Mathematical Logic

Mathematical logic is something that has been around for a very long time. Centuries Ago Greek and other logicians tried to make sense out of mathematical proofs. As time went on other people tried to do the same thing but using only symbols and variables. But I will get into detail about that a little later. There is also something called set theory, which is related with this. In mathematical logic a lot of terms are used such as axiom and proofs. A lot of things in math can be proven, but there are still some things that will probably always remain theories or ideas.

Mathematical Logic is something that has a very long history behind it. It has been debated on for many centuries. If someone were to divide mathematical logic into groups they would get two major groups. Both groups are very long. One is called “The history of formal deduction” and it goes all the way back to Aristotle and Euclid and other people who lived at that time. The other is “the history of mathematical analysis” which goes back to the times of Archimedes, who was in the same era as Aristotle and Euclid. These to groups or streams were separate for a long time until Newton invented Calculus, which brought Math and logic together.

Somebody who studies mathematical logic and gives his or her own concepts about it is called a logician. Some well known logicians include Boole and Frege. They were trying to give a definite form to what formal deduction really was. Aristotle had already done such a thing but he had done it with language, Boole wanted to do it with only Symbols. Frege came up with “Predicate Calculus”.

As time went on people did not make new theories as much as they used to in the time of Aristotle. They mostly concentrated on expanding on theories that have been said centuries ago, proving those theories or putting them into symbolic form.

Table of Logicians*

Boole

Frege

Newton

Gödel

Aristotle

Euclid

Archimedes

Leibnitz

*This Table has a few of the Logicians listed in my book

Words that have to do with logic like and, or, not are given symbols like &, V, or an upside down L reversed. The Letters X, Y, Z and so on are commonly used as variables and P, Q, R are used as predicates, properties or relations.

Sometimes there are theories that have to do with machines that do not exist and usually have things in them that are infinite and they usually work with letters and numbers.