29 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. |
| 19125 | If we define truth, we can eliminate it [Halbach/Leigh] |
| Full Idea: If truth can be explicitly defined, it can be eliminated. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.3) | |
| A reaction: That we could just say p corresponds to the facts, or p coheres with our accepted beliefs, or p is the aim of our enquiries, and never mention the word 'true'. Definition is a strategy for reduction or elimination. |
| 19128 | If a language cannot name all objects, then satisfaction must be used, instead of unary truth [Halbach/Leigh] |
| Full Idea: If axioms are formulated for a language (such as set theory) that lacks names for all objects, then they require the use of a satisfaction relation rather than a unary truth predicate. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 3.3) | |
| A reaction: I take it this is an important idea for understanding why Tarski developed his account of truth based on satisfaction. |
| 19120 | Semantic theories need a powerful metalanguage, typically including set theory [Halbach/Leigh] |
| Full Idea: Semantic approaches to truth usually necessitate the use of a metalanguage that is more powerful than the object-language for which it provides a semantics. It is usually taken to include set theory. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1) | |
| A reaction: This is a motivation for developing an axiomatic account of truth, that moves it into the object language. |
| 19127 | The T-sentences are deductively weak, and also not deductively conservative [Halbach/Leigh] |
| Full Idea: Although the theory is materially adequate, Tarski thought that the T-sentences are deductively too weak. …Also it seems that the T-sentences are not conservative, because they prove in PA that 0=0 and ¬0=0 are different, so at least two objects exist. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 3.2) | |
| A reaction: They are weak because they can't prove completeness. This idea give two reasons for looking for a better theory of truth. |
| 19124 | A natural theory of truth plays the role of reflection principles, establishing arithmetic's soundness [Halbach/Leigh] |
| Full Idea: If a natural theory of truth is added to Peano Arithmetic, it is not necessary to add explicity global reflection principles to assert soundness, as the truth theory proves them. Truth theories thus prove soundess, and allows its expression. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.2) | |
| A reaction: This seems like a big attraction of axiomatic theories of truth for students of metamathematics. |
| 19126 | If deflationary truth is not explanatory, truth axioms should be 'conservative', proving nothing new [Halbach/Leigh] |
| Full Idea: If truth does not have any explanatory force, as some deflationists claim, the axioms of truth should not allow us to prove any new theorems that do not involve the truth predicate. That is, a deflationary axiomatisation of truth should be 'conservative'. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.3) | |
| A reaction: So does truth have 'explanatory force'? These guys are interested in explaining theorems of arithmetic, but I'm more interested in real life. People do daft things because they have daft beliefs. Logic should be neutral, but truth has values? |
| 19129 | The FS axioms use classical logical, but are not fully consistent [Halbach/Leigh] |
| Full Idea: It is a virtue of the Friedman-Sheard axiomatisation that it is thoroughly classical in its logic. Its drawback is that it is ω-inconsistent. That is, it proves &exists;x¬φ(x), but proves also φ(0), φ(1), φ(2), … | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 4.3) | |
| A reaction: It seems the theory is complete (and presumably sound), yet not fully consistent. FS also proves the finite levels of Tarski's hierarchy, but not the transfinite levels. |
| 19130 | KF is formulated in classical logic, but describes non-classical truth, which allows truth-value gluts [Halbach/Leigh] |
| Full Idea: KF is formulated in classical logic, but describes a non-classical notion of truth. It allow truth-value gluts, making some sentences (such as the Liar) both true and not-true. Some authors add an axiom ruling out such gluts. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 4.4) | |
| A reaction: [summary, which I hope is correct! Stanford is not wholly clear] |
| 10121 | Contradiction is not a sign of falsity, nor lack of contradiction a sign of truth [Pascal] |
| Full Idea: Contradiction is not a sign of falsity, nor the lack of contradiction a sign of truth. | |
| From: Blaise Pascal (works [1660]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: [Quoted in Auden and Kronenberger's Book of Aphorisms] Presumably we would now say that contradiction is a purely formal, syntactic notion, and not a semantic one. If you hit a contradiction, something has certainly gone wrong. |
| 19121 | We can reduce properties to true formulas [Halbach/Leigh] |
| Full Idea: One might say that 'x is a poor philosopher' is true of Tom instead of saying that Tom has the property of being a poor philosopher. We quantify over formulas instead of over definable properties, and thus reduce properties to truth. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.1) | |
| A reaction: [compressed] This stuff is difficult (because the axioms are complex and hard to compare), but I am excited (yes!) about this idea. Their point is that you need a truth predicate within the object language for this, which disquotational truth forbids. |
| 19122 | Nominalists can reduce theories of properties or sets to harmless axiomatic truth theories [Halbach/Leigh] |
| Full Idea: The reduction of second-order theories (of properties or sets) to axiomatic theories of truth is a form of reductive nominalism, replacing existence assumptions (e.g. comprehension axioms) by innocuous assumptions about the truth predicate. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.1) | |
| A reaction: I'm currently thinking that axiomatic theories of truth are the most exciting development in contemporary philosophy. See Halbach and Horsten. |
| 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. |
| 536 | We should follow the law in public, and nature in private [Antiphon] |
| Full Idea: A man can best conduct himself in harmony with justice, if when in company of witnesses he upholds the laws, and when alone without witnesses he upholds the edicts of nature. | |
| From: Antiphon (fragments/reports [c.439 BCE], B44), quoted by Anon (Oxy) - Oxyrhynchus Papyrus XI.1364 | |
| A reaction: I'm not sure how you identify the 'edicts of nature', without guidance from other people or the law. Natural behaviour can be pretty grim. |
| 1557 | To gain the greatest advantage only treat law as important when other people are present [Antiphon] |
| Full Idea: The way to get maximum advantage to yourself from justice is to treat the laws as important when other people are present, but when there is nobody else with you to value the demands of nature. | |
| From: Antiphon (fragments/reports [c.439 BCE], B44A), quoted by Anon (Oxy) - Oxyrhynchus Papyrus 1364A | |
| A reaction: This looks like a pretty good description of the majority of people active in politics. |
| 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? |
| 540 | The way you spend your time will form your character [Antiphon] |
| Full Idea: One's character must necessarily grow like that with which one spends the greater part of the day. | |
| From: Antiphon (fragments/reports [c.439 BCE], B62), quoted by John Stobaeus - Anthology 3.31.41 |
| 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). |
| 539 | Nothing is worse for mankind than anarchy [Antiphon] |
| Full Idea: Nothing is worse for mankind than anarchy. | |
| From: Antiphon (fragments/reports [c.439 BCE], B61), quoted by (who?) - where? |
| 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? |