21 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. |
| 17896 | We need to know the meaning of 'and', prior to its role in reasoning [Prior,AN, by Belnap] |
| Full Idea: For Prior, so the moral goes, we must first have a notion of what 'and' means, independently of the role it plays as premise and as conclusion. | |
| From: report of Arthur N. Prior (The Runabout Inference Ticket [1960]) by Nuel D. Belnap - Tonk, Plonk and Plink p.132 | |
| A reaction: The meaning would be given by the truth tables (the truth-conditions), whereas the role would be given by the natural deduction introduction and elimination rules. This seems to be the basic debate about logical connectives. |
| 17898 | Prior's 'tonk' is inconsistent, since it allows the non-conservative inference A |- B [Belnap on Prior,AN] |
| Full Idea: Prior's definition of 'tonk' is inconsistent. It gives us an extension of our original characterisation of deducibility which is not conservative, since in the extension (but not the original) we have, for arbitrary A and B, A |- B. | |
| From: comment on Arthur N. Prior (The Runabout Inference Ticket [1960]) by Nuel D. Belnap - Tonk, Plonk and Plink p.135 | |
| A reaction: Belnap's idea is that connectives don't just rest on their rules, but also on the going concern of normal deduction. |
| 11021 | Prior rejected accounts of logical connectives by inference pattern, with 'tonk' his absurd example [Prior,AN, by Read] |
| Full Idea: Prior dislike the holism inherent in the claim that the meaning of a logical connective was determined by the inference patterns into which it validly fitted. ...His notorious example of 'tonk' (A → A-tonk-B → B) was a reductio of the view. | |
| From: report of Arthur N. Prior (The Runabout Inference Ticket [1960]) by Stephen Read - Thinking About Logic Ch.8 | |
| A reaction: [The view being attacked was attributed to Gentzen] |
| 13836 | Maybe introducing or defining logical connectives by rules of inference leads to absurdity [Prior,AN, by Hacking] |
| Full Idea: Prior intended 'tonk' (a connective which leads to absurdity) as a criticism of the very idea of introducing or defining logical connectives by rules of inference. | |
| From: report of Arthur N. Prior (The Runabout Inference Ticket [1960], §09) by Ian Hacking - What is Logic? |
| 8698 | Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend] |
| Full Idea: The modal structuralist thinks of mathematical structures as possibilities. The application of mathematics is just the realisation that a possible structure is actualised. As structures are possibilities, realist ontological problems are avoided. | |
| From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Michèle Friend - Introducing the Philosophy of Mathematics 4.3 | |
| A reaction: Friend criticises this and rejects it, but it is appealing. Mathematics should aim to be applicable to any possible world, and not just the actual one. However, does the actual world 'actualise a mathematical structure'? |
| 9557 | Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara] |
| Full Idea: Hellman represents statements of pure mathematics as elliptical for modal conditionals of a certain sort. | |
| From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Charles Chihara - A Structural Account of Mathematics 5.3 | |
| A reaction: It's a pity there is such difficulty in understanding conditionals (see Graham Priest on the subject). I intuit a grain of truth in this, though I take maths to reflect the structure of the actual world (with possibilities being part of that world). |
| 10263 | Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman] |
| Full Idea: The usual way to show that a sentence is possible is to show that it has a model, but for Hellman presumably a sentence is possible if it might have a model (or if, possibly, it has a model). It is not clear what this move brings us. | |
| From: comment on Geoffrey Hellman (Mathematics without Numbers [1989]) by Stewart Shapiro - Philosophy of Mathematics 7.3 | |
| A reaction: I can't assess this, but presumably the possibility of the model must be demonstrated in some way. Aren't all models merely possible, because they are based on axioms, which seem to be no more than possibilities? |
| 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'). |
| 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. |
| 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? |