2016年11月1日 · What does mathematical logic mean? In the book Analysis 1 by Terence Tao, it says: The purpose of this appendix is to give a quick introduction to mathematical logic, which is the language one uses to conduct rigourous mathematical proofs. Checking Wikipedia:

$\begingroup$ Open Logic Project - is a collection of teaching materials on mathematical logic aimed at a non-mathematical audience, intended for use in advanced logic courses as taught in many philosophy departments. It is open-source: you can download the LaTeX code.

2013年2月26日 · Mathematical logic is a very broad subject, of which propositional calculus is a very elementary part of, and is very well understood, and is in fact quite trivial. A large portion of modern mathematical logic is concerned with Model Theory, and to some extent is a study of the expression power of formal languages.

If you have mathematical background, I recommend Hannes Leitgeb's Mathematical Logic lecture notes, which introduces modern first-order logic up to Godel's first incompleteness theorem, with a conventional kind of deductive system, and has exercises and solutions.

Here is an attempt to translate them into logic: But as preposition: Everyone but Father left early ...

2017年10月18日 · Back in the days, Joseph Shoenfield's Mathematical Logic was (and still is, in some places) a standard reference, and it does contain a fair bit of model theory (up to Ryll-Nardzewski's categoricity theorem, though do note that there are a lot of important results and definitions in the exercises), some proof theory (say, Herbrand's theorem and ...

The answer to this question is "no". Mathematicians use logic as a language to express mathematical proofs. But to say that these proofs are "based" on logic is analogous to saying that "War and Peace" is based on Russi

2017年3月3日 · Here are some definitions that I found in some lecture notes about mathematical logic: Definition 1. Given two models M and M', an isomorphism of M into M' is a function h such that h is a homomorphism of M into M' and h is one-to-one. A homomorphism is defined as follows: Definition 2.

Mathematically, there are two ways of "translating" "I like neither chocolate nor vanilla" (the two ways are logically equivalent, an instance of de Morgan's laws).

2015年3月8日 · The main difference between "Logic in Philosophy" and "Mathematical Logic" is that in the former case logic is used as a tool, while in the latter it is studied for its own sake. A Logic class in a Philosophy degree will usually cover sentential , predicate and finally first-order logic (by order of increasing complexity and natural way of ...