Can science prove mathematics?

[Atomist]

Can't be proven or aren't proven?

Or are you talking about the fact that we can't have a complete and consistent paradigm a la Godël?

Yeah... Godel... I guess but I mean there are certain truths that can't really be proven... at least not proven rigorously... but I mean for all practical purposes math is "proved"

 

[nrg]

What Gödels incompleteness theorems stated was that it is impossible for mathematics to be entirely consistent because you still have to make the assumption of why arithmetic is consistent because that is the one thing that it cannot prove. It would be circular reasoning.

But what Gödel also proved in his completeness theorem a while before was that if a statement is logically valid you can only deduct one conclusion from it. For example, if I state "Richard has a driver's license. You can only get a driver's license if you're sixteen.", and everything I said is true, then two people cannot arrive at different conclusions regarding if Richard's sixteen or not (again, the statement has to be built by axioms, you cannot say "well, maybe he got it anyway", because the second premise is that you can only get it if you're sixteen).

So, making the one assumption that arithmetic can describe everything but itself consistently, we can then look at mathematical statements and see if they're consistent. Makes sense? Otherwise, I'll have to refer to Occam's razor wich would say that one assumption is good enough to use mathematics the way we use it today, and my English isn't remotely good enough to go there.

 

[jimmyjjohn]

Science (physics and chemistry in particular) tends to be depth first - the classes deal with very few topics, and beat them to death. There's also a context; everything means something. Science is interesting even when you don't quite know what's going on, because there's some hint of what you're supposed to be doing.

Math is breadth first - it covers a huge number of different things, in a very shallow way. There's no context, it's just a bunch of rules. Because of this ***-backwards method of teaching, it takes a looong time to get to a point where math makes as much sense as science does.

Thanks

 

[LuisDantas]

I was watching a "Does God Exist?" debate on youtube the other day. The christian debator, Dr. William Lane Craig, made the claim that science cannot prove mathematical and logical conclusions.

Correct. But it can and does test them. It also tests mathematical and logical models, which makes his objection rather weak.

Further, he claimed that science actually presupposes math, so to claim that it actually proves math would be arguing in a circle.

Nonsense. Math isn't even passible of proof.

What does the RF community make of this? Can mathematical truths be scientifically tested,

Nope. Their applicability to real world situations, however, can and must be. And it is, quite often, with varying results. But that is far more a test of the usefulness of specific models than of math itself.

or do they, so to speak, "prove" themselves?

To an extent they do. But that can only happen while they do not attempt to explain the real world.

 

[Sir Doom]

Math is a language. It is a set of terms designed to allow humans to communicate ideas in a way that other humans understand. The only proof needed is that human beings ACTUALLY communicate ideas to other human beings using math. This happens pretty regularly from what I understand.

 

[LegionOnomaMoi]

What Gödels incompleteness theorems stated was that it is impossible for mathematics to be entirely consistent because you still have to make the assumption of why arithmetic is consistent

More precisely, he proved that for any given formal system (logical, arithmetic, algebraic, etc.), either the system is incomplete, or there are an infinite number of statements/propositions that the system cannot determine to be true or false.

 

[psychoslice]

All I ca say is that as soon as Christianity opens its mouth, it makes one big fool of itself.

 

[captainbryce]

I was watching a "Does God Exist?" debate on youtube the other day. The christian debator, Dr. William Lane Craig, made the claim that science cannot prove mathematical and logical conclusions. Further, he claimed that science actually presupposes math, so to claim that it actually proves math would be arguing in a circle. What does the RF community make of this? Can mathematical truths be scientifically tested, or do they, so to speak, "prove" themselves?

It's a stupid question. It's like asking whether or not microscopes can "prove" calculators. Science and math are both TOOLS! They are a means to an end. They consist of various methods that we use to learn and "figure out" things. The methods used by science can be challenged of course (because science employs theories based on inference), but the whole of science (which is a tool) cannot be "disproved" anymore than a toolbox can be disproved.

 

[ImprobableBeing]

In a sense, mathematics is a science.

The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions".
​

Carl Friedrich Gauss referred to mathematics as "the Queen of the Sciences". In the original Latin Regina Scientiarum, as well as in German Königin der Wissenschaften, the word corresponding to science means (field of) knowledge. Indeed, this is also the original meaning in English, and there is no doubt that mathematics is in this sense a science. The specialization restricting the meaning to natural science is of later date. If one considers science to be strictly about the physical world, then mathematics, or at least pure mathematics, is not a science. Albert Einstein stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."
source

​

Yeah... no.

It's unfortunate enough that you deal with absolute proof (which is anathema to anything scientific since it's unfalsifiable per definition) in mathematics, you also lack any form of objective reference to review your work.

It's not science in itself but it is often used in science to provide measurable predictions that sometimes fail and sometimes work depending on what hypothesis or theory you're working with (with gravity it fails HORRIBLY while it works just fine with electromagnetism).

 

[LegionOnomaMoi]

Yeah... no.

Now the answer is genearlly no. That's a fairly recent development. Mathematics was considered a science more or less right up until Gödel. Even today there are still proponents of this view (I'm not one):
"Many educated people regard mathematics as our most highly developed science, a paradigm for lesser sciences to emulate. Indeed, the more mathematical a science is the more scientists seem to prize it, and traditionally mathematics has been regarded as the 'Queen of Sciences'."
Resnik, M. D. (1997). Mathematics as a Science of Patterns. Oxford University Press.

 

[ImprobableBeing]

Now the answer is genearlly no. That's a fairly recent development. Mathematics was considered a science more or less right up until Gödel. Even today there are still proponents of this view (I'm not one):
"Many educated people regard mathematics as our most highly developed science, a paradigm for lesser sciences to emulate. Indeed, the more mathematical a science is the more scientists seem to prize it, and traditionally mathematics has been regarded as the 'Queen of Sciences'."
Resnik, M. D. (1997). Mathematics as a Science of Patterns. Oxford University Press.

Yeah, i agree with you and disagree with that, it is per definition not a science.

It's closer to alcohol than science.

Saying that using mathematical proofs to provide evidence for a science means that mathematics itself is a science is wrong, it's a tool used in science and i don't know why anyone would argue with that, without the tools we'd have nothing.

 

[Enai de a lukal]

...Dr. William Lane Craig, made the claim that science cannot prove mathematical and logical conclusions.

The claim itself is sort of incoherent, but I guess you could say that's correct. It would probably be more accurate to say that science doesn't need to prove mathematical or logical conclusions- that would be redundant. Mathematical and logical truth is generally a matter of entailment- mathematical/logical truths are true necessarily, and can be known a priori (prior to experience).This post explains the difference, and it also addresses why science would be unnecessary to proving mathematical truths.

Further, he claimed that science actually presupposes math

Another bizarre claim. Science as it exists today heavily relies on mathematics, but I don't know about "presupposes"- once again, this is close to unintelligible (no surprise, coming from Craig).

 

[Revoltingest]

Since he's an old friend, I called up Mathematics to ask his opinion about the OP.
He said....
"Science? I don't need no steenkin natchural science!"

 

[LegionOnomaMoi]

Since he's an old friend, I called up Mathematics to ask his opinion about the OP.

Never trust a guy who's all about Lie groups.

 

[Slapstick]

Yeah, i agree with you and disagree with that, it is per definition not a science.

It's closer to alcohol than science.

Saying that using mathematical proofs to provide evidence for a science means that mathematics itself is a science is wrong, it's a tool used in science and i don't know why anyone would argue with that, without the tools we'd have nothing.

Ol'Einstein for some reason thinks (thought), or did at one time, that "Geometry thus completed is evidently a natural science; we may in fact regard it as the most ancient branch of physics." Einstein, Geometry and Experience

 

[Meow Mix]

Never trust a guy who's all about Lie groups.

Groan.

(Frubal'd anyway)

 

[LegionOnomaMoi]

Groan.

(Frubal'd anyway)

What? Math puns are the "in" thing. Everybody's doing them.
[I was just saying today that we don't see you enough here. You should stop by more]

 

[Revoltingest]

Groan.
(Frubal'd anyway)

Lagroange?

 

[LegionOnomaMoi]

Lagroange?

It's Lagroangian. You Scottish animations never pronounce these correctly.

 

[Slapstick]

Never trust a guy who's all about Lie groups.

I agree, stick with 7-dimensional space and go from there. http://code-laboratory.com/wp-content/uploads/2010/03/piekna_mat_2010_03_23.html