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Single Idea 17774

[filed under theme 2. Reason / D. Definition / 2. Aims of Definition ]

Full Idea

Definition provides us with the means for converting our intuitions into mathematically usable concepts.

Gist of Idea

Definitions make our intuitions mathematically useful

Source

John Mayberry (What Required for Foundation for Maths? [1994], p.405-1)

Book Ref

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.405

The 19 ideas with the same theme [what a definition is trying to achieve]:

16125 To reveal a nature, divide down, and strip away what it has in common with other things [Plato]
16124 No one wants to define 'weaving' just for the sake of weaving [Plato]
17237 Definitions of things that are caused must express their manner of generation [Hobbes]
16541 All the intrinsic properties of a thing should be deducible from its definition [Spinoza]
5618 Definitions exhibit the exhaustive concept of a thing within its boundaries [Kant]
18261 A simplification which is complete constitutes a definition [Kant]
13886 Later Frege held that definitions must fix a function's value for every possible argument [Frege, by Wright,C]
9821 A definition need not capture the sense of an expression - just get the reference right [Frege, by Dummett]
8368 A correct definition is what can be substituted without loss of meaning [Ducasse]
4955 Some definitions aim to fix a reference rather than give a meaning [Kripke]
15527 Defining terms either enables elimination, or shows that they don't require elimination [Lewis]
11225 A definition needs to apply to the same object across possible worlds [Gupta]
11227 The 'revision theory' says that definitions are rules for improving output [Gupta]
17774 Definitions make our intuitions mathematically useful [Mayberry]
20221 Precision is only one of the virtues of a good definition [Zagzebski]
10528 Definitions concern how we should speak, not how things are [Fine,K]
9641 Definitions should be replaceable by primitives, and should not be creative [Brown,JR]
15352 A definition should allow the defined term to be eliminated [Horsten]
16292 An explicit definition enables the elimination of what is defined [Halbach]