3 ms·

Thanks man, will definitely get this book.

• fnrslvr 8y ago
  I'll add, that I strongly advise against beelining for Gödel's Incompleteness theorems. Learn the formal language aspects, like grammar and parsing and structural induction. Learn semantics. Learn a few deductive calculi (say, natural deduction and Hilbert style) and how they interrelate, and actually use them to prove some (very simple) results, ideally from some important axiom systems like Peano arithmetic and ZF set theory. Learn model theory, Gödel's completeness theorem, the compactness theorem, and their more immediate implications. You should also learn how logic interrelates with * Computation, both in the sense of enumerability of deductive proof systems, and in the sense in which expressability in certain logical theories is Turing-complete; and * Set theory, both to grasp the sense in which a first-order set theory like ZF seems to suffice to supply an ontology for the rest of mathematics, and to understand the role of cardinality in e.g. model theory. There isn't really a correct order in which to approach these fields. You'll find that for a proper understanding of any of these topics, you'll have to move back and forth between them frequently. I would put off Gödel's incompleteness theorems until you've done most of this. In particular, learn the completeness theorem, up to a point of confidently being able to apply the compactness theorem, first. Many of the least-informed abuses of the incompleteness theorems come from people who can't distinguish different notions of entailment, and are unfamiliar with the successes of deductive calculi and the categoricity shortcomings of first-order logic.