display all the ideas for this combination of texts
7 ideas
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| Full Idea: Intuitionists in mathematics deny excluded middle, because it is symptomatic of faith in the transcendent existence of mathematical objects and/or the truth of mathematical statements. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2) | |
| A reaction: There are other problems with excluded middle, such as vagueness, but on the whole I, as a card-carrying 'realist', am committed to the law of excluded middle. |
| 21566 | 'Propositional functions' are ambiguous until the variable is given a value [Russell] |
| Full Idea: By a 'propositional function' I mean something which contains a variable x, and expresses a proposition as soon as a value is assigned to x. That is to say, it differs from a proposition solely by the fact that it is ambiguous. | |
| From: Bertrand Russell (The Theory of Logical Types [1910], p.216) | |
| A reaction: This is Frege's notion of a 'concept', as an assertion of a predicate which still lacks a subject. |
| 10316 | We should decide whether singular terms are genuine by their usage [Hale] |
| Full Idea: The criteria for a genuine singular term should pick out not the singular terms themselves but their uses, since they may be genuine in one context and not another. | |
| From: Bob Hale (Abstract Objects [1987], Ch.2.II) | |
| A reaction: [rephrased] This will certainly meet problems with vagueness (e.g. as the reference of a singular term is gradually clarified). |
| 10312 | Often the same singular term does not ensure reliable inference [Hale] |
| Full Idea: In 'the whale is increasingly scarce' and 'the whale is much improved today' (our pet whale), we cannot infer that there is something that is much improved and increasingly scarce, so this singular term fails Dummett's criterion based on inference. | |
| From: Bob Hale (Abstract Objects [1987], Ch.2) | |
| A reaction: [much rephrased] This is not just a problem for a few cunningly selected examples. With contortions almost any singular term can be undermined in this way. Singular terms are simply not a useful guide to the existence of abstracta. |
| 10313 | Plenty of clear examples have singular terms with no ontological commitment [Hale] |
| Full Idea: Some examples where a definite singular noun phrase is not 'genuine' (giving ontological commitment): 'left us in the lurch'; 'for my mother's sake'; 'given the sack'; 'in the nick of time', 'the whereabouts of the PM', 'the identity of the murderer'. | |
| From: Bob Hale (Abstract Objects [1987], Ch.2.II) | |
| A reaction: These are not just freakish examples. If I 'go on a journey', that doesn't involve extra entities called 'journeys', just because the meaning is clearer and a more commonplace part of the language. |
| 10322 | If singular terms can't be language-neutral, then we face a relativity about their objects [Hale] |
| Full Idea: If we lack any general, language-neutral characterization of singular terms, must not a parallel linguistic relativity infect the objects which are to be thought of as their non-linguistic correlates? | |
| From: Bob Hale (Abstract Objects [1987], Ch.2.III) | |
| A reaction: Hale thinks he can answer this, but I would have thought that this problem dooms the linguistic approach from the start. There needs to be more imagination about how very different a language could be, while still qualifying as a language. |
| 21567 | 'All judgements made by Epimenedes are true' needs the judgements to be of the same type [Russell] |
| Full Idea: Such a proposition as 'all the judgements made by Epimenedes are true' will only be prima facie capable of truth if all his judgements are of the same order. | |
| From: Bertrand Russell (The Theory of Logical Types [1910], p.227) | |
| A reaction: This is an attempt to use his theory of types to solve the Liar. Tarski's invocation of a meta-language is clearly in the same territory. |