Abstract
This chapter presents a short history of logic, and we discuss Greek contributions to syllogistic logic, stoic logic, fallacies, and paradoxes. Boole’s symbolic logic was developed by George Boole, and Claude Shannnon demonstrated its application to switching theory and digital computing. We introduce Frege, who was a logician and who is the founder of predicate logic.
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Notes
- 1.
The origin of the word Stoic is from the Stoa Poikile (Στοα Пοιλικη), which was a covered walkway in the Agora of Athens. Zeno taught his philosophy in a public space at this location, and his followers became known as Stoics.
- 2.
Modus ponens is a rule of inference where from P and P→Q we can deduce Q, whereas modus tollens is a rule of inference where from P→Q and ¬Q we can deduce ¬P.
- 3.
De Morgan was a 19th British mathematician based at University College London. De Morgan’s laws in Set Theory and Logic state that: (A \(\cup\) B)c = Ac \(\cap\) Bc and ¬ (A \(\vee\) B) ≡ ¬A \(\wedge\) ¬B.
References
Ackrill JL (1994) Aristotle the philosopher. Clarendon Press Oxford
Boole G (1848) The calculus of logic. Camb Dublin Math J 3:183–198
Boole G (1958) An investigation into the laws of thought. Dover Publications (First published in 1854)
Shannon C (1937) A symbolic analysis of relay and switching circuits. Masters Thesis, Massachusetts Institute of Technology
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O’Regan, G. (2023). A Short History of Logic. In: Mathematical Foundations of Software Engineering. Texts in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-031-26212-8_9
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DOI: https://doi.org/10.1007/978-3-031-26212-8_9
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