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Single Idea 9641

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

Full Idea

The standard requirement of definitions involves 'eliminability' (any defined terms must be replaceable by primitives) and 'non-creativity' (proofs of theorems should not depend on the definition).

Gist of Idea

Definitions should be replaceable by primitives, and should not be creative

Source

James Robert Brown (Philosophy of Mathematics [1999], Ch. 7)

Book Ref

Brown,James Robert: 'Philosophy of Mathematics' [Routledge 2002], p.94

A Reaction

[He cites Russell and Whitehead as a source for this view] This is the austere view of the mathematician or logician. But almost every abstract concept that we use was actually defined in a creative way.

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]