Philosophy and Math

[Kratzer]

I'm taking a class called "the philosophy of math" and for my final I have to write a 15-20 page paper. It can be about pretty much anything, as long as it deals with philosophy and math. Anybody have any ideas?

[cambraceres]

Yeah, paraphrase "Principia"

[bunny]

Personally, I find the question "Do mathematical entities exist or do we make them up?" the most interesting in the philosophy of mathematics. I'd address that question.

[guesswest]

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Personally, I find the question "Do mathematical entities exist or do we make them up?" the most interesting in the philosophy of mathematics. I'd address that question.

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A really interesting read (which isn't to say I agree with much of it) is 'Science Without Numbers' by Harty Field. It's an introduction to the idea of mathematical fictionalism - it has many problems, but if you're looking for overarching criticisms, ie ones that you can apply to all the main schools of philosophy of math (realism, empiricism etc) then you'll find a lot to write about in short order.

[aeest400]

Philip Kicher has a nice philosophy of math book. I read it and wrote a paper arguing about some of the ideas he presents for my phil of math class. Or just google something. Or, alternatively, withdrawl from the course. Based on the content of the OP, option three may be the best.

[DrunkHamster]

Here's (http://www.philosophy.ox.ac.uk/past_papers/FHS/122_-_Philosophy_pf_Mathematics_-_1998-2000.html) a list of old exam titles on my course. All of them are supposed to be about an hour long, but there may well be some interesting stuff that you can write about.

[RJT]

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Here's (http://www.philosophy.ox.ac.uk/past_papers/FHS/122_-_Philosophy_pf_Mathematics_-_1998-2000.html) a list of old exam titles on my course. All of them are supposed to be about an hour long, but there may well be some interesting stuff that you can write about.

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Drunk,

I like this one from your list:

10. What is a set?

One can talk about “trips” and “a set”. Sorry gang, I have yet to have my coffee this morning.

RJT

[pzhon]

What makes an angle right?

If your course is on what I would call the philosophy of mathematics, then I have some real suggestions. Their appropriateness may depend on your background and what has already been covered in the class.

/images/graemlins/diamond.gif Analyze the standard(s) of proof in mathematics, and how this affects the reliability of communicated results. Compare the computer-assisted proofs of the 4-Color Theorem and Kepler's Conjecture with the proof of Fermat's Last Theorem.

/images/graemlins/diamond.gif What makes some statements worth proving as goals, as opposed to other results that are viewed only as intermediate results, or uninteresting provable statements?

/images/graemlins/diamond.gif What is the role of experiments in mathematics?

/images/graemlins/diamond.gif Compare mathematical notions of infinity with each other and with philosophical notions of infinity.

[bluesbassman]

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I'm taking a class called "the philosophy of math" and for my final I have to write a 15-20 page paper. It can be about pretty much anything, as long as it deals with philosophy and math. Anybody have any ideas?

[/ QUOTE ]

Maybe relate the historical development of a specific branch of mathematics/important result to how it might have been influenced or facilitated by a particular philosophic school of thought which occurred concurrently.

One obvious example would be to relate Decartes mathematical advances (analytic geometry, etc) to his metaphysics and/or those of his contemporaries. Russell's work has already been mentioned. I am sure there are many other possibilites along this line.

[etherealpat]

i REALLY like your last one. the math versus the philosophy of infinity is a pretty intense concept, but the mathematical concept of infinity seems a little hard to work with in a paper unless you either drill to semantics or branch out to applications... and both routes yield some to philosophy. if you're going with historical mathematical concept of infinity, it would be easier, but obviously less interesting.

[MathEconomist]

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Personally, I find the question "Do mathematical entities exist or do we make them up?" the most interesting in the philosophy of mathematics. I'd address that question.

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In fact, I'd say it's THE question in philosophy of mathematics. I know when I took a graduate philosophy class in that field that's basically all we worked on. There are other potentially interesting issues, but ultimately it all boils down to what are mathematicians doing and how should we regard the results they produce.

Unfortunately for someone writing an undergrad term paper, it's going to be hard to produce anything new or intersting in that area. The research going on there is pretty technical. I'd stick to something simpler and more narrow for a term paper.

[DrunkHamster]

Also, if it is at all possible, write something to do with Godel's Theorem: this is fascinating stuff.

[Philo]

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It can be about pretty much anything...

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Sounds like an awful class.

[atrifix]

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In fact, I'd say it's THE question in philosophy of mathematics. I know when I took a graduate philosophy class in that field that's basically all we worked on. There are other potentially interesting issues, but ultimately it all boils down to what are mathematicians doing and how should we regard the results they produce.

Unfortunately for someone writing an undergrad term paper, it's going to be hard to produce anything new or intersting in that area. The research going on there is pretty technical. I'd stick to something simpler and more narrow for a term paper.

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I agree the question of realism vs. anti-realism and similar debates are THE question in philosophy of mathematics. I would have no problem writing on it, though, at least, depending on what I thought about the class. I doubt an undergrad will produce anything new or interesting in that field, but presumably a professor (or grader) understands this, and an undergrad won't produce anything new or interesting in any other field anyway. But I don't know enough about the literature on the subject to say whether there is really enough research accessible to an undergrad.

One thing you might want to write about are the rejection of bivalence; perhaps the justification for the move to intuitionism, or the application of intuitionistic logic in some interesting settings. Or you could write about fuzzy logics. Or write about any one of Hilbert's problems (http://mathworld.wolfram.com/HilbertsProblems.html). That should be more than enough to choose from, at any rate.