Three Logicians: Aristotle, Saccheri, Frege
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Aristotle: the Theory of Categorical Syllogism
N.B.: For the references, please see Selected Bibliography on Aristotle's Theory of Categorical Syllogism "When modem logicians in the 1920s and 1930s first turned their attention to the problem of understanding Aristotle’s contribution to logic in modern terms, they were guided both by the Frege-Russell conception of logic as formal ontology and at the same time by a desire to protect Aristotl...
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In the beginning of the 20th century, many prominent logicians and mathematicians, such as Frege, Russell, Hilbert, and many others, felt that mathematics needed a very rigorous foundation in logic. The standard approach in the early part of the 20th century was to use a syntactic or proof-theoretic definition of logical consequence. This says that “for one sentence to be a logical consequence ...
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