15 ideas
| 10928 | Maybe we can quantify modally if the objects are intensional, but it seems unlikely [Quine] |
| Full Idea: Perhaps there is no objection to quantifying into modal contexts as long as the values of any variables thus quantified are limited to intensional objects, but they also lead to disturbing examples. | |
| From: Willard Quine (Reference and Modality [1953], §3) | |
| A reaction: [Quine goes on to give his examples] I take it that possibilities are features of actual reality, not merely objects of thought. The problem is that they are harder to know than actual objects. |
| 11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
| Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], II) | |
| A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts. |
| 11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
| Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table. | |
| From: Ian Rumfitt ("Yes" and "No" [2000]) | |
| A reaction: This is the standard view which Rumfitt sets out to challenge. |
| 11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
| Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], III) | |
| A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value. |
| 10925 | Failure of substitutivity shows that a personal name is not purely referential [Quine] |
| Full Idea: Failure of substitutivity shows that the occurrence of a personal name is not purely referential. | |
| From: Willard Quine (Reference and Modality [1953], §1) | |
| A reaction: I don't think I understand the notion of a name being 'purely' referential, as if it somehow ceased to be a word, and was completely transparent to the named object. |
| 10926 | Quantifying into referentially opaque contexts often produces nonsense [Quine] |
| Full Idea: If to a referentially opaque context of a variable we apply a quantifier, with the intention that it govern that variable from outside the referentially opaque context, then what we commonly end up with is unintended sense or nonsense. | |
| From: Willard Quine (Reference and Modality [1953], §2) |
| 9466 | Nominalists like substitutional quantification to avoid the metaphysics of objects [Jacquette] |
| Full Idea: Some substitutional quantificationists in logic hope to avoid philosophical entanglements about the metaphysics of objects, ..and nominalists can find aid and comfort there. | |
| From: Dale Jacquette (Intro to III: Quantifiers [2002], p.143) | |
| A reaction: This has an appeal for me, particularly if it avoids abstract objects, but I don't see much problem with material objects, so we might as well have a view that admits those. |
| 9465 | Substitutional universal quantification retains truth for substitution of terms of the same type [Jacquette] |
| Full Idea: The substitutional interpretation says the universal quantifier is true just in case it remains true for all substitutions of terms of the same type as that of the universally bound variable. | |
| From: Dale Jacquette (Intro to III: Quantifiers [2002], p.143) | |
| A reaction: This doesn't seem to tell us how it gets started with being true. |
| 10930 | Quantification into modal contexts requires objects to have an essence [Quine] |
| Full Idea: A reversion to Aristotelian essentialism is required if quantification into modal contexts is to be insisted on. An object must be seen as having some of its traits necessarily. | |
| From: Willard Quine (Reference and Modality [1953], §3) | |
| A reaction: This thought leads directly to Kripke's proposal of rigid designation of objects (and Lewis response of counterparts), which really gets modal logic off the ground. Quine's challenge remains - the modal logic entails a huge metaphysical commitment. |
| 14645 | To be necessarily greater than 7 is not a trait of 7, but depends on how 7 is referred to [Quine] |
| Full Idea: To be necessarily greater than 7 is not a trait of a number, but depends on the manner of referring to the number. | |
| From: Willard Quine (Reference and Modality [1953], §2) | |
| A reaction: The most concise quotation of Quine's objection to 'de re' modality. The point is whether the number might have been referred to as 'the number of planets'. So many of these problems are solved by fixing unambiguous propositions first. |
| 9201 | Whether 9 is necessarily greater than 7 depends on how '9' is described [Quine, by Fine,K] |
| Full Idea: Quine's metaphysical argument is that if 9 is 7+2 the number 9 will be necessarily greater than 7, but when 9 is described as the number of planets, the number will not be necessarily greater than 7. The necessity depends on how it is described. | |
| From: report of Willard Quine (Reference and Modality [1953]) by Kit Fine - Intro to 'Modality and Tense' p. 3 | |
| A reaction: Thus necessity would be entirely 'de dicto' and not 'de re'. It sounds like a feeble argument. If I describe the law of identity (a=a) as 'my least favourite logical principle', that won't make it contingent. Describe 9, or refer to it? See Idea 9203. |
| 10927 | Necessity only applies to objects if they are distinctively specified [Quine] |
| Full Idea: Necessity does not properly apply to the fulfilment of conditions by objects (such as the number which numbers the planets), apart from special ways of specifying them. | |
| From: Willard Quine (Reference and Modality [1953], §3) | |
| A reaction: This appears to say that the only necessity is 'de dicto', and that there is no such thing as 'de re' necessity (of the thing in itself). How can Quine deny that there might be de re necessities? His point is epistemological - how can we know them? |
| 9203 | We can't quantify in modal contexts, because the modality depends on descriptions, not objects [Quine, by Fine,K] |
| Full Idea: 'Necessarily 9>7' may be true while the sentence 'necessarily the number of planets < 7' is false, even though it is obtained by substituting a coreferential term. So quantification in these contexts is unintelligible, without a clear object. | |
| From: report of Willard Quine (Reference and Modality [1953]) by Kit Fine - Intro to 'Modality and Tense' p. 4 | |
| A reaction: This is Quine's second argument against modality. See Idea 9201 for his first. Fine attempts to refute it. The standard reply seems to be to insist that 9 must therefore be an object, which pushes materialist philosophers into reluctant platonism. |
| 11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
| Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], IV) | |
| A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role). |
| 10931 | We can't say 'necessarily if x is in water then x dissolves' if we can't quantify modally [Quine] |
| Full Idea: To say an object is soluble in water is to say that it would dissolve if it were in water,..which implies that 'necessarily if x is in water then x dissolves'. Yet we do not know if there is a suitable sense of 'necessarily' into which we can so quantify. | |
| From: Willard Quine (Reference and Modality [1953], §4) | |
| A reaction: This is why there has been a huge revival of scientific essentialism - because Krike seems to offer exacty the account which Quine said was missing. So can you have modal logic without rigid designation? |