1778 – 1831

Logic, a kind of critical thinking, is the study of reasoning. Logic is used in most intellectual activity, but is studied primarily in the disciplines of philosophy, mathematics, and computer science. Logic examines general forms which arguments may take, which forms are valid, and which are fallacies.

Logic is also studied in argumentation theory.

Logic has its origins in several ancient civilizations, including ancient India, China and Greece. Logic was established as a discipline by Aristotle, who established its fundamental place in philosophy. The study of logic is part of the classical trivium.

Averroes defined logic as “the tool for distinguishing between the true and the false”; Richard Whately, ‘”the Science, as well as the Art, of reasoning”; and Frege, “the science of the most general laws of truth”. In the philosophy of mathematics, Benjamin Peirce became known for the statement that “Mathematics is the science that draws necessary conclusions“, and believed, along with George Boole, that mathematics could be used to analyze logic.

The concept of logical form is central to logic, it being held that the validity of an argument is determined by its logical form, not by its content. There four categories of logic: First Formal Logics – the other three being Informal, Symbolic & Mathematical Logic.

Mathematical Logic really refers to two distinct areas of research: the first is the application of the techniques of Formal Logic to mathematics and mathematical reasoning, and the second, in the other direction, the application of mathematical techniques to the representation and analysis of Formal Logic.

Consistency, validity, soundness, and completeness are the important properties that logical systems must have – in that the theorems must not contradict, interfere, guarantee to be true & can be proven.

The earliest use of mathematics and geometry in relation to logic and philosophy goes back to the ancient Greeks such as Euclid, Plato, and Aristotle. Many other ancient and medieval philosophers applied mathematical ideas and methods to their philosophical claims.

For our purpose in simplifying matter & to present an easy illustration, here’s a somewhat “fun” way to look at Mathematical Logic:

If the alphabets: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z were represented as:
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26.

Then:

 H-A-R-D-W-O-R-K . . . 
8+1+18+4+23+15+18+11 = 98%

and K-N-O-W-L-E-D-G-E . . . 11+14+15+23+12+5+4+7+5 = 96%

But , A-T -T -I -T -U -D-E
 . . . 1+20+20+9+20+21+4+5 = 100%

And,

 B-U-L-L-S-H-I-T
 . . . 2+21+12+12+19+8+9+20 = 103%

AND, look how far ass kissing will take you.
:

A-S-S-K-I-S-S-I-N-G . . . 1+19+19+11+9+19+19+9+14+7 = 118%

So, one can conclude with mathematical certainty, that while Hardwork and Knowledge will get you close, and Attitude will get you there, its the Bullshit and Ass Kissing that will put you over the top.

‘REMEMBER SOME PEOPLE ARE ALIVE SIMPLY

BECAUSE IT IS ILLEGAL TO SHOOT THEM’

It goes to show that, for Benjamin Peirce, the great mathematician, true mathematical reasoning is always at the vanguard of thought, and resists logical demonstration.