21 ideas
| 11223 | Definitions usually have a term, a 'definiendum' containing the term, and a defining 'definiens' [Gupta] |
| 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. |
| 11215 | Notable definitions have been of piety (Plato), God (Anselm), number (Frege), and truth (Tarski) [Gupta] |
| 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. |
| 11225 | A definition needs to apply to the same object across possible worlds [Gupta] |
| 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 [Gupta] |
| 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. |
| 11224 | Traditional definitions are general identities, which are sentential and reductive [Gupta] |
| 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 [Gupta] |
| 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) |
| 11221 | A definition can be 'extensionally', 'intensionally' or 'sense' adequate [Gupta] |
| 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) |
| 11217 | Chemists aim at real definition of things; lexicographers aim at nominal definition of usage [Gupta] |
| 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 [Gupta] |
| 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 [Gupta] |
| 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 [Gupta] |
| 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 [Gupta] |
| 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). |
| 10397 | Abelard's mereology involves privileged and natural divisions, and principal parts [Abelard, by King,P] |
| Full Idea: Abelard's theory of substantial integral wholes is not a pure mereology in the modern sense, since he holds that there are privileged divisions; ..the division of a whole must be into its principal parts. Some wholes have a natural division. | |
| From: report of Peter Abelard (works [1135]) by Peter King - Peter Abelard 2 | |
| A reaction: This is a mereology that cuts nature at the joints, rather than Lewis's 'unrestricted composition', so I find Abelard rather appealing. |
| 10396 | If 'animal' is wholly present in Socrates and an ass, then 'animal' is rational and irrational [Abelard, by King,P] |
| Full Idea: Abelard argued that if the universal 'animal' were completely present in both Socrates and an ass, making each wholly an animal, then the same thing, animal, will be simultaneously rational and irrational, with contraries present in the whole thing. | |
| From: report of Peter Abelard (works [1135]) by Peter King - Peter Abelard 2 | |
| A reaction: If we have universals for rationality and irrationality, they can distinguish the two. But we must also say that rationality is not an aspect of animal, which seems to mean that mind isn't either. What is the essence of an animal? Not reason? |
| 10395 | Abelard was an irrealist about virtually everything apart from concrete individuals [Abelard, by King,P] |
| Full Idea: Abelard was an irrealist about universals, but also about propositions, events, times other than the present, natural kinds, relations, wholes, absolute space, hylomorphic composites, and the like. The concrete individual is enough to populate the world. | |
| From: report of Peter Abelard (works [1135]) by Peter King - Peter Abelard 2 | |
| A reaction: If a Nominalist claims that 'only particulars exist', this makes him an extreme nominalist, and remarkably materialistic for his time (though he accepted the soul, as well as God). |
| 15384 | Only words can be 'predicated of many'; the universality is just in its mode of signifying [Abelard, by Panaccio] |
| Full Idea: Abelard concluded that only words can be 'predicated of many'. A universal is nothing but a general linguistic predicate, and its universality depends not on its mode of being, but on its mode of signifying. | |
| From: report of Peter Abelard (works [1135]) by Claude Panaccio - Medieval Problem of Universals 'Peter' | |
| A reaction: Abelard seems to be the originator of what is now called Predicate Nominalism, with Nelson Goodman as his modern representative. If it is just words, is there no fact of two things having the 'same' property? |
| 8481 | The de dicto-de re modality distinction dates back to Abelard [Abelard, by Orenstein] |
| Full Idea: The de dicto-de re modality distinction dates back to Abelard. | |
| From: report of Peter Abelard (works [1135]) by Alex Orenstein - W.V. Quine Ch.7 | |
| A reaction: Most modern philosophers couldn't (apparently) care less where a concept originated, but one of the principles of this database is that such things do matter. I'm not sure why, but if we want the whole picture, we need the historical picture. |
| 15385 | Abelard's problem is the purely singular aspects of things won't account for abstraction [Panaccio on Abelard] |
| Full Idea: Abelard's problem is that it is not clear how singular forms could do the job they are supposed to do - to account for abstraction, namely - if they were purely singular aspects. | |
| From: comment on Peter Abelard (works [1135]) by Claude Panaccio - Medieval Problem of Universals 'Peter' | |
| A reaction: A very nice question! If we say that abstracta are just acquired by ignoring all but that feature in some objects, how do we identify 'that' feature in order to select it? The instances must share something in common to be abstracted. |
| 15383 | Nothing external can truly be predicated of an object [Abelard, by Panaccio] |
| Full Idea: Abelard argued from the commonly accepted definition of a universal as 'what can be predicated of man', that no external thing can ever be predicated of anything. | |
| From: report of Peter Abelard (works [1135]) by Claude Panaccio - Medieval Problem of Universals 'Peter' | |
| A reaction: It sounds to me as if Abelard is confusing predicates with properties! Maybe no external can be a property of anything, but I take predicates to just be part of what you can say about anything, and that had better included external facts. |
| 10398 | Natural kinds are not special; they are just well-defined resemblance collections [Abelard, by King,P] |
| Full Idea: In Abelard's view a natural kind is a well-defined collection of things that have the same features, so that natural kinds have no special status, being no more than discrete integral wholes whose principle of membership is similarity. | |
| From: report of Peter Abelard (works [1135]) by Peter King - Peter Abelard 2 | |
| A reaction: I take a natural kind to be a completely stable and invariant class of things. Presumably this invariance has an underlying explanation, but Abelard seems to take the Humean line that we cannot penetrate beyond the experienced surface. |
| 5467 | Euler said nature is instrinsically passive, and minds cause change [Euler, by Ellis] |
| Full Idea: Euler thought the powers necessary for the maintenance of the changing universe would turn out to be just the passive ones of inertia and impenetrability. There are no active powers, he urged, other than those of God and living beings. | |
| From: report of Leonhard Euler (Letters to a German Princess [1765]) by Brian Ellis - The Philosophy of Nature: new essentialism Ch.4 | |
| A reaction: Very significant, I think, for revealing the religious framework behind early theories of natural laws. If there is nothing external to impose powers and movements on nature, the source must be sought within - hence essentialism. |