8 ideas
| 6564 | To affirm 'p and not-p' is to have mislearned 'and' or 'not' [Quine] |
| Full Idea: To affirm a compound of the form 'p and not-p' is just to have mislearned one or both of these particles. | |
| From: Willard Quine (From Stimulus to Science [1995], p.23), quoted by Robert Fogelin - Walking the Tightrope of Reason Ch.1 | |
| A reaction: Quoted by Fogelin. This summarises the view of logic developed by the young Wittgenstein, that logical terms are 'operators', rather than referring terms. Of course the speaker may have a compartmentalised mind, or not understand 'p' properly. |
| 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. |
| 16639 | Only individual bodies exist [Bacon] |
| Full Idea: Nothing truly exists in nature beyond individual bodies. | |
| From: Francis Bacon (The New Organon [1620]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 182 | |
| A reaction: [Unusually, Pasnau gives no reference in the text; possibly II:1-2] What this leaves out, from even an auster nominalist ontology, is undifferentiated stuff like water. Even electrons don't seem quite distinct from one another. |
| 16033 | There are only individual bodies containing law-based powers, and the Forms are these laws [Bacon] |
| Full Idea: Though nothing exists in nature except individual bodies which exhibit pure individual acts [powers] in accordance with law…It is this law and its clauses which we understand by the term Forms. | |
| From: Francis Bacon (The New Organon [1620], p.103), quoted by Jan-Erik Jones - Real Essence §3 | |
| A reaction: This isn't far off what Aristotle had in mind, when he talks of forms as being 'principles', though there is more emphasis on mechanisms in the original idea. Note that Bacon takes laws so literally that he refers to their 'clauses'. |
| 21950 | Science must clear away the idols of the mind if they are ever going to find the truth [Bacon] |
| Full Idea: We must clear away the idols and false notions which are now in possession of the human understanding, and have taken deep root therein, and so beset men's minds that truth can hardly find an entrance. | |
| From: Francis Bacon (The New Organon [1620], 38), quoted by Mark Wrathall - Heidegger: how to read 2 | |
| A reaction: [He goes on to list the types of idol] |