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16345 | That Peano arithmetic is interpretable in ZF set theory is taken by philosophers as a reduction [Halbach] |
Full Idea: The observation that Peano arithmetic is relatively interpretable in ZF set theory is taken by many philosophers to be a reduction of numbers to sets. | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 23) | |
A reaction: Nice! Being able to express something in a different language is not the same as a reduction. Back to the drawing board. What do you really mean by a reduction? If we model something, we don't 'reduce' it to the model. |
6523 | Positivists regard ontology as either meaningless or stipulated [Ayer, by Robinson,H] |
Full Idea: Positivists tend to be prejudiced against ontology, regarding very general questions about what sort of things exist either as meaningless, or as questions to be settled by stipulation. | |
From: report of A.J. Ayer (Language,Truth and Logic [1936]) by Howard Robinson - Perception IX.4 | |
A reaction: So much the worse for positivists, because they are missing all the fun. I consider one of the central activities of philosophy to be speculating about explanations. Ontology is at the heart of what explanation aims at. |