Development of Logic
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This document outlines the development of logic from ancient times to modern periods. It begins with Nyaya philosophy in India, then covers pre-Aristotelian thinkers who engaged in argumentation. Aristotle is noted for developing syllogistic logic. Subsequent periods expanded on Aristotelian ideas through additions like hypothetical syllogisms. Modern logic revived with symbolic notation and connections to mathematics through thinkers like Leibniz, Frege, Russell and Whitehead. Formal logic systems were then established in the 20th century.
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Development of Logic
- 2. Nyaya Philosophy Pre- Aristotelian Logic Period Aristotelian Logic Period Post - Aristotelian Logic Period Modern Logic Development of Logic
- 3. 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
- 4. Nyaya Philosophy Pre- Aristotelian Logic Period Aristotelian Logic Period Post - Aristotelian Logic Period Modern Logic Development of Logic
- 5. 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
- 6. Nyaya Philosophy Pre- Aristotelian Logic Period Aristotelian Logic Period Post - Aristotelian Logic Period Modern Logic Development of Logic
- 7. 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
- 8. 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.
- 9. Nyaya Philosophy Pre- Aristotelian Logic Period Aristotelian Logic Period Post - Aristotelian Logic Period Modern Logic Development of Logic
- 10. 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
- 11. 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’sTreatises in Reasoning Came to be called LOGIC
- 12. Nyaya Philosophy Pre- Aristotelian Logic Period Aristotelian Logic Period Post - Aristotelian Logic Period Modern Logic Development of Logic
- 13. 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
- 14. 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
- 15. Post-Aristotelian Logic Period GALEN Developed theTheory of the Compound Categorical Syllogism BOETHIUS Coined the term “LOGIC” Translated Aristotle’s works into Latin
- 16. Post-Aristotelian Logic Period PETER ABELARD First major logician of the Middle Ages Reconstructed and refined logic of Aristotle and Chryssipus originated theTheory of Universals WILLIAM OF OCCAM Devoted his attention to Modal Logic
- 17. Post-Aristotelian Logic Period Mid-15th Century Existence of negative reactions against LOGIC LOGIC RHETORIC
- 18. Nyaya Philosophy Pre- Aristotelian Logic Period Aristotelian Logic Period Post - Aristotelian Logic Period Modern Logic Development of Logic
- 19. Modern Logic Period GOTTFRIED WILHELM LEIBNIZ Father of Symbolic Logic SIR FRANCIS BACON Father of Modern Logic
- 20. Modern Logic Period End of 19th century GOTTLOB FREGE Theory of Quantification ALFRED NORTH WHITEHEAD BERTRAND RUSSELL Principia Mathematica
- 21. Modern Logic Period ThreeTraditions ALGEBRAIC SCHOOL by Boole, Pierce & Venn LOGICIST SCHOOL by Russell,Wittgenstein, Frege MATHEMATICAL SCHOOL by Euclid
- 22. Modern Logic Period 20th century Kurt Goedel Formalization of Logical Systems Contribution of Logic to technology