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.