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) |
| 14965 | Truth rests on Elimination ('A' is true → A) and Introduction (A → 'A' is true) [Gupta] |
| Full Idea: The basic principles governing truth are Truth Elimination (sentence A follows from ''A' is true') and the converse Truth Introduction (''A' is true' follows from A), which combine into Tarski's T-schema - 'A' is true if and only if A. | |
| From: Anil Gupta (Truth [2001], 5.1) | |
| A reaction: Introduction and Elimination rules are the basic components of natural deduction systems, so 'true' now works in the same way as 'and', 'or' etc. This is the logician's route into truth. |
| 14968 | A weakened classical language can contain its own truth predicate [Gupta] |
| Full Idea: If a classical language is expressively weakened - for example, by dispensing with negation - then it can contain its own truth predicate. | |
| From: Anil Gupta (Truth [2001], 5.2) | |
| A reaction: Thus the Tarskian requirement to move to a metalanguage for truth is only a requirement of a reasonably strong language. Gupta uses this to criticise theories that dispense with the metalanguage. |
| 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). |
| 14964 | The Liar reappears, even if one insists on propositions instead of sentences [Gupta] |
| Full Idea: There is the idea that the Liar paradox is solved simply by noting that truth is a property of propositions (not of sentences), and the Liar sentence does not express a proposition. But we then say 'I am not now expressing a true proposition'! | |
| From: Anil Gupta (Truth [2001], 5.1) | |
| A reaction: Disappointed to learn this, since I think focusing on propositions (which are unambiguous) rather than sentences solves a huge number of philosophical problems. |
| 14969 | Strengthened Liar: either this sentence is neither-true-nor-false, or it is not true [Gupta] |
| Full Idea: An example of the Strengthened Liar is the following statement SL: 'Either SL is neither-true-nor-false or it is not true'. This raises a serious problem for any theory that assesses the paradoxes to be neither true nor false. | |
| From: Anil Gupta (Truth [2001], 5.4.2) | |
| A reaction: If the sentence is either true or false it reduces to the ordinary Liar. If it is neither true nor false, then it is true. |
| 3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
| Full Idea: Anaxarchus said that he was not even sure that he knew nothing. | |
| From: report of Anaxarchus (fragments/reports [c.340 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.10.1 |
| 6012 | We must choose in which of the virtues we wish to excel [Panaetius] |
| Full Idea: Humans have four roles in life, of which the fourth involves choices, of career, and of the virtue in which one wishes to excel. | |
| From: Panaetius (fragments/reports [c.145 BCE]), quoted by Elizabeth Asmis - Panaetius | |
| A reaction: Panaetius strikes me as exceptionally wise. A big gap in Aristotle is the fact that we cannot excel in all virtues, and that therefore some choice is required. By what criteria? We have the Gauguin problem (excel in one, disgraceful in the others). |
| 6013 | Panaetius said we should live according to our natural starting-points [Panaetius, by Asmis] |
| Full Idea: Panaetius reformulated the Stoic goal as living in accordance with the starting-points given to us by nature. | |
| From: report of Panaetius (fragments/reports [c.145 BCE]) by Elizabeth Asmis - Panaetius | |
| A reaction: This sounds remarkably like the substitution of meritocratic equality of opportunity for communistic actual equality. In other words, it doesn't sound very Stoic. 'Live according to nature' implies more restraint than this ambitious version. |
| 6014 | Panaetius identified courage with great-mindedness, preferring civic courage to military [Panaetius, by Asmis] |
| Full Idea: Panaetius recast the virtue of courage as 'greatmindedness' (Aristotle's paramount virtue), he demoted military valour and gave priority to courage displayed in civic life. | |
| From: report of Panaetius (fragments/reports [c.145 BCE]) by Elizabeth Asmis - Panaetius | |
| A reaction: I find this very appealing, as I am increasingly horrified by our denigration of the people who implement our democracy for us. We urgently need to get back to the Greek idea of civic virtue, and this idea of Panaetius should be widely promulgated. |
| 5888 | Souls are born, since they are sensitive and inherited, so they must perish [Panaetius, by Cicero] |
| Full Idea: Panaetius says that whatever is born must perish, and souls are clearly born, as shown by the resemblance of children to their parents in disposition as well as body; also, anything sensible of pain is susceptible to sickness, and hence perishes. | |
| From: report of Panaetius (fragments/reports [c.145 BCE]) by M. Tullius Cicero - Tusculan Disputations I.xxxii | |
| A reaction: These seem to be rather good arguments. If we actually observe what someone's soul is like (through character) it seems rooted in a family and culture, and it certainly seems susceptible to disease. An empirical approach. |