Tuesday, September 29, 2009

Resemblance Nominalism and Tropes

Here’s the outline of a paper I´m starting to work on. If anybody has some spare time and wants to take a look, comments are very welcome (sorry for the length)!

Nominalists about the ontological constitution of material objects aim to dispense with both universals and bare particulars and yet provide an economic and compelling account of similarity and individuation.
Resemblance nominalism is the view that only concrete particulars exist, and properties are derivative on similarity classes of such particulars. This view has to deal with the traditional Goodmanian objections based on the possibility of coextension, imperfect community and companionship; it must also explain why the very same object couldn’t have any properties whatsoever (since an object’s belonging to a similarity class appears to be a contingent fact). Rodriguez-Pereyra recently defended resemblance nominalism by endorsing counterpart theory (every object possesses its properties - i.e., partakes in specific similarity classes - necessarily) and realism about possible worlds (the coextension problem is solved if similarity classes also comprise merely possible objects); and proposing a complex notion of resemblance, according to which resemblance holds in various degrees and in an iterative way - between pairs of objects, pairs of pairs of objects etc. (this latter move neutralises the problems of imperfect community and companionship). These are, clearly, non-negligible commitments. An alternative would be to give up the assumption that ordinary objects are the ‘unit of discourse’ and assume that the fundamental building blocks of reality are simple (=belonging to one similarity class) concrete particulars. This would immediately solve the Goodmanian difficulties. However, the problem with the contingency of property-possession remains. If one doesn’t like counterpart theory, it would seem, this problem can only be obviated by going trope-theoretic, that is, by identifying each simple concrete object belonging to only one similarity class with its ‘qualitative content’.

Trope theory, however, has the problem that at least some properties appear dependent on objects rather than constitutive of them (think of colour, or shape properties): with respect to their identity (this table’s hardness, not this hardness, which may or may not compose a table) and their number (since I can tear this white sheet in arbitrarily many pieces, it looks as though there is no fixed number of whiteness tropes in it - the so-called boundary problem). The obvious solution is to endorse a sparse and reductionist account according to which only physically basic, simple properties (e.g., the mass or charge of elementary particles) are genuine tropes. However, this seems to go in the direction of resemblance nominalism, as the trope-theorist attempts to defend the view by making tropes concrete, rather than abstract, particulars.

This may seem circular. However, think about the difference between an elementary particle and its qualitative aspects (mass, charge, spin, colour): do they belong to clearly distinct ontological categories? Or would it be plausible to regard mass etc. as material constituents of a more complex, but equally concrete, particular? A third way emerges, in which the nominalist (thanks to the abovementioned sparse-reductionist approach to properties) takes simple, concrete particulars essentially provided with a qualitative content as fundamental entities. Interestingly, this view was proposed by Sellars already in 1963 (‘Particulars’), where he argues in detail that the property/object distinction can and should be overcome, and proposes an ontology of ‘simple particulars’. Perhaps it would be interesting (for nominalists at least) to examine this Sellarsian option in more detail?


  1. Hi Matteo,

    I haven't gotten a chance to read Rodriguez-Pereyra's book yet, but I have a few qualms about his use of counterpart theory, if I understood you correctly.

    You say that, in order to solve the problem of contingency of property possession, R.-P. endorses counterpart theory: "every object possesses its properties necessarily". But counterpart theory is neither sufficient nor necessary to get property essentialism.
    True, in counterpart theory an object exists only at one world. However, the modal statement "x has all its properties essentially" is true iff its counterpart-theoretic translation is true: "every counterpart of x has every property that x actually has". And this happens only in some degenerate cases, for instance when the counterpart relation is identity. It seems to me that R.-P.'s argument conflates the modal language, where we express contingency and essentiality statements, and the language of counterpart theory, which is purely extensional. This is the same kind of confusion that prompted Kripke's well-known "Humphrey objection" to counterpart theory, which was criticized by Hazen in his 1979 paper "Counterpart-theoretic semantics for modal logic" and by Stalnaker in his papers on counterpart semantics.

    On a side note, counterpart theory does not have to be paired with modal realism (pace Lewis). Sure, if you are a modal realist you will most likely endorse counterpart theory to avoid that every necessary statement (that is not a first-order contradiction) is true. But you can be a counterpart theorist without being a modal realist, for example if you reject the notion of transworld identity or if you need a weaker modal logic that any one validated by a class of Kripke frames.

  2. Hi Alessandro, thanks for your comment.
    I didn't express this point very clearly, but as far as I understand, counterpart theory is supposed to allow one to take the joint existence of a and b as a sufficient truthmaker for 'a resembles b'. Indeed, this seems to require the counterpart relation to be identity; but other than this modal notions of contingency and essentiality are not required. Indeed, R-P seems to aim at a purely extensional construction of similarity classes. His realism about possible worlds, on the other hand, follows from an altogether different worry (related to the coextension problem) and is entirely independent of what he says about counterpart theory.

  3. Hi Matteo,

    A few comments:

    1) Isn't the view you sketch in the last paragraph accepted by most people who opt the tropes + bundle theory package? As far as I can see, most of them seem to think that there are only concrete particulars but these are not individuals but tropes and individuals are bundles of tropes. And it's easy to see why, on that view, it is tempting to think of tropes as concrete--if individuals are concrete and they are bundles of tropes, it is tempting to think that the tropes are concrete. How could a bundles of abstract entities make up a concrete entity?

    2) wrt the "boundary problem", clearly a trope + bundle theorist should say that only the most basic individuals (the "simples" which of course on this view are not simple at all) are bundles of tropes. So this white sheet of paper is not a bundle of tropes but is composed of bundles of tropes. (In any case, I hope we all agree that there are no white tropes!).

    3) wrt to the identity of tropes. I think the point you are making is merely epistemic. The fact that we identify tropes by referring to the individuals they compose is no reason to think that the objects have metaphysical priority over the tropes. But maybe I am misunderstanding your point there.

    4) Could you expand on the point you make in your comment at 9:58? "[...] counterpart theory is supposed to allow one to take the joint existence of a and b as a sufficient truthmaker for 'a resembles b'. Indeed, this seems to require the counterpart relation to be identity."

  4. Hi Gabriele,

    W.r.t. to your 1), I definitely agree that this is the way trope theory should be understood, and it is possible that many trope theorists endorse this version of the theory. However, the point worth making - it seems to me - is that if we go along this route then the Sellarsian view that there is no difference between properties and objects becomes compelling. A by-product of this, I also suggest, is a useful synthesis of resemblance nominalism and trope theory. As for 2) and 3), again I agree that these are very plausible ideas, but not all trope theorists endorse a sparse account of properties; and a common criticism (e.g., Lowe (1998)) is that at least some particularised properties cannot be part of the 'alphabet of being' because they cannot be conceived of in abstraction from the objects they are part of. I don't think this is a merely epistemic point.
    As for 4): the problem here is that since the resemblance nominalist only believes in the existence of concrete particulars (objects), s/he cannot use properties to determine which similarity classes objects belong to; instead, s/he has to use objects to determine properties. But then s/he must explain why it isn't possible that the *same* two things belong to a given similarity class in world w1 but not in w2 (which s/he cannot allow, otherwise two universes composed of exactly the same concrete particulars - and nothing else - might exhibit different properties). Counterpart theory offers the tools to equate 'sameness' and participation in the same similarity classes - which means that the counterpart relation is that of exact similarity.
    (Perhaps talk of identity here is incorrect? I am definitely not an expert on counterpart theory...)

  5. A small addition:

    I guess the inference from tropes+bundles to the idea that concrete objects must be composed of tropes as concrete entities only holds if bundles are mereological fusions, which they need not be.

  6. Just to clarify certain points about what I said in the book on Resemblance Nominalism.

    First, I did not commit myself to the idea that counterpart theory means that objects have their properties necessarily. Alessandro is right that this does not follow from counterpart theory, and I did not say or imply that it follows.

    Second, I did not commit myself to the idea that the counterpart relation is that of identity or even that of exact similarity. I don't think anything like that follows from what I said.

    I am not sure I follow Matteo's explanation of why using counterpart theory to account for the truthmakers for "a resembles b" would make the counterpart relation the identity relation or the exact similarity relation. The reason why counterpart theory avoids the possibility that the same thing be a member of different similarity classes in different worlds is simply that no thing, according to counterpart theory, exists in more than one possible world.

    In general, a good way to see that I did not commit myself to any of those things is that the only part of counterpart theory I used was the part that says that individuals are world-bound. I didn't use the other parts of counterpart theory which have to do with the link between resemblance and the counterpart relation and with how the truth of a de re modal statement depends on what happens with counterparts in other worlds.

  7. Hi Gonzalo,

    Of course it wasn't my intention to misrepresent any claims you make in your book. The point we are discussing wasn't even central to my original post.
    I think my talk of 'necessary' property-possession was exactly intended to mean that individuals do not belong to different similarity classes in different worlds. As you point out, it is the worldboundedness of individuals in counterpart theory that gives you this.
    Perhaps you don't need anything else, and I probably misunderstood Alessandro (as I said, I am not an expert in counterpart theory) but I was taking him as suggesting that CT only gives you all this if you make additional assumptions about the counterpart relation.
    Anyway, apologies for this, and I am still curious to see what people think about particulars!

  8. Hi Matteo-- as you are weighing object-class and trope-class nominalisms, I thought I'd chime in with the hope you might find this paper interesting (which I wrote lo! these many years ago): 'Properties and Resemblance Classes', Nous 2002. It tries to undermine the idea that trope-class theories obviously avoid the traditional Goodmanian problem. One way around the issues I raise is to go very sparse with tropes, as you are suggesting. That might provide you with an extra motivation...

  9. Hi David, thanks for this. I was aware of your paper, but never read it. Indeed, it looks very relevant for what I am doing, will definitely take a look!

    As an aside, here's what I think was the misunderstanding in the previous exchanges for this post: I was taking the suggestion to be that, given the requirements for a consistent and credible resemblance nominalism, each object could only be its own counterpart (non-orthodox, but I think not inconsistent with counterpart theory). But of course others understood identity/exact similarity in the 'canonical' way, whence the lack of communication...

  10. Hi Matteo,

    Since this thread seem to have come back to life let me follow up on your comment above that "the inference from tropes+bundles to the idea that concrete objects must be composed of tropes as concrete entities only holds if bundles are mereological fusions, which they need not be".

    I don't think that's the case. I think that it's a more fundamental intuition that while you can "get" the abstract from the concrete (e.g. a set of concrete objects is an abstract entity), you cannot get the concrete from the abstract because any metaphysical "glue" that keeps them together is not going to make the resulting object any less abstract. All this is very vague but I have a strong intuition that something along these lines is true. I'd be curious to hear what people think of it.

  11. Hi Gabriele,

    Well, I share your intuition, however the point was whether it is *necessarily* the case that, assuming trope theory, tropes must be concrete because the objects they constitute are. And I do think the answer is negative. Implausible as this may sound, it is possible to postulate compresence relations that 'reify' property instances that otherwise only belong to abstract similarity classes.
    This having been said, it is exactly my intention to argue that nominalism is best understood (and trope nominalism must be understood) in terms of (ultimately, simple) concrete entities.
    For instance, Williams' seminal paper on tropes clearly states that tropes are the alphabet of being and yet are abstract. At the same time, though, Williams offers an analysis according to which the concrete lollipop can be analysed in terms of concrete parts (e.g., the stick) and abstract parts (e.g., the color of its edible part). It seems very plausible to me that, as the limit of fundamental constituents is reached, the difference between properties and objects disappears. Which, obviously enough, means that the abstract is 'absorbed' by the concrete.
    A worry I didn't mention earlier is that, if the world is gunky, this limit is never reached! Perhaps, since it constitutes a refutation of the idea that there is a fundamental level, this also refutes the Sellarsian conjecture I aim to defend?