What this amounts to, and what deserves further elaboration, is that our ordinary conception is already correct.  This understanding places the burden on the theorist to explain why the ordinary conception is right.  It is the theorist, after all, who claims things mean something other than they appear.  It is the theorist's most honest course to resolve these problems as his or her own.  To claim the ordinary conception is wrong is to read a belief into someone not holding that belief—something akin to placing the burden of proof on the accused.

I will desist from elaboration for a while though.  I will only note that having touched on implication—a target topic here for quite some time—it too deserves elaboration.  Simply keeping it in mind is elaboration enough, but for the pure stimulation of the activity, the reward from the development of clear conceptions creates the merit in elaboration.  And seeing the fixed as the implied of our choice, and our choice as implicit in the grasp of things discerned fixed is something open to explanation now.  Understanding discovery, surprise and the insisted upon as explained by implication allows us to resolve what problems we as theorists propose.  Seeing what we ordinarily do with our problems and happy circumstances as nothing other than examples of those things we as theorist provide in explanation will provide confirmation of our understanding.

A page containing these entries in-line and in sequence can be found at http://patheffect.com/.  It contains nothing other than what you may have already read here, except with occasional corrections.  Though I imagine one day having corrected there the myriad typos and other minor inaccuracies this blog seems to have seduced me into making, all the major flaws will stay, even there.  It's a short read, and perhaps I should keep it that way, but I make no promises.

So, thanks for stopping by, and I'll see you around, distinguished ladies and gentlemen.

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 univers 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 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 is 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.

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.

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, 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 your 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 later 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 for investigation 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 designate 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 is like an essay, as in simile, 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.

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.

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 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 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.

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.

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.

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.

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.

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.