22 ideas
| 16000 | Fixed ideas should be tackled aggressively [Kierkegaard] |
| Full Idea: Fixed ideas are like a cramp in your foot: the best remedy is to stomp on them. | |
| From: Søren Kierkegaard (The Journals of Kierkegaard [1850], JP-III, 635) | |
| A reaction: Sound philosophical advice at any time. [SY] Does this apply in seminars, as well as in private meditation? [PG] |
| 16012 | Philosophy can't be unbiased if it ignores language, as that is no more independent than individuals are [Kierkegaard] |
| Full Idea: If the claim of philosophers to be unbiased were all it pretends to be, it would have to take account of language and its significance...Language is partly given and partly develops freely. As individuals cannot be truly independent, so too with language. | |
| From: Søren Kierkegaard (The Journals of Kierkegaard [1850], 1840.07.18) | |
| A reaction: A surprisingly prophetic entry from Kierkegaard anticipating the linguistic turn. [SY] |
| 18951 | For scientific purposes there is a precise concept of 'true-in-L', using set theory [Putnam] |
| Full Idea: For a language L there is a predicate 'true-in-L' which one can employ for all scientific purposes in place of intuitive truth, and this predicate admits of a precise definition using only the vocabulary of L itself plus set theory. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.2) | |
| A reaction: He refers, of course, to Tarski's theory. I'm unclear of the division between 'scientific purposes' and the rest of life (which is why some people embrace 'minimal' theories of ordinary truth). I'm struck by set theory being a necessary feature. |
| 18953 | Modern notation frees us from Aristotle's restriction of only using two class-names in premises [Putnam] |
| Full Idea: In modern notation we can consider potential logical principles that Aristotle never considered because of his general practice of looking at inferences each of whose premises involved exactly two class-names. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.3) | |
| A reaction: Presumably you can build up complex inferences from a pair of terms, just as you do with pairs in set theory. |
| 18949 | The universal syllogism is now expressed as the transitivity of subclasses [Putnam] |
| Full Idea: On its modern interpretation, the validity of the inference 'All S are M; All M are P; so All S are P' just expresses the transitivity of the relation 'subclass of'. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.1) | |
| A reaction: A simple point I've never quite grasped. Since lots of syllogisms can be expressed as Venn Diagrams, in which the circles are just sets, it's kind of obvious really. So why does Sommers go back to 'terms'? See 'Term Logic'. |
| 18952 | '⊃' ('if...then') is used with the definition 'Px ⊃ Qx' is short for '¬(Px & ¬Qx)' [Putnam] |
| Full Idea: The symbol '⊃' (read 'if...then') is used with the definition 'Px ⊃ Qx' ('if Px then Qx') is short for '¬(Px & ¬Qx)'. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.3) | |
| A reaction: So ⊃ and → are just abbreviations, and not really a proper part of the language. Notoriously, though, this is quite a long way from what 'if...then' means in ordinary English, and it leads to paradoxical oddities. |
| 18958 | In type theory, 'x ∈ y' is well defined only if x and y are of the appropriate type [Putnam] |
| Full Idea: In the theory of types, 'x ∈ y' is well defined only if x and y are of the appropriate type, where individuals count as the zero type, sets of individuals as type one, sets of sets of individuals as type two. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.6) |
| 18954 | Before the late 19th century logic was trivialised by not dealing with relations [Putnam] |
| Full Idea: It was essentially the failure to develop a logic of relations that trivialised the logic studied before the end of the nineteenth century. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.3) | |
| A reaction: De Morgan, Peirce and Frege were, I believe, the people who put this right. |
| 18956 | Asserting first-order validity implicitly involves second-order reference to classes [Putnam] |
| Full Idea: The natural understanding of first-order logic is that in writing down first-order schemata we are implicitly asserting their validity, that is, making second-order assertions. ...Thus even quantification theory involves reference to classes. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.3) | |
| A reaction: If, as a nominalist, you totally rejected classes, presumably you would get by in first-order logic somehow. To say 'there are no classes so there is no logical validity' sounds bonkers. |
| 18962 | Unfashionably, I think logic has an empirical foundation [Putnam] |
| Full Idea: Today, the tendency among philosophers is to assume that in no sense does logic itself have an empirical foundation. I believe this tendency is wrong. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.9) | |
| A reaction: I agree, not on the basis of indispensability to science, but on the basis of psychological processes that lead from experience to logic. Russell and Quine are Putnam's allies here, and Frege is his opponent. Putnam developed a quantum logic. |
| 18961 | We can identify functions with certain sets - or identify sets with certain functions [Putnam] |
| Full Idea: Instead of identifying functions with certain sets, I might have identified sets with certain functions. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.9) |
| 18955 | Having a valid form doesn't ensure truth, as it may be meaningless [Putnam] |
| Full Idea: I don't think all substitution-instances of a valid schema are 'true'; some are clearly meaningless, such as 'If all boojums are snarks and all snarks are egglehumphs, then all boojums are egglehumphs'. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.3) | |
| A reaction: This seems like a very good challenge to Quine's claim that it is only form which produces a logical truth. Keep deductive and semantic consequence separate, with two different types of 'logical truth'. |
| 18959 | Sets larger than the continuum should be studied in an 'if-then' spirit [Putnam] |
| Full Idea: Sets of a very high type or very high cardinality (higher than the continuum, for example) should today be investigated in an 'if-then' spirit. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.7) | |
| A reaction: This attitude goes back to Hilbert, but it fits with Quine's view of what is indispensable for science. It is hard to see a reason for the cut-off, just looking at the logic of expanding sets. |
| 18957 | Nominalism only makes sense if it is materialist [Putnam] |
| Full Idea: Nominalists must at heart be materialists, or so it seems to me: otherwise their scruples are unintelligible. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.5) | |
| A reaction: This is modern nominalism - the rejection of abstract objects. I largely plead guilty to both charges. |
| 18950 | Physics is full of non-physical entities, such as space-vectors [Putnam] |
| Full Idea: Physics is full of references to such 'non-physical' entities as state-vectors, Hamiltonians, Hilbert space etc. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.2) | |
| A reaction: I take these to be concepts which are 'abstracted' from the physical facts, and so they don't strike me as being much of an ontological problem, or an objection to nominalism (which Putnam takes them to be). |
| 18960 | Most predictions are uninteresting, and are only sought in order to confirm a theory [Putnam] |
| Full Idea: Scientists want successful predictions in order to confirm their theories; they do not want theories in order to obtain the predictions, which are in some cases of not the slightest interest in themselves. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.8) | |
| A reaction: Equally, we might only care about the prediction, and have no interest at all in the theory. Farmers want weather predictions, not a PhD in meteorology. |
| 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? |
| 16003 | If people marry just because they are lonely, that is self-love, not love [Kierkegaard] |
| Full Idea: People despair about being lonely and therefore get married. But is this love? I should say it is self-love. | |
| From: Søren Kierkegaard (The Journals of Kierkegaard [1850], JP-III, 40-41) | |
| A reaction: If you decide to marry someone because you don't want to be an old maid/bachelor in your elder years, try to actually love the person you're marrying. Not just for money or sex. [SY] |
| 21910 | Our destiny is the highest pitch of world-weariness [Kierkegaard] |
| Full Idea: Our destiny in this life is to be brought to the highest pitch of world-weariness. | |
| From: Søren Kierkegaard (The Journals of Kierkegaard [1850], 1855.09.25), quoted by Alastair Hannay - Kierkegaard 10 | |
| A reaction: The beginning of his last entry. Hardly a great general truth, but interesting. Should we aspire to exhaust life? |
| 16001 | Life may be understood backwards, but it has to be lived forwards [Kierkegaard] |
| Full Idea: Philosophy is perfectly right in saying that life must be understood backwards. But then it forgets the other side - that it must be lived forwards. | |
| From: Søren Kierkegaard (The Journals of Kierkegaard [1850], JP-III, 635) | |
| A reaction: Some of the best philosophers dwell too much on philosophy, history and the past, while forgetting to actually live and enjoy their lives. [SY] |
| 16008 | The best way to be a Christian is without 'Christianity' [Kierkegaard] |
| Full Idea: One best becomes a Christian - without 'Christianity'. | |
| From: Søren Kierkegaard (The Journals of Kierkegaard [1850], JP-1:214) | |
| A reaction: A very healthy attitude for followers of Jesus, given today's television evangelists, religious fundamentalist and zealots. [SY] |
| 20735 | We need to see that Christianity cannot be understood [Kierkegaard] |
| Full Idea: The problem is not to understand Christianity, but to understand that it cannot be understood. | |
| From: Søren Kierkegaard (The Journals of Kierkegaard [1850], p.146), quoted by Kevin Aho - Existentialism: an introduction 1 'Roots' | |
| A reaction: This seems to cut us intellectually adrift. We could say the same of supporting Real Madrid. There has to be some magnetism which holds our attention, and there must be something to say about that. |