Logic in philosophy and mathematics Textbook

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Hello,


Lately, I have been interested in philosophy and in particular the branches of philosophy where there is a tie with mathematics and physics. From this point, I think the best branch to start studying would be the most robust one for scientists. i.e Logic.

But I am having a problem finding a textbook to read from. Mathematicians usually focus on, well "math"! While philosophers goes for the whole spectrum of logic, but without using the privilege of mathematical notation.

So I am basically searching for a broad textbook that cover Logic as whole, but includes mathematical notations as well. (So that I can link my knowledge of math with the logic).
Note: I already know introductory set theory.

Can Anyone help me finding a suitable textbook?
 

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I have Popper's Logic of Science but from a mathematical point of view, I cannot recommend it. It is basically a book which belongs to philosophy and its influence on science has to be considered critical. At least it contains the letters Einstein wrote who wasn't a fan either.

I've also searched the net for Russel's book about set theory, but it is so full of special notations, that it is hard to read. So it might be better to read about Russel than to read Russel himself.

So, all in all I have not really a good idea. If you asked for a good book in the field of popular science, I would recommend Hofstadter's Gödel, Escher, Bach. It's a good book, but it isn't meant to be scientific.

From a mathematical point of view, I would chose an introductory book on set theory, leaving the philosophical part outside. Another idea is to look for mathematical history of the late 19th and early 20th century, say 1840 - 1960, when the mathematical revolution took place (Cantor, Hilbert, Gödel). A further approach is to study the various systems and models of logic. We basically use only the predicate logic, but there are more. In how far these systems influenced or affected philosophy is beyond my knowledge. I'm a fan of Kant and not very interested in what came after.
 
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