scientific community is deeply committed

Andrew Wiles had a proof of Fermat's Last Theorem that had a hole, but then he corrected the hole and got a legitimate proof. This would mean, according to Popper's "falsifiability" theory, that mathematics is a pseudo-science.

The scientific community is deeply committed to a view of its own destiny which is well articulated by theoretical physicists. Historically, science is a series of commitments to mathematical apparatuses which, once they are established, are endlessly elaborated, but never discarded. One builds on Newton, Maxwell, etc., by recycling them; one never repudiates them.

In pure mathematics, the equivalent to this stance is that nobody wants to change the decision for the infinity of primes or the irrationality of [root]2 which was made at the outset of rational mathematics. These tenets are held to be valid by the latest, "Left-wing" standards--and to be the source and guiding light for all that followed them in mathematical history. The profession does not want the Greeks--who adopted the elementary theorems on the basis of elementary proofs--to have taken any other course.

>>29

And who decides, what "belongs" and what doesnt? Consensus? You should apologize to Shermer.

Why should I apologize to Shermer? Is there something relevant in that PDF or are you confusing me with another poster? >>27 was my only post, >>28 is not me.

Mathematical correctness is decided when the given proof is logically valid based on the given assumptions and ideas that create the system the proof is "working in." If you're going to question any part of that process, it makes more sense to question the underlying foundations of the argument, not the argument itself. As such, you can change *any* basic property of mathematics you want to anything you like, but it has to follow from what you've outlined as properties or axioms. In that sense, everything we've "decided" about mathematics is really a deduction from a hierarchy of simple ideas. If you wish to create a mathematical world where different things are true, nobody is stopping you from picking different properties and going nuts. In fact, for an example of where this has already happened, look at non-Euclidean geometry.

That's the Platonic ideal of mathematics, at least. If you want to argue that our mathematical community is a circlejerk that churns garbage, and that correctness "in the real world" is decided up by people, go right ahead (I'm going to need some evidence to support it, but that's irrelevant). But don't mix up the two, because when you do it makes your argument at best hard to follow and at worst invalid.

Mathematics is just a very large game. As such, I still don't object to you claiming it's not a science, because in a sense it isn't. However, I really don't think Popper's classification is the best tool for refuting its status as a science, at least not in the way you used it above.

Now, what *is* interesting, is the idea that you could create any axiomatic system to support any proposition. That might almost fit the definition Popper used, but there's still another point to be considered: while I can create any arbitrary system to support my ideas, in order to fit within that system things still have to be proven, so there are still ideas that either will or will not work within * that * system.

Also coming in on your side, I think, are Gödel's incompleteness theorems. You can decide if "undecidable" propositions break math's status as a science.

It seems to me that it just comes down to semantic wordplay, and this whole mess assumes you accept Popper's definition anyway. The cold hard fact is that while some science comes down to an incestuous relationship with mathematics, the imperfect, arbitrary models we come up with *do* work well enough to provide usable predictions. It's a long way off from being a deity, but science *does* give us at least some control over nature, and the math *does* back that up at least a little.

tl;dr - I don't think it matters a whole hell of a lot, as long as you remain sensible about math and don't claim to find proof of God's existence in a Calculus book.