Gottlob Frege
(Copyright © 2005 Piero Scaruffi | Legal restrictions - Termini d'uso )

Logic
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Synopsis:
  • Lotze's theory (arithmetic propositions can be demonstrated without any recourse to intuition)
  • Removing intuition from arithmetic requires replacing natural language with logic (Boole's program)
  • Quantifiers and variables allow for "predicate calculus"
  • Mathematics becomes a branch of Logic (Cantor's program)
  • "Sense" (intension) vs "reference" (extension): "the star of the morning" and "the star of the evening" (same extension because they refer to the same thing, but different intensions)
  • Propositions of Logic can only have one of two referents, true or false, but many senses
  • Logic as an objective (not subjective) discipline
  • Cardinal numbers constructed by a purely logical method (not relying on intuition: Kant was wrong)

(Copyright © 2005 Piero Scaruffi | Legal restrictions - Termini d'uso )