28 ideas
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
| A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
| A reaction: Each expansion brings a limitation, but then you can expand again. |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
| 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. |
| 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. |
| 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? |
| 15473 | How does anything get outside itself? [Fodor, by Martin,CB] |
| Full Idea: Fodor asks the stirring and basic question 'How does anything get outside itself?' | |
| From: report of Jerry A. Fodor (works [1986]) by C.B. Martin - The Mind in Nature 03.6 | |
| A reaction: Is this one of those misconceived questions, like major issues concerning 'what's it like to be?' In what sense am I outside myself? Is a mind any more mysterious than a shadow? |
| 2981 | Is intentionality outwardly folk psychology, inwardly mentalese? [Lyons on Fodor] |
| Full Idea: For Fodor the intentionality of the propositional-attitude vocabulary of our folk psychology is the outward expression of the inward intentionality of the language of the brain. | |
| From: comment on Jerry A. Fodor (works [1986]) by William Lyons - Approaches to Intentionality p.39 | |
| A reaction: I would be very cautious about this. Folk psychology works, so it must have a genuine basis in how brains work, but it breaks down in unusual situations, and might even be a total (successful) fiction. |
| 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. |
| 2985 | Are beliefs brains states, but picked out at a "higher level"? [Lyons on Fodor] |
| Full Idea: Fodor holds that beliefs are brain states or processes, but picked out at a 'higher' or 'special science' level. | |
| From: comment on Jerry A. Fodor (works [1986]) by William Lyons - Approaches to Intentionality p.82 | |
| A reaction: I don't think you can argue with this. Levels of physical description exist (e.g. pure physics tells you nothing about the weather), and I think 'process' is the best word for the mind (Idea 4931). |
| 3135 | Is thought a syntactic computation using representations? [Fodor, by Rey] |
| Full Idea: The modest mentalism of the Computational/Representational Theory of Thought (CRTT), associated with Fodor, says mental processes are computational, defined over syntactically specified entities, and these entities represent the world (are also semantic). | |
| From: report of Jerry A. Fodor (works [1986]) by Georges Rey - Contemporary Philosophy of Mind Int.3 | |
| A reaction: This seems to imply that if you built a machine that did all these things, it would become conscious, which sounds unlikely. Do footprints 'represent' feet, or does representation need prior consciousness? |
| 2983 | Maybe narrow content is physical, broad content less so [Lyons on Fodor] |
| Full Idea: Fodor is concerned with producing a realist and physicalist account of 'narrow content' (i.e. wholly in-the-head content). | |
| From: comment on Jerry A. Fodor (works [1986]) by William Lyons - Approaches to Intentionality p.54 | |
| A reaction: The emergence of 'wide' content has rather shaken Fodor's game plan. We can say "Oh dear, I thought I was referring to H2O", so there must be at least some narrow aspect to reference. |
| 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. |