26 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. |
| 13838 | A decent modern definition should always imply a semantics [Hacking] |
| Full Idea: Today we expect that anything worth calling a definition should imply a semantics. | |
| From: Ian Hacking (What is Logic? [1979], §10) | |
| A reaction: He compares this with Gentzen 1935, who was attempting purely syntactic definitions of the logical connectives. |
| 13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
| Full Idea: 'Dilution' (or 'Thinning') provides an essential contrast between deductive and inductive reasoning; for the introduction of new premises may spoil an inductive inference. | |
| From: Ian Hacking (What is Logic? [1979], §06.2) | |
| A reaction: That is, inductive logic (if there is such a thing) is clearly non-monotonic, whereas classical inductive logic is monotonic. |
| 13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
| Full Idea: If A |- B and B |- C, then A |- C. This generalises to: If Γ|-A,Θ and Γ,A |- Θ, then Γ |- Θ. Gentzen called this 'cut'. It is the transitivity of a deduction. | |
| From: Ian Hacking (What is Logic? [1979], §06.3) | |
| A reaction: I read the generalisation as 'If A can be either a premise or a conclusion, you can bypass it'. The first version is just transitivity (which by-passes the middle step). |
| 13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
| Full Idea: Only the cut rule can have a conclusion that is less complex than its premises. Hence when cut is not used, a derivation is quite literally constructive, building up from components. Any theorem obtained by cut can be obtained without it. | |
| From: Ian Hacking (What is Logic? [1979], §08) |
| 13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
| Full Idea: I don't believe English is by nature classical or intuitionistic etc. These are abstractions made by logicians. Logicians attend to numerous different objects that might be served by 'If...then', like material conditional, strict or relevant implication. | |
| From: Ian Hacking (What is Logic? [1979], §15) | |
| A reaction: The idea that they are 'abstractions' is close to my heart. Abstractions from what? Surely 'if...then' has a standard character when employed in normal conversation? |
| 13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
| Full Idea: First-order logic is the strongest complete compact theory with a Löwenheim-Skolem theorem. | |
| From: Ian Hacking (What is Logic? [1979], §13) |
| 13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
| Full Idea: Henkin proved that there is no first-order treatment of branching quantifiers, which do not seem to involve any idea that is fundamentally different from ordinary quantification. | |
| From: Ian Hacking (What is Logic? [1979], §13) | |
| A reaction: See Hacking for an example of branching quantifiers. Hacking is impressed by this as a real limitation of the first-order logic which he generally favours. |
| 13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
| Full Idea: Second-order logic has no chance of a completeness theorem unless one ventures into intensional entities and possible worlds. | |
| From: Ian Hacking (What is Logic? [1979], §13) |
| 13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
| Full Idea: My doctrine is that the peculiarity of the logical constants resides precisely in that given a certain pure notion of truth and consequence, all the desirable semantic properties of the constants are determined by their syntactic properties. | |
| From: Ian Hacking (What is Logic? [1979], §09) | |
| A reaction: He opposes this to Peacocke 1976, who claims that the logical connectives are essentially semantic in character, concerned with the preservation of truth. |
| 13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
| Full Idea: For some purposes the variables of first-order logic can be regarded as prepositions and place-holders that could in principle be dispensed with, say by a system of arrows indicating what places fall in the scope of which quantifier. | |
| From: Ian Hacking (What is Logic? [1979], §11) | |
| A reaction: I tend to think of variables as either pronouns, or as definite descriptions, or as temporary names, but not as prepositions. Must address this new idea... |
| 13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
| Full Idea: A Löwenheim-Skolem theorem holds for anything which, on my delineation, is a logic. | |
| From: Ian Hacking (What is Logic? [1979], §13) | |
| A reaction: I take this to be an unusually conservative view. Shapiro is the chap who can give you an alternative view of these things, or Boolos. |
| 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. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 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? |