A &#39;Mere Cambridge&#39; Test to Demarcate Extrinsic from Intrinsic Properties1

Roger Harris

I argue that a 'mere Cambridge' test can yield a mutually exclusive, jointly exhaustive, partition of properties between the intrinsic and the extrinsic. Unlike its rivals, this account can be extended to partition 2 nd and higher order properties of properties. A property F is intrinsic, I claim, iff the same relation of resemblance holds between all and only possible instances of F. By contrast, each possible bearer of an extrinsic property has a determinate relation to some independently contingent concrete object(s). Such a relation can hold for concrete and abstract objects, of objects which are not remotely duplicates, and can vary from one possible duplicate to another. I compare this with accounts which do not allow extension to 2 nd and higher order properties and give preliminary rebuttals for some main difficulties raised for the account advocated. Intrinsic; extrinsic; 'mere Cambridge' change; Lewis; Francescotti. 1. Preamble I defend and explain an account of intrinsicality which can be summarised as: – Those properties are intrinsic which are stable across all possible worlds. Where possessed by concrete objects, they are possessed by all possible duplicates of those objects. Their possession by properties and abstract objects signals the stable identities of those properties and abstract objects across all possible worlds. Intrinsic properties are united in being stable in virtue of their lack of any disqualifying dependence on any relation2 to independently contingent concrete things which are wholly distinct 3 from their bearers and whose existence and/or character varies from one possible world to another. Properties which do depend on such a relation are subject to possible variations which are 'mere Cambridge changes' to the bearers of those properties that vary in this manner, and are consequently extrinsic.

A ‘Mere Cambridge’ Test to Demarcate Extrinsic from Intrinsic Properties I am indebted to an anonymous referee for many helpful comments which have enabled me hopefully to clarify the claims that follow. (Pre-print of article available as 'Online First': http://link.springer.com/article/10.1007/s12136-017-0336-1please cite published version.) Abstract I argue that a ‘mere Cambridge’ test can yield a mutually exclusive, jointly exhaustive, partition of properties between the intrinsic and the extrinsic. Unlike its rivals, this account can be extended to partition 2nd and higher order properties of properties. A property F is intrinsic, I claim, iff the same relation of resemblance holds between all and only possible instances of F. By contrast, each possible bearer of an extrinsic property has a determinate relation to some independently contingent concrete object(s). Such a relation can hold for concrete and abstract objects, of objects which are not remotely duplicates, and can vary from one possible duplicate to another. I compare this with accounts which do not allow extension to 2nd and higher order properties and give preliminary rebuttals for some main difficulties raised for the account advocated. Intrinsic; extrinsic; ‘mere Cambridge’ change; Lewis; Francescotti. 1. Preamble I defend and explain an account of intrinsicality which can be summarised as: – Those properties are intrinsic which are stable across all possible worlds. Where possessed by concrete objects, they are possessed by all possible duplicates of those objects. Their possession by properties and abstract objects signals the stable identities of those properties and abstract objects across all possible worlds. Intrinsic properties are united in being stable in virtue of their lack of any disqualifying dependence on any relation For this I depend on the insight developed in detail by Francescotti 1999b in his characterisation of ‘d-relational’ properties, of which more below. to independently contingent concrete things which are wholly distinct I.e. having no part in common. from their bearers and whose existence and/or character varies from one possible world to another. Properties which do depend on such a relation are subject to possible variations which are ‘mere Cambridge changes’ to the bearers of those properties that vary in this manner, and are consequently extrinsic. In brief, the rationale for the account advocated here is as follows. To begin with, I take the ways in which objects may resemble or be distinct from one another to be properties, and I take abstract objects, such as properties and numbers to be ‘real’ enough to possess such 2nd and higher order properties as intrinsic and even. I take ‘duplication preserving’ properties to be those shared by every possible duplicate of their instances, where duplicates are objects which could not be more alike. I will argue that talk of possibility depends on assuming the stability of properties as outlined above. The criterion for intrinsicality rests on Geach’s Geach 1969. contrast between ‘real’ and ‘mere Cambridge’ change of which Weatherson & Marshall 2013 write (1.1): Geach noted that we can distinguish between real changes, such as what occurs in Socrates when he dies, from mere changes in which predicates one satisfies, such as occurs in Xanthippe when Socrates dies. The latter he termed ‘mere Cambridge’ change. There is something of a consensus that an object undergoes real change in an event iff there is some intrinsic property they satisfied before the event but not afterwards. Note that Geach does not thereby contrast ‘real’ with unreal change (ask any widow, as Humberstone 1996 notes). Rather, Geach contrasts a change to what x is like with a change to some other wholly distinct object(s) which merely alters x’s relations – i.e. a change to x itself, in contrast to a change to e.g. x’s surroundings. I argue that this yields a way of fixing the identity of an intrinsic or an extrinsic property that is more ‘fine-grained’ than necessary co-extensiveness. Namely, that the characteristic relations in which their bearers participate fix the identities of both intrinsic and extrinsic properties: i.e. for any intrinsic property FI, the same relation of resemblance holds between all and only possible instances of FI; for any extrinsic property FE, each of its possible bearers has a determinate relation to some wholly distinct independently contingent concrete object(s). Thus, an intrinsic property FI of a concrete object x is possessed by all possible duplicates of its instances. By contrast, an extrinsic property FE of x is one that x has in virtue of a relation to some wholly distinct, independently contingent concrete object(s) in which x participates, such as next to me, having the same owner as, being the tallest tree in the forest, etc. Many very different kinds of things may participate in the same relation on which FE depends. FE can consequently hold of objects which are not remotely duplicates, and vary from one possible duplicate to another just as the wholly distinct independently contingent concrete relata, on which it depends, can vary from world to possible world. A ‘mere Cambridge change’ to a concrete thing x is a change to the extrinsic properties of x which makes no difference to what x is like. By the same token, extrinsic properties are those which can vary between possible duplicates of their bearers. The ‘mere Cambridge’ test that I propose is that an extrinsic property is one that may be lost through a ‘mere Cambridge’ change, while intrinsic properties are just those that cannot. A ‘mere Cambridge’ property is, by contrast, a more restrictive category: these properties can only be lost through a ‘mere Cambridge’ change and make no difference to what their bearers are like (e.g. in London, next to me, having the same owner, etc.) So, all ‘mere Cambridge’ properties are extrinsic, but not vice-versa. We cannot take only Discussed in Francescotti 1999a, who raises the difficulty discussed here, previously raised by Humberstone 1996, which I hope I rebut below in §6. ‘mere Cambridge’ properties to be extrinsic because, if FE is e.g. having the same mass See Hoffmann-Kolss 2010 as one’s own son, then FE can be gained or lost by a parent through a ‘mere Cambridge’ change to the parent (the son gains or loses mass) or through an intrinsic, ‘real’ change (the parent gains or loses mass). Such properties, while they may make a difference to what their bearers are like, are still extrinsic by the test proposed: they may be lost through a ‘mere Cambridge’ change, which does not make a difference to what their bearers are like, and, consequently, they can vary between possible duplicates of their bearers, even though they may also be lost through an intrinsic, ‘real change’ to their bearers. In §6. I argue that all properties like having the same mass as one’s own son are intrinsic/extrinsic compounds which can be resolved into wholly intrinsic and wholly extrinsic (mere Cambridge) disjuncts or conjuncts. Take, e.g. concrete By contrast, 2nd order superlatives, true of properties, numbers, shapes etc. are intrinsic: e.g. Platonic solid with the fewest faces. superlatives: T can cease to be the tallest tree in the forest either if another tree grows taller (a ‘mere Cambridge’ change to T) or if T is felled (a real change to T). ‘T is the tallest tree in the forest’ = ‘T is H metres high (intrinsic to T) and T belongs to set of trees F (extrinsic to T) such that every other member of F is less than H metres high’. The cross-world stability of intrinsic properties of concrete objects arises, I shall argue, because, for every intrinsic property F of concrete objects, there is no possible concrete F thing which does not resemble all other actual and possible F things in being F – i.e. for an intrinsic property F the same relation of resemblance holds between all and only possible instances of F. However, if ‘intrinsic’ is an epithet properly applicable to properties of concrete objects, then properties themselves may I write ‘may’ since it is possible to, and some do, disallow or restrict the application of 2nd and higher order properties. The costs of doing so are discussed in Cowling 2017. He argues that neither theories of tropes nor of universals can be developed without invoking 2nd order intrinsicality. While noting that 2nd order intrinsicality poses problems for many current criteria proposed to mark the intrinsic/extrinsic distinction he does not directly address the question of a criterion that will suffice., in turn, be the bearers of 2nd and higher order intrinsic or extrinsic properties – intrinsic itself being a case in point. It is intrinsic to magnetism that magnetism is an intrinsic property, but magnetism can, in turn, have the extrinsic property investigated by Faraday. If so, no account of intrinsicality/extrinsicality can be given by a criterion applicable solely to the (1st order) properties of concrete objects – a drawback for all those criteria whose genealogy can be traced back to Kim’s 1982 suggestion (see §2 below) that intrinsic properties are those whose possession is compatible with loneliness ‘Loneliness’ is an object’s existing as the sole object in some possible world., since it does not seem that properties can be lonely. The account I advocate here has an advantage over very many of the criteria proposed in the literature to distinguish intrinsic, since these are applicable only to the properties of concrete objects (see §2.). I am after a criterion that applies equally to 2nd and higher order properties of properties, like intrinsic itself. The stability of intrinsic properties of properties and abstract objects arises, I shall argue, because for every intrinsic property GI of a property or abstract object F, there is no possible world at which property F does not possess GI. This is so irrespective of what may vary from one possible world to another, including those in which F has no instances (because e.g. red is required to specify the intrinsic character of possible world W~R which contains no red thing One might argue that possible worlds merely need to be characterised positively by exhaustively listing those properties which its contents do display. Against this, I say that, so long as the actual world cannot be characterised in this way (who knows all the properties actual things possess?), nor can those deviations from the actual world we specify by adding or subtracting properties. ). By contrast, I will argue, an abstract object F can have an extrinsic property GE in virtue of a relation F has to some independently contingent concrete object(s) wholly distinct from bearers of F – e.g. the same colour as a tomato, investigated by Faraday, entertained by Descartes, etc. This can vary from one possible world to another just as those wholly distinct relata vary (tomatoes might have been blue, Faraday might have been a botanist, Descartes an empiricist and so on, and each might not exist). Moreover, many very different kinds of abstracta may participate in the same relation on which GE depends, so no single relation of resemblance holds between all and only possible instances of GE (Faraday might have investigated all sorts of different properties). A ‘mere Cambridge change’ to any property or abstract object F is a change to an extrinsic property GE of F which makes no difference to what any possible instance of F is like, or to the cross-world identity of the property or abstract object F. The requirement on intrinsic properties to be stable across all possible worlds provides an overall rationale uniting the ‘duplication preserving’ and ‘non-relational’ criteria for intrinsicality. It mitigates both the apparent circularity of the former – Lewis’s worry in his 1983 – (“duplicates are objects which are alike in all their intrinsic properties; intrinsic properties are those which are unchanged between duplicates”) and the apparent arbitrariness of the latter in proscribing some but not all relational properties. (After all, likeness is a relation that instances of any intrinsic property bear to one another.) The justification for both lies in the need for a class of properties picking out resemblance classes stable across all possible worlds in order to frame comparisons between such worlds. So, making comparisons between possible worlds does not explain the necessity that, for every intrinsic property FI – say triangular – there is no possible abstract or concrete triangular thing which does not resemble all other actual and possible triangular things in being triangular. Rather, it is a condition which must be met before any such comparisons between worlds can possibly succeed in explaining possibility and necessity, namely that, for any intrinsic property FI, the same relation of resemblance holds between all and only possible instances of FI. Let’s expand on and hopefully justify this cryptic beginning. If being possessed by all possible duplicates of its instances makes F intrinsic, then F is intrinsic in every possible world; and being intrinsic is like unique, which is (and unlike extended, which is not) among those properties which exemplify themselves. The reason the property intrinsic is an intrinsic 2nd order property of red cannot be because it is made intrinsic by its being possessed by all possible duplicates of its instances: as a property, red seems not to have duplicates Unless taken to be tropes, but see §2.1. A duplication preservation criterion for intrinsic needs to be supplemented to account for the intrinsicality of 2nd order properties such as intrinsic itself. Francescotti’s account of d-relations does just this. Weatherson and Marshall 2013 outline four alternative styles of criterion distinguishing intrinsic from non-intrinsic properties Though I assume this, below, not everyone takes all non-intrinsic properties to be extrinsic, see e.g. Lewis 1986). Lewis consequently needs an independent account of extrinsicality. He takes external relations to be exclusively (analogically) spatio-temporal in character and must declare many properties to be neither intrinsic nor extrinsic – e.g. being an uncle, having the same owner, being thought of by John, not being accompanied by a talking donkey – yet their loss or gain would be ‘mere Cambridge’ changes, they depend on d-relations, are lost by ‘lonely duplicates’ and, intuitively, they seem plainly to be extrinsic. : Non-Relational vs. Relational Properties (citing Francescotti’s analysis of those disqualifying d-relations that preclude intrinsicality) Duplication Preserving vs. Duplication Non-Preserving Properties (which they broadly characterise with the ‘platitude’ “F is intrinsic iff F never differs between duplicates.”) Interior vs. Exterior Properties (which they broadly characterise with the ‘platitude’ “Being F is an intrinsic property iff, necessarily, anything that is F is F in virtue of the way it itself, and nothing wholly distinct from it, is.”) Local vs. Non-Local Properties (which they broadly characterise with the ‘platitude’ “F is an intrinsic property iff, necessarily, for any x, an ascription of F to x is entirely about how that thing and its parts are, and not at all about how things wholly distinct from it are.”) They note that no single consistent analysis fits all that writers have taken ‘intrinsic’ to mean (endorsing Humberstone 1996). It is worse than they make out. Thesaurus.com lists many purported ‘synonyms’ of ‘intrinsic’ but includes no instances of I. & II. It mostly inclines towards III. & IV. but includes a cluster of further terms broadly meaning ‘essential’, ‘inherent’ or ‘endogenous’, which Weatherson and Marshall do not discuss, though some philosophers appeal to them (e.g. Figdor 2008). Given all this, it is not surprising to find ‘intuitive’ counterexamples proposed to any consistent putative account of the intrinsic/extrinsic distinction. The view I defend combines what I. & II. suggest, namely that, if duplicates are concrete objects that could not be more alike, then ‘duplication preserving’ (intrinsic) properties of concrete objects are shared by every possible duplicate of their instances; while ‘non-duplication preserving’ (extrinsic) properties are not so shared because they depend on some disqualifying (external This relation is not necessarily symmetrically external – see §3.4 – but is a relation external to the bearer of the extrinsic property.) relation which fails to hold of all possible (duplicates of their) ‘Duplicates’ and ‘counterparts’ in brackets are included because the arguments to follow aim to be neutral as between counterpart theory + 4dimensionalism as opposed to trans-world individuals + endurance. Also, the requisite sorts of ‘disqualifying relations’ can hold of properties, too, whether or not these have duplicates. instances. This yields an account which, I claim, gives fewest hostages to competing philosophical positions. It also decouples intrinsic – an intrinsic property of properties, from inherent, essential, endogenous etc. which are 2nd order extrinsic adverbial properties of the instantiation of 1st order properties in some but not all cases: green sometimes is inherent, essential, endogenous or whatever but not always, while always being an intrinsic property stable across every possible world. For, despite not having Unless taken to be tropes, but see §2.1 duplicates, properties themselves, e.g. magnetism, seem to have 2nd order properties: intrinsic is one; investigated by Faraday is another. Moreover, being extrinsic is, itself, an 3rd order intrinsic feature of the 2nd order property investigated by Faraday, which is how we know that investigated by Faraday would unfailingly be an extrinsic property of any property or object that Faraday might possibly investigate. The nature of the relation to Faraday fixes the identity of the extrinsic property – a relation that is not stable from one possible world to another. I.e. both a concrete historic apparatus, and the property magnetism can have the extrinsic property investigated by Faraday in virtue of such a disqualifying relation. Both can have such a relation to some wholly distinct independently contingent concrete object(s) – in this instance, (counterparts of) Faraday. This will apply even if properties have no duplicates Unless taken to be tropes, but see §2.1, so absence-of-a-disqualifying-relation is a putative criterion for intrinsicality appropriate both for properties of contingent concrete objects and for 2nd and higher order properties of properties. The question remains ‘Why, and under what circumstances, does this kind of relation disqualify a 2nd (or higher) order property from being intrinsic? After all, we can’t proscribe all relations to wholly distinct things. If x has an intrinsic property F, then x must bear the relation resemblance to all other actual or possible bearers of F. So which relations of x are proscribed, and for what reason? The short answer is ‘Those relations of x that change as possible alterations occur to relata which are independently contingent object(s) wholly distinct from x but occur without altering what x is like – relations such as its location, ownership, being accompanied, being thought of, etc.’ These are ‘mere Cambridge’ changes. Intrinsic properties, by contrast, are bona fide respects of resemblance, both between concrete and abstract objects, and, unlike extrinsic properties, are independent of any contingent disqualifying relation. So, object x having a relation to wholly distinct, independently contingent relata, which can vary independently of what x is like, allows properties dependent on such a relation to vary between possible duplicates of x, and, thus, disqualifies such dependent properties from being intrinsic. Likewise, property F having a relation to wholly distinct, independently contingent relata, which can vary independently of the cross-world identity of F, allows properties dependent on such a relation (e.g. investigated by Faraday) to vary between the same property F in different possible worlds, and, thus, disqualifies such dependent properties from being intrinsic. I elaborate on these claims further in §3., but begin, in §2., with some schematic considerations which count against its rivals, III. & IV. §2. Shortcomings of Supposing that a Property’s Being Intrinsic Turns on the Way it is Instantiated. The intuitions regarding intrinsicality embodied in III. & IV. have been surprisingly difficult to formulate precisely. These continuing vicissitudes are surveyed in Weatherson and Marshall 2013. Let me give some cursory justification for failing to discuss them at length. I think there were always reasons not to venture so far with this project. §2.1 III. & IV., along with ‘inherent’, ‘endogenous’, ‘essential’ and the like, initially concern a feature of the instantiation Figdor 2008 points this out by distinguishing ‘intrinsic’ from ‘intrinsically’. of a property by a particular concrete object that makes it ‘locally’ ‘Locally’ as opposed to ‘globally’, not ‘local’ as contrasted in IV. with ‘non-local’. intrinsic, inherent, endogenous, essential etc. to that object, when the same property might not be so to some other object. So, ‘locally’ intrinsic is a 2nd order extrinsic adverbial property (being possessed by x intrinsically) that a property may possess in relation to some (but not necessarily all) of its concrete instances, in the same way being inherent, endogenous, essential etc. can be. Thus, it might seem that green can be ‘intrinsic’ to one thing while not to another, which is just green because it is under a green light, or a magnetic field can be ‘intrinsic’ to a ‘permanent’ magnet but not to an electro-magnet in which it is only present when a current flows. This sort of ‘local’ intrinsicality is a feature of the relation a property has to its bearer, by contrast with a 2nd order intrinsic feature of the properties green and magnetic themselves, namely, that in all possible worlds they should unfailingly be the same property – i.e. ‘globally’ intrinsic. Consequently I don’t think ‘intrinsic’ is used in the same sense when we speak of ‘locally’ and ‘globally’ intrinsic properties. It seems we can generalise from ‘local’ to ‘global’ intrinsicality if we follow a principle from Humberstone that the intrinsic properties are precisely those which are locally intrinsic to all their [possible My interpolation – Humberstone makes clear earlier that he intends to generalise across possible worlds, not just within the actual world.] possessors adapted by Weatherson and Marshall as (GTL) If F is an intrinsic property, then it is necessary that every x that has F has F in an intrinsic fashion (LTG) If it is necessary that every x that has F has F in an intrinsic fashion, then F is an intrinsic property But, on this account, necessary ‘local’ intrinsicality is plainly not a feature of the contingent relation a property has to its bearer which can vary from bearer to bearer as green and magnetic do above, i.e. as any 2nd order extrinsic adverbial property does. The necessity “that every x that has F has F in an intrinsic fashion” has become, instead, a 2nd order intrinsic feature of every intrinsic property. It leaves out of account all those cases where it is contingent whether an x that has F has F in an intrinsic fashion. So, though I have no space to justify this here, I effectively reserve ‘intrinsic’ to describe those properties that are the respects in which all actual and possible resemblances obtain, so as not to treat it as a synonym for ‘inherent’ and its cognates, which cluster round the altogether different 2nd order extrinsic adverbial notion. In any case, the criterion ‘being shared by every duplicate of its instances’ needs to be supplemented to account for the intrinsicality of 2nd order properties such as intrinsic, as it is neither necessary nor sufficient for some F2 to be a 2nd order intrinsic property, at least not in so far as properties and abstract objects are necessarily singular and have no duplicates. (Perhaps they do if tropes are invoked to account for properties, but I started by assuming that properties are ‘real’ enough to possess such 2nd and higher order properties as intrinsic. If we invoke tropes, to avoid taking properties to be universals, it seems we abolish the bearers of the 2nd order property intrinsic as a ‘global’ attribute of properties. Tropes, as (albeit abstract) particulars, could have duplicates, but not because they shared all their intrinsic properties, because tropes do not have 1st order properties – it is precisely the brute resemblance between distinct tropes that supposedly allows us to do without reifying 1st order properties that retain their identities across possible worlds. Moreover, because tropes are particulars, their having duplicates can have no bearing on the intrinsicality of 2nd and higher order properties of properties, which is presently at issue. A related problem is that the intrinsic/extrinsic distinction appears to be required before tropes can be invoked to avoid reifying those ‘properties’ whose instances resemble one another. If our initial domain of ‘properties’ contains ‘mere Cambridge’ properties which are wholly extrinsic, then, characteristically, if FMC is such a property, objects can possess FMC irrespective of any resemblance between them: existing before I was born, outside the orbit of Venus, not anticipated by Newton etc. are all examples. Before an account can be given which invokes resemblances between tropes to block the reification of properties as universals, a partition of properties is needed to distinguish those which do from those which do not attribute resemblance between their instances and to disentangle the respective components of those compound properties like tallest tree in the forest – the aim of this essay.) It seems, moreover, to be a 3rd order intrinsic feature of the 2nd order extrinsic character of the 1st order property next to me that it is unfailingly extrinsic: things next to me have possible duplicates both far from me and in possible worlds from which I am absent, and many disparate things can be next to me, so being next to me is a ‘mere Cambridge’ property and can be no part of what those things are like, in any possible world, since all true duplicates of instances of being next to me could not be more alike, irrespective of whether they are next to me or not This claim is open to a major objection: namely that things often seem to be alike in virtue of extrinsic properties, e.g. coming from Yorkshire or having a common ancestor. I hope to rebut this objections in §5.. So, intrinsicality/extrinsicality seem to be properties which need to be intrinsic features of any property to which they are ascribed. I.e. both are ‘global’ features of the 1st or higher order properties they characterise. So, intrinsicality is unlike both being inherent, which varies from one concrete bearer of a property to another, and investigated by Faraday, which is an extrinsic feature of magnetism, the property, which it does not have in worlds without Faraday. §2.2 The idea behind III. & IV., however, is that ‘intrinsically’ (‘in an intrinsic fashion’) should impose further requirements for F to be an intrinsic property of concrete objects, over and above every duplicate of every instance of F needing to have F, because this seems circular e.g. to Lewis in his 1983. But III. & IV. can supply no criterion for the intrinsicality of 2nd order properties of properties. Let’s see why not. In an indicative statement of the intuition underlying III. & IV., Yablo 1999, writes: You know what an intrinsic property is: it’s a property that a thing has (or lacks) regardless of what may be going on outside of itself. To be intrinsic is to possess the second-order feature of stability-under-variation-in-the-outside-world. But what is it that must “possess the second-order feature of stability-under-variation-in-the-outside-world” in order to be intrinsic? You’d think that 2nd order stability would have to be a condition satisfied by the property, not by the bearer of that property. Why, otherwise, is it “2nd order”? We’ve seen that the 2nd order feature stability of the property is just what I. & II do demand and is, I will argue, both the necessary and sufficient requirement for a property to be intrinsic, so I need to indicate how ‘stability of the bearer’ adds nothing. Most proponents of III. & IV. try to capture what is involved in being “a property that a thing has (or lacks) regardless of what may be going on outside of itself”, by attempting to capture how it is that the bearer rather than the property, exhibits the required stability. The notion, originating with Kim 1982, is that, if F is an intrinsic property, then any bearer x that has F does so irrespective of what anything else is like, of what else there is and even of whether there is anything else. Indicative expressions of this intuition are also found in Lewis 1983, Vallentyne 1997, the ‘indifference to loneliness’ criterion proposed in Langton and Lewis 1998, and Weatherson 2001, who writes (p. 369): It is a platitude that a property F is intrinsic iff whether an object is F does not depend on the way the rest of the world is. However this may be formulated precisely, Cameron 2008 argues that all such formulations imply that, for a property to be intrinsic, all its possible bearers must have a possible ‘lonely duplicate’. Perhaps, ‘interiority’ and ‘locality’ of properties that are possessed intrinsically might be articulated so as not to require the possibility of a ‘lonely duplicate’ of the bearer. Even so it is hard to see how the quasi-spatial metaphors invoked by the interior/exterior and local/non-local contrasts between properties of concrete objects can apply to 2nd order intrinsic properties of properties or abstract objects, since these have no location to which a property might be, or not be “interior” or “local”. (Though it is envisaged by friends of tropes that these are abstract particulars precisely located in space/time, their spatiotemporal locations are not obviously 2nd order properties of the property green – they are, rather, 1st order extrinsic properties of this or that greenness token. If there can be 2nd order properties of properties or numbers – the oddness of 13, say – it is hard to see how these can be analysed as spatiotemporally located abstract particulars.) The larger part of recent literature on the intrinsic/extrinsic distinction has focussed on III. & IV. It has sought to progress Lewis’s metaphysical project, generally requiring intrinsic to reflect ‘Hume’s dictum’ – that there are no necessary connections between ‘distinct existences’. I think ‘intrinsic’ need not carry this neo-Humean burden. Wilson 2010 discusses this knot of issues and notes that a criterion for intrinsic that rests on ‘non-relationality’ does not have to be compatible with Hume’s dictum, while her 2015 documents the centrality of his notion of the intrinsic to Lewis’s entire project. I will argue below that true attribution of every physical property allows us to infer something about the ambient conditions of its bearer and that all are ‘causal’ properties in the relatively ‘weak’ sense that their instantiation complies with specific laws of nature holding in those worlds in which they have instances. §2.3 The first indication that III. & IV add nothing comes when we ask what distinguishes any 2nd order intrinsic feature of a property F from an extrinsic feature. Intrinsic is itself a putative 2nd order intrinsic property of magnetism, while, I maintain, investigated by Faraday is not – the latter is a 2nd order extrinsic property of magnetism. For any F2 to be a globally intrinsic 2nd order property of F, all that is needed is for it to be a feature of every possible instance of F, in every possible world. If intrinsic being unfailingly possessed by every possible instance of F is enough to make intrinsic a 2nd order intrinsic property of F, (as the complementarity of Weatherson and Marshall’s (GTL)&(LTG) above suggests) then a criterion concerning how F is individually possessed by its concrete bearers can add nothing further. It cannot be that ‘stability of the bearer’ distinguishes a 2nd order intrinsic property: F is a property, not a concrete object, and thus, arguably, has no duplicate, ‘lonely’ or otherwise. I argued, in 2.1, that invoking tropes to account for properties allows ‘duplicate tropes’, but, only for properties already identified as intrinsic. Moreover, if tropes are spatially located particulars, it remains problematic to envisage how properties or abstract objects can have, as 2nd order properties, properties they share with concrete objects, like symmetry, investigated by Faraday and so forth. The disqualification of investigated by Faraday arises, I claim, because Faraday is not found in every possible world containing instances of magnetism and so cannot be unfailingly possessed by every possible duplicate of any instance of magnetism. Investigated by Faraday depends, as, I say, all extrinsic properties do, on its bearer’s relation to one or more wholly distinct concrete objects whose character and existence are independently contingent. It is this that disqualifies it from being intrinsic, because investigated by Faraday lacks the cross-world stability required of an intrinsic property: it can vary between possible duplicates and between the same properties in worlds with or without Faraday. In short, at least some intrinsic and extrinsic properties are instantiated by both concrete and abstract objects. This requires a criterion both for what makes some F an intrinsic or extrinsic property of a concrete object and for what makes some F2 an intrinsic or an extrinsic 2nd order property of any number or property. Moreover, there must be a requirement that the 1st & 2nd order property terms ‘intrinsic’ and ‘extrinsic’ both be univocal to some degree – i.e. the way in which magnetism is an intrinsic feature of physical objects must at least resemble the way in which intrinsic is an intrinsic feature of the property magnetism; and, by the same token, the way in which investigated by Faraday is an extrinsic feature of a coil of copper wire must resemble the way in which investigated by Faraday is an extrinsic feature of the property magnetism. I will argue in §3. that the presence or absence of a disqualifying external d-relation does the trick. §2.4 There are problems, too, posed by the 2nd order property intrinsic, for the notion that properties are nothing more than the cross-world sets of their concrete instances (an aspiration of the neo-Humean framework within which the intrinsic is widely discussed). Intrinsic could, indeed, be identified with such a cross-world set, namely the set of all possible sets of possible instances of the intrinsic properties. However, nothing in any possible world has no intrinsic properties, so the membership of the cross-world set intrinsic is nothing short of everything there could possibly be. By the same token, nothing in any possible world lacks extrinsic properties: they all, at least, are either lonely or accompanied Point clarified thanks to referee.. So, if the membership of the putative cross-world set extrinsic is the set of all possible sets of possible instances of the extrinsic properties – it is, again, nothing short of everything there could possibly be. Prima facie, it seems that the theory that properties are cross-world sets of their concrete instances must forbid an intrinsic/extrinsic distinction between properties, because, unavoidably, intrinsic and extrinsic have the very same cross-world extension. Alternatively, we could conclude that, unsurprisingly, this theory cannot cope with hyperintensional 2nd order properties of properties, numbers and the like. §2.5 A further reason not to pursue III. & IV. is that there do not seem to be any properties A point I have already laboured elsewhere (Ref 2.). “that a thing has (or lacks) regardless of what may be going on outside of itself”, for any concrete object. Detonate a nuclear bomb, be on hand for a supernova or drop into a black hole as thought-experiments to test this. Such considerations apply without exception to all the properties attributed by the descriptive vocabulary of the natural sciences These considerations are strengthened in e.g. Earman & Roberts 2005 by appealing to quantum entanglement., including sortal terms and the identities of the 3- or 4-dimensional objects they individuate. The attribution of any physical property consequently always allows us to infer something about the ambient conditions of the bearer of that property. Consequently, attributing any physical property to its bearer is neither entirely about how that thing and its parts are, and not at all about how things wholly distinct from it are nor true in virtue of the way it itself, and nothing wholly distinct from it, is. III. & IV both, therefore, imply that no physical property can be intrinsic. III. & IV imply, too, that no properties can be intrinsic that are ‘causal’, i.e. whose instantiation complies with specific laws of nature holding in those worlds in which they have instances and thus allow inferences about physical circumstances in which they are possessed, yet this is a universal feature of the physical properties science ascribes to the world. §2.6 Indeed, contra III. & IV., there is a strong independent reason to hold that ‘causal’ properties must be intrinsic. Suppose that ‘our’ laws of nature are nothing more than the exceptionless regularities that characterise the actual world, and that other possible worlds can resemble this actual world by sharing the same laws of nature. In that case, laws of nature are, by any criterion (indeed, by III. & IV. themselves) an intrinsic feature of those worlds in which they obtain, since they: do not obtain in virtue of a relation that a possible world has to any other wholly distinct thing (complying with I.); are shared by every possible duplicate of that world (complying with II.) (every possible world W has, as duplicates, proper parts of slightly larger possible worlds with the same laws plus one or more items more than W contains – unless extrinsic differences between the contents of different possible worlds engender intrinsic differences between the containing worlds – in which case those worlds’ properties could not be intrinsic by any criterion that entailed their having ‘lonely duplicates’); obtain of any given possible world “in virtue of the way it itself, and nothing wholly distinct from it, is” (complying with III.); are “entirely about how that thing and its parts are, and not at all about how things wholly distinct from it are” (complying with IV.) It is difficult, then, to find a criterion that allows one to argue that the causal features of any given possible world are not intrinsic features of that world and all it contains. Consequently, I suggest that there are good enough prima facie reasons to allow that causal properties can be as intrinsic as the laws with which their instantiations comply, and to reject ‘interiority’ (III.) and ‘locality’ (IV.) as incapable of providing plausible criteria to distinguish the intrinsic. §2.7 Finally, objecting to a ‘duplicate preservation’ criterion for intrinsic, Weatherson & Marshall 2013 (2.4) write: Say that a has b as a part, and consider the event whereby b is replaced in a by c, which happens to be a duplicate of b. This event seems to constitute a real change in a, not merely a Cambridge change, but it does not constitute a change in qualitative properties, and hence does not constitute a change in duplication preserving properties. But we saw that Geach’s ‘real change’ is a term of art. It does not contrast ‘change which is real’ with the unreal ones. Substitution of a duplicate part is no more unreal than becoming a widow, but each is a ‘mere Cambridge’ change because neither meets Weatherson & Marshall’s own necessary and sufficient condition to be a so-called ‘real’ change in Geach’s sense, since we saw above that they write (note the biconditional – my italics): …an object undergoes real change in an event iff there is some intrinsic property they satisfied before the event but not afterwards and, in this case, there is not, because b and c are duplicates and have exactly the same intrinsic properties. It has been suggested Amongst the comments from the referee. that having part c rather than part b involves an intrinsic change to a because, despite being duplicates, b and c have different ‘identity properties’ or haecceities. I do not take such properties to be intrinsic because I argue (in §4.) that identity cannot be intrinsic if duplicates are possible which share all their intrinsic properties, since neither identity nor haecceities can be shared. §3. Central Argument for Stability of The Property 3.1 Overview In this section, I try to show, both for concrete objects, and for properties and abstract objects (for whose identity there is no ‘numerical/qualitative’ distinction), how the ‘mere Cambridge’ criterion identifies, as extrinsic, properties that can change while making no difference to what their relata are like. This test reconciles non-relationality and duplication-preservation criteria (as far as each goes) in taking stability of the intrinsic property to explain why absence-of-a-disqualifying-relation allows both that intrinsic properties must be shared by all concrete duplicates of their instances and that they are just those retained by that property, number etc. in every possible world, including those in which it has no instances. The detailed task of identifying the nature of this ‘disqualifying relation’ I take to have largely been accomplished by Francescotti’s 1999b account of d-relations. In order not to slow this section’s central exposition, I will return, in §§4 – 6, hopefully to rebut some difficulties that arise as I proceed. 3.2 Stability of Intrinsic Properties The ‘stability of the property’ thesis parallels the notion that intrinsic properties are those that are rigidly designated as necessarily the same property in all possible worlds. The latter is a thesis about the reference of terms rather than about the character of properties and some See LaPorte 2016 §4.2 have argued that the apparatus of rigid designation is unnecessary for property terms so long as ‘magnetism’ has the same meaning no matter in which world we attribute it. I will just use terms in italics – e.g. magnetism – to refer to properties, without asking how that is accomplished. The central rationale for this account is that it is a necessary condition for any comparisons between possibilities (or possible worlds, of whatever stripe Considerations derived from theories of possible worlds impinge on many discussions of intrinsicality. Perhaps they should not, for without the prior stability of properties no comparisons between possible worlds can serve to explain necessity in the first place.) that there should be a class of properties that are stable (i.e. properties that are the same at each of those possible worlds) so that, between possibilities (across possible worlds), like can be compared with like and unlike. If e.g. red, charge, fluid etc. are each not the same property at each possible world Perhaps there are possible worlds where things have properties – frumious and slithy, say – which no actual things possess, but I am not sure that we can know anything beyond this about them., then it would be futile to attempt to compare possibilities (possible worlds) where things and their properties are differently distributed from one to another. So, I claim intrinsic properties to be those that exhibit this stability and are responsible for all actual and possible genuine resemblance. (I argue against objections to this specific claim at greater length in §5.) The stability of the intrinsic property FI consists in the same relation of resemblance holding between all and only the possible instances of FI. Let’s take the existence of, and resemblances between concrete objects to be contingent, Apart from necessary concrete beings. The anonymous referee took me to task for assuming there were none. Whatever these are like, if any exist, no possible world can differ in its necessary concrete contents. Regarding all necessary objects (abstract or concrete), I argue below (§3.4) that only contingent accompaniment is extrinsic. so that, for any possible such concrete object x, it is contingent whether there is: any object exactly like x; one sole object exactly like x; more than one object exactly like x. No specific ‘metric’ of similarity is needed to support the notion that duplicates are objects that could not be more alike. We merely need to note that things can be more or less alike: a raven is not very like a writing desk, but it is very much more like another raven. Resemblance must also be reflexive: each thing cannot help but be exactly like itself. So exact duplicates of concrete objects must always be possible. Because any x is exactly like itself, so some y, too, can possibly be exactly like x, because exactly like x must be a way things may possibly be, since this how x itself possibly is. Plainly, then, yet other things can be less than exactly like x. The ‘mere Cambridge’ test precisely distinguishes the intrinsic properties from the extrinsic properties of concrete things just because the latter are not shared by every possible duplicate of their instances and so may change between possible duplicates, i.e. while not changing what their bearers are like (since they remain duplicates) – these are ‘mere Cambridge’ changes. This chimes with Lewis’s 1986 (p.62) designation of resemblance as an internal relation, namely a relation that supervenes on the intrinsic properties of its relata. However, if 2nd order properties are also considered, we have a case like those Lewis discusses (1986 pp. 14 – 17) where supervenience cannot be readily understood with reference to possible worlds. This is because, for every intrinsic property FI, there is no possible FI thing which does not resemble all other actual and possible FI things in being FI. Put ‘red’, ‘100grams’, ‘silver’ etc. for ‘FI’, and it becomes clear that red, 100grams, silver must each be the same property of a concrete object at every world, so intrinsic is, in turn, an intrinsic property of the properties red, 100grams, silver, etc. Put ‘intrinsic’ (the 2nd order property) for FI and its bearers – properties – are not differently distributed across possible worlds in the way that their concrete instances are so as to ‘explain’ why, necessarily, all FI things must be alike in being FI. Indeed, the boot is on the other foot: the thesis of the stability of intrinsic properties is a profoundly important principle because it explains why the way things are distributed across possible worlds may be used to explain 1st order necessity and possibility. Such comparisons across possible worlds could gain no explanatory ‘purchase’ without this stability. It also delineates, by exclusion, extrinsic properties as those that do not only turn on resemblances between their bearers, because extrinsic properties can vary while making no difference to what their (concrete or abstract) bearers are like. (Unless there are relations which are neither internal nor external, which Lewis claims but I argue there are not.) The ‘stability of the property’ thesis says that an intrinsic property FI – e.g. magnetism – retains its identity – is the very same property – at all possible worlds (including those which are characterised by its absence – i.e. by its having no instances in those worlds): for any 1st order intrinsic property FI the same relation of resemblance holds between all and only possible instances of FI. So, if magnetism being an intrinsic property of concrete magnetic objects entails that magnetism is shared by every possible duplicate of its instances, then magnetism’s having that character is, in turn, intrinsic to the property magnetism, so magnetism is globally intrinsic – intrinsic in every possible world – while magnetism’s having been investigated by Faraday is a property it only has in those worlds which contain (a counterpart of) Faraday and in which he investigated magnetism. Whether it was investigated by Faraday makes no difference to what the property magnetism is like, which has to be the same at every world including those in which Faraday does not appear. (Equally irrelevant to the identity and intrinsic character of magnetism is whether it is inherent, as with a permanent magnet, or depends on the flow of a current, like an electromagnet. Faraday’s great discoveries arose precisely from his recognising this identity.) The relevance of the intrinsic properties of an abstract object to its self-identity is a crucial difference between concrete and abstract objects. Apart, possibly, from tropes (but see §2.1), abstract objects like properties, numbers, sets with actual and possible members, shapes etc. are necessarily singular, can have no duplicates, so they do not have a ‘numerical’ as distinct from a ‘qualitative’ identity. Instead they are ‘present’ at (if not in) every possible world (if ‘present’ at any), even at those where they have no instances/members. Abstract objects are causally inert and do not change. Only in so far as properties are immutable and uniform across times and worlds can they explain how worlds and times can be distinct but comparable in respect of the number and intrinsic character of their contents; and, because their cross-world identities turn on their intrinsic properties, these are, effectively, the essential properties of abstract objects, too. So, for abstract objects, exact resemblance is identity and, as a corollary, so long as identity is necessary, every intrinsic property belonging to a shape, property, number or any other abstract object is essential to it, as are the internal relations which supervene on those intrinsic properties. Another corollary is that only concrete objects can possibly have duplicates or have ‘accidental intrinsics’ (my cat is essentially carnivorous, but accidentally black). One might argue, too, that abstracta instantiate their properties in a wholly different manner from concrete objects, if they instantiate them at all, since 1st order instantiation seems to involve spatio-temporal location. 3.3 Extrinsic Properties Not Shared by All Possible Duplicates Those 2nd order properties of properties like investigated by Faraday, which vary from one possible world to another, play no part in fixing the identity of the property magnetism by characterising what it is like at every possible world. Their being extrinsic (like being intrinsic) is a 3rd order intrinsic feature of 1st order property magnetism’s 2nd order extrinsic property investigated by Faraday. It is this you understand when you see that there is no possible world in which investigated by Faraday is intrinsic to anything, because it is true of magnetism, and true of other properties or things and their duplicates, in only some and not in all possible worlds. This has the consequence that a wholly extrinsic ‘mere Cambridge’ property FE cannot be a respect in which its bearers resemble one another There are extrinsic properties like weight which look like resemblances, but only so long as some extrinsic condition (in this case) distance from a massive body is held constant. The real resemblance is in respect of mass – see §6., because it is not shared by every possible duplicate of its concrete instances, which could not be more alike, nor is it shared in every possible world by its abstract instances. This follows for any x where x is the concrete bearer of a ‘mere Cambridge’ property FMC because x then has a duplicate y which does not possess FMC, yet y’s lacking FMC does not make y any less like its duplicate x which has FMC. It further follows, for any property or abstract object F where F is an abstract bearer of extrinsic property FE, that FE cannot be a 2nd order property that any abstract object must have at every possible world in order to be that very abstract object. It cannot because there are possible worlds in which F does not have FE yet remains that very property F, and no less like other properties that F resembles. E.g. 7 is (intrinsically) a prime at every world, but (extrinsically) lucky only in some. Were it to change to being even, if would no longer be 7. This allows an extrinsic property FE to be identified by the ‘mere Cambridge’ test: if a concrete object x can lose FE, and this does not change what x is like, then a ‘mere Cambridge’ change to x has affected something other than x’s intrinsic character, and, hence, other than the internal relations of x itself, namely some external relation RE x has that, unlike resemblance, does not supervene on its intrinsic properties. An external relation such as RE obtains, instead, between x and one or more things (duplicates of) which do not necessarily accompany (duplicates) of x. if an abstract object F loses FE, then this does not impinge on the cross-world identity of F because a ‘mere Cambridge’ change ‘Properties are immutable’ you might object. But F’s being no longer thought important, does not alter what F is like: it is a ‘mere Cambridge’ change to F (that I hope befalls some properties I discuss here!). to F affects something other than F’s intrinsic character, and, hence, other than the identity and internal relations, of F itself, namely some external relation RE that F has which, unlike resemblance, does not supervene on F’s intrinsic properties. An external relation such as RE obtains, instead, between F and one or more things which, unlike F itself, are not found at every possible world. In neither case does it supervene on the intrinsic properties of any concrete or abstract relatum, because RE is a relation F or x has to some actual or possible wholly distinct object(s) whose character and existence are independently contingent. Consequently, (duplicates of) these actual or possible wholly distinct object(s) do not accompany Or do not fail to accompany F or x, because intrinsic and extrinsic are closed under negation. F or x or its duplicates in all possible worlds containing them. The ‘dependence’ of extrinsic properties on external d-relations is straightforward This answers the criticism, from Hoffmann-Kolss 2010, that Francescotti has a problem with the relation ‘consist in’ between d-relational properties and the relations on which they depend. Contra Weatherson & Marshall 2013, too, ‘iff’ can be employed between two expressions without invoking ‘states of affairs’, ‘events’ or whatever, whose equivalence relations are more obscure than ‘– iff –’ simpliciter.: whether a concrete or an abstract object is an instance of an extrinsic property, each token of an extrinsic property must be identical to a token of the relation on which it ‘depends’: e.g. the external relation x is next to y obtains iff x has the extrinsic property next to y iff y has the extrinsic property next to x. They are necessarily coextensive. However, a more fine-grained identity criterion for properties and relations must be employed in even raising the hyperintensional question to which this is the answer, since the question how extrinsic properties ‘depend’ on external relations could not arise if these properties were not hyperintensionally discriminable from the relations on which they depend. the external relation magnetism was investigated by Faraday obtains iff magnetism has the extrinsic property investigated by Faraday iff Faraday has the intrinsic D-relationality need not be symmetrical – see shortly. property investigator of magnetism. For any concrete object, number, property or whatever that may be the bearer of a putative intrinsic property F, F is intrinsic iff the same relation of resemblance holds between all and only possible instances of F. F is extrinsic if that is not so. The ‘mere Cambridge’ test highlights when loss of F by any bearer makes no difference to what that bearer is like. So, unlike an internal relation, an external relation RE does not supervene on any intrinsic properties of its relata, because not all possible duplicates of its concrete relata participate in RE and because no abstract relatum participates in RE in all possible worlds. The identities of both intrinsic and extrinsic properties can be fixed by the characteristic relations in which their bearers participate. For any extrinsic property FE, each of its possible bearers has a determinate relation to some wholly distinct, independently contingent concrete object(s). This analysis is sufficient to establish mutually exclusive, jointly exhaustive distinctions demarcating intrinsic from extrinsic properties and internal from external relations both for concrete objects and for properties or abstract objects. 3.4 The Disqualifying Relata of D-relations In short, extrinsic properties depend on a sort of relation which disqualifies them from being intrinsic, while intrinsic properties do not, so any property that does not depend on such a disqualifying relation is intrinsic. This is the insight developed in detail by Francescotti 1999b in his detailed characterisation of disqualifying ‘d-relational’ properties, which fleshes out my simplistic characterisation of an extrinsic property F as depending upon a relation F has to some actual or possible wholly distinct concrete object(s) whose character and existence are independently contingent. I have adopted two amendments to his account for which I argued in Ref.1., namely: d-relations can only hold towards independently contingent concrete objects; d-relations must hold towards possible as well as actual independently contingent concrete objects. Francescotti does not require that the other wholly distinct relata of d-relations should be independently contingent or concrete, since he allows numbers to fulfil this role. One reason why these two amendments are needed (and have been assumed so far) is that only the independently contingent variability of these relata between possible worlds can explain why extrinsic properties are those which vary between possible duplicates and between the same property, number etc. from one possible worlds to another. There are also independent reasons to take this view. Let’s look first at why only contingent accompaniment might be extrinsic. In Ref 1. I argued that, if d-relations held towards abstract objects such as numbers, then measurements would be d-relations and could not be intrinsic, yet these must be shared by every possible duplicate of their instances. In his 2014 Francescotti argues that one way in which measurements could be intrinsic would be if numbers did not ‘exist’ as wholly distinct objects: if they do not, then accompanied by 21 would not be a d-relation to a wholly distinct object. However, my argument regarding measurement does not show why other sorts of abstracta cannot be the wholly distinct relata of d-relations. I need a rationale to explain why, more generally, it cannot be an extrinsic property of a concrete object that it coexists with any abstract objects because, if they do exist, abstract objects accompany the contents of every possible world. I claim that, because being accompanied by any necessary object (abstract or concrete) is a property shared by every possible duplicate of every object, and never lost in a ‘mere Cambridge’ change, this consequently makes it trivially intrinsic. I need to justify this. This the problem of Indiscriminately Necessary Properties (INPs) discussed by Weatherson and Marshall 2013 and Francescotti 2014. One way is to start from the requirement to distinguish those objects and properties which are stable across all possible worlds from those that are not. INPs are, while changes to those properties which are not, constitute ‘mere Cambridge’ changes to their bearers. This provides the rationale for choosing which relational properties to proscribe as incapable of being intrinsic – namely those where the bearer has that property in virtue of a relation to an independently contingent, wholly distinct object whose existence or character is, consequently, not constant for every possible duplicate of that bearer. That possibility of change rules out the stability across all possible worlds of such relational properties, and allows them to be identified by the ‘mere Cambridge’ test. INPs all come out as intrinsic on this test. For the existence and character of abstract objects (and necessary concrete objects, if there are any) is constant for every possible duplicate of the bearer of a property possessed in virtue of its relation to a necessary object. That guarantees the stability across all possible worlds of such relational properties, and means they evade the ‘mere Cambridge’ test. If there needs to be a rationale to pick out those relational properties incapable of being intrinsic, then stability of the property provides this, and restricts d-relational properties to those a bearer has in virtue of a relation to an independently contingent, wholly distinct object whose existence or character is, consequently, not constant for every possible duplicate of the bearer. However, despite being part of a coherent scheme, that claim may seem to beg the question in the absence of some independent arguments. Here are two. The first is simple. If there are necessary objects present in every possible world, then their presence is a characteristic (set of INPs) shared by every possible world. Their necessary presence is, by any criterion, an intrinsic feature of those worlds in which they obtain, since they do not obtain in virtue of a relation that a possible world has to any other wholly distinct thing (they are each part of the worlds in which they are necessary) (complying with I.); are shared by every possible duplicate of that world (complying with II); obtain of any given possible world “in virtue of the way it itself, and nothing wholly distinct from it, is” (complying with III.) (they would obtain of world W even if it were the only one); are “entirely about how that thing and its parts are, and not at all about how things wholly distinct from it are” (complying with IV.) (they would obtain of world W even if it were the only one). (However, another INP concerns the ubiquity of the property of self-identity. Criteria III. & IV. (and ‘intuition’) make identity intrinsic I do not, because there could be no intrinsic duplicates if it were. I return to this in §4.) The second argument is a little more involved. It is that accompaniment only seems extrinsic when it is taken to be contingent (as in e.g. coincidence in space/time). 21 is necessarily accompanied by every other number, but, unless we seriously doubt mathematical knowledge, relations between numbers cannot be extrinsic, they are, rather, necessary and intrinsic. If the relation of accompaniment 5 has to 21 does not confer a d-relational property on 5 or 21, why should my being accompanied by 21 confer a d-relational property on me? If the answer is that it is because I am not a number, then does the relation that red has to 21 confer a d-relational property on red? A relation 21 has to me (e.g. older than 21 years) does confer a d-relational property on 21, but not on me. This because d-relationality is not necessarily symmetrical. My age > 21 years is intrinsic to me but extrinsic to 21. This is allowed by the account of the internality/externality of relations I outlined, that turns on which relations do and which do not supervene on the intrinsic properties of their relata A departure from Lewis’s account of external relations. . I have argued for the externality of any d-relation that fails to hold of every duplicate of the bearer of an extrinsic property and so fails to supervene on the intrinsic properties of its relata. If a-R-b is a relation it could supervene on the intrinsic properties of both a and b; the intrinsic properties of neither a nor b; the intrinsic properties either of a or of b. Option 1. makes R internal to both a and b, option 2. makes R external to both a and b, while option 3 allows representation of a relation like father/son as internal (necessary and intrinsic) to sons but external (contingent and extrinsic) to fathers. All sons have fathers, but not all fathers have sons, so father/son supervenes on the intrinsic properties of sons, but not on those of fathers: having a father is an intrinsic property of any son, while having a son is an extrinsic property of every father who does not have only daughters. Indeed, supervenience itself is asymmetrical in the manner of 3. above: it is internal to the supervening items but external to those supervened upon. By the same token, accompanied by me can be extrinsic to 21, while accompanied by 21 is intrinsic to me, and accompanied by every number but itself is intrinsic to every number. The case for my second amendment – that d-relations must hold towards possible as well as actual independently contingent concrete objects – is less involved or controversial. Amongst the negative extrinsic properties that I possess are those that depend on relations I do not have to possible objects: e.g. I do not own a talking donkey; I am not the father of a son; I do not fly in my own aeroplane. It would be a ‘mere Cambridge’ change to me should I beget a possible son I do not have or acquire a plane or talking donkey. Equally, intrinsic uniqueness is an extrinsic property of any x in virtue of the relation x has to its non-existent possible duplicates. For some x to gain or lose its uniqueness through the destruction or production of possible duplicates is clearly a ‘mere Cambridge’ change. §4. Identity Some E.g. Francescotti 1999b consider identity and, with it, all haecceitistic properties, to be intrinsic, yet the ‘mere Cambridge’ test does not pick concrete object identity out as intrinsic. Indeed, intrinsic duplicates are only possible if it is not (which they must be since there are very many actual objects ‘numerically’ but not ‘qualitatively’ distinct from one another). Duplicates which could not be more alike one another cannot be intrinsically distinct from one another, but must be separated from one another by extrinsic differentia alone, so duplicates of x must be externally related to one another and the intrinsic uniqueness of concrete objects must be contingent. The claim that identity is intrinsic is prompted by intuitions III. & IV. quoted in §1. For it is undoubtedly the case that any x is self-identical “in virtue of the way it itself, and nothing wholly distinct from it, is.”, and an ascription of identity to x “is entirely about how that thing and its parts are, and not at all about how things wholly distinct from it are”. However, I discussed in §2. reasons why III. & IV. might not be a good guide to the intrinsic. In ref. 1. I gave the following additional reasons why identity might not be intrinsic: The relation non-identity is a ‘d-relation’ that any x must have with everything distinct from x, and is only hyper-extensionally distinct from self-identity, and being identical with x, so the true attribution to x of self-identity, and of the haecceity being identical with x both depend on (‘consist in’) d-relations to everything distinct from x. I.e. x is self-identical iff x is distinct from every other y iff x uniquely possesses its haecceity as x. The self-identity of x does not supervene on any of x’s intrinsic properties because it can be lost through extrinsic change, e.g. replacement of its parts by their duplicates (i.e. self-identity of x fails the ‘mere Cambridge’ test). The property self-identity has none of the characteristics that ‘intrinsic’ attributes to all the intrinsic properties an object x shares with its actual or possible duplicates, because no object shares its identity and no likeness with any other thing obtains in virtue of x’s self-identity, since the latter obtains irrespective of what x is like. But, in ref.1, I suggest that philosophers who still baulk at supposing that identity is extrinsic might follow Quine’s 1972 suggestion and take identity to be “aloofly logical” and thus to be neither intrinsic nor extrinsic. §5. Resemblance is Intrinsic We have seen that the internality of the relation resemblance – the necessity that every F thing should resemble all other actual and possible F things in being F – cannot be explained by the way concrete objects are distributed across possible worlds. Rather, the way things are distributed across possible worlds itself only explains necessity and possibility if we assume the stability of properties that retain the very same character in every possible instance. Resemblance is an internal relation because, for an intrinsic property F, the same relation of resemblance holds between all and only possible instances of F. I think the question ‘What counts as “the same relation of resemblance”?’ can only be answered by taking resemblance to be primitive. This implies that Geach’s ‘mere Cambridge’ changes have no bearing on the resemblances between concrete objects, or on the identities of their properties from any one possible world to another, while his ‘real changes’ are simply changes in what things are like – changes that involve the loss or gain of distinct intrinsic properties by concrete objects. If we take the relation of resemblance to be ‘primitive’, we can rebut the accusation of circularity against this account’s employing the ‘mere Cambridge’ test. To do that, we need a ‘starting point’ – a way into the circle that cannot be repudiated. Likeness or resemblance itself provides this. For no one doubts that there is a bona fide relation resemblance (for which an explanation would be nice, even though, arguably, since Plato failed, no other philosopher has been able to provide one). No one maintains that, for want of such an explanation, we cannot take there to be any resemblances. So, the relation resemblance is already effectively taken to be primitive, pro tem, while realists, nominalists and others contend, arguably so far in vain, to provide us with the missing authoritative explanation Weatherson and Marshall 2013 write: it is not obvious that Francescotti's account is compatible with any credible theory of properties. In order to properly evaluate Francescotti's account, therefore, proponents of the account need to specify what theories of properties it is compatible with, and why we should believe that at least one of these theories is true. This task has not yet been carried out. If this is an objection, then it confounds not just Francescotti but the bulk of existing philosophical theories on any topic. While we still await a “credible theory of properties”, despite the claims made by some for the identification of properties with the cross-world sets of their instances, it seems that any such theory, when it is presented, should, at least, account for those features of likeness assumed to be primitive in the present account.. My claim is simply, first, that likeness itself is unproblematic, that, secondly, all likeness is intrinsic and, so, the ways in which things are alike are their intrinsic properties, and the exact likeness shared by duplicates is their sharing all their intrinsic properties. Then, because extrinsic properties are not shared by all possible duplicates of their instances, their loss or gain in a mere Cambridge change makes no difference to what their bearers are like; and for that reason, there is no mileage in the notion of wholly ‘extrinsic likeness’. ‘Real’ or ‘intrinsic’ changes are changes to the resemblances between things, while ‘mere Cambridge’ changes are not. There is no ‘circle’ here. It is entirely reasonable to take resemblance to be primitive, since no one questions it despite our having no settled theory of properties. (Those extrinsic properties like tallest tree in the forest and weight, which can be lost through both ‘real’ and ‘mere Cambridge’ changes, I will argue in §6., are compounds of intrinsic and wholly extrinsic ‘mere Cambridge’ properties, which can be lost independently of one another.) It is important, too, to rebut another important class of counterexamples, which I think can be done if causal properties can be intrinsic, as I argued they must be in §2.6. Some extrinsic properties do appear to be ways that things might be alike, e.g. alike in having two siblings; alike in coming from Yorkshire; alike in having the same birth sign; alike in having a common ancestor. I argue that these instances are (or are believed to be) alike in their effects, rather than their manifest (‘categorical’) properties. If causal propensities can be intrinsic, because the nomological laws of a possible world are intrinsic to that world, then these and similar apparent ‘extrinsic likenesses’ are not likenesses in external relations (which I have argued cannot obtain) but are hypothetical likenesses in causal background. It is not that coming from Yorkshire is a simple respect of resemblance between two people. It is rather that the same causal background Yorkshire is taken to have a similar effect on both. People may very well have the same birth sign, but it is very doubtful whether that is the cause of a similar effect on each of them. We suppose that whether someone comes from Yorkshire might make a statistically significant difference to what s/he is like while strongly doubting that having a given birth sign will. Expecting some actual experimental/observational result to be repeatable is expecting a repeat of the causally relevant circumstances to be alike in their effect in other actual times and places. The respect of apparent ‘likeness’ is restricted to those possible worlds which share the relevant laws of nature. The hypothesis of a causal link, in such cases, cannot be entertained unless we refute the so called ‘null hypothesis’, namely the hypothesis that the addition or removal of the factor we suspect to be causally relevant would make no more difference than we could expect from mere coincidence. The parallel with the ‘mere Cambridge test’ is striking. In a survey, variation in birth sign, one suspects, would make no more difference to personality type than you might expect from mere coincidence and the null hypothesis would be upheld. In effect, unlike variations in birthplace, variation in birth sign amounts to no more than a ‘mere Cambridge’ change between the experimental subjects. Apparent counterexamples of ‘extrinsic resemblance’ can therefore be recast as alike in virtue of having two siblings, coming from Yorkshire, having the same birth sign, having a common ancestor, etc. These features are not categorical respects in which people are directly alike, but are, rather, hypotheses about causes of resemblance which may or may not be vindicated. §6. Properties Which Can, Apparently, be Either Intrinsic or Extrinsic or Both Accepting resemblance as primitive, and that duplicates are objects which could not be more alike, allows us to sidestep neo-Humean concerns about the absolute ‘naturalness’ of properties of concrete objects and directly address the difficulty that conjoined and disjunctive ‘properties’ seem to confound criteria demarcating the intrinsic. All that is needed is to put resemblance in the driving seat. Weight, though apparently simple and intrinsic, was discovered to be a conjunction of mass and proximity to a massive body (such as the Earth) and so a complex property with intrinsic and wholly extrinsic components. If F is blue or cubic (so F looks intrinsic) two objects with F can seemingly share all their properties but still not be duplicates: one is blue, the other cubic. If F is next to me or red then x can lose F by undergoing a ‘real’ (intrinsic) or a ‘mere Cambridge’ change, depending on which disjunct is lost – x changes colour or I move. So, let’s just say that resemblances alone are bona fide intrinsic properties and seek the simplest resolution of compound properties into resemblances and ‘mere Cambridge’ properties dependent solely on d-relations. Of course, this crudely cuts the Gordian Knot, but why let it be tied? Remember that a ‘compound property’ can always be gratuitously concocted to confound any criterion, e.g.: under the bed or intrinsic by Z’s criterion; red and extrinsic by A’s criterion. Such concocted ‘properties’ are very far from showing that a mutually exclusive, jointly exhaustive intrinsic/extrinsic distinction is impossible. Just as a change to an object is not simply an alteration to the predicates it satisfies, so, too, it does not acquire irreducible sui generis properties in virtue of its satisfying concocted or covertly compound predicates. Such a distinction plainly should apply in a jointly exhaustive, mutually exclusive fashion to the elements – conjuncts and or disjuncts – from which logical property-forming operations yield such compound properties. By the same token we cannot maintain that weight amounts to a bona fide property that resists reduction to a conjunction of mass and proximity to a massive body. We are thus justified in analysing away those properties in which divergent types of component properties alternate or are conjoined so that, it seems, they can be ‘had’ both intrinsically and extrinsically. In short, the remedy for all these is a requirement to apply the ‘mere Cambridge’ test to separate conjuncts and/or disjuncts within such properties to discriminate the wholly extrinsic ‘mere Cambridge’ properties from the intrinsic components, because it is these intrinsic components, individually, and not their conjunction or disjunction, that duplicates must share in order that they could not be more alike. Because the ‘mere Cambridge’ test yields a jointly exhaustive, mutually exclusive partition of properties, any property whose loss sometimes is, and sometimes is not a ‘mere Cambridge’ change must be complex, with intrinsic and extrinsic components. If the discovery regarding weight is legitimate, then the ‘mere Cambridge’ test can pick out ‘middle level’ intrinsic properties that do not require us to identify a level of absolute simplicity or ‘naturalness’ for an unyieldingly ‘sparse’ repertoire of properties (as envisaged in Lewis 1986). It will suffice to appeal to our normal judgements of resemblance. We can then achieve mutual exclusivity merely by ‘reverse engineering’ relatively simpler properties by unpicking explicit or implicit property-forming operations, as we do for weight, without needing to authenticate any claim to have achieved ultimate simplicity. We only need to disassemble complex properties until we come to conjuncts/disjuncts sufficiently simple to support our current judgements of resemblance and be intrinsic or wholly extrinsic ‘mere Cambridge’ properties by the ‘mere Cambridge test’. We can then apply this to our normal or scientific descriptive framework. Undoubtedly further discoveries will be made that will parallel the case of weight. Are there potential counterexamples to the strategy above? Only two routes suggest themselves: either you construct instances like having the same mass as one’s son or being blue or cubic using logical property-forming operations on disparate conjuncts/disjuncts, or you discover cases, like weight, which can only be argued to straddle the distinction if successfully deconstructed in the way I described. Neither route undermines the approach I propose: both confirm it. §7. In Conclusion I have argued that a ‘mere Cambridge’ test yields a mutually exclusive, jointly exhaustive partition between properties which applies alike to 1st and 2nd and higher order properties, and has a strong claim to coincide with the intrinsic/extrinsic distinction if one is guided by the consensus that an object undergoes real change in an event iff there is some intrinsic property they satisfied before the event but not afterwards. It does not shoulder the ‘Humean burden’ Lewis and others would like the intrinsic to bear. ‘Intrinsic’ has been used with many other meanings: the ‘mere Cambridge’ test does not distinguish properties that are endogenous, essential, inherent, inalienable or independent of their bearers’ circumstances, from those which are not. I suggested that the term ‘intrinsic’ cannot be univocal and encompass all these senses at once, and should be reserved for properties which are stable across possible worlds because the same relation of resemblance holds between all and only possible instances of such properties. This account does not help with philosophically significant notions such as ‘intrinsic value’, ‘intrinsic intentionality’ and the like, but I think the claims regarding these notions concern their being inherent in, essential to the nature of, irreducibly present in whatever possesses them, which, I submit, requires an independent analysis. On behalf of all authors, the corresponding author states that there is no conflict of interest. References Cameron R.P. 2008 Recombination and Intrinsicality Ratio XXI Cowling S. 2017 Intrinsic Properties of Properties Philosophical Quarterly 67: 241-262. Earman & Roberts J.T. 2005 Contact With The Nomic 1 Philosophy and Phenomenological Research Vol. LXXI, No. 1, Figdor C. 2008 Intrinsically/Extrinsically Journal of Philosophy 105 (11):691-718. Francescotti R. 1999a Mere Cambridge Properties American Philosophical Quarterly 36 (4):295-308 Francescotti R. 1999b How to Define Intrinsic Properties Noûs 33 no4: n90-609. Francescotti R. 2014 Intrinsic/Extrinsic: A Relational Account Defended in Companion to Intrinsic Properties, ed. Robert Francescotti, Berlin, de Gruyter Geach P.T., 1969, God and the Soul, London: Routledge and Kegan Paul. Harris, R. 2010a, How to Define Extrinsic Properties Axiomathes 20 (4): 461–478. Harris, R. 2010b, Do Material Things Have Intrinsic Properties? Metaphysica 11 (2):105-117 Hoffmann-Kolss V. 2010 The Metaphysics of Extrinsic Properties Heusenstamm Ontos Verlag Humberstone I. L. 1996 Intrinsic/Extrinsic Synthese, 108: 205–67 Kim J. 1982, Psychophysical Supervenience Philosophical Studies 41: 51-70 Langton R. and Lewis D. 1998 Defining ‘Intrinsic’ Philosophy and Phenomenological Research 58: 333–45 LaPorte, J. 2016 Rigid Designators The Stanford Encyclopedia of Philosophy (Spring 2016 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/spr2016/entries/rigid-designators/>. Lewis D. 1983, ‘Extrinsic Properties’, Philosophical Studies, 44: 197–200 reprinted in David Lewis, Papers in Metaphysics and Epistemology, Cambridge: Cambridge University Press, 1999, pp. 111-5 Lewis D. 1986 On the Plurality of Worlds, Oxford: Blackwell Quine W.V. 1972 review of Munitz M. (ed.) Identity and Individuation in Journal of Philosophy 69 pp 488-97 Thesaurus http://www.thesaurus.com/browse/intrinsic Vallentyne, P. 1997 Intrinsic Properties Defined Philosophical Studies 88: 209-19 Weatherson B. 2001 Intrinsic Properties and Combinatorial Principles Philosophy and Phenomenological Research, 63: 365–80. Weatherson B. & Marshall D. 2013 Intrinsic vs. Extrinsic Properties The Stanford Encyclopedia of Philosophy (Spring 2013 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/spr2013/entries/intrinsic-extrinsic/>. Wilson J. 2010 What is Hume's Dictum, and Why Believe It? Philosophy and Phenomenological Research 80 (3):595 – 637 Wilson J. 2015 Hume's Dictum and Metaphysical Modality: Lewis's Combinatorialism in Barry Loewer & Jonathan Schaffer (eds.), The Blackwell Companion to David Lewis. Blackwell. pp. 138-158. Yablo S. 1999 Intrinsicness Philosophical Topics 26: 479-505 30 ‘Mere Cambridge’ Test

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