12 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. |
| 12149 | Indexicals are a problem for beliefs being just subject-proposition relations [Perry] |
| Full Idea: The essential indexical is a problem for the view that belief is a relation between subjects and propositions conceived as bearers of truth and falsity. | |
| From: John Perry (The Problem of the Essential Indexical [1979], 'Intro') | |
| A reaction: My immediate reaction would be that it depends on how you conceive of 'propositions'. If they are objective, you have a problem. I take them to be subjective events in brains, and the indexical meaning to be evident within the proposition. |
| 12151 | If we replace 'I' in sentences about me, they are different beliefs and explanations of behaviour [Perry] |
| Full Idea: If I leave a trail of sugar, and realise 'that I am making a mess', ...when we replace the word 'I' with other designations of me, we no longer have an explanation of my behaviour, or an attribution of the same belief, so it is an 'essential indexical'. | |
| From: John Perry (The Problem of the Essential Indexical [1979], 'Intro') | |
| A reaction: [compressed] A famous observation of Perry's, which leads him to challenge traditional accounts of belief and of propositions. I don't think I see a problem, if we have a thoroughly non-linguistic account of essentially unambiguous propositions. |
| 18412 | Indexicals individuate certain belief states, helping in explanation and prediction [Perry] |
| Full Idea: We use sentences with indexicals or relativized propositions to individuate belief states, for the purposes of classifying believers in ways useful for explanation and prediction. | |
| From: John Perry (The Problem of the Essential Indexical [1979], 'Obvious') | |
| A reaction: He goes on to apparently connect this with some sort of moral integrity involved in 'owning up' to the fact that the person in question is you (who has spilled the sugar etc.). |
| 12150 | Indexicals reveal big problems with the traditional idea of a proposition [Perry] |
| Full Idea: The problem of the essential indexical reveals that something is badly wrong with the traditional doctrine of propositions. | |
| From: John Perry (The Problem of the Essential Indexical [1979], 'Prob') | |
| A reaction: See the reaction to 12149. The traditional view of propositions, or at least Russell's view, seems to be that they are same as facts, which strikes me as daft. I take propositions to be brain events, probably expressed in mentalese. |
| 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 |
| 15203 | Tense is essential for thought and action [Perry, by Le Poidevin] |
| Full Idea: Tense plays a crucial role in thought and action. | |
| From: report of John Perry (The Problem of the Essential Indexical [1979]) by Robin Le Poidevin - Past, Present and Future of Debate about Tense 3 a | |
| A reaction: This is important, because much of our metaphysics is dominated by a detached 'scientific' description of reality, which is given a rather passive character. If processes take centre stage, which they should, then our own processes are part of it. |
| 15204 | Actual tensed sentences cannot be tenseless, because they can cite their own context [Perry, by Le Poidevin] |
| Full Idea: In the new tenseless theory, no tensed token sentence can be equivalent to a tenseless token, because the former, unlike the latter, draws attention to the context in which it is tokened. | |
| From: report of John Perry (The Problem of the Essential Indexical [1979]) by Robin Le Poidevin - Past, Present and Future of Debate about Tense 3 a | |
| A reaction: So the problem about indexicals was worrying fans of the tenseless B-series view of time (and so it should). I'm inclined to translate sentences containing indexicals into their actual propositions, which tend to avoid them. 'Time/person of utterance'. |
| 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. |