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
I would say logic is an abstraction. There's no evidence that classical Aristotelian logic is part of nature. — fishfry
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
Of course there is such a thing as simultaneity. It's that silly word "absolute" that causes the problem. — Banno
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
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
When they aren't, when they're timeless propositions, then nonsimultaneaty doesn't apply. — Michael Ossipoff
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
My point is without simultaneity, which I think you agree is impossible, there can't be a law of noncontradiction. — TheMadFool
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
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
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
But special relativity implies that it is really the case that both X and not-X are true. — Metaphysician Undercover
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.
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
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 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
The sense that is relevant here is the sense of "simultaneous"... — creativesoul
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
"In the same sense" refers to the meaning of the words of the statement, not the frame of reference. — Metaphysician Undercover
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
But the words have no meaning without the frame of reference, just as speed has no meaning without the frame of reference. — litewave
It is a statement without meaning, and meaningless statements are neither contradictory nor non-contradictory. — litewave
What are you denying Meta?
That A and B are simultaneous for Angie, or that A and B are not simultaneous for Beth? — creativesoul
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
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
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. — Banno
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
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 must be having a lend of us. He's just in it to be contrary. — Banno
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