Talk:Philosophy of mathematics/Archive 2
heh. this is going to be *so* weird to people who think math is real...
It's also a total mess as an encyclopedia article.
This article should describe the various different philosophies of mathematics.
Also, I doubt it should be "weird" to anyone. Anyone who works with math pretty soon hits some philosophical issues.
A lot of scientists (particularly if you get into the social sciences) don't consider mathematics neutral.
- It differs from the philosophy of science by not taking mathematics as a neutral point of view - rather, investigating such subjects as the willingness to accept mathematical proofs, the validity of induction or analogy, what combination of metaphors constitutes an isomorphism, mathematicians' social capital and the meaning of the well-known collaboration graph.
- A lot of 'hard scientists' don't consider 'social science' to be science -- they point to the lack of falsifiability in many of their theories, and assert that abandoning objective standards of mathematical and logical proof removes the basis for falsifiability, leaving only opinion, fashion, and popularity contests.
- There are physicists who do think that. But that's a relatively small minority opinion (something like 10% or so). My experience with "math-fetishists" is that they actually tend to be social scientists. Very few physicists (or even mathematicians) seem to believe that an idea that can't be expressed in mathematics isn't an idea at all, however I've known/read a number of social scientists that seem to think that. The problem is that regarding mathematics in social science *greatly* limits the hypothesis that you can form and the theories that you can test. Also, pretty much anyone who does qualitative research would disagree with non-mathematical means non-falsifible, and I'm pretty sure that most physicists don't think this (even though I know of a few who do).
This article is still a mess. It's confusing, misleading, and in some places, downright wrong....
I guess I'll start by removing the most egregious errors
- asks what makes one theory more acceptable than another despite imperfect empirical validation and limits of the scientific method - and assumes mathematics as a neutral point of view.
I'm not sure what neutral point of view means in this context. If the statement is that mathematics doesn't influence how scientists view the world, then its false.
This is gibberish. It's also inaccurate
- and collaborators, actually mapped onto the physicists' particle physics foundation ontology or if they were simply another sacred geometry like that of Plato - a useful but limited model that awaited understanding of some deeper ontology.