28 ideas
| 18823 | To say there could have been people who don't exist, but deny those possible things, rejects Barcan [Stalnaker, by Rumfitt] |
| Full Idea: Stalnaker holds that there could have been people who do not actually exist, but he denies that there are things that could have been those people. That is, he denies the unrestricted validity of the Barcan Formula. | |
| From: report of Robert C. Stalnaker (Counterparts and Identity [1987]) by Ian Rumfitt - The Boundary Stones of Thought 6.2 | |
| A reaction: And quite right too, I should have thought. As they say, Jack Kennedy and Marilyn Monroe might have had a child, but the idea that we should accept some entity which might have been that child but wasn't sounds like nonsense. Except as fiction….. |
| 10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
| Full Idea: The main objection to the axiom of choice was that it had to be given by some law or definition, but since sets are arbitrary this seems irrelevant. Formalists consider it meaningless, but set-theorists consider it as true, and practically obvious. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §3) |
| 10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
| Full Idea: One can distinguish at least two quite different senses of logic: as an instrument of demonstration, and perhaps as an instrument for the characterization of structures. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: This is trying to capture the proof-theory and semantic aspects, but merely 'characterizing' something sounds like a rather feeble aspiration for the semantic side of things. Isn't it to do with truth, rather than just rule-following? |
| 10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
| Full Idea: Elementary logic cannot characterize the usual mathematical structures, but seems to be distinguished by its completeness. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
| Full Idea: The expressive power of second-order logic is too great to admit a proof procedure, but is adequate to express set-theoretical statements, and open questions such as the continuum hypothesis or the existence of big cardinals are easily stated. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
| Full Idea: In sentential logic there is a simple proof that all truth functions, of any number of arguments, are definable from (say) 'not' and 'and'. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §0) | |
| A reaction: The point of 'say' is that it can be got down to two connectives, and these are just the usual preferred pair. |
| 10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
| Full Idea: The symbols ∀ and ∃ may, to start with, be regarded as extrapolations of the truth functional connectives ∧ ('and') and ∨ ('or') to infinite domains. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §5) |
| 10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
| Full Idea: One might add to one's logic an 'uncountable quantifier', or a 'Chang quantifier', or a 'two-argument quantifier', or 'Shelah's quantifier', or 'branching quantifiers'. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §3) | |
| A reaction: [compressed - just listed for reference, if you collect quantifiers, like collecting butterflies] |
| 10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
| Full Idea: Skolem deduced from the Löwenheim-Skolem theorem that 'the absolutist conceptions of Cantor's theory' are 'illusory'. I think it is clear that this conclusion would not follow even if elementary logic were in some sense the true logic, as Skolem assumed. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §7) | |
| A reaction: [Tharp cites Skolem 1962 p.47] Kit Fine refers to accepters of this scepticism about the arithmetic of infinities as 'Skolemites'. |
| 10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
| Full Idea: The Löwenheim-Skolem property seems to be undesirable, in that it states a limitation concerning the distinctions the logic is capable of making, such as saying there are uncountably many reals ('Skolem's Paradox'). | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
| Full Idea: Soundness would seem to be an essential requirement of a proof procedure, since there is little point in proving formulas which may turn out to be false under some interpretation. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10763 | Completeness and compactness together give axiomatizability [Tharp] |
| Full Idea: Putting completeness and compactness together, one has axiomatizability. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §1) |
| 10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
| Full Idea: In general, if completeness fails there is no algorithm to list the valid formulas. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: I.e. the theory is not effectively enumerable. |
| 10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
| Full Idea: It is strange that compactness is often ignored in discussions of philosophy of logic, since the most important theories have infinitely many axioms. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: An example of infinite axioms is the induction schema in first-order Peano Arithmetic. |
| 10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
| Full Idea: The compactness condition seems to state some weakness of the logic (as if it were futile to add infinitely many hypotheses). To look at it another way, formalizations of (say) arithmetic will admit of non-standard models. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
| Full Idea: A complete logic has an effective enumeration of the valid formulas. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
| Full Idea: Despite completeness, the mere existence of an effective enumeration of the valid formulas will not, by itself, provide knowledge. For example, one might be able to prove that there is an effective enumeration, without being able to specify one. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: The point is that completeness is supposed to ensure knowledge (of what is valid but unprovable), and completeness entails effective enumerability, but more than the latter is needed to do the key job. |
| 11976 | Aristotelian essentialism says essences are not relative to specification [Lewis] |
| Full Idea: So-called 'Aristotelian essentialism' is the doctrine of essences not relative to specifications. | |
| From: David Lewis (Counterpart theory and Quant. Modal Logic [1968], III) | |
| A reaction: In other words, they are so-called 'real essences', understood as de re. Quine says essences are all de dicto, and relative to some specification. I vote for Aristotle. |
| 11978 | Causal necessities hold in all worlds compatible with the laws of nature [Lewis] |
| Full Idea: Just as a sentence is necessary if it holds in all worlds, so it is causally necessary if it holds in all worlds compatible with the laws of nature. | |
| From: David Lewis (Counterpart theory and Quant. Modal Logic [1968], V) | |
| A reaction: I don't believe in the so-called 'laws of nature', so I'm not buying that. Is there no distinction in Lewis's view between those sentences which must hold, and those which happen to hold universally? |
| 11979 | It doesn't take the whole of a possible Humphrey to win the election [Lewis] |
| Full Idea: Even if Humphrey is a modal continuant, it doesn't take the whole of him to do such things as winning. | |
| From: David Lewis (Counterpart theory and Quant. Modal Logic [1968], Post B) | |
| A reaction: This responds to Kripke's famous example, that people only care about what happens to themselves, and not to some 'counterpart' of themselves. |
| 16409 | Unlike Lewis, I defend an actualist version of counterpart theory [Stalnaker] |
| Full Idea: I defend a version of counterpart theory that is quite different from Lewis's version, as it is tied to actualism (all that exists is part of the actual world) rather than possibilism (possible things may exist without actually existing). | |
| From: Robert C. Stalnaker (Counterparts and Identity [1987], 1) | |
| A reaction: This could be the theory I am after. I am sympathetic to both actualism and to counterpart theory. Off to the woodshed…. |
| 16411 | If possible worlds really differ, I can't be in more than one at a time [Stalnaker] |
| Full Idea: Nothing can be in two places at once. If other possible worlds are really other universes, then clearly, you and I cannot be in them if we are here in this one. | |
| From: Robert C. Stalnaker (Counterparts and Identity [1987], 2) | |
| A reaction: This can be sensibly expressed without possible worlds. I can't embody my other possibilities while I am embodying this one (I'm too busy). Insofar as possible worlds are a good framework, they are just a precise map of common sense. |
| 16412 | If counterparts exist strictly in one world only, this seems to be extreme invariant essentialism [Stalnaker] |
| Full Idea: Counterparts involve the thesis that domains of different possible worlds are disjoint: possible individuals exist in at most one possible world. This seems to suggest extreme essentialism, where nothing could differ from how it is. | |
| From: Robert C. Stalnaker (Counterparts and Identity [1987], 2) | |
| A reaction: He quotes Salmon (1981:236) as saying counterpart theory is particularly inflexible essentialism. This is a long way from my use of 'essentialism'. The problem is just the extent to which my counterpart is 'the same' as me. |
| 16994 | Counterpart theory is bizarre, as no one cares what happens to a mere counterpart [Kripke on Lewis] |
| Full Idea: Probably Humphrey could not care less whether someone else, no matter how much resembling him, would have been victorious in another possible world. Thus Lewis's view seems even more bizarre that the usual transworld identification it replaces. | |
| From: comment on David Lewis (Counterpart theory and Quant. Modal Logic [1968]) by Saul A. Kripke - Naming and Necessity notes and addenda note 13 | |
| A reaction: I begin to see this as a devastating reply to a theory I previously found quite congenial. |
| 11974 | Counterparts are not the original thing, but resemble it more than other things do [Lewis] |
| Full Idea: Your counterparts resemble you closely in content and context in important respects. They resemble you more closely than do the other things in their worlds. But they are not really you. | |
| From: David Lewis (Counterpart theory and Quant. Modal Logic [1968], I) | |
| A reaction: It is a dilemma. If my counterpart were exactly me, I couldn't contemplate possibly losing a leg, or my sanity. But if my counterpart isn't exactly me, then I don't have much interest in its fate. Only essences can save us here. Cf. me tomorrow. |
| 11975 | If the closest resembler to you is in fact quite unlike you, then you have no counterpart [Lewis] |
| Full Idea: If whatever thing in world w6 it is that resembles you more closely than anything else in w6 is nevertheless quite unlike you; nothing in w6 resembles you at all closely. If so, you have no counterpart in w6. | |
| From: David Lewis (Counterpart theory and Quant. Modal Logic [1968], I) | |
| A reaction: This is the nub, because the whole theory rests on deciding whether two things resemble sufficiently 'closely'. But then we need a criterion of closeness, so we must start talking about which properties matter. Essences loom. |
| 11977 | Essential attributes are those shared with all the counterparts [Lewis] |
| Full Idea: An essential attribute of something is an attribute it shares with all its counterparts. | |
| From: David Lewis (Counterpart theory and Quant. Modal Logic [1968], III) | |
| A reaction: I don't like this. It ties essence entirely to identity, but I think essence precedes identity. Essence is a nexus of causal and explanatory powers which bestows an identity on each thing. But essence might be unstable, and identity with it. |
| 16410 | Extensional semantics has individuals and sets; modal semantics has intensions, functions of world to extension [Stalnaker] |
| Full Idea: Semantic values in extensional semantics are extensions, like individuals for terms, and sets for predicates. In modal semantics we have intensions, functions from worlds to appropriate extensions. | |
| From: Robert C. Stalnaker (Counterparts and Identity [1987], 2) | |
| A reaction: It seems obvious that the meaning of a word like 'giraffe' must include possible giraffes, as well as actual and deceased giraffes. |