display all the ideas for this combination of philosophers
2 ideas
17774 | Definitions make our intuitions mathematically useful [Mayberry] |
Full Idea: Definition provides us with the means for converting our intuitions into mathematically usable concepts. | |
From: John Mayberry (What Required for Foundation for Maths? [1994], p.405-1) |
10204 | An 'implicit definition' gives a direct description of the relations of an entity [Shapiro] |
Full Idea: An 'implicit definition' characterizes a structure or class of structures by giving a direct description of the relations that hold among the places of the structure. | |
From: Stewart Shapiro (Philosophy of Mathematics [1997], Intro) | |
A reaction: This might also be thought of as a 'functional definition', since it seems to say what the structure or entity does, rather than give the intrinsic characteristics that make its relations and actions possible. |