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Nineteenth Century Philosophy

Philosophy of Mathematics and Logic

What was Gottlob Frege’s main innovation in the philosophy of logic?

Frege treated predicates as functions and subjects as arguments. Thus “Socrates is mortal” becomes “function ‘mortal’ is applied to argument ‘Socrates.’“ In his Conceptual Notation (1879), Frege also introduced a simple way to treat words and terms such as “all” and “there is” as logical quantifiers. Logical quantification is a notational system that connects a variable with what is being talked about. For example, in the sentence “Every person alive today will die some day,” “person alive today” is being talked about and “every” is the quantifier. This treatment of Frege’s still stands today.



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