Combining Texts

All the ideas for 'works', 'Building Blocks of Mathematical Logic' and 'Reals by Abstraction'

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4 ideas

1. Philosophy / G. Scientific Philosophy / 1. Aims of Science
6782 Realism is the only philosophy of science that doesn't make the success of science a miracle [Putnam]
     Full Idea: Realism….is the only philosophy science which does not make the success of science a miracle.
     From: Hilary Putnam (works [1980]), quoted by Alexander Bird - Philosophy of Science Ch.4
     A reaction: This was from his earlier work; he became more pragmatist and anti-realist later. Personally I approve of the remark. The philosophy of science must certainly offer an explanation for its success. Truth seems the obvious explanation.
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
17699 Variables are auxiliary notions, and not part of the 'eternal' essence of logic [Schönfinkel]
     Full Idea: A variable in a proposition of logic ....has the status of a mere auxiliary notion that is really inappropriate to the constant, 'eternal' essence of the propositions of logic.
     From: Moses Schönfinkel (Building Blocks of Mathematical Logic [1924], §1)
     A reaction: He presumably thinks that what the variables stand for (and he mentions 'argument places' and 'operators') will be included in the essence. My attention was caught by the thought that he takes logic to have an essence.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
10632 The real numbers may be introduced by abstraction as ratios of quantities [Hale, by Hale/Wright]
     Full Idea: The real numbers may be introduced by abstraction as ratios of quantities. ..They are not defined by Dedekind cuts; rather, the cuts constitute a domain with the properties that are a necessary precondition.
     From: report of Bob Hale (Reals by Abstraction [1998]) by B Hale / C Wright - Intro to 'The Reason's Proper Study' 3.3
     A reaction: This is Hale's neo-logicist attempt to derive the real numbers from Hume's Principle.
7. Existence / D. Theories of Reality / 4. Anti-realism
22181 Putnam says anti-realism is a bad explanation of accurate predictions [Putnam, by Okasha]
     Full Idea: Putnam's 'no miracle' argument says that being an anti-realist is akin to believing in miracles (because of the accurate predictons). …It is a plausibility argument - an inference to the best explanation.
     From: report of Hilary Putnam (works [1980]) by Samir Okasha - Philosophy of Science: Very Short Intro (2nd ed) 4
     A reaction: [not sure of ref] Putnam later backs off from this argument, but my personal realism rests on best explanation. Does anyone want to prefer an inferior explanation? The objection is that successful theories can turn out to be false. Phlogiston, ether.