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Set Theory and Its Philosophy: A Critical Introduction
Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.
360 pages, Kindle Edition
First published January 1, 2004
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Displaying 1 - 3 of 3 reviews
March 3, 2014
This was a pre-requisite read to one of my courses. It's a quick read and if you are studying mathematics you should read it. Even if you know what a set is it will at least get your mind working with the right terminology.
May 17, 2023
It's helpful for me to reread this every couple of years to avoid errors.
That's really the best thing I can say about it.
That's really the best thing I can say about it.
June 8, 2023
Love the picture of the Tower of Babel on the cover. Hordes of humans scrambling around industriously with all the necessary infrastructure ( towns, roads and ports ... ). And only managing so far to build the first few levels. This is so appropriate.
This book is a bit of a challenge. The author attempts to describe a slightly unorthodox version of set theory - for example and rather pointedly no axiom of replacement - which is interesting enough and covers the basics. But it's a bit sketchy and hard to read. More detail is required to follow fully. He does make very clear the difference between a class and a set. And one of the things he focuses on is the possible inadequacy of the overall interative conception of sets and the possible need for impredicative definitions whilst avoiding contradictions. Good luck with that!!
The last couple of chapters on the Axiom of Choice and the higher infinity axioms were disappointing. Basically unreadable. ( Written by experts for experts - using all the standard tricks to exclude the unwashed and the non-credentialed.)
Which is a pity because that's what I am now primarily interested in. He does mention the work of Harvey Friedman which was intriguing.
I want to repeat a comment from the previous review.
Apparently one can use higher order infinity axioms to prove first order properties of numbers than can't be proved in first order logic ( or even second ... etc ). This blows my mind. It says something deep about the nature of reality. Very high on my bucket list. After decades of being distracted by trivia I have just gotta know how this works.
This book is a bit of a challenge. The author attempts to describe a slightly unorthodox version of set theory - for example and rather pointedly no axiom of replacement - which is interesting enough and covers the basics. But it's a bit sketchy and hard to read. More detail is required to follow fully. He does make very clear the difference between a class and a set. And one of the things he focuses on is the possible inadequacy of the overall interative conception of sets and the possible need for impredicative definitions whilst avoiding contradictions. Good luck with that!!
The last couple of chapters on the Axiom of Choice and the higher infinity axioms were disappointing. Basically unreadable. ( Written by experts for experts - using all the standard tricks to exclude the unwashed and the non-credentialed.)
Which is a pity because that's what I am now primarily interested in. He does mention the work of Harvey Friedman which was intriguing.
I want to repeat a comment from the previous review.
Apparently one can use higher order infinity axioms to prove first order properties of numbers than can't be proved in first order logic ( or even second ... etc ). This blows my mind. It says something deep about the nature of reality. Very high on my bucket list. After decades of being distracted by trivia I have just gotta know how this works.
Displaying 1 - 3 of 3 reviews