Reddit reviews Thinking about Mathematics: The Philosophy of Mathematics
We found 11 Reddit comments about Thinking about Mathematics: The Philosophy of Mathematics. Here are the top ones, ranked by their Reddit score.
Hmm .. try Shapiro's Thinking about Mathematics. It's very good and accessible, and Shapiro is quite eminent.
There's a pretty good reader on the subject called Thinking about Mathematics that I used for a reading course in undergrad. I don't know much about the technical literature beyond that level, though, as my formal philosophy career went on hiatus when I entered my Ph.D. program. Since then, I've been more or less an armchair philosopher.
I've only taken one module in philosophy of mathematics (also the only actual philosophy class I've taken) but Shapiro has a good book we used as a go-to text. Link below bc I don't know how to format on mobile. As far as prerequisite knowledge, you shouldn't need much beyond set/model theory and some mathematical logic, and even that isn't necessary depending on how far your studies are.
https://www.amazon.co.uk/Thinking-About-Mathematics-Philosophy/dp/0192893068
Gives a good overview of various topics in PoM, mainly questions of either:
• Ontology - Do mathematical objects exist? If so, in what sense?
• Epistemology - How do we have mathematical knowledge? How does it apply to the real world?
Aside from the book mentioned above, just do a quick Google and see what you can find in your library catalogue! Ayer, Kant, and Quine are some prominent authors.
Hope that helps some :)
Frege's Foundations of Arithmetic is a classic "primary text" that advocates a specific point of view (that arithmetic can be reduced to logic in some sense).
These are a couple of contemporary introductory books that provide decent surveys of some major views:
http://www.amazon.com/Philosophies-Mathematics-Alexander-George/dp/0631195440
http://www.amazon.com/Thinking-about-Mathematics-The-Philosophy/dp/0192893068/ref=pd_bxgy_b_img_z/181-3737012-4965247
EDIT: If I had to choose, I would pick the Velleman/Alexander book.
You are probably beyond this stage, but I would generally suggest Shapiro, https://www.amazon.com/Thinking-about-Mathematics-Philosophy/dp/0192893068, to a student interested in that topic as a good starting point.
To understand the general history of math, you won't need to understand what you most likely consider to be math. You will, however, need to understand how to put yourself in the shoes of those who came before and see the problems as they saw them, which is a rather different kind of thinking.
But anyway, the history of math is long and complicated. It would take years to understand everything and much of it was work done on paths that are now basically dead ends. Nevertheless, here are some other resources:
Of course, let's not forget what is possibly the most complete single resource available today:
This is a huge area and I applaud you for being interested in it. If you decide to look into it seriously, you WILL find yourself confused, bored, and annoyed at times. Yet it's a beautiful history and one that will illuminate much of the apparently meaningless gibberish in calculus, as well as many other areas.
This is a really good book that I had to use in my philosophy of mathematics course. It's very accessible, and gives you a great introduction to philosophy of mathematics. It keeps things in perspective and reminds you what's at stake, the main questions, all in historical context: http://www.amazon.com/Thinking-about-Mathematics-The-Philosophy/dp/0192893068
Here's a professional review of the book attesting to its awesomeness: http://web.calstatela.edu/faculty/mbalagu/papers/Review%20of%20Stewart%20Shapiro%27s%20Thinking%20About%20Mathematics.pdf
Here are some recent introductory books on the subject:
https://smile.amazon.com/Historical-Introduction-Philosophy-Mathematics-Reader/dp/1472525671/
https://smile.amazon.com/dp/0521533414/
https://smile.amazon.com/Thinking-about-Mathematics-Philosophy/dp/0192893068
https://smile.amazon.com/Philosophy-Mathematics-Princeton-Foundations-Contemporary/dp/0691161402
I'm currently reading http://www.amazon.ca/Thinking-about-Mathematics-The-Philosophy/dp/0192893068 where these sorts of questions about the nature of mathematics are nicely outlined.
I too think that the approach offered is creative, but I don't understand argument tbh. Perhaps he will offer a more basic ontology of mathematics at a future point that will situate his argument within the larger reflections on the nature of math.
I'm also worried that Meillassoux has set up a bit of a straw man argument wrt to the arche-fossil and "correlationism." This is not how I read Kant's transcendental idealism, but I'm unsure at the moment.
Personal note: when I read about SR I went to SEP to try and learn more to see if it was worth pursuing in greater depth, but there were no entries for any of the figures associated with this line of thinking. This concerns me as I can't quite situate SR within a larger philosophical history.
It might be helpful to read an introductory text first. My first philosophy of math course used Stewart Shapiro's [Thinking about mathematics] (http://www.amazon.com/Thinking-about-Mathematics-The-Philosophy/dp/0192893068/ref=sr_1_1?ie=UTF8&qid=1341687670&sr=8-1&keywords=stewart+shapiro) as a supplementary text. I didn't use it too much, but it is pretty good and quite approachable from what I recall. Shapiro is a very well regarded contemporary philosopher of mathematics.
You could also start with the [SEP article] (http://plato.stanford.edu/entries/philosophy-mathematics/). This will give you an overview of the area, its history, and the various sub-disciplines. That can help you narrow down what in particularly you are interested in which will make it easier for you to find appropriate books.
You should just read this book. It's extremely easy and still very useful, and written by the best philosopher of maths currently alive.