Why do you assume that existence presupposes a relative difference from another existent? Couldn't A be different from (in this world) non-existent nothingness? For a horse to be different from a unicorn in not having a horn, why would the unicorn need to exist?

What would A (relatively) be different from? — Daniel

A would stand in contrast to not-A. That is the way the logic goes. The existence of A is wholly dependent on it being not not-A. :grin:

Beautiful, and I agree.

But what is not-A? If it would be something, at all. How do you conceive of this thing which is not A?

Why do you assume that existence presupposes a relative difference from another existent? — absoluteaspiration

Because the idea of something existing when all of its properties cannot be differentiated from each other (the quality of difference does not exist) makes no sense to me. To be honest with you, that is the best answer I can provide, so far (a weak one, I admit). Now, I would like you to pay attention to that state (if a state, at all) in which the quality of difference does not exist, where all is the same. What would exist in such a universe?

Couldn't A be different from (in this world) non-existent nothingness? — absoluteaspiration

This is a hard question (in my opinion), and the "naive" answer would be no, because how could something be different from "something" which does not exist? I have not been able to imagine or think about such scenario; hence my assumption that something exists different from something else, which I think would also exist.

How do you conceive of this thing which is not A? — Daniel

This is why metaphysics employs dialectical or dichotomous arguments - the famous unity of opposites.

If I want to define A, I need to conceive of it as the negation of everything that it is not. So that binds our notions about the existence of things or entities to formally complementary relations. I am measurably A to the degree that I’ve measured myself to be not A.

You thus have a reciprocal or inverse relation. A = 1/not-A. And this answers your other question about wholes and parts. You only ever then end up with a world of things in relation. Things only exist definitely as “what they are” to the degree they manage to distance themselves from “that which they are not”.

The usual folk ontology is that things simply exist. And the contrast then is with them not existing.

But that raises questions, like do they not exist because they are simply still just a possibility, or because they are impossibilities?

Metaphysics has to cut deeper and does so by making what exists a concrete story of existence being defined in terms of what is - relatively, rather than absolutely - absent. That is an expanded view that can deal with possibilities (and so also, impossibilities).

To cut a long story short, this is why metaphysics boils down to a naming of the core dichotomies or polarities that underlie ontological Being.

You get familiar metaphysical-strength distinctions like discrete-continuous.

So is reality fundamentally discrete or continuous? A little thought shows that these opposed answers are each just the limit on the other. To be discrete is to have the least possible degree of continuity. And to be continuous is, vice versa, to have the least possible degree of discreteness.

The temptation is to claim that one or other limitation can exist in absolute fashion. Hence one of the two can be the more fundamental.

Yet in systematic reasoning, we only ever find these two fellows in a complementary relation. We can say one is present only to the degree we can assure the other is absent. So the only thing we can be sure about is the existence of this as a reciprocal relation. A basic form of counterfactuality that usefully characterised the world we inhabit.

The same goes with other metaphysical primitives like parts and wholes - or one-many, local-global, etc.

Parts and wholes are the opposing limits of structural order. And there is no structural order - as a unity - without a system divided into relative partness vs relative wholeness.

This leads you to Aristotle’s hylomorphic form and four causes approach to substantial being. The whole is the rational form of the substance, the parts are its material potentials.

I gave you the example of a horse being different from a non-existent unicorn in not having a horn.

There are many problems importing classical negation wholesale into metaphysics. The most famous is the Raven Paradox.

Suppose you have a theory: x is a raven implies x is black. (1)

Contrapositive: x is not black implies x is not a raven. (2)

If you see a black raven, that increases support for (1). That's understandable.

However, if you see a non-black non-raven like a red apple, that increases support for (2). This is surprising because (1) and (2) are equivalent, and the existence of a red apple says nothing about whether if you see a raven, then it will be black.

How do you conceive of this thing which is not A? — Daniel

A is round and green.

Not-A is neither round nor green

That which is round xor green is Aish.

Humble apologies for buttin' in.

There are many problems importing classical negation wholesale into metaphysics. The most famous is the Raven Paradox. — absoluteaspiration

You are talking about predicate logic rather than dialectical argument.

Ravens clearly aren’t metaphysically general. There is no not-raven to stand opposed to the raven in the universal way that discreteness can be the antithesis of continuity, chance the antithesis of necessity, etc.

Predicate logic presumes a world of mereological composition, which is certainly also a popular ontology if your metaphysics predates the quantum revolution.

If you're not using predicate logic, in what sense are you negating A? I thought you understood this world as something like: There is an x such that x is A and for all y, x=y.

As for the Raven Paradox, this question assumes a world where only one thing exists. This thing, A, is clearly an analogue of a raven rather than something like discreteness or necessity.

If you're not using predicate logic, in what sense are you negating A? — absoluteaspiration

In the dialectical sense. So as I said, you move on from A = not not-A (a statement couched in the language of particulars) to a reciprocal framing where you have inverse generality - some dichotomy where A is not-B, with B being 1/A.

A dichotomy is a a relation that is mutually exclusive and jointly exhaustive. So it opposes two generalities in a reciprocal deal. Each becomes the measure of the other in that each is measurable by its lack of that other.

In Yin-Yang fashion, discrete = 1/continuous and continuous = 1/discrete. Each is true to itself to the extent it negates its other. There is the mutual exclusivity.

Then the joint exhaustivity comes when you multiply them together to recover 1/1 as your unity - the unity of opposites.

As for the Raven Paradox, this question assumes a world where only one thing exists. — absoluteaspiration

Predicate logic fails here because it is trying to reason from the general to the particular, and coupling that with an argument from the particular to the general.

That’s a good way to show up the difference between deduction and induction. Not so much for what I’m doing, which is showing that generality itself has this dichotomous structure. Universals always have to come in reciprocal pairs as everything in good metaphysics is based on a logic of relations.

If I want to define A, I need to conceive of it as the negation of everything that it is not. — apokrisis

I don't think this is correct at all. We define "A" with a description, not by saying what it is not. "Man", for example, was defined by Aristotle as a rational animal. We have a much more refined description now, of "human being", but we clearly do not define "human being" by stating everything which is not human. I really cannot think of anything which is defined by stating what it is not.

I don't think this is correct at all. We define "A" with a description, not by saying what it is not. "Man", for example, was defined by Aristotle as a rational animal. — Metaphysician Undercover

Once again you are confusing the predicate logic approach of reductionism with the dialectical approach of logical holism. You are saying the whole - the A - is composed of some set of particular properties. A is constructed in additive fashion from a selection of parts that it either has, or doesn’t have.

So a man has two legs and a willy. But a one-legged man doesn’t seem to have lost anything formally essential, just something materially accidental. However the castrato? Now the debate may start about whether we have cut into something essential.

The dialectical argument operates at a quite different level - that of metaphysical generality. The discovery of categories or universals themselves. The properties or qualities of Being.

This is where everyday reductionist constructionism must give way to some better understood logic of holism. We are dealing with how sameness and difference themselves can both be “true” of the world. We are talking of the creating relation where wholeness and apartness are two faces of the one coin.

That then leads us to the triadic logic, the hierarchical logic, the systems logic, of the likes of Anaximander, Aristotle, Hegel and - above all - Peirce.

I really cannot think of anything which is defined by stating what it is not. — Metaphysician Undercover

Yet even at the level of a logic of particulars, we have Leibniz and the argument from indiscernibles - the differences that don’t make a difference and so speak to identity as sameness.

The one-legged man story.

You haven't addressed the issue, only attempting to change the subject. The simple fact is that we define a thing by describing what it is, not by saying what it is not.

Sure you can refer to some sort of vague generality such as "Being", and say that it is the opposite of "not-Being", but that is not providing a definition.

Yet even at the level of a logic of particulars, we have Leibniz and the argument from indiscernibles - the differences that don’t make a difference and so speak to identity as sameness. — apokrisis

By Leibniz's principle, "identity of indiscernibles", there is no such thing as a difference which does not make a difference. Any type of difference makes the two things not indiscernible, therefore different things. A difference which does not make a difference is straight forward contradiction. And to ignore a difference with a claim like 'it's a difference which doesn't make a difference, therefore the two are the same', is to violate the law of identity.

The simple fact is that we define a thing by describing what it is, not by saying what it is not. — Metaphysician Undercover

That is not true. Or as you might describe it, that is false, :joke:

But even if it were true and not false, then my argument is about the definition of categories like thingness itself.

How did Aristotle decide matter was not-form, and form was not-matter? Why more generally did he treat contradiction and contrariety as different levels of negation in his square of opposition?

Any type of difference makes the two things not indiscernible, therefore different things. — Metaphysician Undercover

More bollocks. An essential difference is different from an accidental difference. One is treated as signal, the other noise.

But even if it were true and not false, then my argument is about the definition of categories like thingness itself. — apokrisis

Categories also are described, and not defined through reference to opposites, like the categories of colour, heat, etc.. These are not defined by referring to an opposite. What often happens, is that when we create a scale for measurement of a categorized quality, we place the two opposing extremes within the same category forming opposite ends of the scale. So the scale of temperature for example has both the extremes, hot and cold. But hot and cold are not the defining features of temperature, it is defined with reference to the movement of particles. And colour is defined in reference to wavelengths of light. And so on with other categories.

An essential difference is different from an accidental difference. One is treated as signal, the other noise. — apokrisis

But you were talking about particulars, and every accidental difference is significant to the identity of the particular, as a particular.

I think opposition, and negation, are very useful tools for logical processes, but descriptions and definitions are not logical processes.

but descriptions and definitions are not logical processes. — Metaphysician Undercover

You seem to be defining definitions by what they are not.

Victory is mine. :party: :party: :party:

What I seek is the reality of the matter, not victory. You keep reasserting unreal claims, despite my demonstrations that these claims are incorrect. So you provide nothing toward compromise or mutual understanding. And now you claim "victory", as if mutual understanding was never the goal. What's the point to your behaviour?

Very simple, you are forgetting that you are an observer. As long as you exist as something separate from A, then you have a relative entity to A. If only one thing exists, you do not exist. In which case there is no concept of A, nor any concept of there not being A.