gesang reviewed Philosophy and Model Theory by Tim Button
Much needed book
5 stars
An exciting and fantastic book, with concise and no-nonsense philosophical explications and the use of relatively advanced results in model theory. Furthermore it is even helpful for those who is learning model theory to get the theory itself, since model theory is by far the most conceptually confusing field in mathematics I've ever encountered.
The gem of the book lies in the B part, regarding categoricity, where categoricity is introduced in a way better than ordinary textbooks in model theory, and seemingly unconnected problem of (sort-of) mathematical structuralism is scrunitized with the categoricity results. Some naive views that mathematicians hold with regard to mathematical structures and arithmetics are dissected and countered. To the end of the B part arguments in favour of internalism is given, which is suspiciously similar to a proof-theoretic view of the foundations. It was a horizon-enlarging experience.
It is claimed that an 101 logic course should …
An exciting and fantastic book, with concise and no-nonsense philosophical explications and the use of relatively advanced results in model theory. Furthermore it is even helpful for those who is learning model theory to get the theory itself, since model theory is by far the most conceptually confusing field in mathematics I've ever encountered.
The gem of the book lies in the B part, regarding categoricity, where categoricity is introduced in a way better than ordinary textbooks in model theory, and seemingly unconnected problem of (sort-of) mathematical structuralism is scrunitized with the categoricity results. Some naive views that mathematicians hold with regard to mathematical structures and arithmetics are dissected and countered. To the end of the B part arguments in favour of internalism is given, which is suspiciously similar to a proof-theoretic view of the foundations. It was a horizon-enlarging experience.
It is claimed that an 101 logic course should be sufficient for the book but I doubt that. Maybe mathematical logic 1 and 2, including Godel's incompleteness theorem and arithmetization, and some not-naive set theory introducing cumulative hierarchy and cardinal arithmetic is needed for part A and B. Regarding part C, it might be too concise. I'll refrain from making comments since I don't really understand.