8 ideas
10121 | Contradiction is not a sign of falsity, nor lack of contradiction a sign of truth [Pascal] |
Full Idea: Contradiction is not a sign of falsity, nor the lack of contradiction a sign of truth. | |
From: Blaise Pascal (works [1660]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
A reaction: [Quoted in Auden and Kronenberger's Book of Aphorisms] Presumably we would now say that contradiction is a purely formal, syntactic notion, and not a semantic one. If you hit a contradiction, something has certainly gone wrong. |
18935 | Semantic theory should specify when an act of naming is successful [Sawyer] |
Full Idea: A semantic theory of names should deliver a specification of the conditions under which a name names an individual, and hence a specification of the conditions under which a name is empty. | |
From: Sarah Sawyer (Empty Names [2012], 1) | |
A reaction: Naming can be private, like naming my car 'Bertrand', but never tell anyone. I like Plato's remark that names are 'tools'. Do we specify conditions for successful spanner-usage? The first step must be individuation, preparatory to naming. |
18945 | Millians say a name just means its object [Sawyer] |
Full Idea: The Millian view of direct reference says that the meaning of a name is the object named. | |
From: Sarah Sawyer (Empty Names [2012], 4) | |
A reaction: Any theory that says meaning somehow is features of the physical world strikes me as totally misguided. Napoleon is a man, so he can't be part of a sentence. He delegates that job to words (such as 'Napoleon'). |
18934 | Sentences with empty names can be understood, be co-referential, and even be true [Sawyer] |
Full Idea: Some empty names sentences can be understood, so appear to be meaningful ('Pegasus was sired by Poseidon'), ...some appear to be co-referential ('Santa Claus'/'Father Christmas'), and some appear to be straightforwardly true ('Pegasus doesn't exist'). | |
From: Sarah Sawyer (Empty Names [2012], 1) | |
A reaction: Hang on to this, when the logicians arrive and start telling you that your talk of empty names is vacuous, because there is no object in the 'domain' to which a predicate can be attached. Meaning, reference and truth are the issues around empty names. |
18938 | Frege's compositional account of truth-vaues makes 'Pegasus doesn't exist' neither true nor false [Sawyer] |
Full Idea: In Frege's account sentences such as 'Pegasus does not exist' will be neither true nor false, since the truth-value of a sentence is its referent, and the referent of a complex expression is determined by the referent of its parts. | |
From: Sarah Sawyer (Empty Names [2012], 2) | |
A reaction: We can keep the idea of 'sense', which is very useful for dealing with empty names, but tweak his account of truth-values to evade this problem. I'm thinking that meaning is compositional, but truth-value isn't. |
18947 | Definites descriptions don't solve the empty names problem, because the properties may not exist [Sawyer] |
Full Idea: If it were possible for a definite description to be empty - not in the sense of there being no object that satisfies it, but of there being no set of properties it refers to - the problem of empty names would not have been solved. | |
From: Sarah Sawyer (Empty Names [2012], 5) | |
A reaction: Swoyer is thinking of properties like 'is a unicorn', which are clearly just as vulnerable to being empty as 'the unicorn' was. It seems unlikely that 'horse', 'white' and 'horn' would be empty. |
21558 | 'Predicative' norms are those which define a class [Russell] |
Full Idea: Norms (containing one variable) which do not define classes I propose to call 'non-predicative'; those which do define classes I shall call 'predicative'. | |
From: Bertrand Russell (Difficulties of Transfinite Numbers and Types [1905], p.141) |
21559 | We need rules for deciding which norms are predicative (unless none of them are) [Russell] |
Full Idea: We need rules for deciding what norms are predicative and what are not, unless we adopt the view (which has much to recommend it) that no norms are predicative. ...[146] A predative propositional function is one which determines a class. | |
From: Bertrand Russell (Difficulties of Transfinite Numbers and Types [1905], p.141) | |
A reaction: He is referring to his 'no class' theory, which he favoured at that time. |