Why does the world conform to logic?

[RJG]

BiV implies that the everyday propositions we take to be logically true (such as 2 + 2 = 4) are by that token necessarily true…

Agreed, the truths of math/logic are NOT 'man-made'; nor reliant upon the existence of man.

We have no 'means' to refute math/logic. Any attempt to invalidate only invalidates our own invalidation.

The (non changing) truths of math/logic are much more certain than the (constantly changing) 'man-made' truths of science. -- Logic/math is our best means of ascertaining truths. There is no higher authority.

The primary purpose of logic in philosophical discussions it to identify and rule out the logical impossibilities and contradictions. If "married bachelors" are 'logically impossible', then any continued debate, assertions, and posturing of such should cease (...one would think, right?).

...RJG says that the primary purpose of logic is to identify and discard logical impossibilities (my italics). That would render it somewhat trivial - we might as well say that the purpose of Scientology is to rule out Scientological impossibilities. Presumably what RJG means is that the purpose of logic is to rule out impossibilities - in which case we need some explanation as to how it does so, as opposed to merely ruling out inconceivabilities.

Are "inconceivabilities" the same as "logical impossibilties"??

One's inability to see (conceive of) something, seems to be quite different than one's ability to see a 'contradiction'.

Firstly, we (humans, philosophers, scientists, sense-makers) don't all agree which logic is the correct one (or even if there is only one) - metalogicians differ about whether higher-order logics should be allowed, whether fuzzy logics should be allowed, which axioms to choose in the construction of a mathematical logic, and so on. Hilbert systems differ from other logics in the way they prioritise axiom schema over rules for inference, for example.

"X = not-X" is a logical impossibility in "everyone's" logic!

Other logical impossibilities include 'before / after', and 'greater than / less than' relationships. If A>B is true, then A<B is also a logical impossibility.

[parsoff]

logic could be one rule in the human world made so 95% of the humans can understand
as the interaction is between humans, 2 or more, they all need to understand

if something is from a higher intelligent order this doesn't count
doesn't mean it is impossible for humans as they have an option to educate them self for some extra years so they can understand

there also could be another kind of logic that plays in the universal
in the winter there is less food so you need to have some extra body fat to survive the winter better

[Lomax]

Firstly, we (humans, philosophers, scientists, sense-makers) don't all agree which logic is the correct one (or even if there is only one) - metalogicians differ about whether higher-order logics should be allowed, whether fuzzy logics should be allowed, which axioms to choose in the construction of a mathematical logic, and so on. Hilbert systems differ from other logics in the way they prioritise axiom schema over rules for inference, for example.

"X = not-X" is a logical impossibility in "everyone's" logic!

You must be unfamiliar with dialetheism. Either way, you did not make your claims for the principle of contradiction: you made them for logic. Is Pierce's Law in everyone's logic? And since you say that logic is "mathematics in words": is Russell's Theory of Types in everyone's logic? Is set theory in everyone's logic, for that matter?

Are "inconceivabilities" the same as "logical impossibilties"??

Did I imply that they were? I don't quite know what is meant by "logical impossibility" (your term) but I will take it (given your other comments) to mean a statement which implies its own negation within a given logic (as opposed to a statement which simply cannot be generated within that logic: with a nod to Godel here, the difference is important). I will take an inconceivability to be something we cannot imagine being true.

In which case, it's not clear to me whether we can imagine a frequency of 100,000KHz, or a man 50.01 feet tall, or the non-existence of the universe, or infinity, or a new colour. It doesn't follow that any of these things are "logically impossible", or impossible.

Still, your defense of logic rests upon it being impossible for us to refute without also refuting its refutation; upon it being "certain"; and upon it being our best means of ascertaining truth. All of which is an argument about how our minds work, not about how the universe is or has to be. This line of reasoning demonstrates nothing about whether the universe conforms to logic - it only entails (if true) that what we think about the universe conforms to logic (and which logic?). In other words you are dealing in inconceivability, not in impossibilities (or logical impossibilities, whatever they are).

[RJG]

"X = not-X" is a logical impossibility in "everyone's" logic!

You must be unfamiliar with dialetheism. Either way, you did not make your claims for the principle of contradiction: you made them for logic. Is Pierce's Law in everyone's logic? And since you say that logic is "mathematics in words": is Russell's Theory of Types in everyone's logic? Is set theory in everyone's logic, for that matter?

Lomax, do you seriously believe X = not-X is actually possible??? ...yes???

If so, I would LOVE to see your logical proof of this new truth, without logically contradicting yourself. (...hint: it's not possible!)

And while you are at it, please prove that 1>2 is true, when 1<2 is also true. (...hint: this is also logically impossible!)

[Asparagus]

A wave is not a particle.
An electron is a wave.
An electron is a particle.

Law of excluded middle has been challenged. Anything more probably reflects an unfounded bias.

[mitchellmckain]

For the most part it is not the world which conforms to logic, but only that the things we can say meaningfully about the world which must conform to logic. Logic is about the truth value of statements in the human language. If you want to understand the world then the place to look is not logic but science. Yes, science must conform to logic in order to be meaningful, but like I said, this is not about the world but about human language.

And as others have observed, quantum physics has pushed the limits of this a bit -- even to the point of suggesting that a different system of logic may be implied by some of what we are seeing there.

[RJG]

If X = not-X is true, then 'anything' is possible, and 'everything' is non-sense.

If we truly believe this illogic, then any talk of anything is pure foolishness (non-sensical-ness). -- If we have no legs (reference point) from which to make a stand, then no stands can be made.

[mitchellmckain]

If X = not-X is true, then 'anything' is possible, and 'everything' is non-sense.

If we truly believe this illogic, then any talk of anything is pure foolishness (non-sensical-ness). -- If we have no legs (reference point) from which to make a stand, then no stands can be made.

The problem with the excluded middle is not in such rules as non-contradiction but with forcing everything into the black and white categories of either true or false. It is demonstrable that not everything can be so categorized. More generally, the problem is essentially an artifact of language, in the way it requires us to put things into arbitrarily defined categories. Often what this means is that we need a better language (such as mathematics) in order to describe the things of nature (i.e. the universe) more accurately and consistently.

[Asparagus]

If X = not-X is true, then 'anything' is possible, and 'everything' is non-sense.

I think you're working on an argument from anti-nihilism. It's not quite holding together, though. Needs more glue.

How about: If logic doesn't guide us in understanding the world, then we have no hope of understanding it. Is that what you meant?

[RJG]

If X = not-X is true, then 'anything' is possible, and 'everything' is non-sense.

How about: If logic doesn't guide us in understanding the world, then we have no hope of understanding it. Is that what you meant?

Not quite. Logic is NOT a "guide" to understanding. Logic is our 'means' of understanding; it is our 'means' of "making sense".

Without a 'means' of making sense, then there can be no "sense making"; i.e. all is then non-sensical.

If X = not-X is true, then X can equal 'anything' (any non-X)! ...which means 'anything' is possible, including 'married bachelors', 'square circles', and flying pigs!

[Asparagus]

If X = not-X is true, then 'anything' is possible, and 'everything' is non-sense.

Logic is NOT a "guide" to understanding. Logic is our 'means' of understanding; it is our 'means' of "making sense".

Without a 'means' of making sense, then there can be no "sense making"; i.e. all is then non-sensical.

Theories of meaning are like a dark forest to me. Holism, atomism, molecularism that dissolves into holism, holism that becomes far-fetched in the face of millennia of recorded human communication. I get lost in it, likely never to be heard from again.

But meaningfulness is a property of signs and such. We were talking about the world.

[Lomax]

"X = not-X" is a logical impossibility in "everyone's" logic!

You must be unfamiliar with dialetheism. Either way, you did not make your claims for the principle of contradiction: you made them for logic. Is Pierce's Law in everyone's logic? And since you say that logic is "mathematics in words": is Russell's Theory of Types in everyone's logic? Is set theory in everyone's logic, for that matter?

Lomax, do you seriously believe X = not-X is actually possible??? ...yes???

If so, I would LOVE to see your logical proof of this new truth, without logically contradicting yourself. (...hint: it's not possible!)

And while you are at it, please prove that 1>2 is true, when 1<2 is also true. (...hint: this is also logically impossible!)

You keep using the term "logically impossible" while ducking the question of what this actually means. But the question isn't whether I believe in dialetheism. You said the law of non-contradiction was in everyone's logic: the work of Graham Priest empirically disproves this claim.

If I disagreed with the law of non-contradiction then it wouldn't matter to me that my disproof of it was self-contradictory, obviously. So your argument is circular.

The law of commutativity does not hold for quantum mechanics. This is simply a fact. You may not like it, but quantum mechanics works. Your insistence that this is impossible does not demonstrate anything; it does not rise beyond the level of assertion.

Finally: do you hold only that the universe must conform to the principle of non-contradiction (for everything) and to the law of commutativity (for inequalities)? Or do you hold that the universe must conform to Pierce's Lemma and to the Axiom of Choice? These are assertions of logic (and math, which you conflate with logic) also.

[Lomax]

By the way:

Hypothesis: inequality is a noncommutative property
|Premise 1) Rock > Scissors
|Premise 2) Scissors > Paper
|Premise 3) Paper > Rock
|Conclusion 1) Rock > Paper (from Premise 1 & Premise 2; associativity)
|Conclusion 2) Rock > Paper & Paper > Rock (from Premise 3 & Conclusion 1; conjunction)
Conclusion 3) Inequality is not a noncommutative property (from Conclusion 2).

That's all it takes. You don't realise how many other assumptions - modal, mathematical and Aristotlean alike - are smuggled into your far from rigorous arguments for the metaphysical necessity of your supposed axioms.

[RJG]

"X = not-X" is a logical impossibility in "everyone's" logic!

Lomax, do you seriously believe X = not-X is actually possible??? ...yes???

You keep using the term "logically impossible" while ducking the question of what this actually means. But the question isn't whether I believe in dialetheism. You said the law of non-contradiction was in everyone's logic: the work of Graham Priest empirically disproves this claim.

If I disagreed with the law of non-contradiction then it wouldn't matter to me that my disproof of it was self-contradictory, obviously. So your argument is circular.

The law of commutativity does not hold for quantum mechanics. This is simply a fact. You may not like it, but quantum mechanics works. Your insistence that this is impossible does not demonstrate anything; it does not rise beyond the level of assertion.

Finally: do you hold only that the universe must conform to the principle of non-contradiction (for everything) and to the law of commutativity (for inequalities)? Or do you hold that the universe must conform to Pierce's Lemma and to the Axiom of Choice? These are assertions of logic (and math, which you conflate with logic) also.

...By the way:

Hypothesis: inequality is a noncommutative property
|Premise 1) Rock > Scissors
|Premise 2) Scissors > Paper
|Premise 3) Paper > Rock
|Conclusion 1) Rock > Paper (from Premise 1 & Premise 2; associativity)
|Conclusion 2) Rock > Paper & Paper > Rock (from Premise 3 & Conclusion 1; conjunction)
Conclusion 3) Inequality is not a noncommutative property (from Conclusion 2).

That's all it takes. You don't realise how many other assumptions - modal, mathematical and Aristotlean alike - are smuggled into your far from rigorous arguments for the metaphysical necessity of your supposed axioms.

??? ...so does this mean "YES" ...or "NO"?

Lomax, no offense, but it seems that your intellectual indoctrination has blinded you from seeing the monumental importance of this simple little question.

Is "X = not-X" actually possible?

1. The 'Universe' has already spoken and has made this question 'impossible' to answer with a "YES". This impossibility is an 'a priori' truth; hence a logical impossibility.

2. To answer this question with a "YES" immediately invalidates the "YES". If "X = not-X" is true, then X equals 'anything'; any non-X! ...which undercuts any sense-making attempt with pure 'nonsense'-making.

3. Those that argue that "X = not-X" is possible, are unwittingly cutting off the very legs upon which they make their stand. For anyone spouting this as 'true' can only spout non-sense.

4. It is the acceptance of this simple logical impossibility that provides the 'foundation' for all our "sense-making" (reasoning). Again, without it, there can be no sense making, nor 'reason' to continue this discussion.

[Lomax]

I'm sorry to say that the people who make the boldest claims for logic usually know the least about it.

Firstly - RJG - you fail to distinguish between psychological and epistemic questions. The fact that I assent to the principle of non-contradiction does nothing to demonstrate its truth, and the fact that Graham Priest - whose work you obviously haven't bothered to check out despite responding to my posts which repeatedly mention it - dissents from the principle is enough to dispel your previous brave claim that everybody assents to the principle. You can't blame this ignorance on having learned nothing about the developments of logic since the days of Aristotle, because even he acknowledges that Heraclitus appears to be what we now call a dialetheist.

In your response to my point (1) you (impressively) confuse physics, metaphysics, epistemology and logic, all within a single sentence. Facts about the universe are not facts about all possible universes, not the same as facts about what we know (or believe) without resort to evidence, and not facts about formal systems of deduction. The Aristotlean Laws of Thought which you give so much weight are not nearly sufficient to string together the qualitatively different clauses in your implied syllogism.

In your response to (2) you confuse the principle of non-contradiction [~(P = ~P)] with the law of excluded middle [(P v ~P)]. In an intuitionist logic, I (or Priest) would not be implying '"X = not-X" is true' by denying 'not-(X = not-X)'. I don't mind whether this distinction is too subtle for you because it's beside the point I made. Suppose that I thought "X = not-X" but still had a finite set of beliefs: why would it bother me that this was contradictory? I would already have assented to the viability of contradiction. In other words your assertion, whether true or false, is not a logical proof, and not even evidence.

Again in your response to (3) you confuse truth with possibility, which would fail you a basic course in modal logic. Possibly what you want is the (more rigorous) law of reflexivity, rather than the principle of non-contradiction. But consider the irony: you claim that my reference to dialetheism leaves me capable only of spouting nonsense, and yet you have something against which to argue. So clearly my reference (and Priest's claim) is not of the same nature as "scoihjnklsdn", because you'd have nothing to say to that, would you? In short you demonstrate that it's not necessary for somebody to assent to the principle of non-contradiction in order for them to say something meaningful.

Either way I look forward to you getting around to answering my question: do you hold only that the universe necessarily conforms to non-contradiction (and perhaps commutativity, which you seem to have dropped) or does it necessarily conform to all the axioms and tautologies of logic (and math)? Again I cite the controversial examples of Pierce's Lemma and the Axiom of Choice. This question is not insignificant.

[RJG]

Lomax, do you believe what you say (above) 'makes sense'?

If you say “yes”, then you have proved my point. If you say “no”, then why should I or anyone listen to you?

Note: there is no way to “make sense” without a ‘means’ to make sense. Logic is our innate (a priori) means to make sense.

[Lomax]

Lomax, do you believe what you say (above) 'makes sense'?

Is it because of 'what you say', or is it because you have a 'means' of making sense?

What comes first?

Yes I do, and it is because we have a means of making sense. That is, with a nod to Wittgenstein and Davidson: understanding gives rise to meaning, not the other way around.

Could you link this to the OP?

[RJG]

Yes I do, and it is because we have a means of making sense.

Agreed.

And if "X=not-X" is true, then we would no longer have a 'means' to make sense (...as every word/meaning ("X") then would be replaced/represented with a different word/meaning (i.e. a "not-X"), ...and that which previously made sense would then be jibberish, and non-sensical).

That is, with a nod to Wittgenstein and Davidson: understanding gives rise to meaning, not the other way around.

Interesting, but not logically possible. One cannot 'understand' without 'something' to understand. Understanding is the recognition of meanings (bits of sensory experiences that form the 'meaningful' words and concepts).

Without 'something' to see, there can be no seeing. And likewise, without 'something' to understand, there can be no understanding. -- Without some pre-existing 'meanings' (sensory experiences), there is nothing to understand.

In other words, the 'content' (the 'meanings') comes BEFORE and determines the 'knowing-of-the-content' (the 'understanding'), ...not the other way around!

[Lomax]

Yes I do, and it is because we have a means of making sense.

Agreed.

And if "X=not-X" is true, then we would no longer have a 'means' to make sense (...as every word/meaning ("X") then would be replaced/represented with a different word/meaning (i.e. a "not-X")

I see no reason why it would be. Rather than repeating yourself - and repeatedly ducking my questions - and failing to address the OP, which asked about the world, not human language - you might better spend your time looking up the arguments of dialetheists, Graham Priest in particular.

That is, with a nod to Wittgenstein and Davidson: understanding gives rise to meaning, not the other way around.

Interesting, but not logically possible. One cannot 'understand' without 'something' to understand.

Ha, there we go with "logically possible" again. You still haven't told me what on Earth that means, or how it differs from "possible". Still, your argument here does not qualify as logically valid; rather it involves equivocation. I did not say that we are "without something to understand" or anything equivalent to that. I said understanding gives rise to meaning. Again, perhaps your lack of acquaintance with the "private language argument" and semantic externalism makes it harder for you to understand this claim. Rather than its lack of meaning ;)

[RJG]

Ha, there we go with "logically possible" again. You still haven't told me what on Earth that means, or how it differs from "possible".

Do you know what "mathematically possible/impossible" means?

Still, your argument here does not qualify as logically valid; rather it involves equivocation. I did not say that we are "without something to understand" or anything equivalent to that. I said understanding gives rise to meaning. Again, perhaps your lack of acquaintance with the "private language argument" and semantic externalism makes it harder for you to understand this claim. Rather than its lack of meaning ;)

Sorry, but "understanding" does NOT "give rise" to meaning, or to anything!. "Understanding" is just a passive 'non-causal' experience; a mere after-effect.

[Lomax]

Ha, there we go with "logically possible" again. You still haven't told me what on Earth that means, or how it differs from "possible".

Do you know what "mathematically possible/impossible" means?

No. Does it mean "consistent (or not) with all of the axioms of mathematics"? If so, which mathematics? Peano? ZFC? Quantum? String?

Ha, there we go with "logically possible" again. You still haven't told me what on Earth that means, or how it differs from "possible".

Sorry, but "understanding" does NOT "give rise" to meaning, or to anything!. "Understanding" is just a passive 'non-causal' experience; a mere after-effect.

You're clearly not interested in debating the point, supporting it with evidence, answering questions, or looking anything up. You just repeat your convictions ad nauseum. Feel free. I might see you later.

[RJG]

Lomax, apparently we are not understanding each other. Have a good day.

[Positor]

I have just read the linked Stanford article on dialetheism. All the examples of dialetheias given in section 3 of that article seem to boil down to either equivocation ("true in one sense and not-true in another") or vagueness ("half-true and half not-true" or "sort of true and sort of not-true" or "true in a manner of speaking...").

I have discussed the Liar Paradox in the past, and I believe it comes into the "true and not-true in different senses" category. The Liar sentence is not unqualifiedly "both true and not-true"; it has different (logically sequential) aspects of truth and untruth, which can be rigorously distinguished so that no contradiction arises. On that understanding, it can loosely be described as "partly true and partly not-true".

Section 6 of the Stanford article mentions the problematic nature of inconsistent objects and/or states of affairs. It seems that, for a realist dialetheist, objects and states of affairs cannot be inconsistent "in themselves", but only in a "derived" sense, i.e. statements about them can be both true and not-true.

[Lomax]

I have discussed the Liar Paradox in the past, and I believe it comes into the "true and not-true in different senses" category. The Liar sentence is not unqualifiedly "both true and not-true"; it has different (logically sequential) aspects of truth and untruth, which can be rigorously distinguished so that no contradiction arises. On that understanding, it can loosely be described as "partly true and partly not-true".

I'm not a dialetheist and I only brought it up to dispel RJG's argument that certain principles of logic are true because everyone believes them (we might call this the "banality model of truth"), but I'll take you up on this. What aspect of "this sentence is false" is true, and what aspect of it is false?

[Positor]

What aspect of "this sentence is false" is true, and what aspect of it is false?

We discussed this here. See in particular my points 3-5 in that post.

[mitchellmckain]

What aspect of "this sentence is false" is true, and what aspect of it is false?

We discussed this here. See in particular my points 3-5 in that post.

Sounds like Kripke's theory which is not universally accepted and pretty much gives away the issue of contention, throwing out the law of the excluded middle by including an "undefined" state.

[Lomax]

Positor, what constitutes a "stage"? I mean, however long you look at it, "this statement is false" is the same utterance. So when you say

4. Hence it falsely implies that it is false-at-the-first-stage. But it consequently acquires a truth-value, i.e. "false". So now there is a second stage, at which it is false. But the fact still remains that it was not false at the first stage; therefore there is no contradiction.

everything before your "therefore" seems to show that there is a contradiction. I mean, you said it yourself: now it reveals itself to be false, despite the fact it was not false. But it is still it: it hasn't changed.

Gilbert Ryle argued something similar to your position: he said that if we unpack "this statement is false" it reads "A is false", where "A" reads "B is true", where "B" reads "C" is false, and so on ad infinitum. He argues that our assignment of truth value would depend on how much unpacking we do. But this to me seems like no answer at all: if the unpacking process is potentially infinite, then at no point have we effectively unpacked it at all, so every step suffers the same problem as the first.

Graham Priest, on the other hand, argues that it's simpler just to allow that some statements meet the condition "P & ~P". As he writes, the metastructure of the universe does not implode around him. His tongue doesn't tie itself in a knot. His mind doesn't consume itself. So isn't there an Occamist case to be made for his position - just restrict the law of non-contradiction and get on with life?

[Braininvat]

I go with the rule: A sentence cannnot contradict itself, however this one does.

[Braininvat]

Or, put another way: semantics is only of value when it is about meaning, and meaning is only significant when it is about the world, and a sentence is only meaningful when it is about something other than itself (i.e. the world). So sentences like "this sentence is false" are essentially void of meaning. A set of mirrors arranged to reflect each other, if there is no object in the field of view, show nothing but the mirrors infinitely receding. The field of view is a visual analogy to the Kripkean "undefined."

[Lomax]

I go with the rule: A sentence cannnot contradict itself, however this one does.

Well my position is that if we're willing to simply call the sentence true (like Graham Priest does) then we hould be just as willing to call it false. The retort that "if it's false and it states that it's false then it must be true" is an expression of confusion - consider the following proposition:

"This sentence is true and this sentence is false"

Now it looks like a straightforward contradiction, right? So we're comfortable calling it false - even though it claims to be false. Yet the above sentence is wholly implicit in the shorter proposition "this sentence is false". So the only real problem with the liar paradox is that it's misleading.

But the fact that we have this choice - between calling it a false contradiction or admitting the existence of a true contradiction - itself ought to suggest that our logic is not something sewn into the fabric of the universe. It's a formalisation of the way we think, or think we ought to think. And the fact that the Axiom of Choice is both an axiom of a formal logic and a highly controversial axiom suggests to me that "X is a logical axiom" does not entail "X is necessarily true". We have different logics for different purposes, and so we should.