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| 11215 | Notable definitions have been of piety (Plato), God (Anselm), number (Frege), and truth (Tarski) |
| Full Idea: Notable examples of definitions in philosophy have been Plato's (e.g. of piety, in 'Euthyphro'), Anselm's definition of God, the Frege-Russell definition of number, and Tarski's definition of truth. | |||
| From: Anil Gupta (Definitions [2008], Intro) | |||
| A reaction: All of these are notable for the extensive metaphysical conclusions which then flow from what seems like a fairly neutral definition. We would expect that if we were defining essences, but not if we were just defining word usage. |
| 11223 | Definitions usually have a term, a 'definiendum' containing the term, and a defining 'definiens' |
| Full Idea: Many definitions have three elements: the term that is defined, an expression containing the defined term (the 'definiendum'), and another expression (the 'definiens') that is equated by the definition with this expression. | |||
| From: Anil Gupta (Definitions [2008], 2) | |||
| A reaction: He notes that the definiendum and the definiens are assumed to be in the 'same logical category', which is a right can of worms. |
| 11225 | A definition needs to apply to the same object across possible worlds |
| Full Idea: In a modal logic in which names are non-vacuous and rigid, not only must existence and uniqueness in a definition be shown to hold necessarily, it must be shown that the definiens is satisfied by the same object across possible worlds. | |||
| From: Anil Gupta (Definitions [2008], 2.4) |
| 11227 | The 'revision theory' says that definitions are rules for improving output |
| Full Idea: The 'revision theory' of definitions says definitions impart a hypothetical character, giving a rule of revision rather than a rule of application. ...The output interpretation is better than the input one. | |||
| From: Anil Gupta (Definitions [2008], 2.7) | |||
| A reaction: Gupta mentions the question of whether such definitions can extend into the trans-finite. |
| 11221 | A definition can be 'extensionally', 'intensionally' or 'sense' adequate |
| Full Idea: A definition is 'extensionally adequate' iff there are no actual counterexamples to it. It is 'intensionally adequate' iff there are no possible counterexamples to it. It is 'sense adequate' (or 'analytic') iff it endows the term with the right sense. | |||
| From: Anil Gupta (Definitions [2008], 1.4) |
| 11224 | Traditional definitions are general identities, which are sentential and reductive |
| Full Idea: Traditional definitions are generalized identities (so definiendum and definiens can replace each other), in which the sentential is primary (for use in argument), and they involve reduction (and hence eliminability in a ground language). | |||
| From: Anil Gupta (Definitions [2008], 2.2) |
| 11226 | Traditional definitions need: same category, mention of the term, and conservativeness and eliminability |
| Full Idea: A traditional definition requires that the definiendum contains the defined term, that definiendum and definiens are of the same logical category, and the definition is conservative (adding nothing new), and makes elimination possible. | |||
| From: Anil Gupta (Definitions [2008], 2.4) |
| 11217 | Chemists aim at real definition of things; lexicographers aim at nominal definition of usage |
| Full Idea: The chemist aims at real definition, whereas the lexicographer aims at nominal definition. ...Perhaps real definitions investigate the thing denoted, and nominal definitions investigate meaning and use. | |||
| From: Anil Gupta (Definitions [2008], 1.1) | |||
| A reaction: Very helpful. I really think we should talk much more about the neglected chemists when we discuss science. Theirs is the single most successful branch of science, the paradigm case of what the whole enterprise aims at. |
| 11216 | If definitions aim at different ideals, then defining essence is not a unitary activity |
| Full Idea: Some definitions aim at precision, others at fairness, or at accuracy, or at clarity, or at fecundity. But if definitions 'give the essence of things' (the Aristotelian formula), then it may not be a unitary kind of activity. | |||
| From: Anil Gupta (Definitions [2008], 1) | |||
| A reaction: We don't have to accept this conclusion so quickly. Human interests may shift the emphasis, but there may be a single ideal definition of which these various examples are mere parts. |
| 11218 | Stipulative definition assigns meaning to a term, ignoring prior meanings |
| Full Idea: Stipulative definition imparts a meaning to the defined term, and involves no commitment that the assigned meaning agrees with prior uses (if any) of the term | |||
| From: Anil Gupta (Definitions [2008], 1.3) | |||
| A reaction: A nice question is how far one can go in stretching received usage. If I define 'democracy' as 'everyone is involved in decisions', that is sort of right, but pushing the boundaries (children, criminals etc). |
| 11220 | Ostensive definitions look simple, but are complex and barely explicable |
| Full Idea: Ostensive definitions look simple (say 'this stick is one meter long', while showing a stick), but they are effective only because a complex linguistic and conceptual capacity is operative in the background, of which it is hard to give an account. | |||
| From: Anil Gupta (Definitions [2008], 1.2) | |||
| A reaction: The full horror of the situation is brought out in Quine's 'gavagai' example (Idea 6312) |
| 11222 | The ordered pair <x,y> is defined as the set {{x},{x,y}}, capturing function, not meaning |
| Full Idea: The ordered pair <x,y> is defined as the set {{x},{x,y}}. This does captures its essential uses. Pairs <x,y> <u,v> are identical iff x=u and y=v, and the definition satisfies this. Function matters here, not meaning. | |||
| From: Anil Gupta (Definitions [2008], 1.5) | |||
| A reaction: This is offered as an example of Carnap's 'explications', rather than pure definitions. Quine extols it as a philosophical paradigm (1960:§53). |