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| 9023 | If you say that a contradiction is true, you change the meaning of 'not', and so change the subject |
| Full Idea: Those who regard the conjunction p.not-p as true think they are talking about negation, 'not', but this ceases to be recognisable as negation. The deviant logician's predicament is when he tries to deny the doctrine he only changes the subject. | |||
| From: Willard Quine (Philosophy of Logic [1970], Ch.6) | |||
| A reaction: The charge of 'changing the subject' has become a classic move in modern discussions of non-standard logics. It is an important idea in discussions of arguments, and is found in Kant's account of the Ontological Argument. |
| 9012 | Talk of 'truth' when sentences are mentioned; it reminds us that reality is the point of sentences |
| Full Idea: The truth predicate has its utility in places where we are compelled to mention sentences. It then serves to point through the sentence to the reality; it serves as a reminder that though sentences are mentioned, reality is still the whole point. | |||
| From: Willard Quine (Philosophy of Logic [1970], Ch.1) | |||
| A reaction: A sensible interpretation of the Tarskian account of truth as disquotation. Quine neatly combines a common sense correspondence with a sophisticated logicians view of the role of truth. So what does "I want the truth here" mean? |
| 9011 | Truth is redundant for single sentences; we do better to simply speak the sentence |
| Full Idea: Rather than speak of truth, we do better simply to say the sentence and so speak not about language but about the world. Of singly given sentences, the perfect theory of truth is the 'disappearance theory of truth' (Sellars). | |||
| From: Willard Quine (Philosophy of Logic [1970], Ch.1) | |||
| A reaction: Quine defends truth as the crucial link between language and reality, but only for large groups of sentences. If someone accuses you of lying or being incorrect, you can respond by repeating your sentence in a firmer tone of voice. |
| 9013 | We can eliminate 'or' from our basic theory, by paraphrasing 'p or q' as 'not(not-p and not-q)' |
| Full Idea: The construction of 'alternation' (using 'or') is useful in practice, but superfluous in theory. It can be paraphrased using only negation and conjunction. We say that 'p or q' is paraphrased as 'not(not-p and not-q)'. | |||
| From: Willard Quine (Philosophy of Logic [1970], Ch.2) | |||
| A reaction: Quine treats 'not' and 'and' as the axiomatic logical connectives, and builds the others from those, presumably because that is the smallest number he could get it down to. I quite like it, because it seems to mesh with basic thought procedures. |
| 9020 | My logical grammar has sentences by predication, then negation, conjunction, and existential quantification |
| Full Idea: We chose a standard grammar in which the simple sentences are got by predication, and all further sentences are generated from these by negation, conjunction, and existential quantification. | |||
| From: Willard Quine (Philosophy of Logic [1970], Ch.3) | |||
| A reaction: It is interesting that we 'choose' our logic, apparently guided by an imperative to achieve minimal ontology. Of these basic ingredients, negation and predication are the more mysterious, especially the latter. Quine is a bit of an 'ostrich' about that. |
| 9028 | Maybe logical truth reflects reality, but in different ways in different languages |
| Full Idea: Perhaps the logical truths owe their truth to certain traits of reality which are reflected in one way by the grammar of our language, in another way by the grammar of another language, and in a third way by the grammar and lexicon of a third language. | |||
| From: Willard Quine (Philosophy of Logic [1970], Ch.7) | |||
| A reaction: This explains Quine's subsequent interest in translation, and the interest of his pupil Davidson in charity, and whether there could actually be rival conceptual schemes. I like the link between logical truths and reality, which follows Russell. |
| 10014 | Quine rejects second-order logic, saying that predicates refer to multiple objects |
| Full Idea: Quine is unwilling to suppose second-order logic intelligible. He holds to Mill's account of the referential role of a predicate: it multiply denotes any and all objects to which it applies, and there is no need for a further 'predicative' entity. | |||
| From: report of Willard Quine (Philosophy of Logic [1970]) by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.130 | |||
| A reaction: If we assume that 'quantifying over' something is a commitment to its existence, then I think I am with Quine, because you end up with a massive commitment to universals, which I prefer to avoid. |
| 10828 | Quantifying over predicates is treating them as names of entities |
| Full Idea: To put the predicate letter 'F' in a quantifier is to treat predicate position suddenly as name position, and hence to treat predicates as names of entities of some sort. | |||
| From: Willard Quine (Philosophy of Logic [1970], Ch.5) | |||
| A reaction: It is tricky to distinguish quantifying over predicates in a first-order way (by reifying them), and in a second-order way (where it is not clear whether you are quantifying over a property or a unified set of things. |
| 9024 | Excluded middle has three different definitions |
| Full Idea: The law of excluded middle, or 'tertium non datur', may be pictured variously as 1) Every closed sentence is true or false; or 2) Every closed sentence or its negation is true; or 3) Every closed sentence is true or not true. | |||
| From: Willard Quine (Philosophy of Logic [1970], Ch.6) | |||
| A reaction: Unlike many top philosophers, Quine thinks clearly about such things. 1) is the classical bivalent reading of excluded middle; 2) is the purely syntactic version; 3) leaves open how we interpret the 'not-true' option. |
| 10012 | Quantification theory can still be proved complete if we add identity |
| Full Idea: Complete proof procedures are available not only for quantification theory, but for quantification theory and identity together. Gödel showed that the theory is still complete if we add self-identity and the indiscernability of identicals. | |||
| From: Willard Quine (Philosophy of Logic [1970], Ch.5) | |||
| A reaction: Hence one talks of first-order logic 'with identity', even though, as Quine observes, it is unclear whether identity is actually a logical or a mathematical notion. |
| 9016 | Names are not essential, because naming can be turned into predication |
| Full Idea: Names are convenient but redundant, because Fa is equivalent to (an x)(a=x,Fx), so a need only occur in the context a=, but this can be rendered as a simple predicate A, so that Fa gives way to (an x)(Ax.Fx). | |||
| From: Willard Quine (Philosophy of Logic [1970], Ch.2) | |||
| A reaction: In eliminating names from analysis, Quine takes Russell's strategy a step further. It is probably this which provoked Kripke into going right back to Mill's view of names as basic labels. The name/description boundary is blurred. Mr Gradgrind. |
| 9015 | Universal quantification is widespread, but it is definable in terms of existential quantification |
| Full Idea: Universal quantification is prominent in logical practice but superfluous in theory, since (for all x)Fx obviously amounts to not(exists an x)not-Fx. | |||
| From: Willard Quine (Philosophy of Logic [1970], Ch.2) | |||
| A reaction: The equivalence between these two works both ways, some you could take the universal quantifier as primitive instead, which would make general truths prior to particular ones. Is there something deep at stake here? |
| 9025 | You can't base quantification on substituting names for variables, if the irrationals cannot all be named |
| Full Idea: A customary argument against quantification based on substitution of names for variables refers to the theorem of set theory that irrational numbers cannot all be assigned integers. Although the integers can all be named, the irrationals therefore can't. | |||
| From: Willard Quine (Philosophy of Logic [1970], Ch.6) | |||
| A reaction: [He names Ruth Marcus as a source of substitutional quantification] This sounds like more than a mere 'argument' against substitutional quantification, but an actual disproof. Or maybe you just can't quantify once you run out of names. |
| 9026 | Some quantifications could be false substitutionally and true objectually, because of nameless objects |
| Full Idea: An existential quantification could turn out false when substitutionally construed and true when objectually construed, because of there being objects of the purported kind but only nameless ones. | |||
| From: Willard Quine (Philosophy of Logic [1970], Ch.6) | |||
| A reaction: (Cf. Idea 9025) Some irrational numbers were his candidates for nameless objects, but as decimals they are infinite in length which seems unfair. I don't take even pi or root-2 to be objects in nature, so not naming irrationals doesn't bother me. |
| 10705 | Putting a predicate letter in a quantifier is to make it the name of an entity |
| Full Idea: To put the predicate letter 'F' in a quantifier is to treat predicate positions suddenly as name positions, and hence to treat predicates as names of entities of some sort. | |||
| From: Willard Quine (Philosophy of Logic [1970], Ch.5) | |||
| A reaction: Quine's famous objection to second-order logic. But Quine then struggles to give an account of predicates and properties, and hence is accused by Armstrong of being an 'ostrich'. Boolos 1975 also attacks Quine here. |
| 9027 | A sentence is logically true if all sentences with that grammatical structure are true |
| Full Idea: A sentence is logically true if all sentences with that grammatical structure are true. | |||
| From: Willard Quine (Philosophy of Logic [1970], Ch.7) | |||
| A reaction: Quine spends some time on the tricky question of deciding which parts of a sentence are grammatical structure ('syncategorematic'), and which parts are what he calls 'lexicon'. I bet there is a Quinean argument which blurs the boundary. |
| 9017 | Predicates are not names; predicates are the other parties to predication |
| Full Idea: Predicates are not names; predicates are the other parties to predication. | |||
| From: Willard Quine (Philosophy of Logic [1970], Ch.2) | |||
| A reaction: Does a wife only exist as party to a marriage? There's something missing here. We are taking predication to be primitive, but we then seem to single out one part of the process - the object - while ignoring the remainder. What are Quinean objects? |
| 9018 | A physical object is the four-dimensional material content of a portion of space-time |
| Full Idea: We might think of a physical object as simply the whole four-dimensional material content, however sporadic and heterogeneous, of some portion of space-time. If it is firm and coherent internally, we call it a body. | |||
| From: Willard Quine (Philosophy of Logic [1970], Ch.2) | |||
| A reaction: An early articulation of one of the two standard views of objects in recent philosophy. I think I prefer the Quinean view, but I am still looking into that one... |
| 9019 | Four-d objects helps predication of what no longer exists, and quantification over items from different times |
| Full Idea: The four-dimensional view of objects aids relativity, and the grammar of tenses, but in logic it makes sense of applying a predicate to something that no longer exists, or of quantifying over objects that never coexisted at any one time. | |||
| From: Willard Quine (Philosophy of Logic [1970], Ch.2) | |||
| A reaction: Since you can predicate of or quantify over hypothetical or fictional objects ('Hamlet is gloomy', 'phlogiston explained fire quite well', 'peace and quiet would be nice') I don't see the necessity for this bold ontological commitment, on these grounds. |
| 9014 | Some conditionals can be explained just by negation and conjunction: not(p and not-q) |
| Full Idea: Often the purpose of a conditional, 'if p, q', can be served simply by negation and conjunction: not(p and not-q), the so-called 'material conditional'. | |||
| From: Willard Quine (Philosophy of Logic [1970], Ch.2) | |||
| A reaction: Logicians love the neatness of that, but get into trouble elsewhere with conditionals, particularly over the implications of not-p. |
| 9009 | Single words are strongly synonymous if their interchange preserves truth |
| Full Idea: We can define, it would seem, a strong synonymy relation for single words by them being interchangeable salva veritate. | |||
| From: Willard Quine (Philosophy of Logic [1970], Ch.1) | |||
| A reaction: This is a first step in Quine's rejection of synonymous sentences. He goes on to raise the problem of renate/cordate. Presumably any two word types can have different connotations, and hence not always be interchangeable - in poetry, for example. |
| 9007 | It makes no sense to say that two sentences express the same proposition |
| Full Idea: My objection to propositions is not parsimony, or disapproval of abstract entities, ..but that propositions induce a relation of synonymy or equivalence between sentences (expressing the same proposition), and this makes no objective sense. | |||
| From: Willard Quine (Philosophy of Logic [1970], Ch.1) | |||
| A reaction: Personally I think propositions are unavoidable when you try to connect language to activities of the brain, and also when you consider animal thought. And also when you introspect about your own language processes. Mr Quine, he wrong. |
| 9008 | There is no rule for separating the information from other features of sentences |
| Full Idea: There is no evident rule for separating the information from the stylistic or other immaterial features of the sentences. | |||
| From: Willard Quine (Philosophy of Logic [1970], Ch.1) | |||
| A reaction: There is no rule for deciding precisely when night falls, so I don't believe in night. I take a proposition, prima facie, as an answer to the question 'What exactly do you mean by that remark?' How do you extract logical form from sentences? |
| 9010 | We can abandon propositions, and just talk of sentences and equivalence |
| Full Idea: Why not just talk of sentences and equivalence and let the propositions go? Propositions have been projected as shadows of sentences, but at best they will give us nothing the sentences will not give. | |||
| From: Willard Quine (Philosophy of Logic [1970], Ch.1) | |||
| A reaction: I don't understand how you decide that two sentences are equivalent. 'There's someone in that wood'; 'yes, there's a person amongst those trees'. Identical truth-conditions. We can formulate a non-linguistic fact about those truth-conditions. |
| 9021 | A good way of explaining an expression is saying what conditions make its contexts true |
| Full Idea: A reasonable way of explaining an expression is by saying what conditions make its various contexts true. | |||
| From: Willard Quine (Philosophy of Logic [1970], Ch.3) | |||
| A reaction: I like the circumspect phrasing of this, which carefully avoids any entities such as 'meanings' or 'truth conditions'. Maybe the whole core of philosophy of language should shift from theories of meaning to just trying to 'explain' sentences. |