Logic

Logic is a language for reasoning.
It is a collection of rules
we use when doing logical reasoning. Human reasoning has been
observed over centuries from at least the times of Greeks, and patterns appearing
in reasoning have been extracted, abstracted, and streamlined.
The foundation of the logic
we are going
to learn here was laid down by a British
mathematician George Boole in the middle
of the 19th century, and
it was further developed and used in an attempt to derive all of mathematics
by Gottlob Frege,
a German
mathematician,
towards the end of the 19th century.
A British philosopher/mathematician, Bertrand Russell, found a flaw in
basic assumptions in Frege's attempt but he, together with Alfred Whitehead,
developed Frege's work further and repaired the damage. The logic we study today
is more or less along this line.

In logic we are interested in true or false of statements, and
how the truth/falsehood of a statement can be determined from other statements.
However, instead of dealing with individual specific statements, we are going to use
symbols to represent arbitrary statements so that the results can be used in many
similar but different cases. The formalization also promotes the clarity of thought
and eliminates mistakes.

There are various types of logic such as logic of sentences (propositional logic),
logic of objects (predicate logic), logic involving uncertainties, logic dealing with
fuzziness, temporal logic etc. Here we are going to be concerned with propositional logic
and predicate logic, which are fundamental to all types of logic.

**
Next -- Introduction to Propositional Logic **

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