I heard that there are philosophy classes that teach philosophy in a very rigorous and formal and mathematical manner. Are there books that do this? I would like some recommendations.
There is a particular school of philosophy, called "analytic philosophy" which aspires to formal rigor, and there is a subject area within philosophy, called "formal logic" which is very closely related to mathematics and is often taught in a mathematical manner. Researching either of those topics should lead you to a wealth of good sources for what you are looking for.
@user107952 - you can supplement Chris' answer with SEP entry about Analysis and use the biblio and the Related Entries' list. Jun 30, 2014 at 14:45
1It should be noted, however, that 'analytic philosophy' is a much broader term than 'formal philosophy'. The former covers most (but not all) philosophy practiced in philosophy departments in the English-speaking world. It tries to do philosophy in a rigorous and precise manner, sometimes appealing to some formal tools (especially logic). The latter is more of a niche, and takes the mathematical character of analytic philosophy much further, typically to mathematically model various philosophical ideas, using logic, probability theory and other mathematical tools.– J.P.Jun 30, 2014 at 15:51
Check out this course on Coursera:
+1. The philosophy department at Munich (where the course is from), and especially MCMP is somewhat of a global centre for mathematical and formal philosophy at the moment.– J.P.Jun 30, 2014 at 15:53