Science

[Cythraul]

What's objective about mathematics? It is completely made up. You define your axioms which can be completely arbitrary and go on from there. There could be two different branches of mathematics which completely negate each other - say non-Euclidean and normal geometry.

It depends on what you mean by 'objective'. If by 'objective' you mean 'provides a true description of the world' then mathematics is in the same boat as the rest of empirical science. If by 'objective' you mean 'produces results whose truth is not determined by the opinion or subjective preferences of a particular individual or group' then mathematics seems to be quite objective. What is more objective than '2 + 2 = 4' in this sense?

 

[kmik]

It depends on what you mean by 'objective'. If by 'objective' you mean 'provides a true description of the world' then mathematics is in the same boat as the rest of empirical science. If by 'objective' you mean 'produces results whose truth is not determined by the opinion or subjective preferences of a particular individual or group' then mathematics seems to be quite objective. What is more objective than '2 + 2 = 4' in this sense?

It's not true. The foundation of mathematics is in axioms chosen arbitrarily. Can't think of other branches in mathematics where 2 + 2 = 4 does not hold, but there are axioms in geometry which don't always hold (for example in non-Euclidean geometry). Mathematics don't describe the world, it provides a specific framework to filter the world through. It is human invented knowledge so mathematics can be objective and true in the sense that there are rules of grammar, but it does not necessarily have anything to do with reality.

 

[Cythraul]

It's not true. The foundation of mathematics is in axioms chosen arbitrarily. Can't think of other branches in mathematics where 2 + 2 = 4 does not hold, but there are axioms in geometry which don't always hold (for example in non-Euclidean geometry). Mathematics don't describe the world, it provides a specific framework to filter the world through. It is human invented knowledge so mathematics can be objective and true in the sense that there are rules of grammar, but it does not necessarily have anything to do with reality.

I didn't literally mean that mathematics could describe the world. Also, what follows from a set of axioms is objective in the latter sense that I described. The fact that the axioms themselves may be arbitrarily chosen is pretty uncontroversial.

 

[kmik]

Of course it is objective in the sense that its truths are independent of viewer, but that's only if the viewer accepts the axioms. Suppose I say "B is C". Then for all people who agree that "B is C" (accept my axioms), "B is C". But "B is C" has no meaning in itself. A good analogy is the rules of a game. If you accept the rules then we can objectively agree which move is legal and which is not, but this is still an abstract system of knowledge.

 

[Blowtus]

You don't have to 'accept' the rules, merely accept that *if* they are the rules, then x is the case.

 

[Seditious]

Physics is easy to pick on cause it's difficult to understand, but what about Darwinian evolution? Do you think that speciation could be explained in other terms besides nonrandom survival of random mutations?

even the religious zealots of America seem unable to conceive of that, and thus grant its existence.

 

[Cythraul]

You don't have to 'accept' the rules, merely accept that *if* they are the rules, then x is the case.

Thank you kind sir. That was a hell of a lot more succinct than what I probably would've said.

 

[kmik]

Ah, of course I agree with that. But if that's the case, how is mathematics in the same boat as empirical science? Mathematics alone describe nothing; it's a tool to be applied to empirical science. Like a language with specific rules of grammar, where a sentence can be said to be grammatically correct if one accepts the "rules" but which means nothing