8 ideas
| 21597 | Logical connectives have the highest precision, yet are infected by the vagueness of true and false [Russell, by Williamson] |
| Full Idea: Russell says the best chance of avoiding vagueness are the logical connectives. ...But the vagueness of 'true' and 'false' infects the logical connectives too. All words are vague. Russell concludes that all language is vague. | |
| From: report of Bertrand Russell (Vagueness [1923]) by Timothy Williamson - Vagueness 2.4 | |
| A reaction: This relies on the logical connectives being defined semantically, in terms of T and F, but that is standard. Presumably the formal uninterpreted syntax is not vague. |
| 8698 | Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend] |
| Full Idea: The modal structuralist thinks of mathematical structures as possibilities. The application of mathematics is just the realisation that a possible structure is actualised. As structures are possibilities, realist ontological problems are avoided. | |
| From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Michèle Friend - Introducing the Philosophy of Mathematics 4.3 | |
| A reaction: Friend criticises this and rejects it, but it is appealing. Mathematics should aim to be applicable to any possible world, and not just the actual one. However, does the actual world 'actualise a mathematical structure'? |
| 9557 | Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara] |
| Full Idea: Hellman represents statements of pure mathematics as elliptical for modal conditionals of a certain sort. | |
| From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Charles Chihara - A Structural Account of Mathematics 5.3 | |
| A reaction: It's a pity there is such difficulty in understanding conditionals (see Graham Priest on the subject). I intuit a grain of truth in this, though I take maths to reflect the structure of the actual world (with possibilities being part of that world). |
| 10263 | Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman] |
| Full Idea: The usual way to show that a sentence is possible is to show that it has a model, but for Hellman presumably a sentence is possible if it might have a model (or if, possibly, it has a model). It is not clear what this move brings us. | |
| From: comment on Geoffrey Hellman (Mathematics without Numbers [1989]) by Stewart Shapiro - Philosophy of Mathematics 7.3 | |
| A reaction: I can't assess this, but presumably the possibility of the model must be demonstrated in some way. Aren't all models merely possible, because they are based on axioms, which seem to be no more than possibilities? |
| 9051 | Since natural language is not precise it cannot be in the province of logic [Russell, by Keefe/Smith] |
| Full Idea: Russell takes it that logic assumes precision, and since natural language is not precise it cannot be in the province of logic at all. | |
| From: report of Bertrand Russell (Vagueness [1923]) by R Keefe / P Smith - Intro: Theories of Vagueness §1 | |
| A reaction: I find this view congenial. It seems to me that the necessary prelude to logic is to do everything you can to eliminate ambiguity and vagueness from the sentences at issue. We want the proposition, or logical form. If there isn't one, forget it? |
| 9054 | Vagueness is only a characteristic of representations, such as language [Russell] |
| Full Idea: Vagueness and precision alike are characteristics which can only belong to a representation, of which language is an example. | |
| From: Bertrand Russell (Vagueness [1923], p.62) | |
| A reaction: Russell was the first to tackle the question of vagueness, and he may have got it right. If we are unable to decide which set an object belongs in (red or orange) that is a problem for our conceptual/linguistic scheme. The object still has a colour! |
| 19508 | Contextualism needs a semantics for knowledge sentences that are partly indexical [Schiffer,S] |
| Full Idea: Contextualist semantics must capture the 'indexical' nature of knowledge claims, the fact that different utterances of a knowledge sentence with no apparent indexical terms can express different propositions. | |
| From: Stephen Schiffer (Contextualist Solutions to Scepticism [1996], p.325), quoted by Keith DeRose - The Case for Contextualism 1.5 | |
| A reaction: Schiffer tries to show that this is too difficult, and DeRose defends contextualism against the charge. |
| 19509 | The indexical aspect of contextual knowledge might be hidden, or it might be in what 'know' means [Schiffer,S] |
| Full Idea: One might have a 'hidden-indexical' theory of knowledge sentences: they contain constituents that are not the semantic values of any terms; ...or 'to know' itself might be indexical, as in 'I know[easy] I have hands' or 'I know[tough] I have hands'. | |
| From: Stephen Schiffer (Contextualist Solutions to Scepticism [1996], p.326-7), quoted by Keith DeRose - The Case for Contextualism 1.5 | |
| A reaction: [very compressed] Given the choice, I would have thought it was in 'know', since to say 'either you know p or you don't' sounds silly to me. |