30 ideas
| 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. |
| 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. |
| 9476 | If dispositions are more fundamental than causes, then they won't conceptually reduce to them [Bird on Lewis] |
| Full Idea: Maybe a disposition is a more fundamental notion than a cause, in which case Lewis has from the very start erred in seeking a causal analysis, in a traditional, conceptual sense, of disposition terms. | |
| From: comment on David Lewis (Causation [1973]) by Alexander Bird - Nature's Metaphysics 2.2.8 | |
| A reaction: Is this right about Lewis? I see him as reducing both dispositions and causes to a set of bald facts, which exist in possible and actual worlds. Conditionals and counterfactuals also suffer the same fate. |
| 16776 | Substance is an intrinsic thing, so parts of substances can't also be intrinsic things [Duns Scotus] |
| Full Idea: Substance ...is an ens per se. No part of a substance is an ens per se when it is part of a substance, because then it would be a particular thing, and one substance would be a particular thing from many things, which does not seem to be true. | |
| From: John Duns Scotus (In Praed. [1300], 15.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 26.1 | |
| A reaction: The tricky bit is 'when it is a part of a substance', meaning a substance must cease to be a substance when it is subsumed into some greater substance. Maybe. Drops of water? Molecules? Bricks? Cells? |
| 8425 | For true counterfactuals, both antecedent and consequent true is closest to actuality [Lewis] |
| Full Idea: A counterfactual is non-vacuously true iff it takes less of a departure from actuality to make the consequent true along with the antecedent than it does to make the antecedent true without the consequent. | |
| From: David Lewis (Causation [1973], p.197) | |
| A reaction: Almost every theory proposed by Lewis hangs on the meaning of the word 'close', as used here. If you visited twenty Earth-like worlds (watch Startrek?), it would be a struggle to decide their closeness to ours in rank order. |
| 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. |
| 8424 | Determinism says there can't be two identical worlds up to a time, with identical laws, which then differ [Lewis] |
| Full Idea: By determinism I mean that the prevailing laws of nature are such that there do not exist any two possible worlds which are exactly alike up to that time, which differ thereafter, and in which those laws are never violated. | |
| From: David Lewis (Causation [1973], p.196) | |
| A reaction: This would mean that the only way an action of free will could creep in would be if it accepted being a 'violation' of the laws of nature. Fans of free will would probably prefer to call it a 'natural' phenomenon. I'm with Lewis. |
| 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. |
| 8420 | A proposition is a set of possible worlds where it is true [Lewis] |
| Full Idea: I identify a proposition with the set of possible worlds where it is true. | |
| From: David Lewis (Causation [1973], p.193) | |
| A reaction: As it stands, I'm baffled by this. How can 'it is raining' be a set of possible worlds? I assume it expands to refer to the truth-conditions, among possibilities as well as actualities. 'It is raining' fits all worlds where it is raining. |
| 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. |
| 8405 | A theory of causation should explain why cause precedes effect, not take it for granted [Lewis, by Field,H] |
| Full Idea: Lewis thinks it is a major defect in a theory of causation that it builds in the condition that the time of the cause precede that of the effect: that cause precedes effect is something we ought to explain (which his counterfactual theory claims to do). | |
| From: report of David Lewis (Causation [1973]) by Hartry Field - Causation in a Physical World | |
| A reaction: My immediate reaction is that the chances of explaining such a thing are probably nil, and that we might as well just accept the direction of causation as a given. Even philosophers balk at the question 'why doesn't time go backwards?' |
| 8427 | I reject making the direction of causation axiomatic, since that takes too much for granted [Lewis] |
| Full Idea: One might stipulate that a cause must always precede its effect, but I reject this solution. It won't solve the problem of epiphenomena, it rejects a priori any backwards causation, and it trivializes defining time-direction through causation. | |
| From: David Lewis (Causation [1973], p.203) | |
| A reaction: [compressed] Not strong arguments, I would say. Maybe apparent causes are never epiphenomenal. Maybe backwards causation is impossible. Maybe we must use time to define causal direction, and not vice versa. |
| 10392 | It is just individious discrimination to pick out one cause and label it as 'the' cause [Lewis] |
| Full Idea: We sometimes single out one among all the causes of some event and call it 'the' cause. ..We may select the abnormal causes, or those under human control, or those we deem good or bad, or those we want to talk about. This is invidious discrimination. | |
| From: David Lewis (Causation [1973]) | |
| A reaction: This is the standard view expressed by Mill - presumably the obvious empiricist line. But if we specify 'the pre-conditions' for an event, we can't just mention ANY fact prior to the effect - there is obvious relevance. So why not for 'the' cause as well? |
| 8419 | The modern regularity view says a cause is a member of a minimal set of sufficient conditions [Lewis] |
| Full Idea: In present-day regularity analyses, a cause is defined (roughly) as any member of any minimal set of actual conditions that are jointly sufficient, given the laws, for the existence of the effect. | |
| From: David Lewis (Causation [1973], p.193) | |
| A reaction: This is the view Lewis is about to reject. It seem to summarise the essence of the Mackie INUS theory. This account would make the presence of oxygen a cause of almost every human event. |
| 8421 | Regularity analyses could make c an effect of e, or an epiphenomenon, or inefficacious, or pre-empted [Lewis] |
| Full Idea: In the regularity analysis of causes, instead of c causing e, c might turn out to be an effect of e, or an epiphenomenon, or an inefficacious effect of a genuine cause, or a pre-empted cause (by some other cause) of e. | |
| From: David Lewis (Causation [1973], p.194) | |
| A reaction: These are Lewis's reasons for rejecting the general regularity account, in favour of his own particular counterfactual account. It is unlikely that c would be regularly pre-empted or epiphenomenal. If we build time's direction in, it won't be an effect. |
| 17525 | The counterfactual view says causes are necessary (rather than sufficient) for their effects [Lewis, by Bird] |
| Full Idea: The Humean idea, developed by Lewis, is that rather than being sufficient for their effects, causes are (counterfactual) necessary for their effects. | |
| From: report of David Lewis (Causation [1973]) by Alexander Bird - Causation and the Manifestation of Powers p.162 |
| 17524 | Lewis has basic causation, counterfactuals, and a general ancestral (thus handling pre-emption) [Lewis, by Bird] |
| Full Idea: Lewis's basic account has a basic causal relation, counterfactual dependence, and the general causal relation is the ancestral of this basic one. ...This is motivated by counterfactual dependence failing to be general because of the pre-emption problem. | |
| From: report of David Lewis (Causation [1973]) by Alexander Bird - Causation and the Manifestation of Powers p.161 | |
| A reaction: It is so nice when you struggle for ages with a topic, and then some clever person summarises it clearly for you. |
| 8397 | Counterfactual causation implies all laws are causal, which they aren't [Tooley on Lewis] |
| Full Idea: Some counterfactuals are based on non-causal laws, such as Newton's Third Law of Motion. 'If no force one way, then no force the other'. Lewis's counterfactual analysis implies that one force causes the other, which is not the case. | |
| From: comment on David Lewis (Causation [1973]) by Michael Tooley - Causation and Supervenience 5.2 | |
| A reaction: So what exactly does 'cause' my punt to move forwards? Basing causal laws on counterfactual claims looks to me like putting the cart before the horse. |
| 8423 | My counterfactual analysis applies to particular cases, not generalisations [Lewis] |
| Full Idea: My (counterfactual) analysis is meant to apply to causation in particular cases; it is not an analysis of causal generalizations. Those presumably quantify over particulars, but it is hard to match natural language to the quantifiers. | |
| From: David Lewis (Causation [1973], p.195) | |
| A reaction: What authority could you have for asserting a counterfactual claim, if you only had one observation? Isn't the counterfactual claim the hallmark of a generalisation? For one case, 'if not-c, then not-e' is just a speculation. |
| 8426 | One event causes another iff there is a causal chain from first to second [Lewis] |
| Full Idea: One event is the cause of another iff there exists a causal chain leading from the first to the second. | |
| From: David Lewis (Causation [1973], p.200) | |
| A reaction: It will be necessary to both explain and identify a 'chain'. Some chains are extremely tenuous (Alexander could stop a barrel of beer). Go back a hundred years, and the cause of any present event is everything back then. |
| 4795 | Lewis's account of counterfactuals is fine if we know what a law of nature is, but it won't explain the latter [Cohen,LJ on Lewis] |
| Full Idea: Lewis can elucidate the logic of counterfactuals on the assumption that you are not at all puzzled about what a law of nature is. But if you are puzzled about this, it cannot contribute anything towards resolving your puzzlement. | |
| From: comment on David Lewis (Causation [1973]) by L. Jonathan Cohen - The Problem of Natural Laws p.219 | |
| A reaction: This seems like a penetrating remark. The counterfactual theory is wrong, partly because it is epistemological instead of ontological, and partly because it refuses to face the really difficult problem, of what is going on out there. |