43 ideas
6675 | The heart has its reasons of which reason knows nothing [Pascal] |
Full Idea: The heart has its reasons of which reason knows nothing. | |
From: Blaise Pascal (Pensées [1662], 423 (277)) | |
A reaction: This romantic remark has passed into folklore. I am essentially against it, but the role of intuition and instinct are undeniable in both reasoning and ethics. I don't feel inclined, though, to let my heart overrule my reason concerning what exists. |
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. |
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. |
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. |
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. |
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. |
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. |
22011 | The first principles of truth are not rational, but are known by the heart [Pascal] |
Full Idea: We know the truth not only through our reason but also through our heart. It is through that latter that we know first principles, and reason, which has nothing to do with it, tries in vain to refute them. | |
From: Blaise Pascal (Pensées [1662], 110 p.58), quoted by Terry Pinkard - German Philosophy 1760-1860 04 n4 | |
A reaction: This resembles the rationalist defence of fundamental a priori principles, needed as a foundation for knowledge. But the a priori insights are not a feature of the 'natural light' of reason, and are presumably inexplicable (of the 'heart'). |
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. |
6681 | We only want to know things so that we can talk about them [Pascal] |
Full Idea: We usually only want to know something so that we can talk about it. | |
From: Blaise Pascal (Pensées [1662], 77 (152)) | |
A reaction: This may be right, but I wouldn't underestimate it as a worthy end (though Pascal, as usual, calls it 'vanity'). Good talk might even be the highest human good (how many people like, more than anything, chatting in pubs?), and good talk is knowledgeable. |
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). |
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. |
6676 | Painting makes us admire things of which we do not admire the originals [Pascal] |
Full Idea: How vain painting is, exciting admiration by its resemblance to things of which we do not admire the originals. | |
From: Blaise Pascal (Pensées [1662], 40 (134)) | |
A reaction: A lesser sort of painting simply depicts things we admire, such as a nice stretch of landscape. For Pascal it is vanity, but it could be defended as the highest achievement of art, if the purpose of artists is to make us see beauty where we had missed it. |
6680 | It is a funny sort of justice whose limits are marked by a river [Pascal] |
Full Idea: It is a funny sort of justice whose limits are marked by a river; true on this side of the Pyrenees, false on the other. | |
From: Blaise Pascal (Pensées [1662], 60 (294)) | |
A reaction: Pascal gives nice concise summaries of our intuitions. Legal justice may be all we can actually get, but everyone knows that what happens to someone could be 'fair' on one side of a river, and very 'unfair' on the other. |
6677 | Imagination creates beauty, justice and happiness, which is the supreme good [Pascal] |
Full Idea: Imagination decides everything: it creates beauty, justice and happiness, which is the world's supreme good. | |
From: Blaise Pascal (Pensées [1662], 44 (82)) | |
A reaction: Compare Fogelin's remark in Idea 6555. I see Pascal's point, but these ideals are also responses to facts about the world, such as human potential and human desire and successful natural functions. |
6678 | We live for the past or future, and so are never happy in the present [Pascal] |
Full Idea: Our thoughts are wholly concerned with the past or the future, never with the present, which is never our end; thus we never actually live, but hope to live, and since we are always planning to be happy, it is inevitable that we should never be so. | |
From: Blaise Pascal (Pensées [1662], 47 (172)) | |
A reaction: A very nice expression of the importance of 'living for the moment' as a route to happiness. Personally I am occasionally startled by the thought 'Good heavens, I seem to be happy!', but it usually passes quickly. How do you plan for the present? |
20732 | If man considers himself as lost and imprisoned in the universe, he will be terrified [Pascal] |
Full Idea: Let man consider what he is in comparison with what exists; let him regard himself as lost, and from this little dungeon the universe, let him learn to take the earth and himself at their proper value. Anyone considering this will be terrified at himself. | |
From: Blaise Pascal (Pensées [1662], p.199), quoted by Kevin Aho - Existentialism: an introduction Pref 'What? | |
A reaction: [p.199 of Penguin edn] Cited by Aho as a forerunner of existentialism. Montaigne probably influenced Pascal. Interesting that this is to be a self-inflicted existential crisis (for some purpose, probably Christian). |
6682 | Majority opinion is visible and authoritative, although not very clever [Pascal] |
Full Idea: Majority opinion is the best way because it can be seen, and is strong enough to command obedience, but it is the opinion of those who are least clever. | |
From: Blaise Pascal (Pensées [1662], 85 (878)) | |
A reaction: A nice statement of the classic dilemma faced by highly educated people over democracy. Plato preferred the clever, Aristotle agreed with Pascal, and with me. Politics must make the best of it, not pursue some ideal. Education is the one feeble hope. |
6679 | It is not good to be too free [Pascal] |
Full Idea: It is not good to be too free. | |
From: Blaise Pascal (Pensées [1662], 57 (379)) | |
A reaction: All Americans, please take note. I agree with this, because I agree with Aristotle that man is essentially a social animal (Idea 5133), and living in a community is a matter of compromise. Extreme libertarianism contradicts our natures, and causes misery. |
7455 | Pascal knows you can't force belief, but you can make it much more probable [Pascal, by Hacking] |
Full Idea: Pascal knows that one cannot decide to believe in God, but he thinks one can act so that one will very probably come to believe in God, by following a life of 'holy water and sacraments'. | |
From: report of Blaise Pascal (Pensées [1662], 418 (233)) by Ian Hacking - The Emergence of Probability Ch.8 | |
A reaction: This meets the most obvious and simple objection to Pascal's idea, and Pascal may well be right. I'm not sure I could resist belief after ten years in a monastery. |
7457 | Pascal is right, but relies on the unsupported claim of a half as the chance of God's existence [Hacking on Pascal] |
Full Idea: Pascal's argument is valid, but it is presented with a monstrous premise of equal chance. We have no good reason for picking a half as the chance of God's existence. | |
From: comment on Blaise Pascal (Pensées [1662], 418 (233)) by Ian Hacking - The Emergence of Probability Ch.8 | |
A reaction: That strikes me as the last word on this rather bizarre argument. |
7456 | The libertine would lose a life of enjoyable sin if he chose the cloisters [Hacking on Pascal] |
Full Idea: The libertine is giving up something if he chooses to adopt a pious form of life. He likes sin. If God is not, the worldly life is preferable to the cloistered one. | |
From: comment on Blaise Pascal (Pensées [1662], 418 (233)) by Ian Hacking - The Emergence of Probability Ch.8 | |
A reaction: This is a very good objection to Pascal, who seems to think you really have nothing at all to lose. I certainly don't intend to become a monk, because the chances of success seem incredibly remote from where I am sitting. |
6684 | If you win the wager on God's existence you win everything, if you lose you lose nothing [Pascal] |
Full Idea: How will you wager if a coin is spun on 'Either God is or he is not'? ...If you win you win everything, if you lose you lose nothing. | |
From: Blaise Pascal (Pensées [1662], 418 (233)) | |
A reaction: 'Sooner safe than sorry' is a principle best used with caution. Do you really 'lose nothing' by believing a falsehood for the whole of your life? What God would reward belief on such a principles as this? |