Download History of Logic

Mr. Cervone
History of Logic - Aristotle
 Aristotle
 Greek philosopher
 384 BC – 322 BC
 Born in Stageira, Chalcidice
(Thessaloniki – Greece)
 Studied at Plato’s Academy of
Athens since he was 18
 Father of logic
 Believed that logic should be
build out of syllogism
History of Logic - Syllogism
 Syllogism:
 Starting from true
statements followed by
statements that must be true
as well
 I.e. “If all monkeys are
primates, and all primates are
mammals, then all monkeys
are mammals”.
 Learn new knowledge based
on old knowledge
History of Logic – George Boole
 George Boole
 English mathematician &
phylosopher
 11/2/1815 – 12/8/1864
 Inventor of Boolean Logic
 Gave rise to computer
science
History of Logic – Boolean Logic
 Boolean Logic
 Truth values 0 and 1
 Conjunction
 Disjunction
 Negation
Logic & Geometry
 What is Geometry?
 Branch of mathematics that defines and relates the basic
properties and measurement of line segments and angles
 I.e. All angles in a triangle add up to 180°, etc.
 What does Logic have to do with Geometry?
 investigate how these geometric properties interact to
form a logical system
 logical system must start with generally accepted terms
and concepts that are building blocks of the system.
Logic & Geometry
 Truth:
 Begin somewhere with truths that are accepted
without argument  Axioms




I.e. Point is that which has no part
I.e. Line is breathless length
I.e. Set as a collection of objects
I.e. Plane as a set of points forming a surface
What is Logic
Examples
Sentence
Type
The Brooklyn Bridge is in New York
True mathematical sentence (T)
The capital of California is Los Angeles False mathematical sentence (F)
Did you have soccer practice today?
Nonmathemtical sentence
19-2
Nonmathemtical sentence
5x = 10
Open sentence: the variable is x
Jenny found it behind the sofa
Open sentence: the variable is it
Negation
 The negation of a statement always has the opposite
truth value of the given or original statement and is
usually formed by adding the word not to the given
statement.
Examples
Statement
Neil Armstrong walked on the moon
True (p)
Negation
Neil Armstrong did not walk on the moon
False (~p)
Statement
A duck is a mammal
False (~k)
Negation
A duck is not a mammal
True (k)
Statement
A carpenter works with wood
True (t)
Negation
It is not true that a carpenter works with wood.
False (~t)
Negation
A carpenter does not work with wood
False (~t)