history and development of logic
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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
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