So, there is no such thing as a contradiction (at least with propositions about the physical world). — TheMadFool

Well, first off, as you indicate, the law of non-contradiction applies to propositions, not the world outside our heads. Not knowing the difference between those two is one of the primary mental, or at least intellectual, disorders displayed on this forum.

But, if we decide to play the game you have set up, I'd say this - Although AE's theory of special relativity is more comprehensive, IN's laws of motion still apply with almost perfect accuracy at human scale. Therefore, unless one of the propositions is travelling near the speed of light, simultaneity occurs.

I would say that the part "at the same time" in Wikipedia's definition of the law of non-contradiction is superfluous. "In the same sense" is enough, because it also includes whatever is meant by "at the same time" (in the context of theory of relativity it means "at the same time from the perspective/reference frame of the same observer").

Well, first off, as you indicate, the law of non-contradiction applies to propositions, not the world outside our heads. Not knowing the difference between those two is one of the primary mental, or at least intellectual, disorders displayed on this forum. — T Clark

This is a stretch but thoughts, propositions included, are, so far as we know, matter-based. Is it too much, then, to say that the ToR applies to propositions that aren't about our physical world?

I mean, in the time when I think x = 2 AND x = 3 (contradictory non-physical propositions), my brain moves through space and this simple fact obviates any possibility of simultaneity. This makes contradictions, which require simultaneity, impossible.

Therefore, unless one of the propositions is travelling near the speed of light, simultaneity occurs. — T Clark

The ToR is applicable at all speeds. It's just unnoticeable at our scale. Time differences at our scale may be (guessing) 0.00000001 seconds. Simultaneity, which requires a time difference of zero, is impossible. So, contradictions of physical propositions are impossible.

I would say that the part "at the same time" in Wikipedia's definition of the law of non-contradiction is superfluous. "In the same sense" is enough, because it also includes whatever is meant by "at the same time" (in the context of theory of relativity it means "at the same time from the perspective/reference frame of the same observer"). — litewave

First, the phrase ''at the same time is important for the law of noncontradiction. Take two propositions: ''it's raining'' and ''it's not raining''. If I say both at exactly 2:00 PM then we have a contradiction but if I say one at 2:00 PM and the other at 4:00 AM then there's no contradiction.

The problem is no point of reference is more correct than the other. There is no absolute time - no universal temporal reference. We could say, very loosely, that time is subjective and so simultaneity for one person is not for another. This means that the contradictions are either impossible or are illusions.

The ToR is applicable at all speeds. It's just unnoticeable at our scale. Time differences at our scale may be (guessing) 0.00000001 seconds. Simultaneity, which requires a time difference of zero, is impossible. So, contradictions of physical propositions are impossible. — TheMadFool

I have to drive to New Haven tomorrow morning. I'll meet you at 9:15 at the McDonalds at the rest stop on I90 west right before the I84 exit. Ok? 2013 Toyota Corolla. Goldish color. Small dent in rear bumper on passenger side. Do you think we can do simultaneity?

I have to drive to New Haven tomorrow morning. I'll meet you at 9:15 at the McDonalds at the rest stop on I90 west right before the I84 exit. Ok? 2013 Toyota Corolla. Goldish color. Small dent in rear bumper on passenger side. Do you think we can do simultaneity? — T Clark

Well, IF we're in the same frame of reference, we can achieve simultaneity. However, from another frame of reference you may arrive at 9:15 and I at another time. No frame of refernce being more correct than the other, it follows that what we perceive as simultaneity is, to say the least, only a local phenomena.

Well, IF we're in the same frame of reference, we can achieve simultaneity. However, from another frame of reference you may arrive at 9:15 and I at another time. No frame of refernce being more correct than the other, it follows that what we perceive as simultaneity is, to say the least, only a local phenomena. — TheMadFool

If you can be there, I'll PM my cell phone number and we can talk about it. I think we can achieve the required level of simultaneity.

If you can be there, I'll PM my cell phone number and we can talk about it. I think we can achieve the required level of simultaneity. — T Clark

Well, by ''required level of simultaneity'' I assume you mean an approximation. That's fine.

Well, by ''required level of simultaneity'' I assume you mean an approximation. That's fine. — TheMadFool

So, will you be there?

One is a principle of classical logic; and the other is a principle of modern physics.

It's like asking why you can't score touchdowns in basketball, or put hotels on Boardwalk and Park Place in chess.

One is a principle of classical logic; and the other is a principle of modern physics.

It's like asking why you can't score touchdowns in basketball, or put hotels on Boardwalk and Park Place in chess. — fishfry

Well, ToR applies to Earth and Logic is an earthly thing. I can see the overlap of the two worlds.

So, will you be there? — T Clark

In one context, yes. In another, slightly late or early.

Logic is an earthly thing — TheMadFool

I would say logic is an abstraction. There's no evidence that classical Aristotelian logic is part of nature. And much evidence that it's not. Relativity for one thing!!

The best you can say is that logic is an aspect of the human mind. So is illogic.

But logic, as an aspect of the human mind, is an abstraction. Like numbers. Like justice, or law, or religion. These are abstractions of the mind that become part of the real world only through common agreement. Social truths, as in Searle's idea of the Construction of Social Reality.

I can barely think of anything in the real world that follows classical Aristotelian logic. Not anything that matters.

The OP is a classic case of a philosophical knot. Not easy to unpick, but it might be interesting.

A) According to Theory of Relativity (ToR) there is no such thing as simultaneity because:

1. Everything is in motion relative to something else and thus spatially separated moment to moment.
2. If everything is spatially separated then simultaneity isn't absolute (for everything). — TheMadFool

Of course there is such a thing as simultaneity. It's that silly word "absolute" that causes the problem.

Suppose that for Angie, events A and B occur at the same time; But for Beth, A occurs before B. The transformation formulas in special relativity allow both Angie and Beth to agree with these two statements:

From Angie's frame of reference, events A and B occur at the same time.
From Beth's frame of reference, A occurs before B.

That is, both Angie and Beth, and anyone else that cares to do the calculations, will agree that for Angie, events A and B are simultaneous.

Here's the law of non-contradiction:

~(p ^ ~p)

It's a rule of grammar; if you find that you have broken it, then you have written something down wrong. It's not confined to Aristotelian logic - or you are using some other grammar, perhaps three-valued logic or Dialetheism.

Now from my previous two posts, I hope it is apparent that, since for Angie, A and B are simultaneous, and similarly for Beth, A and B are not simultaneous, there is no one for whom A and B are both simultaneous and not simultaneous.

The Knot falls out.

the law of non-contradiction applies to propositions, not the world outside our heads. — T Clark

Er, unless those propositions are about the world "outside our heads".

As if language did not apply to the various things that make up our world.

I would say that the part "at the same time" in Wikipedia's definition of the law of non-contradiction is superfluous. "In the same sense" is enough, because it also includes whatever is meant by "at the same time" (in the context of theory of relativity it means "at the same time from the perspective/reference frame of the same observer"). — litewave

That's a good point. One might take "...at the same time" as a colloquial simplification of "...in the same frame of reference"

I don't agree. Logic underpins the language of physics as much as of anything else. It would be absurd to think of logic and physics as incommensurate.

Of course there is such a thing as simultaneity. It's that silly word "absolute" that causes the problem.

Suppose that for Angie, events A and B occur at the same time; But for Beth, A occurs before B. The transformation formulas in special relativity allow both Angie and Beth to agree with these two statements:

From Angie's frame of reference, events A and B occur at the same time.
From Beth's frame of reference, A occurs before B.

That is, both Angie and Beth, and anyone else that cares to do the calculations, will agree that for Angie, events A and B are simultaneous. — Banno

Now from my previous two posts, I hope it is apparent that, since for Angie, A and B are simultaneous, and similarly for Beth, A and B are not simultaneous, there is no one for whom A and B are both simultaneous and not simultaneous.

The Knot falls out. — Banno

Well done Banno...

(Y)

Cheers.

First, the phrase ''at the same time is important for the law of noncontradiction. — TheMadFool

Time may be one of the components of the sense of a statement/proposition. But what is time? According to theory of relativity time is relative, at least in our world. So if you are making statements involving simultaneity you must define the frame of reference. Otherwise the sense of your statements is not sufficiently defined and you cannot judge the consistency of insufficiently defined statements.

The problem is no point of reference is more correct than the other. There is no absolute time - no universal temporal reference. We could say, very loosely, that time is subjective and so simultaneity for one person is not for another. This means that the contradictions are either impossible or are illusions. — TheMadFool

The law of non-contradiction states that contradictory statements cannot both be true in the same sense. So if you completely define the sense of your statements, including the temporal component if relevant, and they are contradictory in the same sense, then they cannot both be true.

It is easy to make contradictions also in the context of the theory of relativity. For example, statements (1) "Peter is watching TV and simultaneously Paul is sleeping according to reference frame X" and (2) "Peter is watching TV and simultaneously Paul is not sleeping according to reference frame X" are contradictory. However, statements (3) "Peter is watching TV and simultaneously Paul is sleeping" and (4) "Peter is watching TV and simultaneously Paul is not sleeping" are insufficiently defined and so it cannot be judged whether they are contradictory.

Not all propositions are about things or events in spacetime.

When they aren't, when they're timeless propositions, then nonsimultaneaty doesn't apply.

Besides, even in spacetime, nonsimultaneaty is only about separate objects with mutually-relative speed. You could still a coin has heads up and also has tails up, and that would be a contradiction.

Besides, if an object is a cube, vs a sphere, the difference in those shapes remains even when they're changed by relativistic flattening, and you can still speak of something's shape as round vs angular regardless of its motion relative to you. if it's round, and stays round, nonsimultaneity wouldn't prevent you from making contradictory statements that it's round, spherical or elliptical and has corners and flat sides.

Michael Ossipoff

Er, unless those propositions are about the world "outside our heads".

As if language did not apply to the various things that make up our world. — Banno

You're playing language games. You haven't untied any knots at all. There never were any.

Logic underpins the language of physics as much as of anything else. It would be absurd to think of logic and physics as incommensurate. — Banno

The axiomitization of physics is still an open problem. This supports my point.

https://en.wikipedia.org/wiki/Hilbert%27s_sixth_problem

In particular:

However, physics as a whole has not [been axiomitized, and in fact the Standard Model is not even logically consistent with general relativity, indicating the need for a still unknown theory of quantum gravity. The solution of Hilbert's sixth problem thus remains open.

You could not, in other words, use classical sentential logic to describe the current state of modern physics

Axioms are not what they used to be.

There are unprovable, yet true statements in any sufficiently interesting axiomatic system. Physics is surely sufficiently interesting to include such.

Nor are axioms so important in logic as they were in Hilbert's time. Natural deduction systems abound.

Nor is sentential logic the whole of logic.

And finally, it is now a philosophical commonplace that one man's axiom is another's deduction.

Why bother axiomatising physics at all?

the Standard Model is not even logically consistent with general relativity, — fishfry

This claim is unreferenced in the article. What is this purported inconsistency?

Even the most flippant topologist knows there are knots that are not knots. X-)

Why bother axiomatising physics at all? — Banno

You're the one claiming physics is based on sentential logic from 2000 years ago. Today we have paraconsistent logic, denial of the law of the excluded middle, and a resurgence of interest in intuitionistic logic. You should Google around. Your understanding of logic is a couple of thousand years out of date.

https://en.wikipedia.org/wiki/Paraconsistent_logic

https://en.wikipedia.org/wiki/Intuitionistic_logic

https://en.wikipedia.org/wiki/Brouwer%E2%80%93Heyting%E2%80%93Kolmogorov_interpretation

You're the one claiming physics is sentential logic from 2000 years ago. — fishfry

Well, no, I'm not. I just pointed out that logic is the basic grammar we use in conversation. Indeed, I was at pains to point out that if one sort of logic does not work, it is open to choose or even develop another:

- or you are using some other grammar, perhaps three-valued logic or Dialetheism. — Banno