I want to study Mathematical Logic. One concept that confuses me, is that implication is equivalent to '-P or Q'. So, I want to start from the book where this idea first started; but I'm not looking only for this idea, but also other basic ideas of Mathematical Logic.
I guess Boole's Boolean Algebra helped build Mathematical Logic. Can you give a brief explanation of how it and other ideas did (Like the previously mentioned implication definition), where they first started (in which books), and what other classic books talk about them?
Best Answer
What you are referring to with your example is the propositional calculus, also knowns as the sentential calculus, which can be traced back to the ancient Greeks and the Aristotelian logic that emerged from that era.
Boole's study of Boolean algebras is an algebraization of Aristotelian logic, providing an algebraic model and rules of algebra that faithfully mimic Aristotelian deductions.
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.
Related to Boole's boolean algebras are Heyting algebras. These provide an algebraization of a different type of logical system, known as Intuitionism.
I hope this gives you a very rough idea about what mathematical logic might be, and what it certainly is not.