41 ideas
| 16512 | Semantic facts are preferable to transcendental philosophical fiction [Wiggins] |
| Full Idea: Semantical fact is almost always more interesting than transcendental philosophical fiction. | |
| From: David Wiggins (Sameness and Substance [1980], 3.1 n4) | |
| A reaction: An interesting expression of a more sophisticated recent allegiance to linguistic philosophy. There is still a strong allegiance to semantics as a major branch of philosophy, despite caution (e.g. from Nathan Salmon) about its scope. |
| 17453 | The meaning of a number isn't just the numerals leading up to it [Heck] |
| Full Idea: My knowing what the number '33' denotes cannot consist in my knowing that it denotes the number of decimal numbers between '1' and '33', because I would know that even if it were in hexadecimal (which I don't know well). | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5) | |
| A reaction: Obviously you wouldn't understand '33' if you didn't understand what '33 things' meant. |
| 17457 | A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck] |
| Full Idea: An appreciation of the connection between sameness of number and equinumerosity that it reports is essential to even the most primitive grasp of the concept of cardinal number. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 6) |
| 17448 | In counting, numerals are used, not mentioned (as objects that have to correlated) [Heck] |
| Full Idea: One need not conceive of the numerals as objects in their own right in order to count. The numerals are not mentioned in counting (as objects to be correlated with baseball players), but are used. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 3) | |
| A reaction: He observes that when you name the team, you aren't correlating a list of names with the players. I could correlate any old tags with some objects, and you could tell me the cardinality denoted by the last tag. I do ordinals, you do cardinals. |
| 17455 | Is counting basically mindless, and independent of the cardinality involved? [Heck] |
| Full Idea: I am not denying that counting can be done mindlessly, without making judgments of cardinality along the way. ...But the question is whether counting is, as it were, fundamentally a mindless exercise. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5) | |
| A reaction: He says no. It seems to me like going on a journey, where you can forget where you are going and where you have got to so far, but those underlying facts are always there. If you just tag things with unknown foreign numbers, you aren't really counting. |
| 17456 | Counting is the assignment of successively larger cardinal numbers to collections [Heck] |
| Full Idea: Counting is not mere tagging: it is the successive assignment of cardinal numbers to increasingly large collections of objects. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5) | |
| A reaction: That the cardinals are 'successive' seems to mean that they are ordinals as well. If you don't know that 'seven' means a cardinality, as well as 'successor of six', you haven't understood it. Days of the week have successors. Does PA capture cardinality? |
| 17529 | Maybe the concept needed under which things coincide must also yield a principle of counting [Wiggins] |
| Full Idea: My thesis C says that to specify something or other under which a and b coincide is to specify a concept f which qualifies for this purpose only if it yields a principle of counting for fs. ...I submit that C is false, though a near miss. | |
| From: David Wiggins (Sameness and Substance [1980], 1.1) |
| 17530 | The sortal needed for identities may not always be sufficient to support counting [Wiggins] |
| Full Idea: My principle C seems unnecessary ...since it is one thing to see how many fs there are...but another to have a perfectly general method. ...One could answer whether this f-compliant is the same as that one, but there are too many ways to articulate it. | |
| From: David Wiggins (Sameness and Substance [1980], 2.8) | |
| A reaction: His famous example is trying to count the Pope's crown, which is made of crowns. A clearer example might be a rectangular figure divided up into various overlapping rectangles. Individuation is easy, but counting is contextual. |
| 17450 | Understanding 'just as many' needn't involve grasping one-one correspondence [Heck] |
| Full Idea: It is far from obvious that knowing what 'just as many' means requires knowing what a one-one correspondence is. The notion of a one-one correspondence is very sophisticated, and it is far from clear that five-year-olds have any grasp of it. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 4) | |
| A reaction: The point is that children decide 'just as many' by counting each group and arriving at the same numeral, not by matching up. He cites psychological research by Gelman and Galistel. |
| 17451 | We can know 'just as many' without the concepts of equinumerosity or numbers [Heck] |
| Full Idea: 'Just as many' is independent of the ability to count, and we shouldn't characterise equinumerosity through counting. It is also independent of the concept of number. Enough cookies to go round doesn't need how many cookies. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 4) | |
| A reaction: [compressed] He talks of children having an 'operational' ability which is independent of these more sophisticated concepts. Interesting. You see how early man could relate 'how many' prior to the development of numbers. |
| 17459 | Frege's Theorem explains why the numbers satisfy the Peano axioms [Heck] |
| Full Idea: The interest of Frege's Theorem is that it offers us an explanation of the fact that the numbers satisfy the Dedekind-Peano axioms. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 6) | |
| A reaction: He says 'explaining' does not make it more fundamental, since all proofs explain why their conclusions hold. |
| 17454 | Children can use numbers, without a concept of them as countable objects [Heck] |
| Full Idea: For a long time my daughter had no understanding of the question of how many numerals or numbers there are between 'one' and 'five'. I think she lacked the concept of numerals as objects which can themselves be counted. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5) | |
| A reaction: I can't make any sense of numbers actually being objects, though clearly treating all sorts of things as objects helps thinking (as in 'the victory is all that matters'). |
| 17458 | Equinumerosity is not the same concept as one-one correspondence [Heck] |
| Full Idea: Equinumerosity is not the same concept as being in one-one correspondence with. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 6) | |
| A reaction: He says this is the case, even if they are coextensive, like renate and cordate. You can see that five loaves are equinumerous with five fishes, without doing a one-one matchup. |
| 17449 | We can understand cardinality without the idea of one-one correspondence [Heck] |
| Full Idea: One can have a perfectly serviceable concept of cardinality without so much as having the concept of one-one correspondence. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 3) | |
| A reaction: This is the culmination of a lengthy discussion. It includes citations about the psychology of children's counting. Cardinality needs one group of things, and 1-1 needs two groups. |
| 16523 | Realist Conceptualists accept that our interests affect our concepts [Wiggins] |
| Full Idea: The realist conceptualist may cheerfully admit that the sortal concepts of which we are possessed are the creatures of our interests; …and also that there need be no one way in which we must articulate reality. | |
| From: David Wiggins (Sameness and Substance [1980], 5.2) | |
| A reaction: Wiggins calls himself a 'realist conceptualist'. In his terminology, I seem to be an 'anti-conceptualist realist'. The issue concerns aspects of reality that extend beyond our concepts. The 99th d.p. of the mass of the electron. |
| 16524 | Conceptualism says we must use our individuating concepts to grasp reality [Wiggins] |
| Full Idea: What Conceptualism entails is that, although horses and stars are not inventions or artefacts, in order to single out these things we must deploy a conceptual scheme which has been formed in such a way as to make singling them out possible. | |
| From: David Wiggins (Sameness and Substance [1980], 5.5) | |
| A reaction: I don't quite see why the 'singling out' role of the concepts is the only one that generates them, or makes them fit for purpose. In general, of course, our conceptual scheme is necessarily a response to our experience of the world. |
| 16526 | Animal classifications: the Emperor's, fabulous, innumerable, like flies, stray dogs, embalmed…. [Wiggins] |
| Full Idea: A Chinese encyclopedia classifies animals as belonging to the Emperor, embalmed, tame, sucking pigs, sirens, fabulous, stray dogs, included in this classification, frenzied, innumerable, drawn with a fine brush, etcetera, or look for afar like flies. | |
| From: David Wiggins (Sameness and Substance [1980], 5.7 n18) | |
| A reaction: [This glorious quotation comes from a story by Borges, first spotted by Foucault] |
| 16492 | Individuation needs accounts of identity, of change, and of singling out [Wiggins] |
| Full Idea: A theory of individuation must comprise at least three things: an elucidation of the primitive concept of identity or sameness; what it is to be a substance that persists through change; and what it is for a thinker to single out the same substance. | |
| From: David Wiggins (Sameness and Substance [1980], Pre 1) | |
| A reaction: [compressed] Metaphysics seems to need a theory of identity, but I am not yet convinced that it also needs a theory of 'individuation'. Never mind, press on and create one, and see how it looks. Aristotle wanted to explain predication too. |
| 16493 | Individuation can only be understood by the relation between things and thinkers [Wiggins] |
| Full Idea: Understanding the concepts involved in individuation can only be characterised by reference to observable commerce between things singled out and thinkers who think or find their way around the world precisely by singling them out. | |
| From: David Wiggins (Sameness and Substance [1980], Pre 1) | |
| A reaction: I take individuation to be relatively uninteresting, because I understand identity independently of how we single things out, but Wiggins's reliance on sortals implies that the very identity of things in the world is knee deep in mental activity. |
| 16496 | Singling out extends back and forward in time [Wiggins] |
| Full Idea: The singling out of a substance at a time reaches backwards and forwards to time before and after that time. | |
| From: David Wiggins (Sameness and Substance [1980], Pre 2) | |
| A reaction: Presumably this is an inferred history and persistence conditions. Sounds fine in a stable world. We assume (a priori?) that any object will have a space-time line for its duration. |
| 16495 | The only singling out is singling out 'as' something [Wiggins] |
| Full Idea: There could be no singling out tout court unless there could be singling out 'as'. | |
| From: David Wiggins (Sameness and Substance [1980], Pre 2) | |
| A reaction: I find this claim baffling. Do animals categorise everything they engage with? Are we unable to engage with something if we have not yet categorised it? Surely picking it out is prior to saying that sort of thing it is? |
| 16501 | In Aristotle's sense, saying x falls under f is to say what x is [Wiggins] |
| Full Idea: To say that x falls under f - or that x is an f - is to say what x is (in the sense Aristotle isolated). | |
| From: David Wiggins (Sameness and Substance [1980], 2.1) | |
| A reaction: This is a key claim in Wiggins's main principle. I'm not convinced. He wants one main sortal to do all the work. I don't think Aristotle at all intended the 'nature' of an individual thing to be given by a single sortal under which it falls. |
| 16506 | Every determinate thing falls under a sortal, which fixes its persistence [Wiggins] |
| Full Idea: We can expect that, for every completely determinate continuant, there will be at least one sortal concept that it falls under and that determines a principle of persistence for it. | |
| From: David Wiggins (Sameness and Substance [1980], 2.4) | |
| A reaction: I think he has the 'determines' relation the wrong way round! Being a tiger doesn't determine anything about persistence. It is having that nature and those persistence conditions which make it a tiger. And why does he optimistically 'expect' this? |
| 16674 | The quantity is just the matter, in that it has extended parts and is diffuse [Charleton] |
| Full Idea: The extension or quantity of a thing is merely modus materiae, or (rather) the matter itself composing that thing; insomuch as it consists not in a point, but has parts posited without parts, in respect whereof it is diffuse. | |
| From: Walter Charleton (Physiologia [1654], III.10.1.4), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 14.2 |
| 16509 | Natural kinds are well suited to be the sortals which fix substances [Wiggins] |
| Full Idea: Among the best candidates to play the roles of sortal and substantial predicates are the natural kind words. | |
| From: David Wiggins (Sameness and Substance [1980], 3.1) | |
| A reaction: There is always a danger of circularity with this kind of approach. How do we distinguish the genuine natural kinds from the dubious ones? |
| 16514 | Artefacts are individuated by some matter having a certain function [Wiggins] |
| Full Idea: Ordinary artefacts are individuated, rather indeterminately and arbitrarily, by reference to a parcel of matter so organised as to subserve a certain function. | |
| From: David Wiggins (Sameness and Substance [1980], 3.3) |
| 16510 | Nominal essences don't fix membership, ignore evolution, and aren't contextual [Wiggins] |
| Full Idea: Nominal essences are unsatisfactory because they fail either of necessity or of sufficiency for membership of the intended kind, they leave unexplained how sortals can evolve, and there is no room for culture or context in our reference to kinds. | |
| From: David Wiggins (Sameness and Substance [1980], 3.1) | |
| A reaction: [a compression of a paragraph] I would have thought that Locke would just say it is tough luck if nominal essences can't do all these things, because that's just the way it is, folks. |
| 16503 | 'What is it?' gives the kind, nature, persistence conditions and identity over time of a thing [Wiggins] |
| Full Idea: The question 'what is it?' refers to the persistence and lifespan of an entity, and so manifests the identity over time of an entity and its persistence, between persistence and existence, and between its existence and being the kind of thing it is. | |
| From: David Wiggins (Sameness and Substance [1980], 2.1) | |
| A reaction: The idea that establishing the kind of a thing can do all this work strikes me as false. The lifespan of a 'human' can be between five minutes and a hundred years. Humans have a clear death, but thunderstorms don't. |
| 16499 | A restored church is the same 'church', but not the same 'building' or 'brickwork' [Wiggins] |
| Full Idea: We can say of Hume's church that the present church is the same 'church' as the old parish church but not the same 'building' or the same 'stonework' as the old parish church. | |
| From: David Wiggins (Sameness and Substance [1980], 1.5) | |
| A reaction: Unconvinced. This seems to make a 'church' into an abstraction, which might even exist in the absence of any building. And it seems to identify a building with its stonework. Wiggins yearns for a neat solution, but it ain't here. |
| 16515 | A thing begins only once; for a clock, it is when its making is first completed [Wiggins] |
| Full Idea: A thing starts existing only once; and in the case of a clock its proper beginning was at about the time when its maker finished it. | |
| From: David Wiggins (Sameness and Substance [1980], 3.3) | |
| A reaction: I love the example that challenges this. Take the clock's parts and use them to make other clocks, then collect them up and reassemble the first clock. If the first clock has persisted through this, you have too many clocks. Wiggins spots some of this. |
| 16517 | Priests prefer the working ship; antiquarians prefer the reconstruction [Wiggins] |
| Full Idea: Dispute might break out between priests who favoured the working ship and antiquarians who preferred the reconstruction. | |
| From: David Wiggins (Sameness and Substance [1980], 3.3) | |
| A reaction: This captures the contextual nature of the dispute very succinctly. Wiggins, of course, thinks that sortals will settle the matter. Fat chance. |
| 16497 | Leibniz's Law (not transitivity, symmetry, reflexivity) marks what is peculiar to identity [Wiggins] |
| Full Idea: The principle of Leibniz's Law marks off what is peculiar to identity and differentiates it in a way in which transitivity, symmetry and reflexivity (all shared by 'exact similarity, 'equality in pay', etc.) do not. | |
| From: David Wiggins (Sameness and Substance [1980], 1.2) |
| 16502 | Identity is primitive [Wiggins] |
| Full Idea: Identity is a primitive notion. | |
| From: David Wiggins (Sameness and Substance [1980], 2.1) | |
| A reaction: To be a true primitive it would have to be univocal, but it seems to me that 'identity' comes in degrees. The primitive concept is the minimal end of the degrees, but there are also more substantial notions of identity. |
| 16498 | Identity cannot be defined, because definitions are identities [Wiggins] |
| Full Idea: Since any definition is an identity, identity itself cannot be defined. | |
| From: David Wiggins (Sameness and Substance [1980], 1.2 n7) | |
| A reaction: This sounds too good to be true! I can't think of an objection, so, okay, identity cannot possibly be defined. We can give synonyms for it, I suppose. [Wrong, says Rumfitt! Definitions can also be equivalences!] |
| 16521 | A is necessarily A, so if B is A, then B is also necessarily A [Wiggins] |
| Full Idea: The famous proof of Barcan Marcus about necessity of identity comes down to simply this: Hesperus is necessarily Hesperus, so if Phosphorus is Hesperus, Phosphorus is necessarily Hesperus. | |
| From: David Wiggins (Sameness and Substance [1980], 4.3) | |
| A reaction: Since the identity of Hesperus and Phosphorus was an a posteriori discovery, this was taken to be the inception of the idea that there are a posteriori necessities. The conclusion seems obvious. One thing is necessarily one thing. |
| 16505 | By the principle of Indiscernibility, a symmetrical object could only be half of itself! [Wiggins] |
| Full Idea: The full Identity of Indiscernibles excludes the existence in this world of a symmetrical object, which is reduced to half of itself by the principle. If symmetrical about all planes that bisect it, it is precluded altogether from existence. | |
| From: David Wiggins (Sameness and Substance [1980], 2.2) | |
| A reaction: A really nice objection. Do the parts even need to be symmetrical? My eyeballs can't be identical to one another, presumably. Electrons already gave the principle big trouble. |
| 16494 | We want to explain sameness as coincidence of substance, not as anything qualitative [Wiggins] |
| Full Idea: The notion of sameness or identity that we are to elucidate is not that of any degree of qualitative similarity but of coincidence as a substance - a notion as primitive as predication. | |
| From: David Wiggins (Sameness and Substance [1980], Pre 2) | |
| A reaction: This question invites an approach to identity through our descriptions of it, rather than to the thing itself. There is no problem in ontology of two substances being 'the same', because they are just one substance. |
| 16522 | It is hard or impossible to think of Caesar as not human [Wiggins] |
| Full Idea: It is hard or impossible to conceive of Caesar's not being a man (human). | |
| From: David Wiggins (Sameness and Substance [1980], 4.5) | |
| A reaction: So is it 'hard' or is it 'impossible'? Older generations of philosophers simply didn't read enough science fiction. Any short story could feature Caesar's failure to be a man. His assassination was a disaster for the Martian invasion of 44 BCE. |
| 16525 | Our sortal concepts fix what we find in experience [Wiggins] |
| Full Idea: What sortal concepts we can bring to bear upon experience determines what we can find there. | |
| From: David Wiggins (Sameness and Substance [1980], 5.6) | |
| A reaction: Wiggins would wince at being classed among linguistic relativists of the Sapir-Whorf type, but that's where I'm putting this idea. Wiggins is a realist, who knows there are things out there our concepts miss. He compares it to a fishing net. He's wrong. |
| 16518 | We conceptualise objects, but they impinge on us [Wiggins] |
| Full Idea: The mind conceptualises objects, yet objects impinge upon the mind. | |
| From: David Wiggins (Sameness and Substance [1980], 3.5) | |
| A reaction: A very nice statement of the relationship, and the fact that we don't just make our concepts up. |
| 16511 | A 'conception' of a horse is a full theory of what it is (and not just the 'concept') [Wiggins] |
| Full Idea: A 'conception' of horse is a theory of what a horse is, or what it is to be a horse. The conception is in no way the same as the concept. The conception is of the concept. | |
| From: David Wiggins (Sameness and Substance [1980], 3.1) | |
| A reaction: Wiggins sounds confident about a sharp distinction here, which I doubt, but some such distinction seems to required. I quite like Williams's 'fat' and 'thin' concepts. |