| 2001 | Abstract Objects |
| 'Non-spat' | p.3 | 8912 | Nowadays abstractions are defined as non-spatial, causally inert things |
| Full Idea: If any characterization of the abstract deserves to be regarded as the modern standard one, it is this: an abstract entity is a non-spatial (or non-spatiotemporal) causally inert thing. This view presents a number of perplexities... | |||
| From: Gideon Rosen (Abstract Objects [2001], 'Non-spat') | |||
| A reaction: As indicated in other ideas, the problem is that some abstractions do seem to be located somewhere in space-time, and to have come into existence, and to pass away. I like 'to exist is to have causal powers'. See Ideas 5992 and 8300. |
| 'Non-spat' | p.4 | 8913 | Chess may be abstract, but it has existed in specific space and time |
| Full Idea: The natural view of chess is not that it is a non-spatiotemporal mathematical object, but that it was invented at a certain time and place, that it has changed over the years, and so on. | |||
| From: Gideon Rosen (Abstract Objects [2001], 'Non-spat') | |||
| A reaction: This strikes me as being undeniable, and being an incredibly important point. Logicians seem to want to subsume things like games into the highly abstract world of logic and numbers. In fact the direction of explanation should be reversed. |
| 'Non-spat' | p.5 | 8914 | Sets are said to be abstract and non-spatial, but a set of books can be on a shelf |
| Full Idea: It is thought that sets are abstract, abstract objects do not exist in space, so sets must not exist in space. But it is not unnatural to say that a set of books is located on a certain shelf in the library. | |||
| From: Gideon Rosen (Abstract Objects [2001], 'Non-spat') | |||
| A reaction: The arguments against non-spatiality of abstractions seem to me to be conclusive. Not being able to assign a location to the cosine function is on a par with not knowing where my thoughts are located in my brain. |
| 'Way of Abs' | p.7 | 8918 | Functional terms can pick out abstractions by asserting an equivalence relation |
| Full Idea: On Frege's suggestion, functional terms that pick out abstract expressions (such as 'direction' or 'equinumeral') have a typical form of f(a) = f(b) iff aRb, where R is an equivalence relation, a relation which is reflexive, symmetric and transitive. | |||
| From: Gideon Rosen (Abstract Objects [2001], 'Way of Abs') | |||
| A reaction: [Wright and Hale are credited with the details] This has become the modern orthodoxy among the logically-minded. Examples of R are 'parallel' or 'just as many as'. It picks out an 'aspect', which isn't far from the old view. |
| 'Way of Abs' | p.7 | 8917 | The Way of Abstraction used to say an abstraction is an idea that was formed by abstracting |
| Full Idea: The simplest version of the Way of Abstraction would be to say that an object is abstract if it is a referent of an idea that was formed by abstraction, but this is wedded to an outmoded philosophy of mind. | |||
| From: Gideon Rosen (Abstract Objects [2001], 'Way of Abs') | |||
| A reaction: This presumably refers to Locke, who wields the highly ambiguous term 'idea'. But if we sort out that ambiguity (by using modern talk of mental events, concepts and content?) we might reclaim the view. But do we have a 'genetic fallacy' here? |
| 'Way of Abs' | p.9 | 8919 | Abstraction by equivalence relationships might prove that a train is an abstract entity |
| Full Idea: It seems possible to define a train in terms of its carriages and the connection relationship, which would meet the equivalence account of abstraction, but demonstrate that trains are actually abstract. | |||
| From: Gideon Rosen (Abstract Objects [2001], 'Way of Abs') | |||
| A reaction: [Compressed. See article for more detail] A tricky example, but a suggestive line of criticism. If you find two physical objects which relate to one another reflexively, symmetrically and transitively, they may turn out to be abstract. |
| 'Way of Con' | p.6 | 8916 | Conflating abstractions with either sets or universals is a big claim, needing a big defence |
| Full Idea: The Way of Conflation account of abstractions (identifying them sets or with universals) is now relatively rare. The claim sets or universals are the only abstract objects would amount to a substantive metaphysical thesis, in need of defence. | |||
| From: Gideon Rosen (Abstract Objects [2001], 'Way of Con') | |||
| A reaction: If you produce a concept like 'mammal' by psychological abstraction, you do seem to end up with a set of things with shared properties, so this approach is not silly. I can't think of any examples of abstractions which are not sets or universals. |
| 'Way of Ex' | p.6 | 8915 | How we refer to abstractions is much less clear than how we refer to other things |
| Full Idea: It is unclear how we manage to refer determinately to abstract entities in a sense in which it is not unclear how we manage to refer determinately to other things. | |||
| From: Gideon Rosen (Abstract Objects [2001], 'Way of Ex') | |||
| A reaction: This is where problems of abstraction overlap with problems about reference in language. Can we have a 'baptism' account of each abstraction (even very large numbers)? Will descriptions do it? Do abstractions collapse into particulars when we refer? |
| 2006 | The Limits of Contingency |
| 02 | p.15 | 18848 | Something may be necessary because of logic, but is that therefore a special sort of necessity? |
| Full Idea: It is one thing to say that P is necessary in some generic sense because it is a truth of logic (true in all models of a language, perhaps). It is something else to say that P therefore enjoys a special sort of necessity. | |||
| From: Gideon Rosen (The Limits of Contingency [2006], 02) | |||
| A reaction: This encourages my thought that there is only one sort of necessity (what must be), and the variety comes from the different types of necessity makers (everything there could be, nature, duties, promises, logics, concepts...). |
| 02 | p.16 | 18850 | 'Metaphysical' modality is the one that makes the necessity or contingency of laws of nature interesting |
| Full Idea: 'Metaphysical' modality is the sort of modality relative to which it is an interesting question whether the laws of nature are necessary or contingent. | |||
| From: Gideon Rosen (The Limits of Contingency [2006], 02) | |||
| A reaction: Being an essentialist here, I take it that the stuff of the universe necessitates the so-called 'laws'. The metaphysically interesting question is whether the stuff might have been different. Search me! A nice test of metaphysical modality though. |
| 02 | p.16 | 18849 | Metaphysical necessity is absolute and universal; metaphysical possibility is very tolerant |
| Full Idea: If P is metaphysically necessary, then it is absolutely necessary, and necessary in every real (non-epistemic) sense; and if P is possible in any sense, then it's possible in the metaphysical sense. | |||
| From: Gideon Rosen (The Limits of Contingency [2006], 02) | |||
| A reaction: Rosen's shot at defining metaphysical necessity and possibility, and it looks pretty good to me. In my terms (drawing from Kit Fine) it is what is necessitated or permitted 'by everything'. So if it is necessitated by logic or nature, that's included. |
| 04 | p.18 | 18851 | Pairing (with Extensionality) guarantees an infinity of sets, just from a single element |
| Full Idea: In conjunction with Extensionality, Pairing entails that given a single non-set, infinitely many sets exist. | |||
| From: Gideon Rosen (The Limits of Contingency [2006], 04) |
| 04 | p.20 | 18852 | A Meinongian principle might say that there is an object for any modest class of properties |
| Full Idea: Meinongian abstraction principles say that for any (suitably restricted) class of properties, there exists an abstract entity (arbitrary object, subsistent entity) that possesses just those properties. | |||
| From: Gideon Rosen (The Limits of Contingency [2006], 04) | |||
| A reaction: This is 'Meinongian' because there will be an object which is circular and square. The nub of the idea presumably resides in what is meant by 'restricted'. An object possessing every conceivable property is, I guess, a step too far. |
| 05 | p.23 | 18853 | A proposition is 'correctly' conceivable if an ominiscient being could conceive it |
| Full Idea: To a first approximation, P is correctly conceivable iff it would be conceivable for a logically ominiscient being who was fully informed about the nature of things. | |||
| From: Gideon Rosen (The Limits of Contingency [2006], 05) | |||
| A reaction: Isn't the last bit covered by 'ominiscient'? Ah, I think the 'logically' only means they have a perfect grasp of what is consistent. This is to meet the standard problem, of ill-informed people 'conceiving' of things which are actually impossible. |
| 08 | p.34 | 18854 | The MRL view says laws are the theorems of the simplest and strongest account of the world |
| Full Idea: According to the Mill-Ramsey-Lewis account of the laws of nature, a generalisation is a law just in case it is a theorem of every true account of the actual world that achieves the best overall balance of simplicity and strength. | |||
| From: Gideon Rosen (The Limits of Contingency [2006], 08) | |||
| A reaction: The obvious objection is that many of the theorems will be utterly trivial, and that is one thing that the laws of nature are not. Unless you are including 'metaphysical laws' about very very fundamental things, like objects, properties, relations. |
| 08 | p.36 | 18855 | Combinatorial theories of possibility assume the principles of combination don't change across worlds |
| Full Idea: Combinatorial theories of possibility take it for granted ....that possible worlds in general share a syntax, as it were, differing only in the constituents from which they are generated, or in the particular manner of their arrangements. | |||
| From: Gideon Rosen (The Limits of Contingency [2006], 08) | |||
| A reaction: For instance, it might assume that every world has 'objects', to which 'properties' and 'relations' can be attached, or to which 'functions' can apply. |
| 10 | p.38 | 18858 | Sets, universals and aggregates may be metaphysically necessary in one sense, but not another |
| Full Idea: It may be metaphysically necessary in one sense that sets or universals or mereological aggregates exist, while in another sense existence is always a contingent matter. | |||
| From: Gideon Rosen (The Limits of Contingency [2006], 10) | |||
| A reaction: This idea depends on Idea 18856 and 18857. Personally I only think mereological aggregates and sets exist when people decide that they exist, so I don't see how they could ever be necessary. I'm unconvinced about his two concepts. |
| 10 | p.38 | 18857 | Standard Metaphysical Necessity: P holds wherever the actual form of the world holds |
| Full Idea: According to the Standard Conception of Metaphysical Necessity, P is metaphysically necessary when it holds in every possible world in which the laws of metaphysics (about the form or structure of the actual world) hold | |||
| From: Gideon Rosen (The Limits of Contingency [2006], 10) | |||
| A reaction: Rosen has a second meaning, in Idea 18856. He thinks it is crucial to see that there are two senses, because many things come out as metaphysically necessary on one concept, but contingent on the other. Interesting.... |
| 10 | p.39 | 18856 | Non-Standard Metaphysical Necessity: when ¬P is incompatible with the nature of things |
| Full Idea: According to the Non-Standard conception of Metaphysical Necessity, P is metaphysically necessary when its negation is logically incompatible with the nature of things. | |||
| From: Gideon Rosen (The Limits of Contingency [2006], 10) | |||
| A reaction: Rosen's new second meaning of the term. My immediate problem is with it resting on being 'logically' incompatible. Are squares 'logically' incompatible with circles? I like the idea that it rests on 'the nature of things'. (Psst! natures = essences) |
| 2010 | Metaphysical Dependence |
| 01 | p.109 | 14092 | Philosophers are often too fussy about words, dismissing perfectly useful ordinary terms |
| Full Idea: Philosophers can sometimes be too fussy about the words they use, dismissing as 'unintelligible' or 'obscure' certain forms of language that are perfectly meaningful by ordinary standards, and which may be of some real use. | |||
| From: Gideon Rosen (Metaphysical Dependence [2010], 01) | |||
| A reaction: Analytic philosophers are inclined to drop terms they can't formalise, but there is more to every concept than its formalisation (Frege's 'direction' for example). I want to rescue 'abstraction' and 'essence'. Rosen says distinguish, don't formalise. |
| 02 | p.112 | 14093 | An 'intrinsic' property is one that depends on a thing and its parts, and not on its relations |
| Full Idea: One intuitive gloss on 'intrinsic' property is that a property is intrinsic iff whether or not a thing has it depends entirely on how things stand with it and its parts, and not on its relation to some distinct thing. | |||
| From: Gideon Rosen (Metaphysical Dependence [2010], 02) | |||
| A reaction: He offers this as a useful reward for reviving 'depends on' in metaphysical talk. The problem here would be to explain the 'thing' and its 'parts' without mentioning the target property. The thing certainly can't be a bundle of tropes. |
| 03 | p.113 | 14094 | The excellent notion of metaphysical 'necessity' cannot be defined |
| Full Idea: Many of our best words in philosophy do not admit of definition, the notion of metaphysical 'necessity' being one pertinent example. | |||
| From: Gideon Rosen (Metaphysical Dependence [2010], 03) | |||
| A reaction: Rosen is busy defending words in metaphysics which cannot be pinned down with logical rigour. We are allowed to write □ for 'necessary', and it is accepted by logicians as being stable in a language. |
| 04 | p.114 | 14095 | Facts are structures of worldly items, rather like sentences, individuated by their ingredients |
| Full Idea: Facts are structured entities built up from worldly items rather as sentences are built up from words. They might be identified with Russellian propositions. They are individuated by their constituents and composition, and are fine-grained. | |||
| From: Gideon Rosen (Metaphysical Dependence [2010], 04) | |||
| A reaction: I'm a little cautious about the emphasis on being sentence-like. We have Russell's continual warnings against imposing subject-predicate structure on things. I think we should happily talk about 'facts' in metaphysics. |
| 05 | p.116 | 14096 | Explanations fail to be monotonic |
| Full Idea: The failure of monotonicity is a general feature of explanatory relations. | |||
| From: Gideon Rosen (Metaphysical Dependence [2010], 05) | |||
| A reaction: In other words, explanations can always shift in the light of new evidence. In principle this is right, but some explanations just seem permanent, like plate-tectonics as explanation for earthquakes. |
| 07 n10 | p.119 | 14097 | Things could be true 'in virtue of' others as relations between truths, or between truths and items |
| Full Idea: Our relation of 'in virtue of' is among facts or truths, whereas Fine's relation (if it is a relation at all) is a relation between a given truth and items whose natures ground that truth. | |||
| From: Gideon Rosen (Metaphysical Dependence [2010], 07 n10) | |||
| A reaction: This disagreement between two key players in the current debate on grounding looks rather significant. I think I favour Fine's view, as it seems more naturalistic, and less likely to succumb to conventionalism. |
| 10 | p.124 | 14098 | An acid is just a proton donor |
| Full Idea: To be an acid just is to be a proton donor. | |||
| From: Gideon Rosen (Metaphysical Dependence [2010], 10) | |||
| A reaction: My interest here is in whether we can say that we have found the 'essence' of an acid - so we want to know whether something 'deeper' explains the proton-donation. I suspect not. Being a proton donor happens to have a group of related consequences. |
| 10 | p.124 | 14099 | 'Bachelor' consists in or reduces to 'unmarried' male, but not the other way around |
| Full Idea: It sounds right to say that Fred's being a bachelor consists in (reduces to) being an unmarried male, but slightly off to say that Fred's being an unmarried male consists in (or reduces to) being a bachelor. There is a corresponding explanatory asymmetry. | |||
| From: Gideon Rosen (Metaphysical Dependence [2010], 10) | |||
| A reaction: This emerging understanding of the asymmetry of the idea shows that we are not just dealing with a simple semantic identity. Our concepts are richer than our language. He adds that a ball could be blue in virtue of being cerulean. |
| 10 | p.125 | 14100 | Figuring in the definition of a thing doesn't make it a part of that thing |
| Full Idea: From the simple fact that '1' figures in the definition of '2', it does not follow that 1 is part of 2. | |||
| From: Gideon Rosen (Metaphysical Dependence [2010], 10) | |||
| A reaction: He observes that quite independent things can be mentioned on the two sides of a definition, with no parthood relation. You begin to wonder what a definition really is. A causal chain? |
| 13 | p.133 | 14101 | Are necessary truths rooted in essences, or also in basic grounding laws? |
| Full Idea: Fine says a truth is necessary when it is a logical consequence of the essential truths, but maybe it is a consequence of the essential truths together with the basic grounding laws (the 'Moorean connections'). | |||
| From: Gideon Rosen (Metaphysical Dependence [2010], 13) | |||
| A reaction: I'm with Fine all the way here, as we really don't need to clog nature up with things called 'grounding laws', which are both obscure and inexplicable. Fine's story is the one for naturalistically inclined philosophers. |