7 ideas
| 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. |
| 8758 | We could talk of open sentences, instead of sets [Chihara, by Shapiro] |
| Full Idea: Chihara's programme is to replace talk of sets with talk of open sentences. Instead of speaking of the set of all cats, we talk about the open sentence 'x is a cat'. | |
| From: report of Charles Chihara (Constructibility and Mathematical Existence [1990]) by Stewart Shapiro - Thinking About Mathematics 9.2 | |
| A reaction: As Shapiro points out, this is following up Russell's view that sets should be replaced with talk of properties. Chihara is expressing it more linguistically. I'm in favour of any attempt to get rid of sets. |
| 10265 | Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro] |
| Full Idea: Chihara's system is a version of type theory. Translate thus: replace variables of sets of type n with level n variables over open sentences, replace membership/predication with satisfaction, and high quantifiers with constructability quantifiers. | |
| From: report of Charles Chihara (Constructibility and Mathematical Existence [1990]) by Stewart Shapiro - Philosophy of Mathematics 7.4 |
| 8759 | We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro] |
| Full Idea: Chihara's system is similar to simple type theory; he replaces each type with variables over open sentences, replaces membership (or predication) with satisfaction, and replaces quantifiers over level 1+ variables with constructability quantifiers. | |
| From: report of Charles Chihara (Constructibility and Mathematical Existence [1990]) by Stewart Shapiro - Thinking About Mathematics 9.2 | |
| A reaction: This is interesting for showing that type theory may not be dead. The revival of supposedly dead theories is the bread-and-butter of modern philosophy. |
| 10264 | Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro] |
| Full Idea: Chihara has proposal a modal primitive, a 'constructability quantifier'. Syntactically it behaves like an ordinary quantifier: Φ is a formula, and x a variable. Then (Cx)Φ is a formula, read as 'it is possible to construct an x such that Φ'. | |
| From: report of Charles Chihara (Constructibility and Mathematical Existence [1990]) by Stewart Shapiro - Philosophy of Mathematics 7.4 | |
| A reaction: We only think natural numbers are infinite because we see no barrier to continuing to count, i.e. to construct new numbers. We accept reals when we know how to construct them. Etc. Sounds promising to me (though not to Shapiro). |
| 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. |
| 19384 | Space and time are the order of all possibilities, and don't just relate to what is actual [Leibniz] |
| Full Idea: Space and time taken together constitute the order of possibilities of the one entire universe, so that these orders relate not only to what actually is, but also to anything that could be put in its place. | |
| From: Gottfried Leibniz (Reply to 'Rorarius' 2nd ed [1702], GP iv 568), quoted by Richard T.W. Arthur - Leibniz 7 'Space and Time' | |
| A reaction: A very nice idea. Rather like the 'space of reasons', where all rational thought must exist, space and time are the 'space of existence and action'. Their concepts involve more than relations between what actually exists. |