45 ideas
| 10308 | Questions about objects are questions about certain non-vacuous singular terms [Hale] |
| Full Idea: I understand questions about the Fregean notion of an object to be inseparable from questions in the philosophy of language - questions of the existence of objects are tantamount to questions about non-vacuous singular terms of a certain kind. | |
| From: Bob Hale (Abstract Objects [1987], Ch.1) | |
| A reaction: This view hovers somewhere between Quine and J.L. Austin, and Dummett is its originator. I am instinctively deeply opposed to the identification of metaphysics with semantics. |
| 10314 | An expression is a genuine singular term if it resists elimination by paraphrase [Hale] |
| Full Idea: An expression ... should be reckoned a genuine singular term only if it resists elimination by paraphrase. | |
| From: Bob Hale (Abstract Objects [1987], Ch.2.II) | |
| A reaction: This strikes me as extraordinarily optimistic. It will be relative to a language, and the resources of a given speaker, and seems open to the invention of new expressions to do the job (e.g. an equivalent adjective for every noun in the dictionary). |
| 10676 | The Axiom of Choice is a non-logical principle of set-theory [Hossack] |
| Full Idea: The Axiom of Choice seems better treated as a non-logical principle of set-theory. | |
| From: Keith Hossack (Plurals and Complexes [2000], 4 n8) | |
| A reaction: This reinforces the idea that set theory is not part of logic (and so pure logicism had better not depend on set theory). |
| 10686 | The Axiom of Choice guarantees a one-one correspondence from sets to ordinals [Hossack] |
| Full Idea: We cannot explicitly define one-one correspondence from the sets to the ordinals (because there is no explicit well-ordering of R). Nevertheless, the Axiom of Choice guarantees that a one-one correspondence does exist, even if we cannot define it. | |
| From: Keith Hossack (Plurals and Complexes [2000], 10) |
| 10687 | Maybe we reduce sets to ordinals, rather than the other way round [Hossack] |
| Full Idea: We might reduce sets to ordinal numbers, thereby reversing the standard set-theoretical reduction of ordinals to sets. | |
| From: Keith Hossack (Plurals and Complexes [2000], 10) | |
| A reaction: He has demonstrated that there are as many ordinals as there are sets. |
| 10677 | Extensional mereology needs two definitions and two axioms [Hossack] |
| Full Idea: Extensional mereology defs: 'distinct' things have no parts in common; a 'fusion' has some things all of which are parts, with no further parts. Axioms: (transitivity) a part of a part is part of the whole; (sums) any things have a unique fusion. | |
| From: Keith Hossack (Plurals and Complexes [2000], 5) |
| 10316 | We should decide whether singular terms are genuine by their usage [Hale] |
| Full Idea: The criteria for a genuine singular term should pick out not the singular terms themselves but their uses, since they may be genuine in one context and not another. | |
| From: Bob Hale (Abstract Objects [1987], Ch.2.II) | |
| A reaction: [rephrased] This will certainly meet problems with vagueness (e.g. as the reference of a singular term is gradually clarified). |
| 10312 | Often the same singular term does not ensure reliable inference [Hale] |
| Full Idea: In 'the whale is increasingly scarce' and 'the whale is much improved today' (our pet whale), we cannot infer that there is something that is much improved and increasingly scarce, so this singular term fails Dummett's criterion based on inference. | |
| From: Bob Hale (Abstract Objects [1987], Ch.2) | |
| A reaction: [much rephrased] This is not just a problem for a few cunningly selected examples. With contortions almost any singular term can be undermined in this way. Singular terms are simply not a useful guide to the existence of abstracta. |
| 10313 | Plenty of clear examples have singular terms with no ontological commitment [Hale] |
| Full Idea: Some examples where a definite singular noun phrase is not 'genuine' (giving ontological commitment): 'left us in the lurch'; 'for my mother's sake'; 'given the sack'; 'in the nick of time', 'the whereabouts of the PM', 'the identity of the murderer'. | |
| From: Bob Hale (Abstract Objects [1987], Ch.2.II) | |
| A reaction: These are not just freakish examples. If I 'go on a journey', that doesn't involve extra entities called 'journeys', just because the meaning is clearer and a more commonplace part of the language. |
| 10322 | If singular terms can't be language-neutral, then we face a relativity about their objects [Hale] |
| Full Idea: If we lack any general, language-neutral characterization of singular terms, must not a parallel linguistic relativity infect the objects which are to be thought of as their non-linguistic correlates? | |
| From: Bob Hale (Abstract Objects [1987], Ch.2.III) | |
| A reaction: Hale thinks he can answer this, but I would have thought that this problem dooms the linguistic approach from the start. There needs to be more imagination about how very different a language could be, while still qualifying as a language. |
| 10671 | Plural definite descriptions pick out the largest class of things that fit the description [Hossack] |
| Full Idea: If we extend the power of language with plural definite descriptions, these would pick out the largest class of things that fit the description. | |
| From: Keith Hossack (Plurals and Complexes [2000], 3) |
| 10666 | Plural reference will refer to complex facts without postulating complex things [Hossack] |
| Full Idea: It may be that plural reference gives atomism the resources to state complex facts without needing to refer to complex things. | |
| From: Keith Hossack (Plurals and Complexes [2000], 1) | |
| A reaction: This seems the most interesting metaphysical implication of the possibility of plural quantification. |
| 10669 | Plural reference is just an abbreviation when properties are distributive, but not otherwise [Hossack] |
| Full Idea: If all properties are distributive, plural reference is just a handy abbreviation to avoid repetition (as in 'A and B are hungry', to avoid 'A is hungry and B is hungry'), but not all properties are distributive (as in 'some people surround a table'). | |
| From: Keith Hossack (Plurals and Complexes [2000], 2) | |
| A reaction: The characteristic examples to support plural quantification involve collective activity and relations, which might be weeded out of our basic ontology, thus leaving singular quantification as sufficient. |
| 10675 | A plural comprehension principle says there are some things one of which meets some condition [Hossack] |
| Full Idea: Singular comprehension principles have a bad reputation, but the plural comprehension principle says that given a condition on individuals, there are some things such that something is one of them iff it meets the condition. | |
| From: Keith Hossack (Plurals and Complexes [2000], 4) |
| 10673 | Plural language can discuss without inconsistency things that are not members of themselves [Hossack] |
| Full Idea: In a plural language we can discuss without fear of inconsistency the things that are not members of themselves. | |
| From: Keith Hossack (Plurals and Complexes [2000], 4) | |
| A reaction: [see Hossack for details] |
| 10680 | The theory of the transfinite needs the ordinal numbers [Hossack] |
| Full Idea: The theory of the transfinite needs the ordinal numbers. | |
| From: Keith Hossack (Plurals and Complexes [2000], 8) |
| 10684 | I take the real numbers to be just lengths [Hossack] |
| Full Idea: I take the real numbers to be just lengths. | |
| From: Keith Hossack (Plurals and Complexes [2000], 9) | |
| A reaction: I love it. Real numbers are beginning to get on my nerves. They turn up to the party with no invitation and improperly dressed, and then refuse to give their names when challenged. |
| 10674 | A plural language gives a single comprehensive induction axiom for arithmetic [Hossack] |
| Full Idea: A language with plurals is better for arithmetic. Instead of a first-order fragment expressible by an induction schema, we have the complete truth with a plural induction axiom, beginning 'If there are some numbers...'. | |
| From: Keith Hossack (Plurals and Complexes [2000], 4) |
| 10681 | In arithmetic singularists need sets as the instantiator of numeric properties [Hossack] |
| Full Idea: In arithmetic singularists need sets as the instantiator of numeric properties. | |
| From: Keith Hossack (Plurals and Complexes [2000], 8) |
| 10685 | Set theory is the science of infinity [Hossack] |
| Full Idea: Set theory is the science of infinity. | |
| From: Keith Hossack (Plurals and Complexes [2000], 10) |
| 10512 | The abstract/concrete distinction is based on what is perceivable, causal and located [Hale] |
| Full Idea: The 'concrete/abstract' distinction has a strong intuitive feel, and can seem to be drawable by familiar contrasts, between what can/cannot be perceived, what can/cannot be involved in causal interactions, and is/is not located in space and time. | |
| From: Bob Hale (Abstract Objects [1987], Ch.3.I) | |
| A reaction: Problems arise, needless to say. The idea of an abstraction can be causal, and abstractions seem to change. If universals are abstract, we seem to perceive some of them. They can hardly be non-spatial if they have a temporal beginning and end. |
| 10517 | Colours and points seem to be both concrete and abstract [Hale] |
| Full Idea: It might seem that colours would qualify both as concrete and as abstract objects. ...and geometrical points also seem to be borderline. | |
| From: Bob Hale (Abstract Objects [1987], Ch.3.II) | |
| A reaction: The theory of tropes exploits this uncertainty. Dummett (1973:ch.14) notes that we can point to colours, but also slip from an adjectival to a noun usage of colour-terms. He concludes that colours are concrete. I think I agree. |
| 10519 | The abstract/concrete distinction is in the relations in the identity-criteria of object-names [Hale] |
| Full Idea: Noonan suggests that the distinction between abstract and concrete objects should be seen as derivative from a difference between the relations centrally involved in criteria of identity associated with names of objects. | |
| From: Bob Hale (Abstract Objects [1987], Ch.3.III) | |
| A reaction: [He cites Noonan 1976, but I've lost it] I don't understand this, but collect it as a lead to something that might be interesting. A careful reading of Hale might reveal what Noonan meant. |
| 10520 | Token-letters and token-words are concrete objects, type-letters and type-words abstract [Hale] |
| Full Idea: In familiar, though doubtless not wholly problematic jargon, token-letters and token-words are concrete objects, type-letters and type-words abstract. | |
| From: Bob Hale (Abstract Objects [1987], Ch.3.III) | |
| A reaction: This is indeed problematic. The marks may be tokens, but the preliminary to identifying the type is to see that the marks are in fact words. To grasp the concrete, grasp the abstraction. An excellent example of the blurring of the distinction. |
| 10524 | There is a hierarchy of abstraction, based on steps taken by equivalence relations [Hale] |
| Full Idea: The domain of the abstract can be seen as exemplifying a hierarchical structure, with differences of level reflecting the number of steps of abstraction, via appropriate equivalence relations, required for recognition at different levels. | |
| From: Bob Hale (Abstract Objects [1987], Ch.3.III) | |
| A reaction: I think this is right, and so does almost everyone else, since people cheerfully talk of 'somewhat' abstract and 'highly' abstract. Don't dream of a neat picture though. You might reach a level by two steps from one direction, and four from another. |
| 10668 | We are committed to a 'group' of children, if they are sitting in a circle [Hossack] |
| Full Idea: By Quine's test of ontological commitment, if some children are sitting in a circle, no individual child can sit in a circle, so a singular paraphrase will have us committed to a 'group' of children. | |
| From: Keith Hossack (Plurals and Complexes [2000], 2) | |
| A reaction: Nice of why Quine is committed to the existence of sets. Hossack offers plural quantification as a way of avoiding commitment to sets. But is 'sitting in a circle' a real property (in the Shoemaker sense)? I can sit in a circle without realising it. |
| 10521 | If F can't have location, there is no problem of things having F in different locations [Hale] |
| Full Idea: If Fs are incapable of spatial location, it is impossible for a and b to be at the same time in different places and yet be the same F. | |
| From: Bob Hale (Abstract Objects [1987], Ch.3.III) | |
| A reaction: A passing remark from Hale which strikes me as incredibly significant. The very idea of a 'one-over-many' is that there are many locations for the thing, so to conclude that the thing is therefore non-located seems to negate the original problem. |
| 10511 | It is doubtful if one entity, a universal, can be picked out by both predicates and abstract nouns [Hale] |
| Full Idea: The traditional conception of universals, resting as it does upon the idea that some single type of entity is picked out by expressions of such radically different logical types as predicates and abstract nouns, is of doubtful coherence. | |
| From: Bob Hale (Abstract Objects [1987], Ch.3 Intro) | |
| A reaction: A striking case of linguistic metaphysics in action. I don't believe in universals, but I don't find this persuasive, as our capacity to express the same proposition by means of extremely varied syntax is obvious. Is 'horse' an abstract noun? |
| 10318 | Realists take universals to be the referrents of both adjectives and of nouns [Hale] |
| Full Idea: On the traditional realist's view abstract qualities (universals) are the common referents of two quite different sorts of expression - of ordinary adjectives (predicates), and of abstract nouns referring to them. | |
| From: Bob Hale (Abstract Objects [1987], Ch.2.II) | |
| A reaction: This fact alone should make us suspicious, especially as there isn't an isomorphism between the nouns and the adjectives, and the match-up will vary between languages. |
| 10310 | Objections to Frege: abstracta are unknowable, non-independent, unstatable, unindividuated [Hale] |
| Full Idea: Objections to Frege's argument for abstract objects: that the objects would not have the right sort of independence; that we could have no knowledge of them; that the singular term statements can't be had; that thoughts of abstracta can't be identified. | |
| From: Bob Hale (Abstract Objects [1987], Ch.1) | |
| A reaction: [compressed] [See Idea 10309 for the original argument] It is helpful to have this list, even if Hale rejects them all. They are also created but then indestructible, and exist in unlimited profusion, and seem relative to a language. Etc! |
| 10518 | Shapes and directions are of something, but games and musical compositions are not [Hale] |
| Full Idea: While a shape or a direction is necessarily of something, games, musical compositions or dance routines are not of anything at all. | |
| From: Bob Hale (Abstract Objects [1987], Ch.3.II) | |
| A reaction: This seems important, because Frege's abstraction principle works nicely for abstractions 'of' some objects, but is not so clear for abstracta that are sui generis. |
| 10513 | Many abstract objects, such as chess, seem non-spatial, but are not atemporal [Hale] |
| Full Idea: There are many plausible example of abstract objects which, though non-spatial, do not appear to satisfy the suggested requirement of atemporality, such as chess, or the English language. | |
| From: Bob Hale (Abstract Objects [1987], Ch.3.1) | |
| A reaction: Given the point that modern physics is committed to 'space-time', with no conceivable separation of them, this looks dubious. Though I think the physics could be challenged. Try Idea 7621, for example. |
| 10514 | If the mental is non-spatial but temporal, then it must be classified as abstract [Hale] |
| Full Idea: If mental events are genuinely non-spatial, but not atemporal, its effect is to classify them as abstract; the distinction between the abstract and the mental simply collapses. | |
| From: Bob Hale (Abstract Objects [1987], Ch.3.1) | |
| A reaction: This is important. You can't discuss this sort of metaphysics in isolation from debates about the ontology of mind. Functionalists do treat mental events as abstractions. |
| 10523 | Being abstract is based on a relation between things which are spatially separated [Hale] |
| Full Idea: The abstract/concrete distinction is, roughly, between those sortals whose grounding relations can hold between abstract things which are spatially but not temporally separated, those concrete things whose grounding relations cannot so hold. | |
| From: Bob Hale (Abstract Objects [1987], Ch.3.III) | |
| A reaction: Thus being a father is based on 'begat', which does not involve spatial separation, and so is concrete. The relation is one of equivalence. |
| 10307 | The modern Fregean use of the term 'object' is much broader than the ordinary usage [Hale] |
| Full Idea: The notion of an 'object' first introduced by Frege is much broader than that of most comparable ordinary uses of 'object', and is now fairly standard and familiar. | |
| From: Bob Hale (Abstract Objects [1987], Ch.1) | |
| A reaction: This makes it very difficult to get to grips with the metaphysical issues involved, since the ontological claims disappear into a mist of semantic vagueness. |
| 10315 | We can't believe in a 'whereabouts' because we ask 'what kind of object is it?' [Hale] |
| Full Idea: Onotological outrage at such objects as the 'whereabouts of the Prime Minister' derives from the fact that we seem beggared for any convincing answer to the question 'What kind of objects are they?' | |
| From: Bob Hale (Abstract Objects [1987], Ch.2.II) | |
| A reaction: I go further and ask of any object 'what is it made of?' When I receive the answer that I am being silly, and that abstract objects are not 'made' of anything, I am tempted to become sarcastic, and say 'thank you - that makes it much clearer'. |
| 10664 | Complex particulars are either masses, or composites, or sets [Hossack] |
| Full Idea: Complex particulars are of at least three types: masses (which sum, of which we do not ask 'how many?' but 'how much?'); composite individuals (how many?, and summing usually fails); and sets (only divisible one way, unlike composites). | |
| From: Keith Hossack (Plurals and Complexes [2000], 1) | |
| A reaction: A composite pile of grains of sand gradually becomes a mass, and drops of water become 'water everywhere'. A set of people divides into individual humans, but redescribe the elements as the union of males and females? |
| 10678 | The relation of composition is indispensable to the part-whole relation for individuals [Hossack] |
| Full Idea: The relation of composition seems to be indispensable in a correct account of the part-whole relation for individuals. | |
| From: Keith Hossack (Plurals and Complexes [2000], 7) | |
| A reaction: This is the culmination of a critical discussion of mereology and ontological atomism. At first blush it doesn't look as if 'composition' has much chance of being a precise notion, and it will be plagued with vagueness. |
| 10665 | Leibniz's Law argues against atomism - water is wet, unlike water molecules [Hossack] |
| Full Idea: We can employ Leibniz's Law against mereological atomism. Water is wet, but no water molecule is wet. The set of infinite numbers is infinite, but no finite number is infinite. ..But with plural reference the atomist can resist this argument. | |
| From: Keith Hossack (Plurals and Complexes [2000], 1) | |
| A reaction: The idea of plural reference is to state plural facts without referring to complex things, which is interesting. The general idea is that we have atomism, and then all the relations, unities, identities etc. are in the facts, not in the things. I like it. |
| 10682 | The fusion of five rectangles can decompose into more than five parts that are rectangles [Hossack] |
| Full Idea: The fusion of five rectangles may have a decomposition into more than five parts that are rectangles. | |
| From: Keith Hossack (Plurals and Complexes [2000], 8) |
| 10522 | The relations featured in criteria of identity are always equivalence relations [Hale] |
| Full Idea: The relations which are featured in criteria of identity are always equivalence relations. | |
| From: Bob Hale (Abstract Objects [1987], Ch.3.III) | |
| A reaction: This will only apply to strict identity. If I say 'a is almost identical to b', this will obviously not be endlessly transitive (as when we get to k we may have lost the near-identity to a). Are 'two threes' identical to 'three twos'? |
| 10321 | We sometimes apply identity without having a real criterion [Hale] |
| Full Idea: Not every (apparent) judgement of identity involves application of anything properly describable as a criterion of identity, ...such as being able to pronounce that mercy is the quality of being merciful. | |
| From: Bob Hale (Abstract Objects [1987], Ch.2.II) | |
| A reaction: This suggests some distinction between internal criteria (e.g. grammatical, conceptual) and external criteria (existent, sensed). |
| 10663 | A thought can refer to many things, but only predicate a universal and affirm a state of affairs [Hossack] |
| Full Idea: A thought can refer to a particular or a universal or a state of affairs, but it can predicate only a universal and it can affirm only a state of affairs. | |
| From: Keith Hossack (Plurals and Complexes [2000], 1) | |
| A reaction: Hossack is summarising Armstrong's view, which he is accepting. To me, 'thought' must allow for animals, unlike language. I think Hossack's picture is much too clear-cut. Do animals grasp universals? Doubtful. Can they predicate? Yes. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 10683 | We could ignore space, and just talk of the shape of matter [Hossack] |
| Full Idea: We might dispense with substantival space, and say that if the distribution of matter in space could have been different, that just means the matter of the Universe could have been shaped differently (with geometry as the science of shapes). | |
| From: Keith Hossack (Plurals and Complexes [2000], 9) |