11 ideas
| 13655 | The Löwenheim-Skolem theorems show that whether all sets are constructible is indeterminate [Putnam, by Shapiro] |
| Full Idea: Putnam claims that the Löwenheim-Skolem theorems indicate that there is no 'fact of the matter' whether all sets are constructible. | |
| From: report of Hilary Putnam (Models and Reality [1977]) by Stewart Shapiro - Foundations without Foundationalism | |
| A reaction: [He refers to the 4th and 5th pages of Putnam's article] Shapiro offers (p.109) a critique of Putnam's proposal. |
| 9915 | V = L just says all sets are constructible [Putnam] |
| Full Idea: V = L just says all sets are constructible. L is the class of all constructible sets, and V is the universe of all sets. | |
| From: Hilary Putnam (Models and Reality [1977], p.425) |
| 9913 | The Löwenheim-Skolem Theorem is close to an antinomy in philosophy of language [Putnam] |
| Full Idea: The Löwenheim-Skolem Theorem says that a satisfiable first-order theory (in a countable language) has a countable model. ..I argue that this is not a logical antinomy, but close to one in philosophy of language. | |
| From: Hilary Putnam (Models and Reality [1977], p.421) | |
| A reaction: See the rest of this paper for where he takes us on this. |
| 9914 | It is unfashionable, but most mathematical intuitions come from nature [Putnam] |
| Full Idea: Experience with nature is undoubtedly the source of our most basic 'mathematical intuitions', even if it is unfashionable to say so. | |
| From: Hilary Putnam (Models and Reality [1977], p.424) | |
| A reaction: Correct. I find it quite bewildering how Frege has managed to so discredit all empirical and psychological approaches to mathematics that it has become a heresy to say such things. |
| 304 | Beautiful things must be different from beauty itself, but beauty itself must be present in each of them [Plato] |
| Full Idea: Are fine things different from or identical to fineness? They are different from fineness itself, but fineness itself is in a sense present in each of them. | |
| From: Plato (Euthydemus [c.379 BCE], 301a) |
| 16120 | Knowing how to achieve immortality is pointless without the knowledge how to use immortality [Plato] |
| Full Idea: If there exists the knowledge of how to make men immortal, but without the knowledge of how to use this immortality, there seems to be no value in it. | |
| From: Plato (Euthydemus [c.379 BCE], 289b) | |
| A reaction: I take this to be not a gormless utilitarianism about knowledge, but a plea for holism, that knowledge only has value as part of some larger picture. The big view is the important view. He's wrong, though. Work out the use later. |
| 303 | Say how many teeth the other has, then count them. If you are right, we will trust your other claims [Plato] |
| Full Idea: If each of you says how many teeth the other has, and when they are counted we find you do know, we will believe your other claims as well. | |
| From: Plato (Euthydemus [c.379 BCE], 294c) | |
| A reaction: This is the clairvoyant problem for reliabilism, if truth is delivered for no apparent reason. Useful, but hardly knowledge. HOW did you know the number of teeth? |
| 16383 | Puzzled Pierre has two mental files about the same object [Recanati on Kripke] |
| Full Idea: In Kripke's puzzle about belief, the subject has two distinct mental files about one and the same object. | |
| From: comment on Saul A. Kripke (A Puzzle about Belief [1979]) by François Recanati - Mental Files 17.1 | |
| A reaction: [Pierre distinguishes 'London' from 'Londres'] The Kripkean puzzle is presented as very deep, but I have always felt there was a simple explanation, and I suspect that this is it (though I will leave the reader to think it through, as I'm very busy…). |
| 302 | What knowledge is required to live well? [Plato] |
| Full Idea: What knowledge would enable us to live finely for the rest of our lives? | |
| From: Plato (Euthydemus [c.379 BCE], 293a) | |
| A reaction: A successful grasp of other people's points of view might lead to respect for them. Also a realisation that we are not isolated individuals. We really are all in it together. |
| 301 | Only knowledge of some sort is good [Plato] |
| Full Idea: Nothing is good except knowledge of some sort. | |
| From: Plato (Euthydemus [c.379 BCE], 292b) | |
| A reaction: I've heard it suggested that truth is the only value. This is the Socratic idea that moral goodness is a matter of successful rational judgement. Not convinced, but interesting. |
| 305 | Something which lies midway between two evils is better than either of them [Plato] |
| Full Idea: Something which is composed of two factors which are bad for different purposes and lies midway between them is better than either of the factors. | |
| From: Plato (Euthydemus [c.379 BCE], 306a) |