31 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. |
| 16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
| Full Idea: It seems unavoidable that the facts about logically necessary relations between levels of facts are themselves logically distinct further facts, irreducible to the microphysical facts. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], C) | |
| A reaction: I'm beginning to think that rejecting every theory of reality that is proposed by carefully exposing some infinite regress hidden in it is a rather lazy way to do philosophy. Almost as bad as rejecting anything if it can't be defined. |
| 16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
| Full Idea: Logical supervenience, restricted to individuals, seems to imply strong reduction. It is said that where the B-facts logically supervene on the A-facts, the B-facts simply re-describe what the A-facts describe, and the B-facts come along 'for free'. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], C) | |
| A reaction: This seems to be taking 'logically' to mean 'analytically'. Presumably an entailment is logically supervenient on its premisses, and may therefore be very revealing, even if some people think such things are analytic. |
| 16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
| Full Idea: The root intuition behind nonreductive materialism is that reality is composed of ontologically distinct layers or levels. …The upper levels depend on the physical without reducing to it. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], B) | |
| A reaction: A nice clear statement of a view which I take to be false. This relationship is the sort of thing that drives people fishing for an account of it to use the word 'supervenience', which just says two things seem to hang out together. Fluffy materialism. |
| 16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
| Full Idea: Jessica Wilson (1999) says what makes physicalist accounts different from emergentism etc. is that each individual causal power associated with a supervenient property is numerically identical with a causal power associated with its base property. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], n 11) | |
| A reaction: Hence the key thought in so-called (serious, rather than self-evident) 'emergentism' is so-called 'downward causation', which I take to be an idle daydream. |
| 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. |
| 14508 | A 'thisness' is a thing's property of being identical with itself (not the possession of self-identity) [Adams,RM] |
| Full Idea: A thisness is the property of being identical with a certain particular individual - not the property that we all share, of being identical with some individual, but my property of being identical with me, your property of being identical with you etc. | |
| From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 1) | |
| A reaction: These philosophers tell you that a thisness 'is' so-and-so, and don't admit that he (and Plantinga) are putting forward a new theory about haecceities, and one I find implausible. I just don't believe in the property of 'being-identical-to-me'. |
| 14511 | There are cases where mere qualities would not ensure an intrinsic identity [Adams,RM] |
| Full Idea: I have argued that there are possible cases in which no purely qualitative conditions would be both necessary and sufficient for possessing a given thisness. | |
| From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 6) | |
| A reaction: Are we perhaps confusing our epistemology with our ontology here? We can ensure that something has identity, or ensure that its identity is knowable. If it is 'something', then it has identity. Er, that's it? |
| 16463 | Adams says actual things have haecceities, but not things that only might exist [Adams,RM, by Stalnaker] |
| Full Idea: Adams favours haecceitism about actual things but no haecceities for things that might exist but don't. | |
| From: report of Robert Merrihew Adams (Actualism and Thisness [1981]) by Robert C. Stalnaker - Mere Possibilities 4.2 | |
| A reaction: This contrasts with Plantinga, who proposes necessary essences for everything, even for what might exist. Plantinga sounds crazy to me, Adams merely interesting but not too plausible. |
| 12031 | Essences are taken to be qualitative properties [Adams,RM] |
| Full Idea: Essences have normally been understood to be constituted by qualitative properties. | |
| From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 1) | |
| A reaction: I add this simple point, because it might be challenged by the view that an essence is a substance, rather than the properties of anything. I prefer that, and would add that substances are individuated by distinctive causal powers. |
| 12034 | If the universe was cyclical, totally indiscernible events might occur from time to time [Adams,RM] |
| Full Idea: There is a temporal argument for the possibility of non-identical indiscernibles, if there could be a cyclical universe, in which each event was preceded and followed by infinitely many other events qualitatively indiscernible from itself. | |
| From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 3) | |
| A reaction: The argument is a parallel to Max Black's indiscernible spheres in space. Adams offers the reply that time might be tightly 'curved', so that the repetition was indeed the same event again. |
| 14510 | Two events might be indiscernible yet distinct, if there was a universe cyclical in time [Adams,RM] |
| Full Idea: Similar to the argument from spatial dispersal, we can argue against the Identity of Indiscernibles from temporal dispersal. It seems there could be a cyclic universe, ..and thus there could be distinct but indiscernible events, separated temporally. | |
| From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 3) | |
| A reaction: See Idea 14509 for spatial dispersal. If cosmologists decided that a cyclical universe was incoherent, would that ruin the argument? Presumably there might even be indistinguishable events in the one universe (in principle!). |
| 16455 | Black's two globes might be one globe in highly curved space [Adams,RM] |
| Full Idea: If God creates a globe reached by travelling two diameters in a straight line from another globe, this can be described as two globes in Euclidean space, or a single globe in a tightly curved non-Euclidean space. | |
| From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 3) | |
| A reaction: [my compression of Adams's version of Hacking's response to Black, as spotted by Stalnaker] Hence we save the identity of indiscernibles, by saying we can't be sure that two indiscernibles are not one thing, unusually described. |
| 14507 | Are possible worlds just qualities, or do they include primitive identities as well? [Adams,RM] |
| Full Idea: Is the world - and are all possible worlds - constituted by purely qualitative facts, or does thisness hold a place beside suchness as a fundamental feature of reality? | |
| From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], Intro) | |
| A reaction: 'Thisness' and 'suchness' aim to capture Aristotelian notions of the entity and its attributes. Aristotle talks of 'a this'. Adams is after adding 'haecceities' to the world. My intuitive answer is no, there are no 'pure' identities. We add those. |
| 11964 | Possible worlds are world-stories, maximal descriptions of whole non-existent worlds [Adams,RM, by Molnar] |
| Full Idea: According to a theory proposed by Adams, possible worlds are world-stories, that is maximally complete consistent sets of propositions which between them describe non-existent whole worlds. | |
| From: report of Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979]) by George Molnar - Powers 12.2.2 | |
| A reaction: Presumably this places an additional constraint on the view that a world is just a maximal set of propositions. It seems to require coherence as well as consistency. Suppose an object destroys all others objects. Is that a world? |
| 16451 | Adams says anti-haecceitism reduces all thisness to suchness [Adams,RM, by Stalnaker] |
| Full Idea: The anti-haecceitist thesis (according to Adams's version) is that all thisnesses are reducible to, or supervenient upon, suchnesses. | |
| From: report of Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979]) by Robert C. Stalnaker - Mere Possibilities 3.5 |
| 11901 | Haecceitism may or may not involve some logical connection to essence [Adams,RM, by Mackie,P] |
| Full Idea: Moderate Haecceitism says that thisnesses and transworld identities are primitive, but logically connected with suchnesses. ..Extreme Haecceitism involves the rejection of all logical connections between suchness and thisness, for persons. | |
| From: report of Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979]) by Penelope Mackie - How Things Might Have Been | |
| A reaction: I am coming to the conclusion that they are not linked. That thisness is a feature of our conceptual thinking, and is utterly atomistic and content-free, while suchness is rich and a feature of reality. |
| 14512 | Moderate Haecceitism says transworld identities are primitive, but connected to qualities [Adams,RM] |
| Full Idea: My position, according to which thisnesses and transworld identities are primitive but logically connected to suchnesses, we may call 'Moderate Haecceitism'. | |
| From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 6) | |
| A reaction: The rather tentative connection to qualities is to block the possibility of Aristotle being a poached egg, which he (quite reasonably!) holds to be counterintuitive. It all feels like a mess to me. |
| 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. |
| 12032 | Direct reference is by proper names, or indexicals, or referential uses of descriptions [Adams,RM] |
| Full Idea: Direct reference is commonly effected by the use of proper names and indexical expressions, and sometimes by what has been called (by Donnellan) the 'referential' use of descriptions. | |
| From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 2) | |
| A reaction: One might enquire whether the third usage should be described as 'direct', but then I am not sure that there is much of a distinction between references which are or are not 'direct'. Either you (or a sentence) refer or you (or it) don't. |
| 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. |