Salandriagado wrote:Sociobiology wrote:sorry my bad, wrong soundness, it was the logic part that took me right to sound arguments.
yes, I know what axiomatic formalism is. do you know what deductivist formalism is?
Yes. It strikes me as irrelevant pedantry, to be honest. There is no significant difference between "statement X within system Y is true" and "statement X is true if we accept that the premises of system Y are true".
well yes thats why it always confuses me when people say mathematics is not science, it only works with an artificially narrow definition of science.
so all math theorems ever proposed are true? By your logic no scientific theory has ever been wrong because they are not proven to begin with.
No, every mathematical theorem ever proven is true. And always will be.
see deductivist formalism
there are testable assumptions here because there are more than one axiomatic systems.
I know this.Scientific theory =/= mathematical theorem. They are too entirely different concepts.
why would you expect to see a proof in an experimental paper?
If you don't see a description of an experimental approach in that paper, I can only conclude you don't know what an experiment is.
And of course it is a paper about experimentation, what else would I show you?
A paper actually conducting experiments in the aid of establishing the truth or falsity of some mathematical result. (In other news: I just noticed that I know one of those authors). It even says it, right there in that paper:Note that we do value proofs: experimentally inspired results that can be proved are more desirable than conjectural ones. However, we
do publish significant conjectures or explorations in the hope of inspiring other, perhaps better-equipped researchers to carry on the investigation. The objective of Experimental Mathematics is to play a role in the discovery of formal proofs, not to displace them.
It also speaks primarily about the best practices for teaching and disseminating mathematics and building intuition to allow you to do more mathematics, not for deriving it in the first place.
and?
I think you think I am claiming something I am not.
I never claimed mathematics did not need proofs.
proven through experimental means.
No, disproven by counterexample. That is nowhere near the same thing.
It is like the vast majority of experiments.
which is true of all experimental knowledge, and indeed all knowledge, unless you claim mathematics has never accepted any ideas that were later shown to be conjecture.
I claim precisely that: until it's proven, mathematics does not accept it, regardless of how likely we may think it is.
nor does science, but both accept it as worthy of future research.
although to be fair in science everything is various levels of likelihood. which will be true of any contingent statement.
like I said, I don't think you know what an experiment is.
exhaustive counter example is pretty common form of experimentation.
OK, for a weird and arbitrary definition of "experiment", sure.
for the empiric definition.
my own research in paleontology relies on exhaustive counter example.
which I never claimed they constituted proofs, they do however constitute evidence.
No they don't. There's no such thing as "evidence" in mathematics.
disregarding the paper I sourced and you quoted.
hence my statement about mathematics being one large theory.
It is one large hypothetical and logical deductivist construct.
No it isn't. It's not hypothetical. We make zero claims about our statements having relationships to things in the real world.
thats not what hypothetical means.
If scientists want to turn up later and find some way in which they can use them, that's their own prerogative.
not what I am talking about.
value being defined as?
Value in mathematics. Something that increases our knowledge of mathematics. A part of the body of the things that are known about mathematics.
I'm going to quote your own quote.
Note that we do value proofs: experimentally inspired results that can be proved are more desirable than conjectural ones. However, we
do publish significant conjectures or explorations in the hope of inspiring other, perhaps better-equipped researchers to carry on the investigation. The objective of Experimental Mathematics is to play a role in the discovery of formal proofs, not to displace them.
sounds like that fits your definition of value.
yes multiple axiom system, in other words there can be no one overarching set of axioms.
That's not a problem. There's no need for a single set of axioms, Hilbert just thought it would be neat.
there is a need if you want to eliminate the value judgment of which axiomatic set to use in a case.
specifically any one that includes 1+1=2
Yeah. There's plenty of maths that you can do without that.
I know, but you made it sound like it only applied to some obscure rarely used branch.
that would be called hypothesis construction and modelling in science.
No, it isn't. Because we don't then test to see if we can find evidence for it being true. We simply prove that they are true, within our own universe.
that is what a hypothetical construct is.
you can go further an see if it matches the real world, but that is testing the construct not creating it, and of course sciences measure of truth is different. And of course their was a time when science tried to be purely theoretical as well.
yet had applicable validity. meaning it had achieved the state of a law not a theory, scientifically. which is exactly what you should expect.
No, it didn't. It had no validity, at all, in any way, anywhere in mathematics. [/quote]
not according to your own quote.
but we may be running into a conflict of jargon here.
science is actually both, and I have always been told mathematics is the same.I realize now we are running to a problem of wording, Mathematics is the thing being tested not individual propositions.
Mathematics is a process. It is not the body of proven statements, much the same a science is a process, rather than the totality of all theories/laws/etc.