33 ideas
| 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. |
| 15435 | If you think universals are immanent, you must believe them to be sparse, and not every related predicate [Lewis] |
| Full Idea: Any theorist of universals as immanent had better hold a sparse theory; it is preposterous on its face that a thing has as many nonspatiotemporal parts as there are different predicates that it falls under, or different classes that it belongs to. | |
| From: David Lewis (Against Structural Universals [1986], 'Why believe') | |
| A reaction: I am firmly committed to sparse universal, and view the idea that properties are just predicates as the sort of nonsense that results from approaching philosophy too linguistically. |
| 15451 | I assume there could be natural properties that are not instantiated in our world [Lewis] |
| Full Idea: It is possible, I take it, that there might be simple natural properties different from any that instantiated within our world. | |
| From: David Lewis (Against Structural Universals [1986], 'Uninstantiated') | |
| A reaction: Interesting. Fine for Lewis, of course, for whom possibilities seem (to me) to be just logical possibilities. Even a scientific essentialist, though, must allow that different stuff might exist, which might have different intrinsic properties. |
| 15433 | Tropes are particular properties, which cannot recur, but can be exact duplicates [Lewis] |
| Full Idea: Tropes are supposed to be particularized properties: nonspatiotemporal parts of their instances which cannot occur repeatedly, but can be exact duplicates. | |
| From: David Lewis (Against Structural Universals [1986], 'Intro') | |
| A reaction: Russell's objection is that 'duplication' appears to be a non-trope universal. The account seems wrong for very close resemblance, which is accepted by everyone as being the same (e.g. in colour, for football shirts). |
| 15436 | Universals are meant to give an account of resemblance [Lewis] |
| Full Idea: Perhaps the main job of a theory of universals is to give an account of resemblance. | |
| From: David Lewis (Against Structural Universals [1986], 'Why believe') | |
| A reaction: This invites the quick reply, popular with some nominalists, of taking resemblance as primitive, and hence beyond explanation. |
| 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. |
| 15438 | We can add a primitive natural/unnatural distinction to class nominalism [Lewis] |
| Full Idea: To class nominalism we can add a primitive distinction between natural and unnatural classes. | |
| From: David Lewis (Against Structural Universals [1986], 'Why believe') | |
| A reaction: Lewis explores this elsewhere, but this looks like a very complex concept to play the role of a 'primitive'. Human conventions seem to be parts of nature. |
| 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). |
| 15448 | The 'magical' view of structural universals says they are atoms, even though they have parts [Lewis] |
| Full Idea: The 'magical' conception of structural universals says 'simple' must be distinguished from 'atomic'. A structural universal is never simple; it involves other, simpler, universals, but it is mereologically atomic. The other universals are not its parts. | |
| From: David Lewis (Against Structural Universals [1986], 'The magical') | |
| A reaction: Hence the 'magic' is for it to be an indissoluble unity, while acknowledging that it has parts. Personally I don't see much problem with this view, since universals already perform the magical feat of being 'instantiated', whatever that means. |
| 15449 | If 'methane' is an atomic structural universal, it has nothing to connect it to its carbon universals [Lewis] |
| Full Idea: What is it about the universal carbon that gets it involved in necessary connections with methane? Why not rubidium instead? The universal 'carbon' has nothing more in common with the universal methane than the universal rubidium has! | |
| From: David Lewis (Against Structural Universals [1986], 'The magical') | |
| A reaction: This is his objection to the 'magical' unity of structural universals. The point is that if methane is an atomic unity, as claimed, it can't have anything 'in common' with its components. |
| 15439 | The 'pictorial' view of structural universals says they are wholes made of universals as parts [Lewis] |
| Full Idea: On the 'pictorial' conception, a structural universal is isomorphic to its instances. ...It is an individual, a mereological composite, not a set. ...It is composed of simpler universals which are literally parts of it. | |
| From: David Lewis (Against Structural Universals [1986], 'The pictorial') | |
| A reaction: I'm not clear why Lewis labels this the 'pictorial' view. His other two views of structural universals are 'linguistic' and 'magical'. The linguistic is obviously wrong, and the magical doesn't sound promising. Must I vote for pictorial? |
| 15441 | The structural universal 'methane' needs the universal 'hydrogen' four times over [Lewis] |
| Full Idea: What is wrong with the pictorial conception is that if the structural universal 'methane' is to be an isomorph of the molecules that are its instances, it must have the universal 'hydrogen' as a part not just once, but four times over. | |
| From: David Lewis (Against Structural Universals [1986], 'The pictorial') | |
| A reaction: The point is that if hydrogen is a universal it must be unique, so there can't be four of them. To me this smacks of the hopeless mess theologians get into, because of bad premisses. Drop universals, and avoid this kind of stuff. |
| 15445 | Butane and Isobutane have the same atoms, but different structures [Lewis] |
| Full Idea: The stuctural universal 'isobutane' consists of the universal carbon four times over, hydrogen ten times over, and the universal 'bonded' thirteen times over - just like the universal 'butane'. | |
| From: David Lewis (Against Structural Universals [1986], 'Variants') | |
| A reaction: The point is that isobutane and butane have the same components in different structures. At least this is Lewis facing up to the problem of the 'flatness' of mereological wholes. |
| 15434 | Structural universals have a necessary connection to the universals forming its parts [Lewis] |
| Full Idea: There is a necessary connection between the instantiating of a structural universal by the whole and the instantiating of other universals by its parts. We can call the relation 'involvement', a nondescript word. | |
| From: David Lewis (Against Structural Universals [1986], 'What are') | |
| A reaction: In the case of a shape, I suppose the composing 'universals' [dunno what they are] will all be essential to the shape - that is, part of the very nature of the thing, loss of which would destroy the identity. |
| 15437 | We can't get rid of structural universals if there are no simple universals [Lewis] |
| Full Idea: We can't dispense with structural universals if we cannot be sure that there are any simples which can be involved in them. | |
| From: David Lewis (Against Structural Universals [1986], 'Why believe') | |
| A reaction: Lewis cites this as Armstrong's strongest reason for accepting structural universals (and he takes their requirement for an account of laws of nature as the weakest). I can't comprehend a world that lacks underlying simplicity. |
| 15446 | Composition is not just making new things from old; there are too many counterexamples [Lewis] |
| Full Idea: Not just any operation that makes new things from old is a form of composition! There is no sense in which my parents are part of me, and no sense in which two numbers are parts of their greatest common factor. | |
| From: David Lewis (Against Structural Universals [1986], 'Variants') | |
| A reaction: One of those rare moments when David Lewis seems to have approached a really sensible metaphysics. Further on he rejects all forms of composition apart from mereology. |
| 15440 | A whole is distinct from its parts, but is not a further addition in ontology [Lewis] |
| Full Idea: A whole is an extra item in our ontology only in the minimal sense that it is not identical to any of its proper parts; but it is not distinct from them either, so when we believe in the parts it is no extra burden to believe in the whole. | |
| From: David Lewis (Against Structural Universals [1986], 'The pictorial') | |
| A reaction: A little confusing, to be 'not identical' and yet 'not different'. As Lewis says elsewhere, the whole is one, and the parts are not. A crux. Essentialism implies a sort of holism, that parts with a structure constitute a new thing. |
| 15444 | Different things (a toy house and toy car) can be made of the same parts at different times [Lewis] |
| Full Idea: Different things can be made of the same parts at different times, as when the tinkertoy house is taken apart and put back together as a tinkertoy car. | |
| From: David Lewis (Against Structural Universals [1986], 'Variants') | |
| A reaction: More important than it looks! This is Lewis's evasion of the question of the structure of the parts. Times will individuate different structures, but if I take type-identical parts and make a house and a car simultaneously, are they type-identical? |
| 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. |
| 15450 | Maybe abstraction is just mereological subtraction [Lewis] |
| Full Idea: We could say that abstraction is just mereological subtraction of universals. | |
| From: David Lewis (Against Structural Universals [1986], 'Uninstantiated') | |
| A reaction: This only works, of course, for the theories that complex universals have simpler universals as 'parts'. This is just a passing surmise. I take it that abstraction only works for a thing whose unity survives the abstraction. |
| 15443 | Mathematicians abstract by equivalence classes, but that doesn't turn a many into one [Lewis] |
| Full Idea: When mathematicians abstract one thing from others, they take an equivalence class. ....But it is only superficially a one; underneath, a class are still many. | |
| From: David Lewis (Against Structural Universals [1986], 'The pictorial') | |
| A reaction: This is Frege's approach to abstraction, and it is helpful to have it spelled out that this is a mathematical technique, even when applied by Frege to obtaining 'direction' from classes of parallels. Too much philosophy borrows inappropriate techniques. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |