Question II
Assuming that for two things (i.e., A and B) to exist relative to each other, they must be different (in at least one property) from each other, what would be the analogy for when only one thing exists (i.e., A). What would A (relatively) be different from?
Comments (20)
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?
Quoting 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?
Quoting 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.
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 Ive 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 Aristotles hylomorphic form and four causes approach to substantial being. The whole is the rational form of the substance, the parts are its material potentials.
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.
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.
You are talking about predicate logic rather than dialectical argument.
Ravens clearly arent 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.
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.
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.
Quoting 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.
Thats a good way to show up the difference between deduction and induction. Not so much for what Im 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.
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.
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 doesnt have.
So a man has two legs and a willy. But a one-legged man doesnt 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.
Quoting Metaphysician Undercover
Yet even at the level of a logic of particulars, we have Leibniz and the argument from indiscernibles - the differences that dont 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.
Quoting 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.
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?
Quoting Metaphysician Undercover
More bollocks. An essential difference is different from an accidental difference. One is treated as signal, the other noise.
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.
Quoting 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.
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?