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From Graham Priest and the SEP it seems like the world doesn't have to be a certain way with the PNC being necessary for "scientific inquiry, reasoning and communication" (SEP).

The world could be any which way, but to engage in one of the above activities, we have to form some boundary to it according to Aristotle, since speakers can contradict themselves. This very post requires me not contradicting myself, but seems to say little about the world outside communication.

Aristotle, in the most powerful argument for the PNC, uses elenchus not to say an interlocutor can't contradict themself, but that we can't communicate, reason, or inquire once demonstrated they have.

According to the same SEP, PNC can be seen as a transcendental argument, but how? If communication requires non-contradiction, the world could still have them or not. Either case of the world could explain the PNC being necessary for X.

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    Aristotle's is not the most powerful argument for PNC, ex falso quodlibet is, and he was missing it because his syllogistic was too weak. But he does anticipate what it entails, that contradictions trivialize claims and deprive knowledge of its content. SEP's transcendental argument comparison is, indeed, misleading, but, charitably, Kant uses transcendental arguments not so much to infer that the world is a certain way (it is unknowable, after all), but rather that our faculties must function a certain way, e.g. conform to PNC.
    – Conifold
    Sep 1, 2023 at 21:41
  • @conifold is the principle of explosion metaphysically more powerful or just logically? Does it go beyond “scientific inquiry, reasoning and communication”, e.g. a fourth faculty is also shown to follow the PNC, or, empirically we never observe everything? (Or something else?) Does the PoE also suggest speakers can’t actually contradict themselves contra what I wrote in my post? (I won’t make this a long chain of comments, just trying to tease out a tiny bit more)
    – J Kusin
    Sep 1, 2023 at 23:12
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    Aristotle and scholastics worked in a different ("Parmenidian") paradigm of correspondence theory, mostly abandoned after middle ages, where true thoughts were directly "equated" with "true" things. So it sufficed for him to establish epistemic necessity of PNC to infer metaphysical conformity of the world to it. We now (after Kant especially) distinguish features of representations from features of what they represent, and must face the question you ask the way Aristotle did not. To us, his projection of PNC onto metaphysics is an implausible (and almost nonsensical) leap.
    – Conifold
    Sep 1, 2023 at 23:45

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From a modern perspective, we are accustomed to distinguishing between the way the universe is, and our experience of it. The universe is complex and weird and we struggle to understand it and navigate our way through it. Our thoughts and beliefs are an attempt to make sense of our experiences. Our theories and even our logic are an attempt to organise and systematise our experiences and render them into a form that has predictive and explanatory value.

But this is not how ancient philosophers saw things. They imagined a kind of direct correspondence between thought and the way the world is. The world contains true propositions and the job of a rational person is to believe these.

On the modern view, it does not make sense to say that the universe 'contains' contradictions. Contradictions are a feature of our understanding and our language, not a property of the universe. The universe just does what it does. Contradictions arise only when we attempt to describe it. In the most commonly used logics, including classical logic, no contradictions are true. This is not a statement about how the universe is, but a statement about how we choose to organise our information. We typically find it inconvenient and unsatisfactory to allow that contradictary propositions are true.

On the ancient view, a contradiction would mean that the world has some conflicting and impossible combination of properties. The ancient Greeks, at least, held that the world is rational and so this was assumed to be unthinkable.

Kant can perhaps be thought of as the dividing line between these positions. Kant held that the world as the thing-in-itself is unknowable. But he held that because we understand the world in particular ways (the categories) we can formulate transcendental arguments about the way the world must be in order for us to have any knowledge of it. For Kant, this gives rise to a priori knowledge, including logic.

As to Aristotle himself, as the article from SEP shows, Aristotle presents three different versions of the principle of non-contradiction. (1) He says that it is impossible for a thing both to have a particular property and also not to have it, at the same time and in the same respect. (2) He says that it is impossible to believe a thing both to be and not to be. (3) He says that opposite assertions cannot be true at the same time.

All of these are different, and we would express them differently in modern logic, and it is not clear whether Aristotle regarded them as distinct, and if so, how they are related. In the way that Aristotle defends the principle with his elenctic argument, he seems to be leaning on the claim that reasoning and belief would be incoherent without it. This might be considered similar to a transcendental argument since it is not so much holding that contradictions are impossible, only that we would be unable to think and communicate rationally if we believed contradictions. And since we are capable of thinking and communicating rationally, contradictions must be rejected as false.

Switching back to the modern perspective again, this argument could be said to be question-begging. Why should we suppose that any and all contradictions completely subvert rational belief and communication? People do seem to be able to cope with inconsistent beliefs without becoming completely dysfunctional. Dialetheists, while being in a small minority, allow that some contradictions are true without triviality and without explosion.

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  • I am very sympathetic to the modern view I suppose. But, how do philosophers like Graham Priest say "there are real contradictions"? Do they still have the modern sense in mind?
    – J Kusin
    Sep 2, 2023 at 1:36
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    Dialetheists like Graham Priest hold that it is correct to say of some sentences that they are both true and false. For example, in the case of semantic paradoxes. These are 'real' in the sense that dialetheists maintain they are not just linguistic puzzles that can be resolved in some other way.
    – Bumble
    Sep 2, 2023 at 3:49
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If memory serves, Aristotle investigated temporal propositions, those about the future (sea battle). The story goes that someone (adapting it to present times) claims S = a sea battle will occur in Jan 2024 Is S, in the here and now, true/false? Aristotle decided that the truth value for S should be unknown i.e. neither true nor false, wrecking the Law of Excluded Middle or LEM. Arisitotle was a genius.


I'm much intrigued by the OP's comment on communication vis-à-vis the LNC. Worth a second look.

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    I think you are confusing LNC with LEM. Aristotle's discussion of tomorrow's sea battle is sometimes interpreted as introducing indeterminate S ∨ ~S that violate LEM, but not LNC. Presumably, he wanted LEM restricted for future contingents to avoid fatalism about the future.
    – Conifold
    Sep 2, 2023 at 0:56
  • @Conifold, true that. I went back to the source and found out Aristotle realized something hadta give, if you know what I mean. We all know the choice he made, which is to say, the OP has picked up a rather intriguing scent.
    – Hudjefa
    Sep 2, 2023 at 7:50

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