36 ideas
| 9023 | If you say that a contradiction is true, you change the meaning of 'not', and so change the subject [Quine] |
| 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 [Quine] |
| 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 [Quine] |
| 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)' [Quine] |
| 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 [Quine] |
| 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 [Quine] |
| 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 [Quine, by Hodes] |
| 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 [Quine] |
| 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 [Quine] |
| 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 [Quine] |
| 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 [Quine] |
| 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 [Quine] |
| 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 [Quine] |
| 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 [Quine] |
| 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 [Quine] |
| 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 [Quine] |
| 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 [Quine] |
| 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 [Quine] |
| 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 [Quine] |
| 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) [Quine] |
| 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. |
| 21506 | A coherence theory of justification can combine with a correspondence theory of truth [Bonjour] |
| Full Idea: There is no manifest absurdity in combining a coherence theory of justification with a correspondence theory of truth. | |
| From: Laurence Bonjour (The Structure of Empirical Knowledge [1985], 5.1) | |
| A reaction: His point is to sharply (and correctly) distinguish coherent justification from a coherence theory of truth. Personally I would recommend talking of a 'robust' theory of truth, without tricky commitment to 'correspondence' between very dissimilar things. |
| 21509 | There will always be a vast number of equally coherent but rival systems [Bonjour] |
| Full Idea: On any plausible conception of coherence, there will always be many, probably infinitely many, different and incompatible systems of belief which are equally coherent. | |
| From: Laurence Bonjour (The Structure of Empirical Knowledge [1985], 5.5) | |
| A reaction: If 'infinitely many' theories are allowed, that blocks the coherentist hope that widening and precisifying the system will narrow down the options and offer some verisimilitude. If we stick to current English expression, that should keep them finite. |
| 21503 | Empirical coherence must attribute reliability to spontaneous experience [Bonjour] |
| Full Idea: An empirical coherence theory needs, for the beliefs of a cognitive system to be even candidates for empirical justification, that the system must contain laws attributing a high degree of reliability to a variety of spontaneous cognitive beliefs. | |
| From: Laurence Bonjour (The Structure of Empirical Knowledge [1985], 7.1) | |
| A reaction: Wanting such a 'law' seems optimistic, and not in the spirit of true coherentism, which can individually evaluate each experiential belief. I'm not sure Bonjour's Observation Requirement is needed, since it is incoherent to neglect observations. |
| 21511 | A well written novel cannot possibly match a real belief system for coherence [Bonjour] |
| Full Idea: It is not even minimally plausible that a well written novel ...would have the degree of coherence required to be a serious alternative to anyone's actual system of beliefs. | |
| From: Laurence Bonjour (The Structure of Empirical Knowledge [1985], 5.5) | |
| A reaction: This seems correct. 'Bleak House' is wonderfully consistent, but its elements are entirely verbal, and nothing occupies the space between the facts that are described. And Lady Dedlock is not in Debrett. I think this kills a standard objection. |
| 21510 | The objection that a negated system is equally coherent assume that coherence is consistency [Bonjour] |
| Full Idea: Sometimes it is said that if one has an appropriately coherent system, an alternative system can be produced simply be negating all of the components of the first system. This would only be so if coherence amounted simply to consistency. | |
| From: Laurence Bonjour (The Structure of Empirical Knowledge [1985], 5.5) | |
| A reaction: I associate Russell with this original objection to coherentism. I formerly took this to be a serious problem, and am now relieved to see that it clearly isn't. |
| 21505 | A coherent system can be justified with initial beliefs lacking all credibility [Bonjour] |
| Full Idea: It is simply not necessary in order for [the coherence] view to yield justification to suppose that cognitively spontaneous beliefs have some degree of initial or independent credibility. | |
| From: Laurence Bonjour (The Structure of Empirical Knowledge [1985], 7.2) | |
| A reaction: This is thoroughly and rather persuasively criticised by Erik Olson. But he always focuses on the coherence of a 'system' with multiple beliefs. I take the credibility of each individual belief to need coherent assessment against a full background. |
| 21504 | The best explanation of coherent observations is they are caused by and correspond to reality [Bonjour] |
| Full Idea: The best explanation for a stable system of beliefs which rely on observation is that the beliefs are caused by what they depict, and the system roughly corresponds to the independent reality it describes. | |
| From: Laurence Bonjour (The Structure of Empirical Knowledge [1985], 8.3) | |
| A reaction: [compressed] Anyone who links best explanation to coherence (and to induction) warms the cockles of my heart. Erik Olson offers a critique, but doesn't convince me. The alternative is to find a better explanation (than reality), or give up. |
| 21508 | Anomalies challenge the claim that the basic explanations are actually basic [Bonjour] |
| Full Idea: The distinctive significance of anomalies lies in the fact that they undermine the claim of the allegedly basic explanatory principles to be genuinely basic. | |
| From: Laurence Bonjour (The Structure of Empirical Knowledge [1985], 5.3) | |
| A reaction: This seems plausible, suggesting that (rather than an anomaly flatly 'falsifying' a theory) an anomaly may just demand a restructuring or reconceptualising of the theory. |
| 9009 | Single words are strongly synonymous if their interchange preserves truth [Quine] |
| 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 [Quine] |
| 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 [Quine] |
| 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 [Quine] |
| 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 [Quine] |
| 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. |
| 5049 | Intelligent pleasure is the perception of beauty, order and perfection [Leibniz] |
| Full Idea: An intelligent being's pleasure is simply the perception of beauty, order and perfection. | |
| From: Gottfried Leibniz (A Résumé of Metaphysics [1697], §18) | |
| A reaction: Leibniz seems to have inherited this from the Greeks, especially Pythagoras and Plato. Buried in Leibniz's remark I see the Christian fear of physical pleasure. He should have got out more. Must an intelligent being always be intelligent? |
| 5048 | Perfection is simply quantity of reality [Leibniz] |
| Full Idea: Perfection is simply quantity of reality. | |
| From: Gottfried Leibniz (A Résumé of Metaphysics [1697], §11) | |
| A reaction: An interesting claim, but totally beyond my personal comprehension. I presume he inherited 'quantity of reality' from Plato, e.g. as you move up the Line from shadows to Forms you increase the degree of reality. I see 'real' as all-or-nothing. |
| 5050 | Evil serves a greater good, and pain is necessary for higher pleasure [Leibniz] |
| Full Idea: Evils themselves serve a greater good, and the fact that pains are found in minds is necessary if they are to reach greater pleasures. | |
| From: Gottfried Leibniz (A Résumé of Metaphysics [1697], §23) | |
| A reaction: How much pain is needed to qualify for the 'greater pleasures'? Some people receive an awful lot. I am not sure exactly how an evil can 'serve' a greater good. Is he recommending evil? |