31 ideas
| 16943 | Philosophy is continuous with science, and has no external vantage point [Quine] |
| Full Idea: I see philosophy not as an a priori propaedeutic or groundwork for science, but as continuous with science. I see philosophy and science as in the same boat. …There is no external vantage point, no first philosophy. | |
| From: Willard Quine (Natural Kinds [1969], p.126) | |
| A reaction: Philosophy is generalisation. Science holds the upper hand, because it settles the subject-matter to be generalised. |
| 11064 | Classes can be reduced to propositional functions [Russell, by Hanna] |
| Full Idea: Russell held that classes can be reduced to propositional functions. | |
| From: report of Bertrand Russell (Mathematical logic and theory of types [1908]) by Robert Hanna - Rationality and Logic 2.4 | |
| A reaction: The exact nature of a propositional function is disputed amongst Russell scholars (though it is roughly an open sentence of the form 'x is red'). |
| 21677 | How can the not-true fail to be false, or the not-false fail to be true? [Cicero] |
| Full Idea: How can something that is not true not be false, or how can something that is not false not be true? | |
| From: M. Tullius Cicero (On Fate ('De fato') [c.44 BCE], 16.38) | |
| A reaction: We must at least distinguish between whether the contrary thing is not actually true, or whether we are prepared to assert that it is not true. The disjunction may seem to be a false dichotomy. 'He isn't good' may not entail 'he is evil'. |
| 6407 | The class of classes which lack self-membership leads to a contradiction [Russell, by Grayling] |
| Full Idea: The class of teaspoons isn't a teaspoon, so isn't a member of itself; but the class of non-teaspoons is a member of itself. The class of all classes which are not members of themselves is a member of itself if it isn't a member of itself! Paradox. | |
| From: report of Bertrand Russell (Mathematical logic and theory of types [1908]) by A.C. Grayling - Russell Ch.2 | |
| A reaction: A very compressed version of Russell's famous paradox, often known as the 'barber' paradox. Russell developed his Theory of Types in an attempt to counter the paradox. Frege's response was to despair of his own theory. |
| 16949 | Klein summarised geometry as grouped together by transformations [Quine] |
| Full Idea: Felix Klein's so-called 'Erlangerprogramm' in geometry involved characterizing the various branches of geometry by what transformations were irrelevant to each. | |
| From: Willard Quine (Natural Kinds [1969], p.137) |
| 10418 | Type theory seems an extreme reaction, since self-exemplification is often innocuous [Swoyer on Russell] |
| Full Idea: Russell's reaction to his paradox (by creating his theory of types) seems extreme, because many cases of self-exemplification are innocuous. The property of being a property is itself a property. | |
| From: comment on Bertrand Russell (Mathematical logic and theory of types [1908]) by Chris Swoyer - Properties 7.5 | |
| A reaction: Perhaps it is not enough that 'many cases' are innocuous. We are starting from philosophy of mathematics, where precision is essentially. General views about properties come later. |
| 10047 | Russell's improvements blocked mathematics as well as paradoxes, and needed further axioms [Russell, by Musgrave] |
| Full Idea: Unfortunately, Russell's new logic, as well as preventing the deduction of paradoxes, also prevented the deduction of mathematics, so he supplemented it with additional axioms, of Infinity, of Choice, and of Reducibility. | |
| From: report of Bertrand Russell (Mathematical logic and theory of types [1908]) by Alan Musgrave - Logicism Revisited §2 | |
| A reaction: The first axiom seems to be an empirical hypothesis, and the second has turned out to be independent of logic and set theory. |
| 23478 | Type theory means that features shared by different levels cannot be expressed [Morris,M on Russell] |
| Full Idea: Russell's theory of types avoided the paradoxes, but it had the result that features common to different levels of the hierarchy become uncapturable (since any attempt to capture them would involve a predicate which disobeyed the hierarchy restrictions). | |
| From: comment on Bertrand Russell (Mathematical logic and theory of types [1908]) by Michael Morris - Guidebook to Wittgenstein's Tractatus 2H |
| 21718 | Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets [Russell, by Linsky,B] |
| Full Idea: A defence of the ramified theory of types comes in seeing it as a system of intensional logic which includes the 'no class' account of sets, and indeed the whole development of mathematics, as just a part. | |
| From: report of Bertrand Russell (Mathematical logic and theory of types [1908]) by Bernard Linsky - Russell's Metaphysical Logic 6.1 | |
| A reaction: So Linsky's basic project is to save logicism, by resting on intensional logic (rather than extensional logic and set theory). I'm not aware that Linsky has acquired followers for this. Maybe Crispin Wright has commented? |
| 18126 | A set does not exist unless at least one of its specifications is predicative [Russell, by Bostock] |
| Full Idea: The idea is that the same set may well have different canonical specifications, i.e. there may be different ways of stating its membership conditions, and so long as one of these is predicative all is well. If none are, the supposed set does not exist. | |
| From: report of Bertrand Russell (Mathematical logic and theory of types [1908]) by David Bostock - Philosophy of Mathematics 8.1 |
| 18128 | Russell is a conceptualist here, saying some abstracta only exist because definitions create them [Russell, by Bostock] |
| Full Idea: It is a conceptualist approach that Russell is relying on. ...The view is that some abstract objects ...exist only because they are definable. It is the definition that would (if permitted) somehow bring them into existence. | |
| From: report of Bertrand Russell (Mathematical logic and theory of types [1908]) by David Bostock - Philosophy of Mathematics 8.1 | |
| A reaction: I'm suddenly thinking that predicativism is rather interesting. Being of an anti-platonist persuasion about abstract 'objects', I take some story about how we generate them to be needed. Psychological abstraction seems right, but a bit vague. |
| 18124 | Vicious Circle says if it is expressed using the whole collection, it can't be in the collection [Russell, by Bostock] |
| Full Idea: The Vicious Circle Principle says, roughly, that whatever involves, or presupposes, or is only definable in terms of, all of a collection cannot itself be one of the collection. | |
| From: report of Bertrand Russell (Mathematical logic and theory of types [1908], p.63,75) by David Bostock - Philosophy of Mathematics 8.1 | |
| A reaction: This is Bostock's paraphrase of Russell, because Russell never quite puts it clearly. The response is the requirement to be 'predicative'. Bostock emphasises that it mainly concerns definitions. The Principle 'always leads to hierarchies'. |
| 16939 | Mass terms just concern spread, but other terms involve both spread and individuation [Quine] |
| Full Idea: 'Yellow' and 'water' are mass terms, concerned only with spread; 'apple' and 'square' are terms of divided reference, concerned with both spread and individuation. | |
| From: Willard Quine (Natural Kinds [1969], p.124) | |
| A reaction: Would you like some apple? Pass me that water. It is helpful to see that it is a requirement of 'individuation' that is missing from terms for stuff. |
| 16948 | Once we know the mechanism of a disposition, we can eliminate 'similarity' [Quine] |
| Full Idea: Once we can legitimize a disposition term by defining the relevant similarity standard, we are apt to know the mechanism of the disposition, and so by-pass the similarity. | |
| From: Willard Quine (Natural Kinds [1969], p.135) | |
| A reaction: I love mechanisms, but can we characterise mechanisms without mentioning powers and dispositions? Quine's dream is to eliminate 'similarity'. |
| 16945 | We judge things to be soluble if they are the same kind as, or similar to, things that do dissolve [Quine] |
| Full Idea: Intuitively, what qualifies a thing as soluble though it never gets into water is that it is of the same kind as the things that actually did or will dissolve; it is similar to them. | |
| From: Willard Quine (Natural Kinds [1969], p.130) | |
| A reaction: If you can judge that the similar things 'will' dissolve, you can cut to the chase and judge that this thing will dissolve. |
| 16944 | Science is common sense, with a sophisticated method [Quine] |
| Full Idea: Sciences differ from common sense only in the degree of methodological sophistication. | |
| From: Willard Quine (Natural Kinds [1969], p.129) | |
| A reaction: Science is normal thinking about the world, but it is teamwork, with the bar set very high. |
| 16940 | Induction is just more of the same: animal expectations [Quine] |
| Full Idea: Induction is essentially only more of the same: animal expectation or habit formation. | |
| From: Willard Quine (Natural Kinds [1969], p.125) | |
| A reaction: My working definition of induction is 'learning from experience', but that doesn't disagree with Quine. Lipton has a richer account of different types of induction. Quine's point is that it rests on resemblance. |
| 16941 | Induction relies on similar effects following from each cause [Quine] |
| Full Idea: Induction expresses our hopes that similar causes will have similar effects. | |
| From: Willard Quine (Natural Kinds [1969], p.125) | |
| A reaction: Some top philosophers are also top teachers, and Quine was one of them, in his writings. He boils it down for the layman. Once again, he is pointing to the fundamental role of the similarity relation. |
| 16933 | Grue is a puzzle because the notions of similarity and kind are dubious in science [Quine] |
| Full Idea: What makes Goodman's example a puzzle is the dubious scientific standing of a general notion of similarity, or of kind. | |
| From: Willard Quine (Natural Kinds [1969], p.116) | |
| A reaction: Illuminating. It might be best expressed as revealing a problem with sortal terms, as employed by Geach, or by Wiggins. Grue is a bit silly, but sortals are subject to convention and culture. 'Natural' properties seem needed. |
| 16934 | General terms depend on similarities among things [Quine] |
| Full Idea: The usual general term, whether a common noun or a verb or an adjective, owes its generality to some resemblance among the things referred to. | |
| From: Willard Quine (Natural Kinds [1969], p.116) | |
| A reaction: Quine has a nice analysis of the basic role of similarity in a huge amount of supposedly strict scientific thought. |
| 16938 | To learn yellow by observation, must we be told to look at the colour? [Quine] |
| Full Idea: According to the 'respects' view, our learning of yellow by ostension would have depended on our first having been told or somehow apprised that it was going to be a question of color. | |
| From: Willard Quine (Natural Kinds [1969], p.122) | |
| A reaction: Quine suggests there is just one notion of similarity, and respects can be 'abstracted' afterwards. Even the ontologically ruthless Quine admits psychological abstraction! |
| 8486 | Standards of similarity are innate, and the spacing of qualities such as colours can be mapped [Quine] |
| Full Idea: A standard of similarity is in some sense innate. The spacing of qualities (such as red, pink and blue) can be explored and mapped in the laboratory by experiments. They are needed for all learning. | |
| From: Willard Quine (Natural Kinds [1969], p.123) | |
| A reaction: This reasserts Hume's original point in more scientific terms. It is one of the undeniable facts about our perceptions of qualities and properties, no matter how platonist your view of universals may be. |
| 16947 | Similarity is just interchangeability in the cosmic machine [Quine] |
| Full Idea: Things are similar to the extent that they are interchangeable parts of the cosmic machine. | |
| From: Willard Quine (Natural Kinds [1969], p.134) | |
| A reaction: This is a major idea for Quine, because it is a means to gradually eliminate the fuzzy ideas of 'resemblance' or 'similarity' or 'natural kind' from science. I love it! Two tigers are same insofar as they are substitutable. |
| 16932 | Projectible predicates can be universalised about the kind to which they refer [Quine] |
| Full Idea: 'Projectible' predicates are predicates F and G whose shared instances all do count, for whatever reason, towards confirmation of 'All F are G'. ….A projectible predicate is one that is true of all and only the things of a kind. | |
| From: Willard Quine (Natural Kinds [1969], p.115-6) | |
| A reaction: Both Quine and Goodman are infuriatingly brief about the introduction of this concept. 'Red' is true of all ripe tomatoes, but not 'only' of them. Hardly any predicates are true only of one kind. Is that a scholastic 'proprium'? |
| 21667 | Oratory and philosophy are closely allied; orators borrow from philosophy, and ornament it [Cicero] |
| Full Idea: There is a close alliance between the orator and the philosophical system of which I am a follower, since the orator borrows subtlely from the Academy, and repays the loan by giving to it a copious and flowing style and rhetorical ornament. | |
| From: M. Tullius Cicero (On Fate ('De fato') [c.44 BCE], 02.03) | |
| A reaction: It is a misundertanding to think that rhetoric and philosophy are seen as in necessary opposition. Philosophers just seemed to think that oratory works a lot better if it is truthful. |
| 21678 | If desire is not in our power then neither are choices, so we should not be praised or punished [Cicero] |
| Full Idea: If the cause of desire is not situated within us, even desire itself is also not in our power. ...It follows that neither assent nor action is in our power. Hence there is no justice in either praise or blame, either honours or punishments. | |
| From: M. Tullius Cicero (On Fate ('De fato') [c.44 BCE], 17.40) | |
| A reaction: This is the view of 'old philosophers', but I'm unsure which ones. Cicero spurns this view. It is obvious that the causes of our desires are largely out of our control. Responsibility seems to concern what we do about our desires. |
| 7375 | Quine probably regrets natural kinds now being treated as essences [Quine, by Dennett] |
| Full Idea: The concept of natural kinds was reintroduced by Quine, who may now regret the way it has become a stand-in for the dubious but covertly popular concept of essences. | |
| From: report of Willard Quine (Natural Kinds [1969]) by Daniel C. Dennett - Consciousness Explained 12.2 n2 | |
| A reaction: He is right that Quine would regret it, and he is right that we can't assume that there are necessary essences just because there seem to be stable natural kinds, but personally I am an essentialist, so I'm not that bothered. |
| 16935 | If similarity has no degrees, kinds cannot be contained within one another [Quine] |
| Full Idea: If similarity has no degrees there is no containing of kinds within broader kinds. If colored things are a kind, they are similar, but red things are too narrow for a kind. If red things are a kind, colored things are not similar, and it's too broad. | |
| From: Willard Quine (Natural Kinds [1969], p.118) | |
| A reaction: [compressed] I'm on Quine's side with this. We glibly talk of 'kinds', but the criteria for sorting things into kinds seems to be a mess. Quine goes on to offer a better account than the (diadic, yes-no) one rejected here. |
| 16936 | Comparative similarity allows the kind 'colored' to contain the kind 'red' [Quine] |
| Full Idea: With the triadic relation of comparative similarity, kinds can contain one another, as well as overlapping. Red and colored things can both count as kinds. Colored things all resemble one another, even though less than red things do. | |
| From: Willard Quine (Natural Kinds [1969], p.119) | |
| A reaction: [compressed] Quine claims that comparative similarity is necessary for kinds - that there be some 'foil' in a similarity - that A is more like C than B is. |
| 16937 | You can't base kinds just on resemblance, because chains of resemblance are a muddle [Quine] |
| Full Idea: If kinds are based on similarity, this has the Imperfect Community problem. Red round, red wooden and round wooden things all resemble one another somehow. There may be nothing outside the set resembling them, so it meets the definition of kind. | |
| From: Willard Quine (Natural Kinds [1969], p.120) | |
| A reaction: [ref. to Goodman 'Structure' 2nd 163- , which attacks Carnap on this] This suggests an invocation of Wittgenstein's family resemblance, which won't be much help for natural kinds. |
| 16942 | It is hard to see how regularities could be explained [Quine] |
| Full Idea: Why there have been regularities is an obscure question, for it is hard to see what would count as an answer. | |
| From: Willard Quine (Natural Kinds [1969], p.126) | |
| A reaction: This is the standard pessimism of the 20th century Humeans, but it strikes me as comparable to the pessimism about science found in Locke and Hume. Regularities are explained all the time by scientists, though the lowest level may be hopeless. |