false division of reality no more than the clear multitude of “not-happy” argues that “Not ‘I am happy’”, denotes rather than asserts that which is in contrast to “I am happy”—“I am sullen”, “I am concerned”, and so on.

Intuitionism in mathematics is well-known for its rejection of the principle of excluded middle—that for any statement, A, either A or not A is true.  An intuitionist requires that we be able to constructively determine which is the case, A is true or A is false, before we can state “A or not A”.  The classical view says that our reasoning with the phrase otherwise being sound, “A or not A” must always, regardless of the particular A we fill the phrase in with, be true.  We can see from the perspective presented here we're already prepared to defend the intuitionistic view as the statement A, even when given in what could be read as an assertive form, need not represent a truth value.  When “not” is seen as merely presenting a thing distinct from its argument, “A or not A” does not necessarily represent truth.

A further consequence of the intuitionistic view is that “A = not not A” is not an immediate truth for arbitrary A.  Here we have to elaborate further to accept the intuitionistic view.  That which is something other than something which is again something other than A might be taken to be A.  But if we look more closely at what we distinguish in any utterance such as “not not A”, we observe not simply two identical “nots” applied to an “A”, but two distinct “nots”, in that each is at a different place in the phrase.  We might just as well say, “not1 not2 A”.  “Not1” and “not2” can both be discerned distinct things.  Indeed in “A or not A”, the two instances of “A” might be distinct.  We can also envision one of two participants in discussion not even distinguishing “A” from “not A”.  When we compare any two of these statements, as we do in logic, it is up to the discerner to take meaning from them.  The discerner distinguishes components, and if the two “nots” aren't distinguished, the classical rule may take sway.

And of course, not just “not-things”, but all elements distinguished in any laying against of things are distinct, and where we don't distinguish, they aren't.  When we progress, as we may when communicating with another, the agreement of successive distinctions will decide where we progress, or if we are communicating what we set out to.  We can't read too much into our agreement with the intuitionist on these points because we're equally ready to embrace the classical view when we recognize that for a thing to be “not” something else, it is effectively “false” that they are the same.  And we are free to break any of these bounds and take as the sense of the inquiry, not whether a statement is true or false, but the distinction in the sense that would make it true.  We might also hold the sense fixed and distinguish some other denotation—hogwash perhaps, or a titular proper noun and so on.  One thing we can do with the proposition “A = not not A”, regardless of our stance on intuitionism, is distinguish new sense in other of our distinctions given the naming implicit in this distinction.  The propagation of sense via the substitution of a thing for its name is itself distinction, where the distinctiveness is seen before we take the name, and the simplification is seen after taking it, the substitution being the choice not to distinguish the thing from its name.

So the particularity in “not” is explained in that it in fact needn't be anything in particular.  “Not” is perhaps simply some distinction, and it is in the particular distinction that its particularity lay.  And generally, within any communication with another, we will find ourselves distinguishing something in common, with the remainder as the information of our dialog.  So we might find ourselves in confusing times if we see something different in “not” than our collocutor.  But we may just as easily be communicating the very point we wished.

In distinction there is choice.  We see in it alternates or alternatives.  The found alternate is external to we who find it and the alternatives are that from which we choose.  The self is what we are.  What we are not, the rest of it, is the external world.  So we see a boundary between ourselves and the external world in choice.

What we establish by convention is our choice.  Things chosen are created, adopted, unfixed.  They are what we'd have them be, possibly this or possibly that, equally well predicted as contradicted.  What is discovered has its nature without our choice.  Things discovered are fixed, surprising, unchosen.  They are exactly what they are and not anything else—they are noncontradictory.

We will consider here choice and the distinction between the internal and external world from the views of distinction as naming and as contradiction.

In naming is an instance of taking together, something we've taken as distinction itself.  It generalizes the A is B form.  However, this isn't the only way we take things together.  The “is” in “A is B” is a sign of this taking together as truth.  Indeed, we see the “is” in the phrase as but one part of the taking together of A and B in language.  The “A” and the “is”, the “is” and the “B”, the “A” and the “is B”, and any other constituents we see in the linguistic phrase, are all taken together.  In the graphic form of language, even the letters in a word are taken together.  But in discussing “A is B” we are really talking about the A and the B being taken together.

We've already looked at taking “not” together with another thing, but in fact any two things, like “featherless” and “biped” might be taken together to form a distinction.  “Man is a featherless biped”.  “This is exquisitely delicious”.  “That biped is not feathered”.  “I have gone fishing”.  So things described in language with adjectives, adverbs, transitive verbs, compound names all have in them distinct things taken together, laid against each other.  And not just linguistic forms are taken together but all the things we experience.  The surfaces juxtaposed at the joint in a door.  The thing we lay before us and we ourselves.  In mathematics, the argument applied to its function, f(x).  The detail of contour within any diversity taken together as one thing.

In this is both internal choice and external observation.  When taking two things together, we accept the things taken as fixed and our internal choice is the distinction of sense.  When we simply take two of these takings together together again, or when we see distinctiveness within each of the particulars of a given taking together, we are taking distinctions themselves together.  Such is clearly the case in communication where we can see an interesting interplay of choice and observation.  Take the following two similar conversations.

In each conversation a different point is highlighted.  In the first, she is clarifying that the cat is on the box, in the second that the cat is on the box.  In both conversation she utters the same thing, and even communicates partially the same thing, that is, where the cat is.  But the sense is different, and is fixed by what is common to the two utterances.  If he had held his silence while merely thinking that the cat was in the box, yet she had assumed he believed the cat to be on the floor, her utterance would yield a reply from him that would be occasioned by some surprise on her part.

We sometimes fix such sense within one utterance by distinguishing one word with emphasis, as when italicized.  We can imagine our protagonist alone in this search for a cat, wondering at once whether the cat was in the box or on the floor and finding surprise in her own thought that perhaps the cat is on the box.

We find in our distinctions externally existent things yet in our own distinction the source of external things.  This elicits a debate as to whether external things are the way they are exactly because it is “we” who found them that way, or whether we are what we are only because we find external things just as they are.  Whichever we define in terms of the other, one remains fixed and the other ranges free.

We have in past entries described distinction as arising from contradiction.  We say, we can't hold a contradiction, so we resolve it, and that resolution is distinctive, or is our distinction.  The task may be put to our theory of life as born from contradiction to defend itself in the face of reason and clarity, which is at times, if not as often as we'd wish, plainly before us.  From this point of view, the rational reality toward which we resolve contradiction is noncontradiction.  Noncontradiction is rational, fixed external reality.  In noncontradiction is the requirement that distinct things are not the same—a thing is not both true and not true.  We have the external, that which is not us, as noncontradiction, and us, that choice in resolution which remains, as contradiction.

Noncontradiction in philosophy is a general principle about facts.  Facts are independently true things.  These facts have been subdivided in many ways, just some of which are a priori-a posteriori, analytic-synthetic, necessary-contingent.  In each of these subdivisions, noncontradiction is held and truth or falsity is to be found fixed, absolutely in propositions.

Noncontradiction and contradiction are particularly relevant where we see the most stringent of facts and the most freedom of choice, thought.  As much as number may be a convention of our own, once made, we can't choose 2 + 2 into being 5 without breaking our own convention.  But we are free to choose to break or modify our convention by resolving those contradictions we don't object to reject, as we say “P and not P” is only true if we recognize instead of the atomic fact P we have a relation P such that “P(4) and not P(5)”.  Similarly we say there may be no whole number we can add to 3 to get 2, but we can by fiat introduce negative numbers to say -1 + 3 = 2.  Before even mathematics, we resolve contradiction when we see no sameness in two different words in a statement about two names were we not by fiat to take them to name the same thing.

It seems odd to discuss contradiction and noncontradiction as opposites, for it is the role of opposition within these two categories that distinguishes the two categories.  Isn't it the role of noncontradiction to define “opposite” or “not”, and therefore contradictory to speak of noncontradiction's opposite?  We can throw up our hands, and say, once we start talking of all reason, as we are when we discuss noncontradiction, we are inevitably without recourse to reason.  Or we can look again with surprise at the perfect sense in describing “opposition to noncontradiction” as “contradiction”.  To “opposite of contradiction” we object, “contradiction!”, but this objection imputes exactly what it was in objection to.

Taking each of these two categories as wholes, say C and N, we can say any two opposites in C are indistinguishable and any two opposites in N are perfectly distinct.  Indeed, everything in C is indistinguishable from everything else in C, and within N is a vast sea of distinguished particularity.  The shared use of “not” in these two categories reflects our choice of distinction—the essence of “not”—as the essence of the two taken together.  We can see distinction as encompassing both N and C if we look at its behavior under this essential complement created by it.

In distinction is that which is distinguished and that which is indiscernible.  In indistinction is that which is distinguished and that which is indiscernible.  The two appear indiscernible in all ways but name.  We might call this latter thing counterdistinction to reflect a role in our discursive account, but being distinguished for the sake of being distinguished is all this new name brings to the discussion.  We could say the difference between distinction and counterdistinction is in which side of a distinction, the distintive and indiscernable, is prior, but this is drawing further distinction, hypothesizing the structure of sides.  Within a distinction itself, priority is a thing to be distinguished and not present at face value.

To summarize simply, in contradiction we have something to resolve, and this is our choice.  In noncontradiction distinctiveness is imposed—a thing and its opposite are different, and we have no choice over this.  So we have our internal truth and external truth.  Both are valid and viewable as by fiat, as is seen in the multiple senses of fiat—a thing arbitrary and a thing by command.

We might ask, how can the external not be fixed first and foremost rather than purely of our own distinction when we clearly find individuals other than ourselves?  Which of us, we might ask, is the creator of reality, and if both, how do we explain conflicts of convention between us in our mutual creations of the external world?  The answer is in our distinction of individual.  Surely the individuals we distinguish in life, if they are to be distinct from ourselves but individuals like ourselves, will appear to us with all we hold fixed in individuality, such as the experience of all reality from a view in which only they have choice over what we see as fixed to ourselves but intrinsic to them.  Just as our distinctions contain fixed facts, so do the conflicting choices of what we distinguish as other individuals appear as impositions to ourselves.

We might ask, if all we can do with the external is discover, does this very observation uncover a truly external fact over which we have no choice?  Clearly the answer depends on what we distinguish in the question.

Our investigation of truth as among the things of reality calls our very deliberation into question when that deliberation is in terms of what is and is not true.  We proposed in Underneath Not an understanding that takes truth as better seen as naming.  Naming is a free act, and so this understanding of truth is a free convention of our own.  This understanding is the creation of a stable platform from which to launch our investigation of the very undeniable presence of truth.  It is not a solved issue, for truth by convention leaves truth as something arbitrary.  Indeed truth does appear to change.  A thing can be more than one thing.  A book is an archive of information in one use and a conveyor of information in another.  It is daytime on one continent and nighttime on another.  There are varying contexts for resolving the truth of which thing each is.  If we can fix our context, we can fix our truth.  But we don't have to.  We do have multiple contexts, and so do seem to be able to change our truths.  What is lost in those contexts when we untether their truths?

In Choice, Self and the External World we argued that the views of life as produced entirely by the individual and as produced entirely by external reality are equally relevant.  However, we ended the piece asking how it could possibly be that external reality isn't first and foremost.  We didn't balance that by asking why it shouldn't be that the individual is first and foremost.  The reason this second question doesn't compel itself more strongly is that we do in fact take our own thought and choice to be first and foremost, but there is no explanation in that.  When we seek explanation for a thing, we look for another thing prior to it.  In foundation is the explication of one thing as found within another.  All our explanations are found in the external world.  Our explanations are where we find truth.

In the self and the external world we have extremes of context.  We have the self, entirely without context, and the external world, the final explanatory, fully disambiguating context.  The fact that we have truth, yet still have choice, puts us at varying points between extremes depending on context.  We will say here, as we give up our self and accept more and more of the imposition of the external world, we create more and more truth.  Essentially we give ourselves greater and greater definition, externalizing our self, placing ourselves in communities.  If I am tall, I find myself among a community of those who are or would be tall.  If I am corporeal, I partake in that attribute that makes me among the community of the embodied.  When seeking explanation of the external world, as we are when explaining truth, we are left only with ourselves to externalize.  And so it is that we see variations of ourself—find them—in communities.  That these variations each resolve our facts, otherwise contradictory, makes community our context.

And indeed this is born out in more than just the differing points of view so clearly found in different social communities.  A great deal of philosophy defines truth by what we are as humans.  If we really wish to find answers to problems such as the mind-body problem, we must move to contexts wider than humanity.  It is hard to envision a community wide enough to solve this problem.  The view of external reality as produced by the self overcomes this limitation at once, but at the same time leaves the problem that it, as we pointed out earlier, isn't actually explanatory.

The truths of experimental science are too found in the community of humankind.  It is by definition of scientific method that among hypotheses, we accept only those that can be and are independently confirmed by different people.  We don't include elephants or institutions as those who's confirmations or denials we accept.  There is a scientific variant of reality as created by the observer in the anthropic principle.  By this principle, our very existence as humankind places bounds on externally observable facts such as the values of fundamental constants in our scientific theories of cosmology.  By untethering these constants, we remove ourselves from the context of the merely human.

A truth is untethered in the Liar's Paradox.  The individual uttering, “I am lying,” clearly doesn't include you and he as among a community of individuals discriminating facts.  More clear is the statement, “this statement is false”.  It is debated what category this statement falls into.  Is it among the community of propositions?

We've reached for the bounds of this approach to explaining truth in The Strange and Beautiful.  To maintain a self in the widest community still observing external truth, we take together the seeming fixed and particular external world with the seeming arbitrary possibility of the distinguishing individual by holding fixed the truism that all we discern is real and all that is real is discernible—in effect holding the two disparate views to be the same.  Holding the two opposing views to be the same, we should expect not only that the particular imposing world is implicit in our own free creation, but that anything we might choose to distinguish can be found already present in the found external world.  In such a view, the very communities we partake in are our alternates, putting ourselves into an exceedingly wide community leaving room for almost all individuality.  Our fellows, our alternates, are all those possible worlds we see here before us.

If we direct our consideration of community to the conflicts in which we participate, we can recognize that when we allow the unpredictable to direct our lives we give up our selves—our individuality and freedom—to enact the external truths of the communities that define those truths.  When we exercise choice in those areas least predictable—as in the considerate, assertive life of our own will—we are living the freest part of our lives.  Our communities contradict each other, but without them we have no truth in which to participate.  So when we find ourselves tugged or tugging to no apparent avail, certainly there is something to be gained simply by distinguishing communities upon and on behalf of which we act.

The statement of The Strange and Beautiful is essentially that all things that aren't true, or don't exist, somehow do exist.  Generally we assume non-existent things must somehow be waiting in the wings for us to apply them in our conception, even while they aren't existent in actuality.  Taking the waiting in the wings metaphor to mean the things that do exist are like the actors on stage in a play, we'd take the alternates to them to be those actors off-stage, in the wings.  Applying this metaphor to present wings, insisting non-existent things must exist somehow, we might say the playhouse has no separate facilities to serve as wings to exit to, so an actor leaving the scene would merely recede to a place on stage where he now functions in a new role—perhaps an onlooking extra.  This metaphor gives us an explanation of the widest, most present sense of the principle of plenitude—that all that could be, in fact, is.  This isn't simply the fullest, most perfect, or eventual actuality of all things, but complete, and complete with contradictory, actuality.  We will retain for this the phrase present wings.

This view is our best effort to externalize our internally produced reality, a necessary act if we are to explain that production.  Since internal production knows no bounds and the externally discovered is fully bounded, our internal possibilities, including contrary, counterfactual things, must all be discoverable.  This discovery explains certain perplexities, such as the nature of knowledge, cause-effect and the mind-body problem, for these perplexities all involve seeing our personal view from the outside.  In knowledge we hold that we hold something discoverable as true; in cause-effect, discovered things are produced; in mind-body, the person causes effect in a discovered body.  So while it is a curious effort to externalize the internal, the perplexities themselves arise from doing exactly that, and so carrying on in the course set for us by our very perplexity, we externalize ourselves in entirety, seeing all our choices as already chosen from one perspective or another.

In Context as Community we regarded the observation of the diverse truths in individual things being multiple things—while truth seems to preclude exactly this multiplicity—as explained by the differing contexts, or communities, in which we see ourselves under the varying verdicts of truth.  In particular, imposed external facts can be seen to be of our own design by recognizing the communities in which we place ourselves.  So, as a Texan among US residents, I'm a southerner, but as a US resident among residents of the Americas, I'm a northerner.  As a biologically persisting being, I need to eat, but as a political protester, I'm free not to.  In those things we have no choice over, our lack of choice is found in our choice not to choose, by setting ourselves against some chosen reference.

As the simplest example of the introduction of fixed truth by community, we can imagine, we as lone individuals reading from and writing on paper can choose any scribble we wish to denote whatever we wish.  There is no contradicting our choice, it being fully a free convention of our own.  However, if we recognize a community of two individuals reading and writing together, it now becomes an external determination of fact as to what means what, else we really aren't participating in that community.

In this simple determination of fact is a kernel of what we mean by knowledge.  Knowledge is related to some other phenomena sharing this kernel.  Aside from knowing something, we can believe it, take it provisionally or treat it as true, suspending our disbelief.  In all of these is 1) holding something—this, a pure internal choice.  To distinguish knowledge we require also that 2) what we hold is true—held in common with a context or community—and that 3) we hold that we hold it.  If the second requirement places us in a context determining the truth of the thing held, then the third requirement—the truth that “we hold this truth”—must place us in a context outside ourselves if it is to determine our very internal production.  Our first requirement presents no problem—there really is no question that we choose.  Our second requirement too can be reduced to choice where we accept our communities as chosen.  Our third requirement presents a problem.  If we look more closely at this problem, we can see how present wings can be seen to solve it.

It is in holding what we hold that we quickly lose our certainty of knowledge.  That we hold something determined is undoubted in retrospect.  And, true, in actively inspecting what we hold, we again hold something.  The problem here is that we hold now an inspection, not the thing inspected—that inspected thing has been externalized.  Once we look to find the facts of the matter on that, we are no longer certain, for what is found is not chosen.  Our one source of certainty—what we willfully do, hold or choose—is gone.  By example, when we finish running, we never say, “if I'd known I was running I'd have ...”.  However, we might ask, mysteriously, “but do I really know I was running?”  This skeptical view doesn't abolish knowledge, for knowledge as a thing certainly exists in those cases we do make this counterfactual usage, “if I'd known that ...”.  It exists, if not in some particular instance, as a counterfactual hypothesis.  To doubt the meaningfulness of knowledge, one must doubt the meaningfulness of counterfactuals, and this is what present wings make meaningful.  In present wings is that community wide enough to determine the fact of whether “we hold this truth”.

Let us consider what we know about knowledge.  We hold some thing.  That thing is indeed fixed and true with respect to the communities that share in holding it.  That we hold ourselves to hold exactly that truth is fixed and true of some one of our alternates discoverable in the many wings of our imposed reality.  We have explained, by finding ourselves in external reality, how each of our requirements of knowledge are met in externally true reality.

The community determining the verdicts of present wings—all verdicts, like or contrary—is the community of all communities.  In each perspective on our currently found distinction is a community, and by varying the community, we see those alternate truths.  How many dimensions of space are there?  To a visual artist with work of art on hand there are at least four: how far to the right, how far in front, how high from the floor and what color of what intensity.  To a conceptual artist there is no orthogonal numerical dimensionality at all, the meaning of the work not being spacial at all.  How can we find winter when its summer?  By considering Australia if we're in Japan.  To the two faces in the classic figure-ground image, a vase may not be present, but it certainly can be considered.

In this plenitude is to be found the answer both to why only this particular effect from this particular cause, and also how one can be dependent on the other.  That we have the strange particulars of conjunctions of causes with effects is seen not to be strange at all, again, simply because any two given things can be taken together to be cause and effect, one of the other.  With all possibilities waiting in the wings, our only task then is finding the right wing.  The relation of one resulting from the other is exactly that concurrence of communities fixed by one cause.  That is, fix what you will to be your cause, and those true verdicts of the communities that share in the distinction of that cause will be the effects of that thing as cause.  Our very requirement of externalizing our own choice explains the discovery of one thing as produced by another.

We don't really need the theory of present wings to explain the mind body problem if we are already willing to see externally found reality and internally produced reality as equivalent.  In this sense our body is simply that boundary of our self in choice.  We choose to look, but in looking is necessarily the function of looking.  Our eyes as function and organ are the same, seen at once as chosen, and again as found.  If we inspect our very choice of looking, we will need explanation of that act, and so something—in this case eyes—will be what we find.  But still, this has that uneasy lack of the explanatory, and it is in this uneasiness that we introduce present wings.  So we look to explicate this relationship, externalizing for ready explanation our choice.

Why does that unchosen thing, the arm, move there and not somewhere else when I, that distinct person, choose to move it?  When we have the existence of any possible alternative discoverable in reality, in fact it does move there, or somewhere else.  We can see examples of the most unbelievable alternates in our everyday lives.  Our arm does move somewhere other than where we choose when we reach out to someone in instinct but refrain through self-discipline.  Our arm does move where we did not choose to move it when we find surprise in its movement but explain the motion as reflex.

How can we have power over something fully externally determined?  Power requires resistance, and in a world where every possibility is present, that the individual is able to distinguish one possibility over another would require no power at all.  That is, if freedom of chosen distinction were significantly greater than the freedom of external observation, it certainly would seem odd that there is a strange preestablished harmony between the two.  But every alternate can be found, and that you have some particular, true, configuration now may reflect more a bias of outcome of the community in which you distinguish yourself.  Why are you not a bird among a community of birds?  This is not a problem for the mind-body relationship, but a happy circumstance, for if you whimsically shape-shifted, you certainly wouldn't ask about the strange impositions of external reality—they not imposing on you at all.  As we wind down this path of what-if to the less and less fixed of truth, we see how qualia such as color are clear to we as lone distinguishers, but become matters of fact, doubt and scientific inquiry into issues such as the physics of electromagnetism when shared with a community.

Yet in all this explanation of the unexplainable, we must bear also the honest truth, that in externalizing the self we have left the self doing the externalizing, so we will not find absolutely every possibility, but some instance of particular fact.  In the case of present wings, we might say one inexorable fact is a principle of conservation.  From every shift from one to another alternative perspective on reality will again be found everything as from the previous alternative.  So we as shape-shifters will find some delimitation of ourselves—that which is not us, not chosen, but fixed and discovered as we non-shape-shifters find our own bodies and physical needs such as rest or nourishment.  But as we distinguish this limiting process of externalization, surely we can see in it the meaning of doing yet discovering.

We've proposed embracing conflict.  In dissecting this proposition we would do well to consider it carefully.  There is, after all, a difference between glamorizing hardship and embracing conflict.  We can hardly consider ourselves discerning individuals if we accept an unwanted imposition when we are not forced to.  We here consider what care we can take, looking at our engagement in coercion.

It is the fundamental problem considered in this series that there seem to be unavoidable necessities.  This is often a good circumstance.  But it is not always, so we are left to wonder why and where we are truly coerced to anything at all.  We've supposed all particularity we come across to be of our own design, and the seeming impositions around us to be implicit in our own choice.  So we find freedom in embracing conflict when it is of the sort for which any path out leaves a circumstance in which we wish to stay.  At that point our recognition of it affords us a proportion in its experience and a certain virtuosity in handling it.  We model our proportionate experience of unwanted conflict on the sort we do want.  Many gratifying things are hard.  Those struggles in which we willingly choose to engage are the ones we experience with proportion.  So it is we look for the contradiction in our undesirable conflicts in hope of finding where it is we who are actively engaging—willfully—in the conflict.

Flat out contradiction can be seen to be embraced every day.  In modeling the world on contradiction we may attach excessive importance to that essential feature of models—that they are distinct from the thing modeled.  The expectation that the essence of contradiction in everyday life should only be extracted after long and difficult deliberation over counterintuitive propositions, places too much weight on the distinctiveness of the model from reality.  Contradiction as distinction does take together two things that are different, but the model is most successful when we find surprise that our seemingly counterintuitive take on things is not always so remote.  It is in this spirit that we say, yes a thing having parts makes that thing of count one have in another sense a count of many.  This contradiction is so easily written off, that we hardly recognize it as the presence of contradiction in actuality.  Surely this isn't a contradiction, we may object.  And surely it isn't, in the sense that contradiction as distinction is just a model.  But that the phenomenon has this resemblance to the model while not being problematic can just as easily be seen as the most compelling evidence that we have a good model.  We will suggest in what follows, further examples of contradiction in everyday life, and those involving coercion in particular.

Commands

Statements, commands and questions are seen with varying degrees of clarity to be modeled by distinction and plain contradiction.  A statement, a proposition, makes a compelling example of distinction.  It carries this sense of contradiction in that most incredulous way we mentioned in the previous paragraph.  The more counterintuitive existence of contradiction can be found in asking the way in which commands and questions are distinctions.  We have a resource in statements that allows us to cast commands as statements.  To achieve coercion with only a statement we can turn to our ability to assert contradictions.  If an individual has one thing on offer, we can coerce from them anything distinct from that offer—in essence commanding them to do something they weren't otherwise going to do.  This method is described in Smullyan's The Riddle of Scheherazade.  He describes a situation in which a father offers his younger daughter's hand in marriage to his elder daughter's suitor if the suitor makes a true statement, and none of his daughters if he makes a false statement.  The suitor answers such that paradox arises in all situations in which the father doesn't give him the elder daughter's hand.  This arrangement can be generally characterized: 1) the coerced who holds certain presuppositions offers a particular action and awaits some true statement while 2) the unsuspected coercer's reply conjoins the fact of the coerced's refraining from action with a desired result and conjoins fact of the coerced's carrying out that action with facts contrary to the presuppositions.  The conclusion from these two as premises is contradictory if not along the coercer's desire.

This use of contradiction is seen to hold the essentials of coercive command.  To further explain questions, we see in them commands to resolve contradictions.  If I make the statement, “it will rain tomorrow”, the time, “tomorrow”, is well-placed.  If I replace the object of time with something quite out of place—like an object of no time at all such as the word “when”—I am only a coercion away from having my contradiction resolved by an answer such as “tomorrow”.  A question is a statement of contradictions, with at least one of those contradictions being itself a statement of another contradiction, all this exemplifying our agility at navigating contradiction.

If this construction carries the essence of the imperative, we've found our freedom from coercion.  In these examples of coercion, the coerced subject must be engaged.  Not every question is met with an answer.  Not every command is followed.  In Smullyan's examples, the coerced subject makes an offer of action, which the coercer deftly manipulates into a necessary result.  We have an undeniable coercion, but not the undeniable imposition, for the engagement of the coerced is required.  If our offer is always present in any imposition, we have our freedom, for it is ours to abstain from it.

Logic

We see contradiction as coercive everywhere.  In simple everyday reasoning, the bare existence of paradoxes coerces us away from arguments that lead to them.  In logic paradox has shaped our landscape.  Paradox forces logicians to avoid the disjunctive syllogism in entailment, to restrict our comprehension in set theory, to introduce types in higher order logic.  In mathematics, the fundamentals of real analysis were driven by the paradox of infinitesimals.  The fact that it seems unsafe to accept “B” simply because we have “A or B” and “not A”, carries both a coercion of paradox as a possibility in our conclusion and in what imperative there is in being compelled to adopt premises.  Do we have freedom to disengage from these premises?  We have argued elsewhere that we do.

Knowledge

We find a ready example of an imposed fact from which we are free to abstain in certain knowledge.  When we ask, is certain knowledge to be had, we have in a sense fixed our answer in the question.  If we wish to be certain about it, we can only answer yes, for a certain no is paradoxical—at once an example of certain knowledge, and at the same time denying the possibility of the same.  If we do not wish to be certain, an uncertain yes or no still leaves open the question.  We seem only to escape the certainty of some certain knowledge by not answering the question.  As we pointed out in our last entry, that knowledge only seems certain in counterfactual situations does not remove the utility of knowledge itself.  By recognizing the border of the possible answers to our question about knowledge, perhaps we can find proportion in those situations where such an answer carries import.

In our suspicion that all coercion requires our engagement we have not conclusively excluded the possibility of impositions over which we have no choice.  We might say we can defeat our suspicion by fiat, contradicting our own choice and finding all resolutions to be against that choice.  But whether or not some impositions are utterly unavoidable, we can only be giving ourselves more freedom by considering in any one circumstance how that imposition may, counterintuitively, not be so imposing after all.

In this entry we return to the view of life as naming.  Of the ideas considered in this series, naming is only less general than distinction itself.  Our recent investigations on the subject await further tools to their task.  Subjects such as present wings and the relation of self to truth having been forthcoming with such tools and characterizing devices, we will now employ them in characterizing naming by showing the relation of naming to these other views.

Face value and the meaning of naming

It is a difficulty for the philosopher who seeks to reduce phenomena to prior principles that the process of so doing never ends.  However, in seeking to understand reality, even in reducing it, we may rely on the practical effect in our life of our investigations.  Observing that the process of reduction does not end, yet in our practical affairs, things do not regress unendingly, we may choose to take this observation of unending reduction as a first principle—putting an end to the reduction by the same fiat we presume to be in effect in our practical affairs.

In Context as Community we observed that science as a method of authoritatively cataloging absolutely true fact falls short of the philosopher's goal, in that the community determining those facts is not the only community in which we participate.  However, scientific method carries a deeper allure.  Scientific truths commend themselves.  We come for ourselves to the same scientific conclusions presented to us in a scientific account.  It is exactly in the method's not being authoritative that it is most compelling.  We observe that we are compelled to accept and benefit from scientific investigation because its results are reproducible, not only because its results have been reproduced.  This same effect on both the author and audience is sought by an author in the indication of first principles.  We as readers make progress when we feel compelled by our own concurrence with what we read.  We here endeavor to establish what we mean by the concept of reality as naming, striving such for self-compelled communication.

What is it an author and reader share when in successful communication of such self-evident ideas?  In Doing Yet Discovering we observed our skepticism about knowledge comes into action when we attempt to hold what we hold—investigate our very apprehension.  When we hold X and look to hold Y, “that we hold X”, Y is now our apprehension, and uncertainty is cast on what we held in X.  This thing we do without self-inspection we will here call holding at face value.

When we discuss something, we treat as fixed among participants the meaning of various of our terms.  A writer may not know that his reader has the same sense in mind for a term as he does, but his writing is no less useful for it.  To the extent the agreement is in, the discussion will be fruitful.  However, for that writer to assume as fixed and then cast doubt on a term, is to bring the meaning of the term under discussion, not the substance of the originally fixed meaning.  This too can be fruitful, but in it is again an assumption of coordination between writer and reader on the terms of that discussion.  This coordination, or concurrence of face value, is always present and holds what effect there is to our first principles.

Face value holds two roles in the present conversation.  In one role, it acts as the medium of our first principles.  In the second role, it characterizes naming itself in that face value is held, as are names to their meanings.  We find ourselves in the same place as our opening paragraph to Underneath Not.  Our topic and its explication are found to be one and the same.  If this is paradoxical, it may not be dishearteningly so, for it is fitting, even necessary, of any explication of all reality.

Another reductive attempt bearing relation to naming is the theory of descriptions as per Russell.  In demonstrating the eliminability of descriptions from pure logic we find their disappearance encourages us that descriptions may in fact be a superb description of reality.  In our search for prior principles to all reality we would be most pleased if when we have exhausted our sequence of priors nothing remains at all.  All priors as among everything should be eliminated if we wish not to provide circular explanations.  If, in an intuitive sense—or if only in what we take at face value in logic—the logical constants and rules of deduction of pure logic are recognized as themselves descriptions, there is no part of pure logic that remains after description has been fully eliminated.

So, by naming we mean that which we hold, or perhaps those descriptions we introduce and eliminate.  We can add to these two characterizations also that naming is the process of identification and substitution of expressions, as well as the convention of this identity relation by an individual or community.  In taking together, naming is seen almost directly to be distinction, and not just identifications but any laying of things against each other, as one finds in compound expressions, is left as first in principle.  We can choose not to take it as first in principle, and derive even this juxtaposition to be an act of identification.  The placement of things in such compound entities is then determined by the letting of, say, “left side = ‘f’” simultaneously with “right side = ‘x’” in fx.  The simultaneity would then be the letting of the two namings themselves to name each other, recognizing in this that basic principle that one thing can be be multiple things—in this case a thing with a left side and a thing with a right side.  In what follows we will compare naming to some views of reality presented previously in this series.

Context and choice

Naming is not self-centric.  Naming as convention has a clear tie to context as community in that communities convene on standards, such as names.  And while external truth may be determined for ourselves by the communities to which we as individual self belong, naming, in and of itself, does not require the individual-centric perspective.  Any community can form a convention.  We are free to consider names with or without the involvement of we the person doing the considering.  In this can be found some freedom from disproportionate conflict, for comprehension of any exigency from this view allows, but doesn't commit, us to examining our own involvement in it.

We observed in Choice, Self and the External World that naming shares with the view of reality in choice and contradiction, internal creation and external observation.  Having now at hand an index between pure self and pure externality in context as community, we can tie also the partial order we imagined in Taking Together to this spectrum of truth.  Under this correspondence, the varying expressions we have for an externally found object act as the conventions of communities determining the truth of that object.  The least explicit expression for an object leaves open the most choice in resolution of its denotation—this corresponding to the self as pure choice.  The most explicit expression for an object is the most determinate, leaving no choice in resolution, corresponding to fully externally discoverable fact.

Incompleteness

There are counterintuitive conclusions one can draw from this identification of reality with naming.  We can expect, as we found in Doing Yet Discovering, present wings to resolve some of these perplexities.  For example, expressions being incomplete depictions of our objects, taking our expressions to be the entirety of our objects leads us to conclude that what is not known about an object from its expression alone is not determined independently of our knowledge of it.  We may ask, is the object going to change to meet whatever expression we provide in elaboration of it?  The answer is no.  On the one, seemingly self-defeating, hand, whatever it might change to can be seen to be whatever it “really” was prior to changing, simply by the presence of all alternates to that thing as discoverable in found reality.  On the other, that original fact of the object truly does contain variability.  And this is not a philosophical problem, but a demand we have on reality.

This demand is that of possibility.  By example, when taking notes, the very determinate piece of paper and very determine inscriptions on it, made very determinately by we ourselves, is held by ourselves not in complete determinate detail.  That is, we don't even know exactly what we have written, but carry an incomplete image or expression for that seemingly determinate fact as and after we write.  If we knew exactly what was written on the paper, the paper would be no useful tool at all, but merely a superfluous copy of what we already know.

We demand incompleteness of our things in universals.  Universals are contrasted exactly with the fully specified, or particular.  When we inspect a universal, specifying it to greater and greater degree, it loses its generality.  If the universal “green” were as determinate as a list of things green, “green” would be specific, not universal.

In one sense, there should be found very little conflict in that which is unknown about a thing being as integral to that thing's essence as what is known about it, for the known and unknown are opposites—in perfect correspondence to each other.  Either, and both, are completely characteristic of the thing.  In relation to context and the separation of self from the external world in choice, we might say, the incompleteness of our fixedness at the varying points of context shy of the completely external is the imperfection of our knowledge of the true nature of things, or the incompleteness and imperfection of the names that demarcate those things.

Metaphor

In present wings we take the possible worlds, w₁ and w₂, to be found within each other.  We say, the particulars of w₁ are the particulars of w₂ under change of perspective.  We can ask, what is this change of perspective?  If we compare our present wing worlds to logical expressions, we will see in their strange particularity something like the particularity of possible predicates—i.e., satisfiable but not valid, or not necessary but not contradictory propositions.  Such predicates carry extensions of interpretations that satisfy them.  We will here imagine an idealized logic for which sense and this extension coincide.  When discussing the entire world we would expect the full context of that world to be present in our predicates.  We take the features of observer perspective implicit in the Earth-bound morning/evening observation of Venus as a star, and the historical particulars of Greece in the names Hesperus and Phosphorus as constants or free variables explicitly visible and admitting interpretation, thereby capturing the sense of the various names for Venus in extension.  The distinction implicit in taking two predicates, P and Q, to be the same is the extension of the larger predicate, P ≡ Q.  And in the same way that sense is most visible in the identification of distinct names, Hesperus = Phosphorus, the identification of two worlds, w₁ = w₂, will capture a sense and the sense will capture the distinction of this alteration of perspective.

This idealization entails contradiction, speaking as it does of all things.  We addressed this in To The Extent.  We there took all things to be all others, to whatever extent they are.  The contradiction in the identification of two distinct things there provides the parameterization of extension whereby the identification is resolved.  The application to present wings can be seen in the movement from one perspective to another.  Taking the figure of two faces to hold in its ground a vase leaves some element of the picture free to interpretation when we take it in its alternate identifications as faces or vase—the free element here well-taken to be figure-ground, or which, black or white, is the figure and which is ground.  We have here again face value in that we, upon first view, take one or the other to be figure and experience the surprise of optical illusion when what we took at face value as figure changes.

There is the tie to naming here in the incompleteness implicit in those contradictions, constants and free variables admitting interpretation—or completion.  This, taken with the holding of some face value in common to two perspectives provides a close tie to metaphor—another topic in which expressions are identified.

We immediately see alternates to our found facts in those very same facts when substituting likes through their analogies.  We directly experience the removal of contradiction in the identification of dissimilars in our full involvement in such analogies.  This full involvement can be seen in Freudian slips and the adage, “when all you have is a hammer, every problem looks like a nail.”  The analogy becomes our reality when we so completely immerse ourselves in it, we experience surprise when drawn out of if.

In both naming and metaphor we take distinct things to be the same.  What is the difference between naming and metaphor?  If we remove the distinction between domain of discourse and the language in which we speak of things within that domain, naming is just metaphor.  Names then are never without sense.  The point at which a name becomes a pure designator is the point at which we no longer distinguish anything in the name.  But when discernibly present, names always have some structure, possibly graphical, auditory, imaginative or otherwise.  If we truly take the name in a sentence “you are John” at face value, then we distinguish nothing in referent to “John”.  But taking the sentence as medium at face value is not to take some meaning of the sentence at face value.  We could as easily have used the word “mountain” instead of “John” and would have essentially the same content as we have yet to distinguish any content.  If we distinguish further we will take different information from each of the two names.  At that point, “John” and “mountain” both carry distinct information in sense.

We can watch the varying sense of a name in the example of “Socrates”.  “You are Socrates.”  Am I saying you respond when “Socrates” is called out, or am I saying you are a deep source of wisdom by comparing you to an ancient philosopher?  In the former what I take at face value has more to do with responses to auditory facts, and what varies from the face value is who responds.  The latter allows me to review you and refer to other things I distinguish in you by their corresponding distinctions in the ancient philosopher.  To the extent you are Socrates you are a conduit to truth through dialectical investigation.  Here I am varying the person and time, and retaining the philosophical activities.  If Socrates is just a proper noun, say just another entry on a list of name suggestions, it will carry still some sense—perhaps that its referent is male.  If I call you “X”, I am purposely using a name that carries little sense, and so carries exactly that sense: not specific, free as possible of connotation, hence its frequent use in exotic or extensible contexts.  We might try to achieve name as pure designator by imagining our sentences to be taken just that degree beyond graphical face value that says, “John”, “Mountain”, “Socrates” and “X” are indistinguishable except in their attachment to “you”.  But even here, it is our face value doing the designation, and we have in face value that very boundary that so well characterizes metaphor, that full involvement.

That our very acts are metaphors can be proposed when we look at the meaning we apprehend in our acts, as is well-exemplified by the act of reading.  Are we now reading words or inspecting graphic images on a page?  When we first sit to a reading, we may find ourselves inspecting the physical object—observing the font and spacing of the text, or the choice of format.  When we move on to immerse ourselves in the reading, we never stop our inspection of the page before us, yet we “lose ourselves” in the content.  We rarely stop to notice the graphical nature until some imperfection such as a typo or illegible print presents itself to us.  We move from a page to an essay.  We don't say, the page forms, is like, or even contains an essay, but that it is an essay, as in metaphor.

The relation we've given here of naming to various other concepts is not crisp, concise and definitive.  The pervasiveness of naming in our lives—here taking us so far as to the audacious claim that naming forms the makeup of reality itself—recommends to us that it will not be well characterized, but rather is better suited to the role of characterizing.  So in proposing these characterizations of naming itself, we hope to gain in their application a crisper, more concise and more definitive understanding of life itself.  Where that is not to be had, we again have a ready resource in the recognition that some imperfections of our lives are implicit, and themselves a source of possibility.

In this entry we carry out an experiment in inspecting distinction.  We don't hold that this is the correct and only way do do this.  Indeed, holding distinction to be the essence of all things, our exposition is guaranteed to be imperfect by the principle that only all reality can accurately model all reality.  We here work by example, or approximation, looking to model distinction and trust in our roles as collocutors to hold only the essentials of the model, thereby capturing a possible essence of distinction.

In distinction is the discerned and the indiscernible.  We model a simple distinction of a diversity of two, D, by { D₁, D₂ }.  D is the original thing upon which we draw a distinction; D₁ and D₂ are the distinguished parts.  When D is what is held at face value, all we see in the distinction D is what we've fixed upon as D₁ and D₂.  We do not see the D.  D at that point is as yet uninspected.  We have in this first act a thing that is both an arbitrary act of distinction and a determinate act of particular fixation.

There are two features of this first model that tell us we have an incomplete apparatus for full distinction.  First, in the fixing of D₁ and D₂ in our model of D we trust ourselves to ignore irrelevancies of letters and subscripts and see neither one of D₁ and D₂ as elevated over the other.  Second, our having named this distinction D is a feature of our account, not a feature of the distinction, leaving us no way to see a whole divided in one distinction.  Yet, we do recognize particulars with emphasis, and we do distinguish wholes to be divided.  Here we may find our bridge between discovery and creation in that emphasizing some among many has the character of discovering them, while recognizing many as parts of a whole has the character of creating those parts or choosing the whole's division.  As a form of distinction bridging these two views we can see in some imagined list of particulars a commonality with some central collection elevated above the rest.  In this sense, the { D₁, D₂ } is just two elements taken to be elevated above the rest on the list, and the view of the whole D is taken to be just that commonality to the many on the list.  We can recognize as somewhere between these two views, distinction as a multiplicity of variations.  A useful element of our model of distinction then will be this bridge between the free and arbitrary visage of particulars, and the discovery of those certain of those particulars as fixed.  Between the bare apprehension of particulars at face value,

(A) { D₁, D₂ },

and the full recognition of the whole,

(B) D₀ = { D₁, D₂ },

we emphasize, or focus on one element—discern it from among many,

(C) { ... F_i, F₀, F_j, ... }.

Let us call this latter distinction F.  We can depict the approximation of the distinction of particulars alone by

(A') { ... D_i, D₁, D₂, D_j, ... }.

and that of the whole with particulars by the distinction of distinctions,

(B') { D₀, { ... D_i, D₁, D₂, D_j, ... }, ... },

With this we can draw further distinctions on our original taking of the whole with its particulars, D₀ = { D₁, D₂ }, discerning in it priority.  Our further application of form F will prioritize which comes first, the discerned or indiscernible:

{ D₀, { D₁, D₂ } }

or

{ D₀, { D₁, D₂ } }.

These two forms of D₀ = { D₁, D₂ } we call E₁ and E₂ respectively.  In E₁ we say D₀, as the focus, is fixed first and seen subsequently to be distinguished.  This is the simplest form of multiplicity creation.  In E₂ we see { D₁, D₂ } as the focus upon which is elaborated that its multiplicity is no more than the whole D₀.  This is the simplest form of the removal of distinction.  These two distinctive acts we will call division and unification or inscription and erasure.

With distinctions such as with E₁ and E₂ we can see in distinctions such as D, naming and community.  Via E₂ and its removal of distinction we can see in dissimilars identity, or indiscernibility: D₁ = D₂.  They are recognized via the unification in E₂ as undistinguished, or the same, or simply, equal.  We may, via E₁, remove an apparent contradiction in D₁ = D₂ by creating a sense in which E₂ holds of { D₁, D₂ }, say by distinguishing in both D₁ and D₂, { G, ... }, so that D₁ = D₂ now, perhaps surprisingly, is fulfilled by { G, ... } = { G, ... }, in which we lose our ability to discern the two by no positive act of distinction at all.

We may distinguish each of the D_i in D as { D_{i, j} }, and via various operations like E₁, see on occasion D_{k, l} = D_{m, n}, and again via operations like E₂, recognize a concomitance of distinction with in a community of discerned things, { D_c1, D_c2, ..., D_i', ...}.

With this experiment we have the elements of taking together, naming, internal-external, choosing-fixing, resolution of contradiction, community and the asymmetry of priority.  There is little that is circular in our construction, though this absence likely reflects certain conveniences we availed ouselves of in concepts such as nested distinction, forms of distinction and the use of forms as operators.  Such concepts will themselves have to be found among distinction itself—distinction as distinction, with no use of singular or plural, object or operation, initial or subsequent.  But compelling approximations are exactly what we seek, for perfect descriptions aren't to be had in fixed expositions.  The distinction captured by the investigator, though, does not carry such limitation.

A thing can be multiple things.  This observation is uncontroversial.  We recognize in it simply a statement of the many true things we can say of any one given thing.  “This is an utterance and this is a sentence.”  “This object is both a bookend and a decoration.”  It is a very direct demonstration of the essential way distinction is part of our reality.  In drawing a distinction on a thing, we see the thing as yet something else, and however one explicates the terms of the conversation, such as “thing”, “can be” and “multiple”, the evidence of the observation remains.

Multiplicity in things, however, is not a principle applied with abandon.  We don’t say, for example, “this utterance is multiple sentences”.  In this we again have distinction, for we are discerning—as one with a discerning palate—in our application of distinction, seeking to equate things only among those varieties that carry some true unity.

These two senses are in opposition.  If distinction alone is our first principle, abandon seems to rule, and there is no constraint on the division and equation that must ensue.  Yet, a distinction held is a particularly fixed thing—by its very grasp, its diversity is withdrawn from contest.

It should perhaps be no surprise we find ourselves drawn to two extremes in our analysis of life.  There is the skeptical extreme that relinquishes the struggle to conclude anything, seeing all as arbitrary, possibly even the judgment ‘all is arbitrary’.  There is the fatalistic extreme of determinism, in which all is necessary and in which conclusions are again undermined, in this case by the independent bareness of pure fact.  But points between extremes do find elucidation in meaning and interdependence.  Caprice comes at a price, and even the best vagaries beset themselves.  If, in our analysis, we wish to resolve all reality into some single underlying principle, as we do with reality as distinction, we must find this meaning, this consequence found between extremes, within that principle.  We will observe here that the diversity of a thing being both arbitrary and fixed is in fact the essence of meaning.  This is a diversity in distinction itself.  We find a bootstrap in distinction too being both arbitrary and fixed, and in that, nothing any more controversial than the principle that a thing can be multiple things—a thing in abandon and a thing in constraint.

Modeling

Considering philosophy to be description of the world focuses our attention on the terms of the description.  The principal term considered here is distinction.  It may be felt that recognizing reality as really just a lot of distinction misses the point.  Isn’t it that reality can be proposed to be, in its true essence, many different things, and it is what we distinguish in these possibilities that tells us which is correct?  That distinction is after the fact?  We demonstrate that two things are indiscernible, and therefore the same.  We highlight a distinction between two things to show that they are not the same.  We point out that a given misunderstanding is explained by the mistaken drawing of an inessential distinction or the failure to draw a distinction that is essential.

It is our thesis here that the erecting and demolishing of distinctions in this way explains how meaning and implication are mediated.  So, if not for the pervasiveness of distinction in our deliberation, and the pervasiveness of deliberation in the experience of reality, then for its value in explaining what meaning we may take in the majority of our philosophical endeavors not based upon distinction as first, distinction is compellingly first taken as first.

Meaning and implication

Meaning and implication are closely related.  Meaning is implicit in expressions and events.  We ask, “what do you mean—what are you implying?”  That the two are mediated by distinction can be seen from the circumstance of two individuals communicating.  What does the first person discern in the second’s exposition?  The second has made discernible impact on the first if successful in communicating something.  What has been distinguished is the meaning taken from the discourse.  We say, however, that the meaning is taken or mediated, and that this requires some explanation.  Discerning something alone does not provide explanation of meaning.  We find distinct in a discourse perhaps sounds or letters.  Within these objects we discern yet other things like words.  Within these we discern ideas, and with those we may discern attributions, and among those, and indefinitely on, we can discern further meaning.  This discernment, at face value, is really metadistinction.  As a thing distinct from pure distinction, metadistinction destroys the unity of our theory.  Left out from our description of reality as distinction is metadistinction—or multiply applied distinction.  It is in facing this that we recognize something similar to the multiplicity discerned in any distinction as characteristic of distinction itself.  Distinction—like things discerned—is distinguished and multiple.  The contact of the various layers of distinction is essential to meaning, and requires explanation.

To understand how meaning is mediated we may examine implication by association.  When one is bolstered or takes offense at a comment regarding some group with which he or she associates, how is that attribution to the group transferred to the member?  “You may not have said I am φ, but you implied it.”  We have in the multiplicity of things that the attribution was indeed of the member, in that the member is not merely associated with that group, the member is that group.  This is the dropping of the distinction between the member and the group.  At that same time, association is between things, so the distinction of member and group does hold.

The view of distinction that puts the self as individuated choice and the external world as the fixed fact of absolute truth provides us again implication as multiplicity in distinction.  We seem not to be able to find implication in absolute truth alone, for the truth of a conclusion is simply true, regardless of any antecedents we may prefix to it.  Implication in an internally created truth cannot be found, for any truth whatsoever may be taken to be the consequent, again, regardless of particular antecedents.  But we have in implication via conditional, ‘A implies B’, both possibility and certainty.  We want the absolutely determined A and B, to have possible alternates demonstrating B to depend on A.  And distinction is exactly those two things: things necessarily fixed and things arbitrarily contradicted.  That we can distinguish in both ways at once is simply a multiplicity in our distinction.

The possible and actual

One type of variation in proposition we may use to determine an implication is the interpretation.  We imagine either a collection of possible worlds or some imagined universe of possible domains of discourse.  We test a proposition for truth, it having various determinations in various worlds or interpretations.  In this way too we draw a distinction that we alternately drop.  We view the expression of a proposition as some distinct interpreted entity, and drop that distinction and attribute subsequently derived logical conclusion of the original expression.

In a less mathematical sense, we say we may drop the distinction between counterfactual things and actual things.  By so doing we remove the difficulty of attributing something of a thing that isn’t.  We must resurrect the distinction to mean something in particular—something in contradistinction to what that thing is not.

Naming

In naming we have designators and designees.  We hold them distinct, and in so doing create the conundrum of how their meaning is mediated.  However, observing we are able to speak with and of sentences, we may be compelled to recognize that our domain of designators and our domain of discourse are the same.  And in this we find something more palatably mediative.  Two things from among the same domain are effortlessly—implicitly—substituted for each other when we draw no distinction between them.  At the same time, we retain the freedom to separate our names from their objects, in that circumstance in which our meaning is accepted and uninvestigated, to avoid of the equally unpalatable prospect of passing around among participants in discourse the very bits of the world we discuss.

Philosophical nominalism provides explanation in the dropping of the distinction of abstraction.  In this is the pragmatic benefit that we are less likely to misattribute character to our things otherwise given independent existence.  If “apple” and “the apple” are two different things, where does one find “apple”?  Does “apple” have extent?  Of the person found in a particular body we may ask, can this soul meander the world independently of this body?  However, we may discuss “apple” or soul independently as concepts and descriptions, so we do, if only in net-effect in nominalism and its opposing views, draw the distinction, holding the abstraction as separate from yet substitutable with its description.  This effect is well-taken to be the meaning and implication of our apprehension.

Where meaning falls

Misattribution points us to a valuable source of information as to where we hold something fixed in relation to its varied alternates.  Our mistakes, when taken not to be mistakes, recover the many missing alternates from our actuality.  By example, when we ask about the strange particularity of our discovered physical space—its three dimensionality or continuity—we can look to what we attribute as error in our discourse for nearby alternates, the context of which remove the appearance of particularity.

Suppose two people to be having a conversation on a stroll, the second interrupting the first to ask, “Exactly where you are going?” meaning to question the purpose in the first's line of reasoning.  The first may answer, “to the garden,” thinking the second to be wondering, to what location in space he is directing himself in the stroll.  “To the garden” and “to a demonstration of the value of temperance” both fit as answers to a question of where.  And in this we may say the demonstration is only metaphorically apt as a destination.  The use of destination in space is first and foremost.  But perhaps destination in space is merely first and foremost to the person considering it the most relevant meaning to a given question.  To the questioner, destination in space is merely alternative and the destination in demonstration was the most apt.  The fact that we can simultaneously have as destination a demonstration and a physical location should point out to us that not all things exist in a physical space—that alternates to continuous, three dimensional space are immediately before us.

In selection bias too we have an informative fallacy.  When we see an error in the breaking of a convention we can at least admit that, if only in a contrived sense, those breaking the convention simply have a convention of their own.  Here we have a multiplicitous truth meeting objections from all sides, “but that is not what is we mean.”  If we introduce an objective third party to sample the behavior and determine the true intended meaning, we still have an arbitrary result, for errant results will simply be written off as examples of selection bias.  The ostensibly objective party is deciding the truth of the convention all over again, in meaning one population to be the correct one.  Treating the error not as error—dropping that distinction—gives us alternates by which to determine dependency, and holding the error fixed gives us the final truth.

The anthropic principle exemplifies the dropping of selection bias as error.  Simply discovering all the facts, as in a Copernican view, and simply necessitating the facts by our presence, as in a Ptolemaic or anthropic view, both deprive our facts of meaning.  However, if both the finder’s bias, and the arbitrariness of what is found fixed are taken together, we find what is implied by our presence.

The existence of absolute truth in the light of the most skeptical considerations is secured in this view.  An internally created view such as the anthropic one brings with it a sense of reality as completely lacking in absolute truth.  We may say, the laws of physics could have been B rather than A, if only it had been something other than me investigating the laws.  But finding meaning in various finders of the universe, we have still the certainty that ‘I imply A’ and that ‘it implies B’.  ‘I’ and ‘it’ are, of course, distinguished presently by one of their alternates (you or me), showing the entire enterprise to admit of possible variation, and those variations to admit of absolute truths.

Hume proposed that in the understanding there can exist necessary connections, genuine dependencies of consequent on antecedent, but that in the empirical we have only concomitance in any relation of distinct things—conjunctions of particulars but no genuine necessity that any given particulars be conjoined.  Kant fixed upon a transcendental boundary between these two, the understanding and the empirical.  This is quite similar to the division we draw here.  The understanding is of the self, and the empirical is fixed externally.  In a sense, Hume drops the distinction of meaning in external things, and Kant restores it.  However, for both of them, necessary connection, or in Kant’s terminology, a priori cognition, resides already in the understanding by first principle.  In reality as distinction, even things determined true a priori are fixed, and therefore essentially external.  From what we propose here, the a priori as a source of such judgments is perhaps well seen to be in the transcendental—or at the boundary between the fixed and unfixed in any case.

Kant does consider this option, and in the process shows us a fallacy that allows us to investigate where our meaning falls.  He, according to the Cambridge edition of the Critique of Pure Reason, in a note in his personal copy at the head of Transcendental Analytic, First Book, The Analytic of Concepts, asks whether a priori principles are themselves transcendent.  In making an experiment of a universal proposition, if the empirical judgment sought does not stand under a universal rule for judging, the concept of this endeavor is a vicious fallacy.

This fallacy, unlike our previous errors, is of the vicious variety.  Indeed we do find in the terms of meaning given here something like a paradox.  While we say that distinction as both abandon and constraint is simply portraying that uncontroversial feature of a thing being multiple things, we do see the two things as contradictory.  If distinction is to be found in the resolution of contradictions, in this particular case we seem to be asking ourselves to both resolve and not resolve it.  And perhaps, in this, we have explanation for why we cannot, in the case of knowledge, hold what we hold with certainty.  In holding meaning, we insist that we not resolve the underlying distinction.

Our theory, as distinct from its object, is expected, no matter how much more elucidating than our intuitive common sense it may be, to describe also this matter of fact world that is its object.  We want to say a rainbow isn't a colored arch in the sky, but an interference pattern of photons resulting from the water droplets through which they pass.  But we want also our theory to leave the undeniable fact, that a rainbow is a colored arch in the sky.  We want to see things in their most ideal aspect, recognizing even logic is just what we choose to single out.  But we want to see, nonetheless, if ‘A’ and ‘A implies B’, then however we might wish to single this out such that ‘not B’, we are stuck with the conclusion B.  We want to see all human conflict as a matter of confusion and that in some context all disagreements are resolved.  But we do not want to lose our footing by misapplying this principle, giving in to our impositions in contexts in which they are not resolved.  We want to see that reality is what we find in it, as by our will.  But we must also see, that external impositions do exist.  This theory is expected to remove conflict, but the multiplicity it must describe implies that this improvement must come while embracing the conflict.  And we have from this embrace meaning itself, which is, after all, what we seek in our theories.

We have application to conflict here in the meaning we appreciate.  It may on occasion appear that we never appreciate a thing until it's gone.  This, if it were a universal rule, would be entirely unacceptable.  If a thing cannot be appreciated until it is lost, there is no point in acquiring it in the first place.  We do appreciate things.  We can strive to acquire and appreciate what can be kept.  Perhaps we need only remember that taking something for granted is itself losing the thing, for the loss of our sense of its possibly being otherwise deprives us of its meaning.  We can keep the objects of our desire by simply appreciating their meaning—holding on to that simultaneous possession of mere possibility and absolute certainty.  The intermittent threats to that certainty can be seen as welcome reminders, the value of what they secure for us outweighing the conflict they inflict upon us.