display all the ideas for this combination of texts
3 ideas
9955 | Contextual definitions replace a complete sentence containing the expression [George/Velleman] |
Full Idea: A contextual definition shows how to analyse an expression in situ, by replacing a complete sentence (of a particular form) in which the expression occurs by another in which it does not. | |
From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2) | |
A reaction: This is a controversial procedure, which (according to Dummett) Frege originally accepted, and later rejected. It might not be the perfect definition that replacing just the expression would give you, but it is a promising step. |
10031 | Impredicative definitions quantify over the thing being defined [George/Velleman] |
Full Idea: When a definition contains a quantifier whose range includes the very entity being defined, the definition is said to be 'impredicative'. | |
From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2) | |
A reaction: Presumably they are 'impredicative' because they do not predicate a new quality in the definiens, but make use of the qualities already known. |
9331 | How do we determine which of the sentences containing a term comprise its definition? [Horwich] |
Full Idea: How are we to determine which of the sentences containing a term comprise its definition? | |
From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §2) | |
A reaction: Nice question. If I say 'philosophy is the love of wisdom' and 'philosophy bores me', why should one be part of its definition and the other not? What if I stipulated that the second one is part of my definition, and the first one isn't? |