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Wednesday, August 29, 2018

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Gottlob Frege (1848-1925) was a German philosopher and mathematician best known for his contributions to logic and the philosophy of mathematics. Frege is also considered the father of analytic philosophy. Mathematician Michael Beeson said,

"Gottlob Frege created modern logic including 'for all', 'there exists' and rules of proof. Leibniz and Boole had dealt only with what we now call 'propositional logic' (that is, no 'for all' or 'there exists'). The also did not concern themselves with rules of proof, since their aim was to reach truth by pure calculation with symbols for the propositions. Frege took the opposite track: instead of trying to reduce logic to calculation, he tried to reduce mathematics to logic, including the concept of number." (Alan Turing: Life and Legacy of a Great Thinker, 2004)

The rest of this post is some quotes from Frege.

"This ideography is a 'formula language', that is, a lingua characterica, a language written with special symbols, 'for pure thought', that is, free from rhetorical embellishments, 'modeled upon that of arithmetic', that is, constructed from specific symbols that are manipulated according to definite rules." (Begriffsschrift, 1879)

"Strictly speaking, it is really scandalous that science has not yet clarified the nature of number. It might be excusable that there is still no generally accepted definition of number if at least there were general agreement on the matter itself. However, science has not even decided on whether number is an assemblage of things, or a figure drawn on the blackboard by the hand of man; whether it is something psychical, about whose generation psychology must give information, or whether it is a logical structure; whether it is created and can vanish, or whether it is eternal." (Uber die Zahlen des Herrn H. Schubert, 1899)

"I hope I may claim in the present work to have made it probable that the laws of arithmetic are analytic judgments and consequently a priori. Arithmetic thus becomes simply a development of logic, and every proposition of arithmetic a law of logic..." (The Foundations of Arithmetic, 1884)

"The novelty of this book does not lie in the theorems but in the development of the proofs and the foundations of which they are based." (Grundgesetze der Arithmetik, 1893)

"Often it is only after immense intellectual effort, which may have continued over centuries, that humanity at last succeeds in achieving knowledge of a concept in its pure form, by stripping off the irrelevant accretions which veil it from the eye of the mind. (Grundgesetze der Arithmetik, 1893)

"We suppose, it would seem, that concepts grow in the individual mind like leaves on a tree, and we think to discover their nature by studying their growth; we seek to define them psychologically, in terms of the human mind. But this account makes everything subjective, and we follow it through to the end, does away with truth. (Grundgesetze der Arithmetik, 1893)

"If the task of philosophy is to break the domination of words over the human mind... then my concept notation, being developed for these purposes, can be a useful instrument for philosophers." (Begriffsschrift, 1879)

"Facts, facts, facts' cries the scientist if he wants to emphasize the necessity of a firm foundation for science. What is a fact? A fact is a thought that is true. But the scientist will surely not recognize something which depends on men's varying states of mind to be the firm foundation of science." (The thought: A logical inquiry, 1956 posthumous)