Philosophy of Mathematics/Scope

This is an introductory meta chapter on the topic. It answers the basic questions about the scope of the course and gives information for deciding on taking the course or not.

Why studying Philosophy of Mathematics?

This is not about either studying PoM or doing (i.e. studying) nothing at all, the question is not 'to study or not to study'. In fact it's about 'this to study or that to study'.

• PoM is better than taking another Maths course, since
  • just doing sth without questioning it is like a hamster in a running wheel that never asks what's outside
  • the valuation of mathematical results itself is not done mathematically
  • communications with nonmathematicians from time to time is unavoidable ( such is life ;o)
• PoM is better than taking another Philosophy of xyz course, since
  • mathematics is THE apriorical science, so here one learns more about the a priori then anywhere else
  • the concept of 'theory' is an elementary one in epistemology, mathematics is where it is defined
  • when talking about mathematics many people appear unconfident, here is clarified what one can and can't expect from it

What does a Philosophy of Mathematics contain?

When doing mathematics 'the usual way' one can easily find that it's not a purely formal science at it's rock bottom. So it can be thought of a mathematical foundation of mathematics. This is usually referred to as metamathematics.

Also one can question the formal method of mathematics at all from a cognitive point of view: is it really better to write confusing lines of symbols then e.g. writing a poem about the stuff? Moreover a mathematician is not alone. There is a whole mathematical community out there and although the results are formal, doing mathematics is highly creative and valuating these results as well as deciding about directions of research is primarily a social problem.

Similarly when thinking about the application mathematics in science, engineering etc. one can take the same two approaches: modelling the situation mathematically and examining the cognitive and community aspects. The application of mathematics can and can't be seen as part of the subject of philosophy of mathematics. Here it is included, but when reasons should appear to source it out to another course this could be done easily.

Exclusions: What it does NOT contain:

• an introduction to logic or model theory
• an introduction to epistemology
• an introduction to cognitive science (should it?)
• an introduction to social science or game theory (should it?)
• any training of mathematical abilities or capabilities
• any issues of non-formal linguistics
• aesthetics of mathematics (as a standalone subject), since this is truly art and not only a subchapter of philosophy. Although it might appear as part of some philosophical considerations.

How is this course structured?

Problem: Philosophers make statements in epistemology and theory of science. Scientists ignore them mainly or even be annoyed about them (or do you know any formal scientist who loves T.S.Kuhn?). But actually Scientists are interested in the philosophical background of their job as well as Philosophers are interested in the justification of their Theories.

Approach: Structuring the whole subject from the perspective of a questioning Mathematician. Such a course structure may be build up along the following questions, expanding the underlying Model of the 'Mathematician's job' step by step.

So the course will be beneficial for Scientists AND Philosophers as well as it enables both sides also to participate in EDITING the content - leveraging the cooperative spirit of Wikiversity!