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Full Idea
Today we expect that anything worth calling a definition should imply a semantics.
Gist of Idea
A decent modern definition should always imply a semantics
Source
Ian Hacking (What is Logic? [1979], §10)
Book Ref
'A Philosophical Companion to First-Order Logic', ed/tr. Hughes,R.I.G. [Hackett 1993], p.239
A Reaction
He compares this with Gentzen 1935, who was attempting purely syntactic definitions of the logical connectives.
| 16094 | You can't define particulars, because accounts have to be generalised [Aristotle] |
| 12983 | A nominal definition is of the qualities, but the real definition is of the essential inner structure [Leibniz] |
| 4417 | Only that which has no history is definable [Nietzsche] |
| 16877 | A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege] |
| 14426 | A definition by 'extension' enumerates items, and one by 'intension' gives a defining property [Russell] |
| 13838 | A decent modern definition should always imply a semantics [Hacking] |
| 11221 | A definition can be 'extensionally', 'intensionally' or 'sense' adequate [Gupta] |
| 11224 | Traditional definitions are general identities, which are sentential and reductive [Gupta] |
| 11226 | Traditional definitions need: same category, mention of the term, and conservativeness and eliminability [Gupta] |
| 9143 | Implicit definitions must be satisfiable, creative definitions introduce things, contextual definitions build on things [Fine,K, by Cook/Ebert] |
| 10143 | 'Creative definitions' do not presuppose the existence of the objects defined [Fine,K] |