41 ideas
| 12223 | It is a fallacy to explain the obscure with the even more obscure [Hale/Wright] |
| Full Idea: The fallacy of 'ad obscurum per obscurius' is to explain the obscure by appeal to what is more obscure. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §3) | |
| A reaction: Not strictly a fallacy, so much as an example of inadequate explanation, along with circularity and infinite regresses. |
| 12230 | Singular terms refer if they make certain atomic statements true [Hale/Wright] |
| Full Idea: Anyone should agree that a justification for regarding a singular term as having objectual reference is provided just as soon as one has justification for regarding as true certain atomic statements in which it functions as a singular term. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §9) | |
| A reaction: The meat of this idea is hidden in the word 'certain'. See Idea 10314 for Hale's explanation. Without that, the proposal strikes me as absurd. |
| 10631 | If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright] |
| Full Idea: If we stipulate that 'x is heterological' iff it does not apply to itself, we speedily arrive at the contradiction that 'heterological' is itself heterological just in case it is not. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2) |
| 10624 | The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright] |
| Full Idea: The incompletability of formal arithmetic reveals, not arithmetical truths which are not truths of logic, but that logical truth likewise defies complete deductive characterization. ...Gödel's result has no specific bearing on the logicist project. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], §2 n5) | |
| A reaction: This is the key defence against the claim that Gödel's First Theorem demolished logicism. |
| 8784 | Neo-logicism founds arithmetic on Hume's Principle along with second-order logic [Hale/Wright] |
| Full Idea: The result of joining Hume's Principle to second-order logic is a consistent system which is a foundation for arithmetic, in the sense that all the fundamental laws of arithmetic are derivable within it as theorems. This seems a vindication of logicism. | |
| From: B Hale / C Wright (Logicism in the 21st Century [2007], 1) | |
| A reaction: The controversial part seems to be second-order logic, which Quine (for example) vigorously challenged. The contention against most attempts to improve Frege's logicism is that they thereby cease to be properly logical. |
| 8787 | The Julius Caesar problem asks for a criterion for the concept of a 'number' [Hale/Wright] |
| Full Idea: The Julius Caesar problem is the problem of supplying a criterion of application for 'number', and thereby setting it up as the concept of a genuine sort of object. (Why is Julius Caesar not a number?) | |
| From: B Hale / C Wright (Logicism in the 21st Century [2007], 3) | |
| A reaction: One response would be to deny that numbers are objects. Another would be to derive numbers from their application in counting objects, rather than the other way round. I suspect that the problem only real bothers platonists. Serves them right. |
| 10629 | If structures are relative, this undermines truth-value and objectivity [Hale/Wright] |
| Full Idea: The relativization of ontology to theory in structuralism can't avoid carrying with it a relativization of truth-value, which would compromise the objectivity which structuralists wish to claim for mathematics. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2 n26) | |
| A reaction: This is the attraction of structures which grow out of the physical world, where truth-value is presumably not in dispute. |
| 10628 | The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright] |
| Full Idea: It is not clear how the view that natural numbers are purely intra-structural 'objects' can be squared with the widespread use of numerals outside purely arithmetical contexts. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2 n26) | |
| A reaction: I don't understand this objection. If they refer to quantity, they are implicitly cardinal. If they name things in a sequence they are implicitly ordinal. All users of numbers have a grasp of the basic structure. |
| 8788 | Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology [Hale/Wright] |
| Full Idea: It is only if logic is metaphysically and epistemologically privileged that a reduction of mathematical theories to logical ones can be philosophically any more noteworthy than a reduction of any mathematical theory to any other. | |
| From: B Hale / C Wright (Logicism in the 21st Century [2007], 8) | |
| A reaction: It would be hard to demonstrate this privileged position, though intuitively there is nothing more basic in human rationality. That may be a fact about us, but it doesn't make logic basic to nature, which is where proper reduction should be heading. |
| 10622 | The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright] |
| Full Idea: The neo-Fregean takes a more optimistic view than Frege of the prospects for the kind of contextual explanation of the fundamental concepts of arithmetic and analysis (cardinals and reals), which he rejected in 'Grundlagen' 60-68. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], §1) |
| 8783 | Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright] |
| Full Idea: Two modern approaches to logicism are the quantificational approach of David Bostock, and the abstraction-free approach of Neil Tennant. | |
| From: B Hale / C Wright (Logicism in the 21st Century [2007], 1 n2) | |
| A reaction: Hale and Wright mention these as alternatives to their own view. I merely catalogue them for further examination. My immediate reaction is that Bostock sounds hopeless and Tennant sounds interesting. |
| 12225 | Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment [Hale/Wright] |
| Full Idea: A third way has been offered to 'make sense' of neo-Fregeanism: we should reject Quine's well-known criterion of ontological commitment in favour of one based on 'truth-maker theory'. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §4 n19) | |
| A reaction: [The cite Ross Cameron for this] They reject this proposal, on the grounds that truth-maker theory is not sufficient to fix the grounding truth-conditions of statements. |
| 12224 | Are neo-Fregeans 'maximalists' - that everything which can exist does exist? [Hale/Wright] |
| Full Idea: It is claimed that neo-Fregeans are committed to 'maximalism' - that whatever can exist does. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §4) | |
| A reaction: [The cite Eklund] They observe that maximalism denies contingent non-existence (of the £20 note I haven't got). There seems to be the related problem of 'hyperinflation', that if abstract objects are generated logically, the process is unstoppable. |
| 12226 | The identity of Pegasus with Pegasus may be true, despite the non-existence [Hale/Wright] |
| Full Idea: Identity is sometimes read so that 'Pegasus is Pegasus' expresses a truth, the non-existence of any winged horse notwithstanding. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §5) | |
| A reaction: This would give you ontological commitment to truth, without commitment to existence. It undercuts the use of identity statements as the basis of existence claims, which was Frege's strategy. |
| 12229 | Maybe we have abundant properties for semantics, and sparse properties for ontology [Hale/Wright] |
| Full Idea: There is a compatibilist view which says that it is for the abundant properties to play the role of 'bedeutungen' in semantic theory, and the sparse ones to address certain metaphysical concerns. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §9) | |
| A reaction: Only a philosopher could live with the word 'property' having utterly different extensions in different areas of discourse. They similarly bifurcate words like 'object' and 'exist'. Call properties 'quasi-properties' and I might join in. |
| 18443 | A successful predicate guarantees the existence of a property - the way of being it expresses [Hale/Wright] |
| Full Idea: The good standing of a predicate is already trivially sufficient to ensure the existence of an associated property, a (perhaps complex) way of being which the predicate serves to express. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §9) | |
| A reaction: 'Way of being' is interesting. Is 'being near Trafalgar Sq' a way of being? I take properties to be 'features', which seems to give a clearer way of demarcating them. They say they are talking about 'abundant' (rather than 'sparse') properties. |
| 10197 | An immanent universal is wholly present in more than one place [Zimmerman,DW] |
| Full Idea: An immanent universal will routinely be 'at some distance from itself', in the sense that it is wholly present in more than one place. | |
| From: Dean W. Zimmerman (Distinct Indiscernibles and the Bundle Theory [1997], p.306) | |
| A reaction: This is the Aristotelian view, which sounds distinctly implausible in this formulation. Though I suppose redness is wholly present in a tomato, in the way that fourness is wholly present in the Horsemen of the Apocalypse. How many rednesses are there? |
| 10626 | Objects just are what singular terms refer to [Hale/Wright] |
| Full Idea: Objects, as distinct from entities of other types (properties, relations or, more generally, functions of different types and levels), just are what (actual or possible) singular terms refer to. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.1) | |
| A reaction: I find this view very bizarre and hard to cope with. It seems either to preposterously accept the implications of the way we speak into our ontology ('sakes'?), or preposterously bend the word 'object' away from its normal meaning. |
| 14508 | A 'thisness' is a thing's property of being identical with itself (not the possession of self-identity) [Adams,RM] |
| Full Idea: A thisness is the property of being identical with a certain particular individual - not the property that we all share, of being identical with some individual, but my property of being identical with me, your property of being identical with you etc. | |
| From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 1) | |
| A reaction: These philosophers tell you that a thisness 'is' so-and-so, and don't admit that he (and Plantinga) are putting forward a new theory about haecceities, and one I find implausible. I just don't believe in the property of 'being-identical-to-me'. |
| 14511 | There are cases where mere qualities would not ensure an intrinsic identity [Adams,RM] |
| Full Idea: I have argued that there are possible cases in which no purely qualitative conditions would be both necessary and sufficient for possessing a given thisness. | |
| From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 6) | |
| A reaction: Are we perhaps confusing our epistemology with our ontology here? We can ensure that something has identity, or ensure that its identity is knowable. If it is 'something', then it has identity. Er, that's it? |
| 16463 | Adams says actual things have haecceities, but not things that only might exist [Adams,RM, by Stalnaker] |
| Full Idea: Adams favours haecceitism about actual things but no haecceities for things that might exist but don't. | |
| From: report of Robert Merrihew Adams (Actualism and Thisness [1981]) by Robert C. Stalnaker - Mere Possibilities 4.2 | |
| A reaction: This contrasts with Plantinga, who proposes necessary essences for everything, even for what might exist. Plantinga sounds crazy to me, Adams merely interesting but not too plausible. |
| 12031 | Essences are taken to be qualitative properties [Adams,RM] |
| Full Idea: Essences have normally been understood to be constituted by qualitative properties. | |
| From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 1) | |
| A reaction: I add this simple point, because it might be challenged by the view that an essence is a substance, rather than the properties of anything. I prefer that, and would add that substances are individuated by distinctive causal powers. |
| 12034 | If the universe was cyclical, totally indiscernible events might occur from time to time [Adams,RM] |
| Full Idea: There is a temporal argument for the possibility of non-identical indiscernibles, if there could be a cyclical universe, in which each event was preceded and followed by infinitely many other events qualitatively indiscernible from itself. | |
| From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 3) | |
| A reaction: The argument is a parallel to Max Black's indiscernible spheres in space. Adams offers the reply that time might be tightly 'curved', so that the repetition was indeed the same event again. |
| 14510 | Two events might be indiscernible yet distinct, if there was a universe cyclical in time [Adams,RM] |
| Full Idea: Similar to the argument from spatial dispersal, we can argue against the Identity of Indiscernibles from temporal dispersal. It seems there could be a cyclic universe, ..and thus there could be distinct but indiscernible events, separated temporally. | |
| From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 3) | |
| A reaction: See Idea 14509 for spatial dispersal. If cosmologists decided that a cyclical universe was incoherent, would that ruin the argument? Presumably there might even be indistinguishable events in the one universe (in principle!). |
| 16455 | Black's two globes might be one globe in highly curved space [Adams,RM] |
| Full Idea: If God creates a globe reached by travelling two diameters in a straight line from another globe, this can be described as two globes in Euclidean space, or a single globe in a tightly curved non-Euclidean space. | |
| From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 3) | |
| A reaction: [my compression of Adams's version of Hacking's response to Black, as spotted by Stalnaker] Hence we save the identity of indiscernibles, by saying we can't be sure that two indiscernibles are not one thing, unusually described. |
| 10198 | If only two indiscernible electrons exist, future differences must still be possible [Zimmerman,DW] |
| Full Idea: If nothing existed except two electrons, which are indiscernible, it remains possible that differences will emerge later. Even if this universe has eternal symmetry, such differences are still logically, metaphysically, physically and causally possible. | |
| From: Dean W. Zimmerman (Distinct Indiscernibles and the Bundle Theory [1997], p.306) | |
| A reaction: The question then is whether the two electrons have hidden properties that make differences possible. Zimmerman assumes that 'laws' of an indeterministic kind will do the job. I doubt that. Can differences be discerned after the event? |
| 10199 | Discernible differences at different times may just be in counterparts [Zimmerman,DW] |
| Full Idea: Possible differences which may later become discernible could be treated as differences in a counterpart, which is similar to, but not identical with, the original object. | |
| From: Dean W. Zimmerman (Distinct Indiscernibles and the Bundle Theory [1997], p.307) | |
| A reaction: [compressed] This is a reply to Idea 10198, which implies that two things could never be indiscernible over time, because of their different possibilities. One must then decide issues about rigid designation and counterparts. |
| 14507 | Are possible worlds just qualities, or do they include primitive identities as well? [Adams,RM] |
| Full Idea: Is the world - and are all possible worlds - constituted by purely qualitative facts, or does thisness hold a place beside suchness as a fundamental feature of reality? | |
| From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], Intro) | |
| A reaction: 'Thisness' and 'suchness' aim to capture Aristotelian notions of the entity and its attributes. Aristotle talks of 'a this'. Adams is after adding 'haecceities' to the world. My intuitive answer is no, there are no 'pure' identities. We add those. |
| 11964 | Possible worlds are world-stories, maximal descriptions of whole non-existent worlds [Adams,RM, by Molnar] |
| Full Idea: According to a theory proposed by Adams, possible worlds are world-stories, that is maximally complete consistent sets of propositions which between them describe non-existent whole worlds. | |
| From: report of Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979]) by George Molnar - Powers 12.2.2 | |
| A reaction: Presumably this places an additional constraint on the view that a world is just a maximal set of propositions. It seems to require coherence as well as consistency. Suppose an object destroys all others objects. Is that a world? |
| 16451 | Adams says anti-haecceitism reduces all thisness to suchness [Adams,RM, by Stalnaker] |
| Full Idea: The anti-haecceitist thesis (according to Adams's version) is that all thisnesses are reducible to, or supervenient upon, suchnesses. | |
| From: report of Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979]) by Robert C. Stalnaker - Mere Possibilities 3.5 |
| 11901 | Haecceitism may or may not involve some logical connection to essence [Adams,RM, by Mackie,P] |
| Full Idea: Moderate Haecceitism says that thisnesses and transworld identities are primitive, but logically connected with suchnesses. ..Extreme Haecceitism involves the rejection of all logical connections between suchness and thisness, for persons. | |
| From: report of Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979]) by Penelope Mackie - How Things Might Have Been | |
| A reaction: I am coming to the conclusion that they are not linked. That thisness is a feature of our conceptual thinking, and is utterly atomistic and content-free, while suchness is rich and a feature of reality. |
| 14512 | Moderate Haecceitism says transworld identities are primitive, but connected to qualities [Adams,RM] |
| Full Idea: My position, according to which thisnesses and transworld identities are primitive but logically connected to suchnesses, we may call 'Moderate Haecceitism'. | |
| From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 6) | |
| A reaction: The rather tentative connection to qualities is to block the possibility of Aristotle being a poached egg, which he (quite reasonably!) holds to be counterintuitive. It all feels like a mess to me. |
| 10630 | Abstracted objects are not mental creations, but depend on equivalence between given entities [Hale/Wright] |
| Full Idea: The new kind of abstract objects are not creations of the human mind. ...The existence of such objects depends upon whether or not the relevant equivalence relation holds among the entities of the presupposed kind. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2) | |
| A reaction: It seems odd that we no longer have any choice about what abstract objects we use, and that we can't evade them if the objects exist, and can't have them if the objects don't exist - and presumably destruction of the objects kills the concept? |
| 8786 | One first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines [Hale/Wright] |
| Full Idea: An example of a first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines; a higher-order example (which refers to first-order predicates) defines 'equinumeral' in terms of one-to-one correlation (Hume's Principle). | |
| From: B Hale / C Wright (Logicism in the 21st Century [2007], 1) | |
| A reaction: [compressed] This is the way modern logicians now treat abstraction, but abstraction principles include the elusive concept of 'equivalence' of entities, which may be no more than that the same adjective ('parallel') can be applied to them. |
| 12227 | Abstractionism needs existential commitment and uniform truth-conditions [Hale/Wright] |
| Full Idea: Abstractionism needs a face-value, existentially committed reading of the terms occurring on the left-hand sides together with sameness of truth-conditions across the biconditional. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §5) | |
| A reaction: They employ 'abstractionism' to mean their logical Fregean strategy for defining abstractions, not to mean the older psychological account. Thus the truth-conditions for being 'parallel' and for having the 'same direction' must be consistent. |
| 12228 | Equivalence abstraction refers to objects otherwise beyond our grasp [Hale/Wright] |
| Full Idea: Abstraction principles purport to introduce fundamental means of reference to a range of objects, to which there is accordingly no presumption that we have any prior or independent means of reference. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §8) | |
| A reaction: There's the rub! They make it sound like a virtue, that we open up yet another heaven of abstract toys to play with. As fictions, they are indeed exciting new fun. As platonic discoveries they strike me as Cloud-Cuckoo Land. |
| 12032 | Direct reference is by proper names, or indexicals, or referential uses of descriptions [Adams,RM] |
| Full Idea: Direct reference is commonly effected by the use of proper names and indexical expressions, and sometimes by what has been called (by Donnellan) the 'referential' use of descriptions. | |
| From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 2) | |
| A reaction: One might enquire whether the third usage should be described as 'direct', but then I am not sure that there is much of a distinction between references which are or are not 'direct'. Either you (or a sentence) refer or you (or it) don't. |
| 12231 | Reference needs truth as well as sense [Hale/Wright] |
| Full Idea: It takes, over and above the possession of sense, the truth of relevant contexts to ensure reference. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §9) | |
| A reaction: Reference purely through sense was discredited by Kripke. The present idea challenges Kripke's baptismal realist approach. How do you 'baptise' an abstract object? But isn't reference needed prior to the establishment of truth? |
| 10627 | Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions [Hale/Wright] |
| Full Idea: There are many statements which are plausibly viewed as conceptual truths (such as 'what is yellow is extended') which do not qualify as analytic under Frege's definition (as provable using only logical laws and definitions). | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2) | |
| A reaction: Presumably this is because the early assumptions of Frege were mathematical and logical, and he was trying to get away from Kant. That yellow is extended is a truth for non-linguistic beings. |
| 14610 | Neither 'moving spotlight' nor 'growing block' views explain why we care what is present or past [Zimmerman,DW] |
| Full Idea: Neither the 'moving spotlight' nor the 'growing block' view of A-theory time can explain why we care so much about whether things (such as a headache) are present or past. | |
| From: Dean W. Zimmerman (The Privileged Present: A-Theory [2008], 3) | |
| A reaction: He goes on the defend Presentism as the best version of the A-series view. You can't deny that the past is more of a 'truthmaker' than the future, so it seems to have a firmer ontological status. Deeply weird. |
| 14608 | A-theorists, unlike B-theorists, believe some sort of objective distinction between past, present and future [Zimmerman,DW] |
| Full Idea: To be an A-theorist is to believe in some sort of objective distinction between what is present and past and future. ..To be a B-theorist is to deny the objectivity of our talk about past, present and future. | |
| From: Dean W. Zimmerman (The Privileged Present: A-Theory [2008], 2) | |
| A reaction: The A/B distinction originates with McTaggart. All my intuitions side with the A-theory, certainly to the extent that the present seems to be objectively privileged in some way (despite special relativity). |