50 ideas
| 21474 | Metaphysics studies the inexplicable ends of explanation [Schopenhauer] |
| Full Idea: The plummet touches the bottom of the sea now at a greater depth, now at a less, but is bound to reach it somewhere sooner or later; the study of this inexplicable devolves upon metaphysics. | |
| From: Arthur Schopenhauer (Parerga and Paralipomena [1851], I:1) | |
| A reaction: This definition of metapysics contains the germ of despair about the subject. Does he hope that metaphysicians can explain what nobody else can? |
| 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. |
| 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. |
| 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. |
| 21470 | For me the objective thing-in-itself is the will [Schopenhauer] |
| Full Idea: Thing in itself signifies that which exists independently of our perception, that which actually is; …to Kant it was '= x'; to me it is will. | |
| From: Arthur Schopenhauer (Parerga and Paralipomena [1851], IV:61) | |
| A reaction: Does he mean his own will, which is plausible since he has direct experience of it, or is he referring will in general - whatever that is? |
| 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. |
| 21479 | Knowledge is not power! Ignorant people possess supreme authority [Schopenhauer] |
| Full Idea: Knowledge is power. The devil it is! One man can have a great deal of knowledge without its giving him the least power, while another possesses supreme authority but next to no knowledge. | |
| From: Arthur Schopenhauer (Parerga and Paralipomena [1851], III:43) | |
| A reaction: He is referring to Bacon's famous adage. Bacon may be right about military affairs, but not about politics. |
| 21476 | A priori propositions are those we could never be seriously motivated to challenge [Schopenhauer] |
| Full Idea: A dictate of reason is the name we give to certain propositions which we hold to be true without investigation, and of which we think ourselves so firmly convinced we should be incapable of seriously testing them even if we wanted to. | |
| From: Arthur Schopenhauer (Parerga and Paralipomena [1851], I:12) | |
| A reaction: This is closer to the cautious way modern thinkers are inclined to express the idea. Even Quine would be reasonably happy with this. |
| 21473 | All knowledge and explanation rests on the inexplicable [Schopenhauer] |
| Full Idea: The fundament upon which all our knowledge and learning rests is the inexplicable. It is to this that every explanation, through few or many intermediary stages, leads. | |
| From: Arthur Schopenhauer (Parerga and Paralipomena [1851], I:1) | |
| A reaction: This is obviously true, and the only question is whether it is a necessary or a contingent truth. |
| 21478 | Half our thinking is unconscious, and we reach conclusions while unaware of premises [Schopenhauer] |
| Full Idea: One might almost believe that half our thinking takes place unconsciously.. Usually we arrive at a conclusion without having clearly thought about the premises which lead to it. | |
| From: Arthur Schopenhauer (Parerga and Paralipomena [1851], III:40) | |
| A reaction: Schopenhauer was a major pioneer of this crucial idea. I'm beginning to think it is much greater than a half. |
| 21477 | We don't control our own thinking [Schopenhauer] |
| Full Idea: Thoughts come not when we want but when they want. | |
| From: Arthur Schopenhauer (Parerga and Paralipomena [1851], III:37) | |
| A reaction: One of my favourite Nietzsche ideas originated in Schopenhauer! |
| 21475 | All of our concepts are borrowed from perceptual knowledge [Schopenhauer] |
| Full Idea: The entire property of a concept consists in nothing more than what has been begged and borrowed from perceptual knowledge, which is the true and inexhaustible source of all insight. | |
| From: Arthur Schopenhauer (Parerga and Paralipomena [1851], I:9) | |
| A reaction: Schopenhauer is usually seen as a sort of idealist, but this is a full endorsement of the empirical view of concepts, to which I largely subscribe. Note that he talks of 'knowledge', rather than of 'experience'. |
| 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. |
| 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. |
| 21372 | Aesthetics concerns how we can take pleasure in an object, with no reference to the will [Schopenhauer] |
| Full Idea: The central problem of aesthetics is how satisfaction with and pleasure in an object are possible without any reference thereof to our willing. | |
| From: Arthur Schopenhauer (Parerga and Paralipomena [1851], II:415), quoted by Christopher Janaway - Schopenhauer 6 'Aesthetic' | |
| A reaction: This does seem a good distinction. We can divide pleasures into willed and unwilled. Compare thinking that some remote stranger (in a photograph) is very beautiful, with falling in love with someone. |
| 21488 | The beautiful is a perception of Plato's Forms, which eliminates the will [Schopenhauer] |
| Full Idea: In the beautiful we always perceive the intrinsic and primary form of animate and inanimate nature, that is to say Plato's Ideas thereof. …When an aesthetic perception occurs the will completely vanishes from consciousness. | |
| From: Arthur Schopenhauer (Parerga and Paralipomena [1851], XIX:205) | |
| A reaction: An essential Schopenauer idea. Iris Murdoch said something similar. |
| 21483 | Man is essentially a dreadful wild animal [Schopenhauer] |
| Full Idea: Man is at bottom a dreadful wild animal. | |
| From: Arthur Schopenhauer (Parerga and Paralipomena [1851], VIII:114) | |
| A reaction: As an example he cites the slave owners in the United States. |
| 1590 | The just man does not harm his enemies, but benefits everyone [Plato] |
| Full Idea: First, Socrates, you told me justice is harming your enemies and helping your friends. But later it seemed that the just man, since everything he does is for someone's benefit, never harms anyone. | |
| From: Plato (Clitophon [c.372 BCE], 410b) | |
| A reaction: Socrates certainly didn't subscribe to the first view, which is the traditional consensus in Greek culture. In general Socrates agreed with the views later promoted by Jesus. |
| 21466 | Pleasure is weaker, and pain stronger, than we expect [Schopenhauer] |
| Full Idea: As a rule we find pleasure much less pleasurable, pain much more painful than we expected. | |
| From: Arthur Schopenhauer (Parerga and Paralipomena [1851], XII:149) | |
| A reaction: Never go on holiday with Schopenhauer. This is more accurate about pain, I think. |
| 21484 | A man's character can be learned from a single characteristic action [Schopenhauer] |
| Full Idea: As a botanist can recognise the whole plant from one leaf, …so an accurate knowledge of a man's character can be arrived at from a single characteristic action. | |
| From: Arthur Schopenhauer (Parerga and Paralipomena [1851], VIII:118) | |
| A reaction: Very true. Great novelists specialise in such observations. One word can reveal a character, as well as one action. |
| 21482 | The five Chinese virtues: pity, justice, politeness, wisdom, honesty [Schopenhauer] |
| Full Idea: The Chinese name five cardinal virtues: pity, justice, politeness, wisdom and honesty. | |
| From: Arthur Schopenhauer (Parerga and Paralipomena [1851], VIII:110) | |
| A reaction: I like politeness being on the list, though it seems rather superficial to be a virtue of character. Respect would be better. |
| 21481 | Buddhists wisely start with the cardinal vices [Schopenhauer] |
| Full Idea: Because of their profounder ethical and metaphysical insight, the Buddhists start not with the cardinal virtues but with cardinal vices, …which are lust, sloth, wrath and avarice (and maybe hatred). | |
| From: Arthur Schopenhauer (Parerga and Paralipomena [1851], VIII:110) | |
| A reaction: This may be right. Our lives are affected much more by the vices of others than by their virtues, and most virtuous behaviour aims at rectifying the bad effects of other people's vices. |
| 21480 | Boredom is only felt by those clever enough to need activity [Schopenhauer] |
| Full Idea: Only in the cleverest animals such as dogs and apes does the need for activity, and with that boredom, make itself felt. | |
| From: Arthur Schopenhauer (Parerga and Paralipomena [1851], III:50) | |
| A reaction: But it is much more frequently young creatures, of almost any kind, that seek constant activity, and get continually restless. The most active adults need not be the cleverest. |
| 21469 | Human life is a mistake, shown by boredom, which is direct awareness of the fact [Schopenhauer] |
| Full Idea: Human life must be some kind of mistake. ...Boredom is a direct proof that existence is in itself valueless, for boredom is nothing other than the sensation of the emptiness of existence. | |
| From: Arthur Schopenhauer (Parerga and Paralipomena [1851], XI:146) | |
| A reaction: I think it is a good advertisement for existentialism that it makes something more out of boredom than Schopenhauer does. |
| 21485 | The state only exists to defend citizens, from exterior threats, and from one another [Schopenhauer] |
| Full Idea: The state is essentially no more than an institution for the protection of the whole against attacks from without, and the protection of its individual members from attacks by one another. | |
| From: Arthur Schopenhauer (Parerga and Paralipomena [1851], IX:123) | |
| A reaction: He then has a swipe at Hegel for his inflated idea of the importance of the state. Schopenhauer is close to Hobbes on this one. |
| 21486 | Poverty and slavery are virtually two words for the same thing [Schopenhauer] |
| Full Idea: Poverty and slavery are only two forms - on might almost say two words for - the same thing, the essence of which is that a man's energies are expended for the most part not on his own behalf but on that of others. | |
| From: Arthur Schopenhauer (Parerga and Paralipomena [1851], IX:125) | |
| A reaction: The modern world is full of people who righteously despise slavery, but think only of the poor that it serves them right. |
| 21487 | The freedom of the press to sell poison outweighs its usefulness [Schopenhauer] |
| Full Idea: Freedom of the press must be regarded as a permit to sell poison. …I very much fear, therefore, that the dangers of press freedom outweigh its usefulness. | |
| From: Arthur Schopenhauer (Parerga and Paralipomena [1851], IX:127) | |
| A reaction: On the whole the modern world disagrees with this view, but watching the popular press in Britain in the last twenty years has made me sympathise with Schopenhauer. |
| 21471 | If suicide was quick and easy, most people would have done it by now [Schopenhauer] |
| Full Idea: Perhaps there is no one alive who would not already have put an end to his life if this end were something purely negative, a sudden cessation of existence. | |
| From: Arthur Schopenhauer (Parerga and Paralipomena [1851], XIII:158) | |
| A reaction: Nonsense, on the whole, but it is a nice question how many people would do it if it only took a painless instant. |
| 21467 | Would humanity still exist if sex wasn't both desired and pleasurable? [Schopenhauer] |
| Full Idea: If the act of procreation were neither the outcome of a desire nor accompanied by feelings of pleasure, but a matter to be decided on the basis of purely rational considerations, is it likely the human race would still exist? | |
| From: Arthur Schopenhauer (Parerga and Paralipomena [1851], XII:156) | |
| A reaction: This is almost certainly correct in the modern world. In tougher economic circumstances people seem desperate to have children who will help them survive. |
| 21472 | Only religion introduces serious issues to uneducated people [Schopenhauer] |
| Full Idea: Religion is the only means of introducing some notion of the high significance of life into the uncultivated heads of the masses. | |
| From: Arthur Schopenhauer (Parerga and Paralipomena [1851], XV:174) | |
| A reaction: Cf Philip Larkin's poem 'Church Going'. On the whole Schopenhauer didn't actually believe that our lives had any 'high significance'. |
| 21468 | The Creator created the possibilities for worlds, so should have made a better one than this possible [Schopenhauer] |
| Full Idea: The Creator created not only the world, but also created possibility itself; therefore he should have created the possibility of a better world than this one. | |
| From: Arthur Schopenhauer (Parerga and Paralipomena [1851], XII:156) | |
| A reaction: This is explicitly a response to Leibniz's claim that the Creator selected the best of all possible worlds from the available options. The Euthyphro Question hovers here: must the Creator accept what is possible (the platonic view), or create possibility? |