Thread: Foundations of mathematics

Hello,
The foundations of mathematics is quite an interesting subject in its own right. However I have not yet come across any good writing that can make this issue and its discussion clear to me. Still the topic is highly mysterious to me because the available writings on the net ( which I have been able to find) are too diffused and also because it is rare that something is said about the foundations in any book on mathematics.
Can somebody please refer me to some book or available writing that can make this issue clearer to me ? It would be better if the available writing was available online.

Regards

UJJWAL

This is the topic that I want to understand better, too. It seems to me that some books on philosophy of mathematics are too concerned with good English and style, and are too vague.

When I was choosing a book on the subject, "The Oxford Handbook of Philosophy of Mathematics and Logic" edited by Shapiro seemed OK, but I only started reading it. I also encountered a quite recent paper "Foundations of Mathematics from the Perspective of Computer Mathematics" by a prominent logician Henk Barendregt, which can be found on his home page. However, it is probably not intended to be a first introduction.

Hello,

My post was useless

I basically refer to the axiom theory, modal theory, set theory, logic etc and things like consistency when I speak of the "Foundations of mathematics "

I have a book by Calvin Clawson titled Mathematical Mysteries you may wish to read.

@wonderboy1953
do you have the e-copy of the book. Is their a link you can direct me to ?

Originally Posted by UJJWAL

@wonderboy1953
do you have the e-copy of the book. Is their a link you can direct me to ?

This is a link, but you'll have to order the book:

Mathematical Mysteries: Calvin C Clawson: Books | Flipkart

If you're planning on studying the foundations, I can recommend the following:

Axiomatic Set Theory, by Patrick Suppes.
Language, Proof, and Logic, by Barwise and Etchemendy.
An Introduction to Mathematical Logic, by Enderton.
Metalogic, by Hunter.

In my experience, "Foundations of mathematics" usually refers to metamathematics, i.e., philosophy of mathematics. On the other hand, set theory, model theory, consistency, etc. are standard topics of mathematical logic, a branch of mathematics. Concerning philosophy, I forgot to mention Stanford Encyclopedia of Philosophy. It has quite a few in-depth articles about platonism, formalism, intuitionism, logicism, etc.