22 ideas
| 18487 | We want to know what makes sentences true, rather than defining 'true' [McFetridge] |
| Full Idea: The generalisation 'What makes a (any) sentence true?' is not a request for definitions of 'true' (the concept), but rather requests for (partial) explanations of why certain particular sentences are true. | |
| From: Ian McFetridge (Truth, Correspondence, Explanation and Knowledge [1977], II) | |
| A reaction: McFetridge is responding to the shortcomings of Tarski's account of truth. The mystery seems to be why some of our representations of the world are 'successful', and others are not. |
| 8472 | Sentential logic is consistent (no contradictions) and complete (entirely provable) [Orenstein] |
| Full Idea: Sentential logic has been proved consistent and complete; its consistency means that no contradictions can be derived, and its completeness assures us that every one of the logical truths can be proved. | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.5) | |
| A reaction: The situation for quantificational logic is not quite so clear (Orenstein p.98). I do not presume that being consistent and complete makes it necessarily better as a tool in the real world. |
| 8476 | Axiomatization simply picks from among the true sentences a few to play a special role [Orenstein] |
| Full Idea: In axiomatizing, we are merely sorting out among the truths of a science those which will play a special role, namely, serve as axioms from which we derive the others. The sentences are already true in a non-conventional or ordinary sense. | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.5) | |
| A reaction: If you were starting from scratch, as Euclidean geometers may have felt they were doing, you might want to decide which are the simplest truths. Axiomatizing an established system is a more advanced activity. |
| 8480 | S4: 'poss that poss that p' implies 'poss that p'; S5: 'poss that nec that p' implies 'nec that p' [Orenstein] |
| Full Idea: The five systems of propositional modal logic contain successively stronger conceptions of necessity. In S4 'it is poss that it is poss that p' implies 'it is poss that p'. In S5, 'it is poss that it is nec that p' implies 'it is nec that p'. | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.7) | |
| A reaction: C.I. Lewis originated this stuff. Any serious student of modality is probably going to have to pick a system. E.g. Nathan Salmon says that the correct modal logic is even weaker than S4. |
| 8474 | Unlike elementary logic, set theory is not complete [Orenstein] |
| Full Idea: The incompleteness of set theory contrasts sharply with the completeness of elementary logic. | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.5) | |
| A reaction: This seems to be Quine's reason for abandoning the Frege-Russell logicist programme (quite apart from the problems raised by Gödel. |
| 8465 | Mereology has been exploited by some nominalists to achieve the effects of set theory [Orenstein] |
| Full Idea: The theory of mereology has had a history of being exploited by nominalists to achieve some of the effects of set theory. | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.3) | |
| A reaction: Some writers refer to mereology as a 'theory', and others as an area of study. This appears to be an interesting line of investigation. Orenstein says Quine and Goodman showed its limitations. |
| 8452 | Traditionally, universal sentences had existential import, but were later treated as conditional claims [Orenstein] |
| Full Idea: In traditional logic from Aristotle to Kant, universal sentences have existential import, but Brentano and Boole construed them as universal conditionals (such as 'for anything, if it is a man, then it is mortal'). | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.2) | |
| A reaction: I am sympathetic to the idea that even the 'existential' quantifier should be treated as conditional, or fictional. Modern Christians may well routinely quantify over angels, without actually being committed to them. |
| 8475 | The substitution view of quantification says a sentence is true when there is a substitution instance [Orenstein] |
| Full Idea: The substitution view of quantification explains 'there-is-an-x-such-that x is a man' as true when it has a true substitution instance, as in the case of 'Socrates is a man', so the quantifier can be read as 'it is sometimes true that'. | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.5) | |
| A reaction: The word 'true' crops up twice here. The alternative (existential-referential) view cites objects, so the substitution view is a more linguistic approach. |
| 8454 | The whole numbers are 'natural'; 'rational' numbers include fractions; the 'reals' include root-2 etc. [Orenstein] |
| Full Idea: The 'natural' numbers are the whole numbers 1, 2, 3 and so on. The 'rational' numbers consist of the natural numbers plus the fractions. The 'real' numbers include the others, plus numbers such a pi and root-2, which cannot be expressed as fractions. | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.2) | |
| A reaction: The 'irrational' numbers involved entities such as root-minus-1. Philosophical discussions in ontology tend to focus on the existence of the real numbers. |
| 8473 | The logicists held that is-a-member-of is a logical constant, making set theory part of logic [Orenstein] |
| Full Idea: The question to be posed is whether is-a-member-of should be considered a logical constant, that is, does logic include set theory. Frege, Russell and Whitehead held that it did. | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.5) | |
| A reaction: This is obviously the key element in the logicist programme. The objection seems to be that while first-order logic is consistent and complete, set theory is not at all like that, and so is part of a different world. |
| 18488 | We normally explain natural events by citing further facts [McFetridge] |
| Full Idea: If one were asked 'What makes salt soluble in water?', the most natural answer would be something of the style 'The fact that it has such-and-such structure'. | |
| From: Ian McFetridge (Truth, Correspondence, Explanation and Knowledge [1977], II) | |
| A reaction: Personally I would want to talk about its 'powers' (dispositional properties), rather than its 'structure' (categorical properties). This defends facts, but you could easily paraphrase 'fact' out of this reply (as McFetridge realised). |
| 8458 | Just individuals in Nominalism; add sets for Extensionalism; add properties, concepts etc for Intensionalism [Orenstein] |
| Full Idea: Modest ontologies are Nominalism (Goodman), admitting only concrete individuals; and Extensionalism (Quine/Davidson) which admits individuals and sets; but Intensionalists (Frege/Carnap/Church/Marcus/Kripke) may have propositions, properties, concepts. | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.3) | |
| A reaction: I don't like sets, because of Idea 7035. Even the ontology of individuals could collapse dramatically (see the ideas of Merricks, e.g. 6124). The intensional items may be real enough, but needn't have a place at the ontological high table. |
| 8457 | The Principle of Conservatism says we should violate the minimum number of background beliefs [Orenstein] |
| Full Idea: The principle of conservatism in choosing between theories is a maxim of minimal mutilation, stating that of competing theories, all other things being equal, choose the one that violates the fewest background beliefs held. | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.2) | |
| A reaction: In this sense, all rational people should be conservatives. The idea is a modern variant of Hume's objection to miracles (Idea 2227). A Kuhnian 'paradigm shift' is the dramatic moment when this principle no longer seems appropriate. |
| 8477 | People presume meanings exist because they confuse meaning and reference [Orenstein] |
| Full Idea: A good part of the confidence people have that there are meanings rests on the confusion of meaning and reference. | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.6) | |
| A reaction: An important point. Everyone assumes that sentences link to the world, but Frege shows that that is not part of meaning. Words like prepositions and conjunctions ('to', 'and') don't have 'a meaning' apart from their function and use. |
| 8471 | Three ways for 'Socrates is human' to be true are nominalist, platonist, or Montague's way [Orenstein] |
| Full Idea: 'Socrates is human' is true if 1) subject referent is identical with a predicate referent (Nominalism), 2) subject reference member of the predicate set, or the subject has that property (Platonism), 3) predicate set a member of the subject set (Montague) | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.3) | |
| A reaction: Orenstein offers these as alternatives to Quine's 'inscrutability of reference' thesis, which makes the sense unanalysable. |
| 8484 | If two people believe the same proposition, this implies the existence of propositions [Orenstein] |
| Full Idea: If we can say 'there exists a p such that John believes p and Barbara believes p', logical forms such as this are cited as evidence for our ontological commitment to propositions. | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.7) | |
| A reaction: Opponents of propositions (such as Quine) will, of course, attempt to revise the logical form to eliminate the quantification over propositions. See Orenstein's outline on p.171. |
| 22384 | A 'double effect' is a foreseen but not desired side-effect, which may be forgivable [Foot] |
| Full Idea: 'Double effect' refers to action having an effect aimed at, and also one foreseen but in now way desired. The 'doctrine' is that it is sometimes permissible to bring about by oblique intention what one may not directly intend. | |
| From: Philippa Foot (Abortion and the Doctrine of Double Effect [1967], p.20) | |
| A reaction: Presumably this can only be justified by a trade-off. The unfortunate side effect must be rated as a price worth paying. If the side effect is not foreseen, that is presumably either understandable, or wickedly negligent. No clear rule is possible. |
| 22385 | The doctrine of double effect can excuse an outcome because it wasn't directly intended [Foot] |
| Full Idea: Supporters of double effect say that sometimes it makes a difference to the permissibility of an action involving harm to others that this harm, although foreseen, is not part of the agent's intention. | |
| From: Philippa Foot (Abortion and the Doctrine of Double Effect [1967], p.22) | |
| A reaction: The obvious major case is the direction of wartime bombing raids. Controversial, because how can someone foresee a side effect and yet claim to have no intention to cause it? Isn't it wickedly self-deluding? |
| 22386 | Double effect says foreseeing you will kill someone is not the same as intending it [Foot] |
| Full Idea: The doctrine of double effect offers us a way out [of the trolley problem], insisting that it is one thing to steer towards someone foreseeing that you will kill him, and another to aim at his death as part of your plan. | |
| From: Philippa Foot (Abortion and the Doctrine of Double Effect [1967], p.23) | |
| A reaction: [She has just created her famous Trolley Problem]. Utilitarians must constantly rely on the doctrine of double effect, as they calculate their trade-offs. |
| 22387 | Without double effect, bad men can make us do evil by threatening something worse [Foot] |
| Full Idea: Rejection of the doctrine of double effect puts us hopelessly in the power of bad men. Anyone who wants us to do something we think is wrong has only to threaten that otherwise he himself will do something we think worse. | |
| From: Philippa Foot (Abortion and the Doctrine of Double Effect [1967], p.25) | |
| A reaction: Her example is they will torture five if you don't torture one. Bernard Williams's famous Jim and the Indians is they will shoot twenty if you don't shoot one. Williams aims it at utilitarian calculations. Double effect is highly relevant. |
| 22388 | Double effect seems to rely on a distinction between what we do and what we allow [Foot] |
| Full Idea: The strength of the doctrine of double effect seems to lie in the distinction it makes between what we do (equated with direct intention) and what we allow (thought of as obliquely intended). | |
| From: Philippa Foot (Abortion and the Doctrine of Double Effect [1967], p.25) | |
| A reaction: She objects (nicely), saying her trolley driver 'does' the side-effect killing, and someone might 'allow' an obvious criminal death. There is also an intermediate class of 'brought about', where you set up a killing, but don't do it. |
| 22383 | Abortion is puzzling because we do and don't want the unborn child to have rights [Foot] |
| Full Idea: One reason why most of us feel puzzled about the problem of abortion is that we want, and do not want, to allow to the unborn child the rights that belong to adults and children. | |
| From: Philippa Foot (Abortion and the Doctrine of Double Effect [1967], p.19) | |
| A reaction: We also do and don't want children to have the same rights as adults. Rights should accrue with development and maturity, it seems. No one thinks sperm and egg have rights. Why stop at 'adult'? Superior adults deserve more rights! |