23 ideas
| 10688 | 'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall] |
| Full Idea: 'Equivocation' is when the terms do not mean the same thing in the premises and in the conclusion. | |
| From: JC Beall / G Restall (Logical Consequence [2005], Intro) |
| 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. |
| 10690 | Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall] |
| Full Idea: Logic is purely formal either when it is invariant under permutation of object (Tarski), or when it has totally abstracted away from all contents, or it is the constitutive norms for thought. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) | |
| A reaction: [compressed] The third account sounds rather woolly, and the second one sounds like a tricky operation, but the first one sounds clear and decisive, so I vote for Tarski. |
| 10691 | Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall] |
| Full Idea: Technical work on logical consequence has either focused on proofs, where validity is the existence of a proof of the conclusions from the premises, or on models, which focus on the absence of counterexamples. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 10695 | Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall] |
| Full Idea: Two different views of logical consequence are necessary truth-preservation (based on modelling possible worlds; favoured by Realists), or truth-preservation based on the meanings of the logical vocabulary (differing in various models; for Anti-Realists). | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) | |
| A reaction: Thus Dummett prefers the second view, because the law of excluded middle is optional. My instincts are with the first one. |
| 10689 | A step is a 'material consequence' if we need contents as well as form [Beall/Restall] |
| Full Idea: A logical step is a 'material consequence' and not a formal one, if we need the contents as well as the structure or form. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) |
| 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) |
| 10696 | A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall] |
| Full Idea: If a conclusion follows from an empty collection of premises, it is true by logic alone, and is a 'logical truth' (sometimes a 'tautology'), or, in the proof-centred approach, 'theorems'. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 4) | |
| A reaction: These truths are written as following from the empty set Φ. They are just implications derived from the axioms and the rules. |
| 10693 | Models are mathematical structures which interpret the non-logical primitives [Beall/Restall] |
| Full Idea: Models are abstract mathematical structures that provide possible interpretations for each of the non-logical primitives in a formal language. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 10692 | Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall] |
| Full Idea: There are many proof-systems, the main being Hilbert proofs (with simple rules and complex axioms), or natural deduction systems (with few axioms and many rules, and the rules constitute the meaning of the connectives). | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 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. |
| 411 | If we succeed in speaking the truth, we cannot know we have done it [Xenophanes] |
| Full Idea: No man has seen certain truth, and no man will ever know about the gods and other things I mentioned; for if he succeeds in saying what is fully true, he himself is unaware of it; opinion is fixed by fate on all things. | |
| From: Xenophanes (fragments/reports [c.530 BCE], B34), quoted by Sextus Empiricus - Against the Professors (six books) 7.49.4 |
| 412 | If God had not created honey, men would say figs are sweeter [Xenophanes] |
| Full Idea: If God had not created yellow honey, men would say that figs were sweeter. | |
| From: Xenophanes (fragments/reports [c.530 BCE], B38), quoted by Herodian - On Peculiar Speech 41.5 |
| 1640 | The basic Eleatic belief was that all things are one [Xenophanes, by Plato] |
| Full Idea: The Eleatic tribe, which had its beginnings from Xenophanes and still earlier, proceed on the grounds that all things so-called are one. | |
| From: report of Xenophanes (fragments/reports [c.530 BCE]) by Plato - The Sophist 242d |
| 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? |
| 3055 | Xenophanes said the essence of God was spherical and utterly inhuman [Xenophanes, by Diog. Laertius] |
| Full Idea: Xenophanes taught that the essence of God was of a spherical form, in no respect resembling man. | |
| From: report of Xenophanes (fragments/reports [c.530 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.2.3 |
| 408 | Ethiopian gods have black hair, and Thracian gods have red hair [Xenophanes] |
| Full Idea: Ethiopians have gods with snub noses and black hair, Thracians have gods with grey eyes and red hair. | |
| From: Xenophanes (fragments/reports [c.530 BCE], B16), quoted by Clement - Miscellanies 7.22.1 |
| 407 | Mortals believe gods are born, and have voices and clothes just like mortals [Xenophanes] |
| Full Idea: Mortals believe the gods to be created by birth, and to have raiment, voice and body like mortals'. | |
| From: Xenophanes (fragments/reports [c.530 BCE], B14), quoted by Clement - Miscellanies 5.109.2 |