5 ideas
| 18201 | General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C] |
| Full Idea: The existence of very general principles in mathematics are universally regarded as obvious, where on an empiricist view one would expect them to be bold hypotheses, about which a prudent scientist would maintain reserve. | |
| From: Charles Parsons (Mathematical Intuition [1980], p.152), quoted by Penelope Maddy - Naturalism in Mathematics | |
| A reaction: This is mainly aimed at Quine's and Putnam's indispensability (to science) argument about mathematics. |
| 9103 | A universal is not a real feature of objects, but only a thought-object in the mind [William of Ockham] |
| Full Idea: I maintain that a universal is not something real that exists in a subject [of inherence], either inside or outside the mind, but that it has being only as a thought-object in the mind. | |
| From: William of Ockham (Ordinatio [1320], DII Qviii prima redactio) | |
| A reaction: [A footnote says that William later abandoned this view] I don't see a clear distinction here between having real existence in the mind, and being a thought-object in the mind. Maybe we should say 'merely' a thought-object? |
| 9104 | A universal is the result of abstraction, which is only a kind of mental picturing [William of Ockham] |
| Full Idea: A universal is not the result of generation, but of abstraction, which is only a kind of mental picturing. | |
| From: William of Ockham (Ordinatio [1320], DII Qviii prima redactio) | |
| A reaction: The phrase 'mental picturing' works very plausibly for the universal 'giraffe', but not so well for 'multiplication' or 'contradiction'. Though we might broaden 'picturing' to being a much less visual concept. Mapping seems basic. |
| 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. |