History and Development of LOGIC

Group 2M-F 3:40-5:20PM

Nyaya Philosophy

Pre-Aristotelian Logic Period

Aristotelian Logic Period

Post -Aristotelian Logic Period

Modern Logic

Development of Logic

Nyaya Philosophy

(5th century BCE)

Attainment of knowledge to be

free from sin through the use of logical arguments

Pre-Aristotelian Logic Period

• Art of Argumentation (Eleatics, Sophists & Megarics)• Dialectics (Zeno of Elea)

• Definition and Induction (Plato & Socrates)

Aristotelian Logic Period

Syllogism (Aristotle)

Post-Aristotelian Logic Period

• Hypothetical Syllogism (Theophrastus)• Logic as Part of Philosophy (Eudemus)

• Logic of Chrysippus• Theory of the Compound Categorical

Syllogism (Galen)• Coinage of the term “logic” (Boethius)• Theory of Universals (Peter Abelard)

• Modal Logic (William of Occam)• Displacement of Logic

Modern Logic Period

• Symbolic Logic (Leibniz)• Inductive Method (Bacon)

• Mathematical Logic (Frege, Whitehead, & Russell)

• Three Traditions of the Development of Logic

• Formalization of Logical Systems (Goedel)

• Logic in Technology

Nyaya Philosophy

Pre-Aristotelian Logic Period

Aristotelian Logic Period

Post -Aristotelian Logic Period

Modern Logic

Development of Logic

NYAYA PHILOSOPHY

Originated in India in 5th century CE

Authored by Siddhartha Gautama

“nyaya” means LOGICAL ARGUMENT or SYLLOGISM

Attainment of knowledge to be free from sin through the use of logical arguments

Nyaya Philosophy

Pre-Aristotelian Logic Period

Aristotelian Logic Period

Post -Aristotelian Logic Period

Modern Logic

Development of Logic

PRE-ARISTOTELIAN LOGIC PERIOD

Arguments about the origin of the universe Later on, arguments of determining the validity of thought-experiences Used ARGUMENTS to be considered trustworthy

Eleatics, Sophists & Megarics devoted to the ART OF ARGUMENTATION

ZENO OF ELEA

Founder of Dialectics

The dialectical method is discourse between two or more people holding

different points of view about a subject, who wish to establish the truth of the

matter guided by reasoned arguments.

Socrates & Plato

Further developed the

dialectical method

Definition and Induction

Nyaya Philosophy

Pre-Aristotelian Logic Period

Aristotelian Logic Period

Post -Aristotelian Logic Period

Modern Logic

Development of Logic

ARISTOTELIAN LOGIC PERIOD

ARISTOTLE

First thinker to devise a logical system

Ideas:

• reduction and absurdum of Zeno

• propositional structure and negation of

Parmenides

• argumentative techniques of Plato

developed the SYLLOGISTIC METHOD

Father of Logic

ARISTOTELIAN LOGIC PERIOD

A syllogism  is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted

or assumed to be true.

ORGANON

Aristotle’s Treatises in Reasoning

Came to be calledLOGIC

Nyaya Philosophy

Pre-Aristotelian Logic Period

Aristotelian Logic Period

Post -Aristotelian Logic Period

Modern Logic

Development of Logic

Post-Aristotelian Logic Period

Theophrastus

Hypothetical Syllogism

Hypothetical syllogism is a valid argument form which is

a syllogism having a conditional statement for one or both of its premises.

Eudemus

Logic as a constitutive part of

Philosophy

Post-Aristotelian Logic Period

CHRYSIPPUS

One of the founders of Stoic

school

Developed a form of logic in which

the fundamental elements were

whole propositions

Post-Aristotelian Logic Period

GALEN

Developed the Theory of the Compound Categorical Syllogism

BOETHIUS

Coined the term “LOGIC” Translated Aristotle’s works into Latin

Post-Aristotelian Logic Period

PETER ABELARD

First major logician of the Middle Ages Reconstructed and refined logic of Aristotle and Chryssipus originated the Theory of Universals

WILLIAM OF OCCAM

Devoted his attention to Modal

Logic

Post-Aristotelian Logic Period

Mid-15th Century

Existence of negative reactions against LOGIC

LOGIC

RHETORIC

Nyaya Philosophy

Pre-Aristotelian Logic Period

Aristotelian Logic Period

Post -Aristotelian Logic Period

Modern Logic

Development of Logic

Modern Logic Period

GOTTFRIED WILHELM LEIBNIZ

Father of Symbolic Logic

SIR FRANCIS BACON

Father of Modern Logic

Modern Logic Period

End of 19th century

GOTTLOB FREGE

Theory of Quantification

ALFRED NORTH WHITEHEADBERTRAND RUSSELL

Principia Mathematica

Modern Logic Period

Three Traditions

ALGEBRAIC SCHOOL by Boole, Pierce &

Venn

LOGICIST SCHOOL byRussell, Wittgenstein,

Frege

MATHEMATICAL SCHOOL by

Euclid

Modern Logic Period

20th century

Kurt Goedel

Formalization of Logical Systems

Contribution of Logic to technology