Assuming the axioms we build logic on remain constant, would any results obtained by using these axioms still be relevant in another universe (multiverse?)?
I know the question is badly worded, but I can’t properly write down the question that I have in my head.
Is logic necessarily relevant in this universe?
Logic is like language - it has its own rules and internal consistencies, but it needn’t be relevant to reality, any more than the grammar of the sentence “the cat sat on the mat” tells us anything about the actual feline.
It really depends on the nature of that other universe.
Do you mean logic or laws of science?
Logic can be one of the tools used to derive the physical laws that govern the universe, another universe may have completely different physical laws but if it enabled sentient life to exist then they may use logic similar to ours to derive the laws of their universe. However we have no way of really knowing, this is just speculation.
I guess is you want to believe the String/M Theorists, all “universes” will have the same fundamental law, and in the sundry vacua/universes (one of which we occupy), certain free parameters accounted for by that law will take on different values.
How might Logic be different in another Universe?
Logic to me is statements like
If we know
( If A is True then B must be True
If B is True then C must be True )
Then Logic allows us to calculate
If A is True then C must be True
Is there consideration of universes where given the above known state
there exists some cases where A is True yet C is false, with B in some sort of other state than true or false.
The question boils down to:
“Is causality fundamental, or merely a manifestation of a higher order of laws which may produce different properties in different systems (universes)?”
Depends on what you mean by “existed”. If you mean such that there is an even infinitesimal chance of sending even one bit of information between the two worlds, then yes, our laws of logic would apply.
However, if there is not possibility of information exchange, then no, our laws of logic wouldn’t have to apply, but then from our perspective it couldn’t really be said to “exist”. And even if it did it would be located outside our space time boundaries, so we couldn’t say it existed “now” or “yesterday” or “10 trillion light years away”, since we wouldn’t be able to reference it in space or , more importantly, in time.
Do you mean to say that if quantum entanglement can act between universes, that the physical laws in each must be identical?
Without logic, how do you expect to answer your own question?
Yes. Because either our logic applies, and therefore our logic applies (A=A), or because or logic doesn’t apply, and therefore the very premise that if not A then not A does not apply, and that means if not A then A, which means that because our logic doesn’t apply, our logic applies.
Actually, I’m beginning to rethink my statement, but as I wrote it originally, I was only referring to the laws of logic, not the physical laws.
However, in any sub-realm of the metaphysics of the parallel universe we could study, would not necessarily be amenable to logic. For instance, things could pop into existence and out based on rules that no one can comprehend, and go from for instance a stationary, particle existence to a universe-spanning waveform without reason or science behind it.
What if that universe were controlled by an infinite stack of logical deconstructionists? That constantly rewrite the way things interact, and which themselves are constantly altered such that they do things in an entirely different way? Any logical preposition you might forward would be instantly rendered meaningless by the constant shifts in causality and physical interactions.
On that world, the study of logic would make as much sense as the study of a random finite state machine in computer science: valid, but not interesting.
So I guess my altered answer is that I cannot conceive of a universe that interacts with ours in which the laws of logic cannot be discovered, but it’s possible they might not have real meaning.
I could answer in gobbledegook, but that would presumably not really be an ‘answer’ under certain definitions. However, neither could I answer my question without language (or, indeed, oxygen, a temperature within a certain threshold, or 3 dimensions of space and one of time: 3D+T for short). All kinds of things are necessary for events called “answering questions” to occur.
What the OP appears to seek to explore is the “reality” of logic: is the absurdity of A & -A a property of the universe, or something which exists only in the minds of humans, and therefore not necessarily the case given a different configuration of space?
The universe is so. It is how it is, not some other way. How it is is 3D+T, containing arrangements of matter, energy and their accompanying fundamental forces. (One end of it might be timeless.) Within this 3D+T region, some matter has a configuration such that it uses language. That language can comprise “The cat sat on the mat”, thus communicating to another language-using configuration the position in time and space of a small, furry configuration.
Now, that sentence “The cat sat on the mat” is only a linguistical construct. It is a series of sounds or letters associated with memories held in the neural networks of those amazing configurations which allow them to in effect exchange memories. However, this “memory exchange” requires a certain protocol of precisely which sounds/letters represent which memories. Thus arise the rules of language.
I consider logic and mathematics also to be kinds of language. Of course, they are enormously complex languages which “write themselves” based on the simplest of grammatical protocols, and they are capable of encoding in just a few letters “memories” which would take far longer to describe in everyday words (e[sup]i[symbol]p[/symbol][/sup]=-1 anyone?). But, just as “The cat sat on the mat” does not necessarily have any relevance to the 3D+T how it is, neither does 1+1=2 or reductio ad absurdans necessarily relate to reality: we impress them onto reality just as we impress “cat, sat, mat” etc. onto reality.
And so what of these “other universes” (which I suggest are more accurately described as “other regions of the universe”? What if How it is was 2D+T, or 4D+T, or 11D without time?
Again, logic would require language-using configurations of matter. How it is would be the case without any reference to logic, mathematics or language. It seems that any number other than 3 dimensions of space involves gravity too weak or too strong for such configurations of matter to evolve, and time (or its illusion) similarly appears to be necessary.
It might well be that the 3D+T region of the universe is the only place where logic exists. But it is still not necessary anywhere.
How is causality linked to logic? (not an accusation, I just don’t know)
I have allways considered causality to be a law of Physics, one that could be broken if for instance time travel is possible, but not a law of logic.
Does anyone have a good link to a cite that links causality with pure logic?
Thanks, Bippy
Ah, but the question was whether logic is always relevant in any given universe. Without logic, that question cannot be answered – indeed, it makes no sense to even ask such a question. And any attempt to claim otherwise would be self-refuting.
Causality is not linked to standard propositional or predicate logic, but it could be the product of other physical laws. The question is, “Is causality independent of the other fundamental laws that govern our universe?”
Causality is not linked to standard propositional or predicate logic, but it could be the product of other physical laws. The question is, “Is causality independent of the other fundamental laws that govern our universe?”
If it did not obey some kind of what we would loosely call logic, I don’t see how we could fairly apply the word “exists” to it.
Since we can only analyze it from the perspective of a world that can be shown to, at least loosely, follow what we would call logic, I can’t describe what such a world would be like were it to really “exist”.
But I have described a world which would be able to exchange information with us, that effectively does not follow any logic.
From my perspective, the Prime Universe can only be said to effectively follow logic anyway, so it makes just as much sense to say ours does follow logic and that other one doesn’t.
Logic and language are necessary to (and therefore relevant to) the entity called “asking questions”. I contend that they are not necessary to (and therefore not necessarily relevant to) the entity called the universe.
Is this not cart-before-horsemanship? Does the fact that we apply the word “exists” to the universe necessitate that the universe “obeys language”? Is logic fundamentally different in this respect?