6 ideas
18200 | Very large sets should be studied in an 'if-then' spirit [Putnam] |
Full Idea: Sets of a very high type or very high cardinality (higher than the continuum, for example), should today be investigated in an 'if-then' spirit. | |
From: Hilary Putnam (The Philosophy of Logic [1971], p.347), quoted by Penelope Maddy - Naturalism in Mathematics | |
A reaction: Quine says the large sets should be regarded as 'uninterpreted'. |
18199 | Indispensability strongly supports predicative sets, and somewhat supports impredicative sets [Putnam] |
Full Idea: We may say that indispensability is a pretty strong argument for the existence of at least predicative sets, and a pretty strong, but not as strong, argument for the existence of impredicative sets. | |
From: Hilary Putnam (The Philosophy of Logic [1971], p.346), quoted by Penelope Maddy - Naturalism in Mathematics II.2 |
8857 | We must quantify over numbers for science; but that commits us to their existence [Putnam] |
Full Idea: Quantification over mathematical entities is indispensable for science..., therefore we should accept such quantification; but this commits us to accepting the existence of the mathematical entities in question. | |
From: Hilary Putnam (The Philosophy of Logic [1971], p.57), quoted by Stephen Yablo - Apriority and Existence | |
A reaction: I'm not surprised that Hartry Field launched his Fictionalist view of mathematics in response to such a counterintuitive claim. I take it we use numbers to slice up reality the way we use latitude to slice up the globe. No commitment to lines! |
5692 | Introspection is not perception, because there are no extra qualities apart from the mental events themselves [Rosenthal] |
Full Idea: Introspection cannot be a form of perceiving, since that invariably involves sensory qualities, and no qualities occur in introspection other than those of the sensations and perceptions we introspect; there are no additional qualities. | |
From: David M. Rosenthal (Instrospection [1998]) | |
A reaction: This sounds pretty conclusive. Presumably introspection is best described as meta-thought rather than perception, which means that it involves beliefs and judgements, rather than new perceptual qualities. It has to be conceptual, and probably linguistic. |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
Full Idea: Archelaus was the first person to say that the universe is boundless. | |
From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |