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2 ideas
23441 | Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo] |
Full Idea: Modern logic requires that logical truths be true in all models, including ones devoid of any mathematical objects. It follows immediately that the existence of mathematical objects can never be a matter of logic alone. | |
From: Øystein Linnebo (Philosophy of Mathematics [2017], 2) | |
A reaction: Hm. Could there not be a complete set of models for a theory which all included mathematical objects? (I can't answer that). |
23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo] |
Full Idea: Game Formalism seeks to banish all semantics from mathematics, and Term Formalism seeks to reduce any such notions to purely syntactic ones. | |
From: Øystein Linnebo (Philosophy of Mathematics [2017], 3.3) | |
A reaction: This approach was stimulated by the need to justify the existence of the imaginary number i. Just say it is a letter! |