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# If the most fundamental laws of nature changed, would axioms of logic and maths watch

1. also change? If they did not, this suggests there is no connection between them and the natural world, which completely contradicts experience.
2. What 'fundamental laws' are you talking about? I don't think the vagueness helps with your question!

With regard to mathematics, the axioms of any particular field are in some sense arbitrary. We could have chosen (and can choose) different ones if we liked; we'd just get a different set of valid inferences and so a different 'mathematics'. The same is true of formal logic, and there are 101 different logics with different rules of inference, valid sentences etc. Which one(s) you take to be 'true' is a strange question to think about.
3. (Original post by Implication)
What 'fundamental laws' are you talking about? I don't think the vagueness helps with your question!

With regard to mathematics, the axioms of any particular field are in some sense arbitrary. We could have chosen (and can choose) different ones if we liked; we'd just get a different set of valid inferences and so a different 'mathematics'. The same is true of formal logic, and there are 101 different logics with different rules of inference, valid sentences etc. Which one(s) you take to be 'true' is a strange question to think about.
The laws, or law that determine the nature of all existence. It's going to be vague because we know nothing of it.
If axioms of logic and maths are arbitrary, how do they manage to work harmoniously alongside empirical inferences and observations?
4. Human's mind never changes. It's always beyond logic & imaginations. It creates different worlds in the same world.

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5. Not really. We'd simply have to change the mathematical equations and expressions, as opposed to the fundamental axioms.
6. (Original post by RobML)
The laws, or law that determine the nature of all existence. It's going to be vague because we know nothing of it.
So like a theory of everything in physics, if such a thing exists?

If axioms of logic and maths are arbitrary, how do they manage to work harmoniously alongside empirical inferences and observations?
Well, we sometimes use mathematics to model reality, and in those cases we choose the constructions that allow us to make good predictions. There are infinitely many ways we could represent a physical system mathematically that would give results that don't match empirical observations!
7. Interesting question.
8. (Original post by Dima-Blackburn)
Not really. We'd simply have to change the mathematical equations and expressions, as opposed to the fundamental axioms.
This brings the question: where do the axioms come from if not from all that exists?

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9. (Original post by Implication)
So like a theory of everything in physics, if such a thing exists?

Well, we sometimes use mathematics to model reality, and in those cases we choose the constructions that allow us to make good predictions. There are infinitely many ways we could represent a physical system mathematically that would give results that don't match empirical observations!
Yup, but not just a law that connects all natural phenomena, but is the cause of all natural phenomena. I use the word "law" because it's difficult to think of anything else to describe it with.

When I speak of axioms I'm bringing to mind things like "a is b therefore b is a"

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10. If think you could change the laws of maths but i'm more sceptical logically impossible universes could exist. if they could, there is no universal way we could semantically say that they could in the first place anyway.

The laws of logic are true in every possible world, which means they are true in every state of affairs that aren't contradictory. If there could be some universe that didn't follow these laws, i don't even think we can meaning refer to it.
11. http://plato.stanford.edu/entries/impossible-worlds/

12. Good question. It's a shame I'm an idiot and the answers people are giving have long words in them
13. (Original post by RobML)
Yup, but not just a law that connects all natural phenomena, but is the cause of all natural phenomena. I use the word "law" because it's difficult to think of anything else to describe it with.
What do you mean by 'cause', though? For example, even in a universe where Newton's law of universal gravitation holds exactly, it's not true to say Newton's law causes gravitation. The law is just one mathematical formalism that can be used to describe the way objects gravitate in that universe. It's not telling us what is 'actually' happening: the same physical predictions could likely be made by many other formalisms (some likely completely alien to us), why should we pick up on this particular formalism and claim that this is the one that's really causing it?

I suppose my point is that it's a mistake to think of fundamental physical laws as telling us what the universe really is, or as 'causes' of what happens in the universe. Instead, they are specific ways of describing how things in the universe behave.

I really think you need to pin down precisely what you mean by 'the cause of all natural phenomena'!

When I speak of axioms I'm bringing to mind things like "a is b therefore b is a"

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Okay, but different logics have different 'axioms' and different valid sentences/inferences, and it's not always obvious which we should regard as 'true' when trying to make legitimate deductions about the universe. For example, do you regard the law of excluded middle as being true?
14. (Original post by Implication)
What do you mean by 'cause', though? For example, even in a universe where Newton's law of universal gravitation holds exactly, it's not true to say Newton's law causes gravitation. The law is just one mathematical formalism that can be used to describe the way objects gravitate in that universe. It's not telling us what is 'actually' happening: the same physical predictions could likely be made by many other formalisms (some likely completely alien to us), why should we pick up on this particular formalism and claim that this is the one that's really causing it?

I suppose my point is that it's a mistake to think of fundamental physical laws as telling us what the universe really is, or as 'causes' of what happens in the universe. Instead, they are specific ways of describing how things in the universe behave.

I really think you need to pin down precisely what you mean by 'the cause of all natural phenomena'!

Okay, but different logics have different 'axioms' and different valid sentences/inferences, and it's not always obvious which we should regard as 'true' when trying to make legitimate deductions about the universe. For example, do you regard the law of excluded middle as being true?
most of those logics have been developed because some philosophers think that classical logic doesn't do with conditionals correctly though. So "the laws of logic" can be taken here to mean, whichever ones in actual fact turn out to be true.
15. (Original post by banterboy)
most of those logics have been developed because some philosophers think that classical logic doesn't do with conditionals correctly though. So "the laws of logic" can be taken here to mean, whichever ones in actual fact turn out to be true.
That's not quite true (for example, vagueness and paradoxes are often motivations for other logics). But yeah I suppose it is mostly irrelevant to the question at hand - whatever the 'laws of logic' happen to be, we can still ask whether and under what circumstances they might change.

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