So Angie and Beth sit facing each other for a meal. Angie orders a soup, and the waiter sets the soup spoon.

For Angie, the soup spoon is on the right.

For Beth, the soup spoon is on the left.

Apparently for @Metaphysician Undercover, this involves a contradiction.

@Metaphysician Undercover; @fishfry

It occurs to me that it might be clearer to re-arange the scope of the statement;

It is true both that:
events A and B occur at the same time from Angie's frame of reference, and
A occurs before B from Beth's frame of reference.

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

Except that our theories and statements about reality include such intuitions, which are propositions itself. The law of non-contradiction also holds true in relativity theory provided they are statements made with regard to a single reference frame. A plane cannot move both forward and backward from me at the same time when it's travelling in a straight line from my point of view for instance.

I would say logic is an abstraction. There's no evidence that classical Aristotelian logic is part of nature. — fishfry

Classical logic can be understood as an approximation of reality. Just as Newton's physics is an approximation of Theory of Relativity.

I see no problem. In fact the world at our scale (size, speed, etc.) seems to obey classical logic rules such as the law of noncontradiction.

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. — fishfry

But, you'll agree, the ''common agreement'' is based on reality. Abstraction is based off off reality, don't you think?

Anyway, my main point is that no particular frame of reference is more ''valid'' than another. That makes simultaneity just an artifact of a particular frame of reference. If this is so, the law of noncontradiction, which depends on the notion of simultaneity, isn't a truth, in an absolute sense.

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

You're right. The term ''absolute'' is key to the issue. The law of noncontradiction is aboslute, isn't it? It's supposed to be true in all possible worlds, otherwise classical logic, as it stands, breaks down to mush.

Therefore, there being no absolute sense of simultaneity, the law of noncontradiction has lost its crucial footing and it simply fades away into meaninglessness.

One could argue that IF we're in the same frame of reference then simultaneity is possible. But, which two objects can ever claim such a sameness? We're all moving at different velocities relative to each other. Given that is the case, no two objects can ever be in the same frame of refernce.

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. — litewave

What does physics say about time? To me, it's simply a frame of reference for the universe. It moves in one direction, ''forward''??

No two objects can ever have the same exact velocity - there are too many variables to manage. Given this, it's obvious that no two objects can ever be in the same frame of reference. Thus, no simultaneity and no law of noncontradiction. So, fixing a frame of reference doesn't solve the problem.

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. — litewave

My point is without simultaneity, which I think you agree is impossible, there can't be a law of noncontradiction. You could say that ''simultaneity'' is meaningless and so, the law of noncontradiction is nonsense.

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

I agree that some propositions are ''timeless''. ''Timeless'' because nothing is really timeless is it? Even abstractions in the mind have to be thought of in a brain (matter). Also, let's leave this issue aside and focus on propositions about the physical world e.g the well known flashlight in a train thought experiment (you can google it). Propositions about the physical world are relative because the physical world is relative. The notion of simultaneity is meaningless in our relativistic world and without simultaneity the law of noncontradiction is nonsense.

No two objects can ever have the same exact velocity - there are too many variables to manage. Given this, it's obvious that no two objects can ever be in the same frame of reference. — TheMadFool

I see no reason why two objects couldn't have the exact same velocity. Of course, velocity is relative too. Two objects can move at exactly the same velocity in relation to me, that is, in relation to the frame of reference in which I am at rest.

My point is without simultaneity, which I think you agree is impossible, there can't be a law of noncontradiction. — TheMadFool

Then you misunderstand what the law of non-contradiction is. It says that two contradictory statements cannot both be true in the same sense, not that two contradictory statements cannot both be true at the same absolute time.

Except that our theories and statements about reality include such intuitions, which are propositions itself. The law of non-contradiction also holds true in relativity theory provided they are statements made with regard to a single reference frame. A plane cannot move both forward and backward from me at the same time when it's travelling in a straight line from my point of view for instance. — Benkei

I haven't participated in this thread since back at the beginning, so I don't know what else has been said, but I have been thinking about the issue. As I snottily noted in the part of my post you quoted, I think the issue of misunderstanding the difference between propositions and the world permeates the arguments on this forum. I've been trying to formulate why it bothers me so much, but haven't gotten it straight yet.

My second point in my previous post - even if relativity were relevant to the law of non-contradiction and vise versa, the proposition would have to be travelling at near the speed of light - say 1/2 c - before it made any significant difference. There's the absurdity - a proposition with velocity.

Third and new point - I think the case can be made that the law of non-contradiction is not true at any speed. That's for another thread.

Contemplate this:
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.

These two statements are both true for both Angie and Beth.

There is no contradiction. — Banno

Yes there is contradiction here. You are saying that from A's frame of reference X is the case, and from B's frame of reference not-X is the case. So you are saying that both X and not-X are the case, and this is contradictory. Introducing a "frame of reference" does not mitigate the contradiction, just like saying that from "my perspective" X is the case and from "your perspective" not-X is the case does not mitigate the contradiction implied by the two incompatible statements, "X is the case", and "not-X is the case".

To mitigate the contradiction, it is required to say that from A's frame of reference X "appears" to be the case, and from B's frame of reference not-X "appears" to be the case. This allows that the incompatible descriptions of what appears to be the case, may be resolved with what is "really" the case. But special relativity implies that it is really the case that both X and not-X are true. This is contradiction, plain and simple.

It is true both that:
events A and B occur at the same time from Angie's frame of reference, and
A occurs before B from Beth's frame of reference. — Banno

Right, "A and B occur at the same time" contradicts "A occurs before B". No matter how you qualify this with frames of reference, you do not negate the contradiction. The contradictory statements refer to the described object, while "frame of reference" refers to the point of observation. What is true or false of the object cannot be changed by changing the point of observation because this implies that mere changes to the point of observation can actually change the object. To avoid contradiction you would have to say that Angie and Beth are observing different things.

I don't think that you're applying an understanding of Einstein's paper Meta. ON THE ELECTRODYNAMICS OF MOVING BODIES

But special relativity implies that it is really the case that both X and not-X are true. — Metaphysician Undercover

No, in the context of special relativity it is meaningless to say that X or not-X is true unless you specify the reference frame in relation to which X or not-X applies. It is just as meaningless as saying that an object moves at speed 300 miles per hour without specifying the reference frame in relation to which the speed applies. There is no "real" speed that exists irrespective of a reference frame.

Banno wrote:

It is true both that:
events A and B occur at the same time from Angie's frame of reference, and
A occurs before B from Beth's frame of reference.

Some context ought help matters out here...

Let A be a gun being fired at night. Let B be the gunfire making a sound. Angie is within 5 feet of the gun wielder. Beth is more than 300 yards away with a clear view.

That doesn't quite make the point of SR(because both Angie and Beth are in the frame of the world), but it ought help one to grasp how simultaneity is relative to one's 'frame' of reference and thus that events A and B occur at the same time from Angie's frame of reference, and A occurs before B from Beth's frame of reference.

No, in the context of special relativity it is meaningless to say that X or not-X is true unless you specify the reference frame in relation to which X or not-X applies. It is just as meaningless as saying that an object moves at speed 300 miles per hour without specifying the reference frame in relation to which the speed applies. There is no "real" speed that exists irrespective of a reference frame. — litewave

We're not talking about the speed of an object though. What we are talking about is simultaneity, whether or not it is meaningless to say "at the same time" without specifying a frame of reference. As the op points out, "at the same time" is a crucial part of the law of non-contradiction. If special relativity allows that the meaning of "at the same time" is dependent on the frame of reference, then it circumvents the law of non-contradiction by giving "frame of reference" a higher priority than "non-contradiction".

If the determination of "is", and "is not" is dependent on the frame of reference, then "frame of reference" is simply given priority over the law of non-contradiction, allowing that both "is" and "is not" are actually the case depending on the frame of reference. How is this any different, in principle, from giving priority to "subjective perspective", such that what "is" and "is not" is dependent on the subject's perspective?

If special relativity allows that the meaning of "at the same time" is dependent on the frame of reference, then it circumvents the law of non-contradiction by giving "frame of reference" a higher priority than "non-contradiction". — Metaphysician Undercover

No, the frame of reference is included in the "in the same sense" part of the law of non-contradiction.

"In the same sense" refers to the meaning of the words of the statement, not the frame of reference. If you take "in the same sense" to refer to the frame of reference, then you are still just circumventing the law of non-contradiction by saying that two statements must be taken within the same frame of reference to have the same meaning. This is like saying that statements could have a different meaning for me than for you, so "in the same sense" is rendered meaningless.

The sense that is relevant here is the sense of "simultaneous"...

No two objects can ever have the same exact velocity - there are too many variables to manage. Given this, it's obvious that no two objects can ever be in the same frame of reference. Thus, no simultaneity and no law of noncontradiction. So, fixing a frame of reference doesn't solve the problem. — TheMadFool

Two objects do not have to be travelling the same speed and direction in order to be in the same frame of reference.

Also, I'm pretty sure that no human has ever travelled fast enough in relation to another such that the difference in simultaneity between them is measurable with the most precise instruments.

The sense that is relevant here is the sense of "simultaneous"... — creativesoul

So, are you saying that the word "simultaneous" means something different in frame of reference A from what it means in frame of reference B. If so, it doesn't, it means the same thing in both frames of reference. What varies is the determination of which events are simultaneous, not the sense of "simultaneous".

It is a fact that A and B can be and/or are simultaneous for Angie but not Beth. That has to do with the difference between the speed of sound and the speed of light. There is no contradiction. Angie is closer, so she sees the flash at the same time she hears the sound. Beth is far enough away that she sees the flash prior to hearing the sound.

It is a fact that A and B can be and/or are simultaneous for Angie but not Beth. That has to do with the difference between the speed of sound and the speed of light. There is no contradiction. — creativesoul

If you don't see the contradiction in stating that it is a fact that A and B are both simultaneous, and not simultaneous, then I can't help you.

What are you denying Meta?

That A and B are simultaneous for Angie, or that A and B are not simultaneous for Beth?

"In the same sense" refers to the meaning of the words of the statement, not the frame of reference. — Metaphysician Undercover

But the words have no meaning without the frame of reference, just as speed has no meaning without the frame of reference. Simultaneity and speed have no meaning without the frame of reference. So, it is not a contradiction to say that a car is moving at the speed of 70 miles per hour and simultaneously it is not moving at the speed of 70 miles per hour. It is just a statement without meaning. But it is a contradiction to say that a car is moving at the speed of 70 miles per hour in relation to the Statue of Liberty and simultaneously it is not moving at the speed of 70 miles per hour in relation to the Statue of Liberty. You can formulate genuine contradictions like this, even in the theory of relativity.

If you don't see the contradiction in stating that it is a fact that A and B are both simultaneous, and not simultaneous, then I can't help you. — Metaphysician Undercover

It is a statement without meaning, and meaningless statements are neither contradictory nor non-contradictory.

But the words have no meaning without the frame of reference, just as speed has no meaning without the frame of reference. — litewave

That's not the case though. Speed might have no meaning without a frame of reference, but words do not require a frame of reference to have meaning, you are just making that up. Words had meaning long before physicists started talking about frames of reference. Also, "simultaneous" has meaning without a frame of reference. Philosophers as far back as Aristotle, and beyond, spoke of simultaneity without a frame of reference. It's only relativity theory, which insists that simultaneity is meaningless without a frame of reference. When people believed in absolute time, the meaning of simultaneous was not dependent on a frame of reference.

It is a statement without meaning, and meaningless statements are neither contradictory nor non-contradictory. — litewave

It is only a meaningless statement if you allow that "simultaneous" is defined by special relativity. Otherwise it is contradictory. That's clear evidence of what I have argued, special relativity circumvents the law of non-contradiction by defining "simultaneous" in a particular way.

What are you denying Meta?

That A and B are simultaneous for Angie, or that A and B are not simultaneous for Beth? — creativesoul

Either A and B are simultaneous, or they are not. As in other cases of objective truth, "for Angie", and "for Beth", are irrelevant to what is at issue, you are just throwing them in as red herrings.

Speed might have no meaning without a frame of reference, but words do not require a frame of reference to have meaning, you are just making that up. — Metaphysician Undercover

In the theory of relativity, simultaneity has no meaning without a frame of reference, just as speed has no meaning without a frame of reference.

Philosophers as far back as Aristotle, and beyond, spoke of simultaneity without a frame of reference. It's only relativity theory, which insists that simultaneity is meaningless without a frame of reference. — Metaphysician Undercover

Yes, but whether we talk about simultaneity in the context of relativity theory or in the context of absolute space and time, is part of the meaning of simultaneity.

You are saying that from A's frame of reference X is the case, and from B's frame of reference not-X is the case. — Metaphysician Undercover

Clearly, that is not what was said.

Meta must be having a lend of us. He's just in it to be contrary.

Clearly, that is not what was said. — Banno

Are you kidding?

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. — Banno

My interpretation:

You are saying that from A's frame of reference X is the case, and from B's frame of reference not-X is the case. — Metaphysician Undercover

Meta, both Angie and Beth agree as to what happened. They agree that the events were simultaneous for Angie, but not for Beth.

Your interpretation is wrong.

Meta must be having a lend of us. He's just in it to be contrary. — Banno

Well, being contrary to the way things are is being wrong. One who doesn't acknowledge the relativity of simultaneity cannot account for how simultaneity works. Not much one can do to help another who refuses to acknowledge the inadequacy inherent to a framework they're using. It's akin to continuing to argue in favor of Zeno's account(paradox), even after being shown how Newton dissolved it with calculus.