@Janus: One thought I keep coming back to is that in rejecting the reality of types, one must - or at least this is what I want to argue - reject the reality of particulars
as well. I mean, at the most basic level this is just a matter of intelligible discourse: a token is only a token in relation to a type and vice versa, and each only has meaning in relation to the other. So I don't think that a consistent nominalism can be reduced to the idea that 'there are only particulars, no types'. So there's got to be something deeper and more interesting going on. One way to get to this 'deeper thing' is to look at how abstraction functions:
Say we've got two apples. We say that the apples are two tokens of the type 'apple' and we do so precisely by abstracting from the particularity of
this apple such that we discard certain of it's features (this apple is bruised, that one is not, yet we ignore this).
Already at this level we can see that particularity is
abstract from the get-go: that
this is a particular apple (read = 'belongs to the type apple') and that
that is a particular apple is already to ignore, paradoxically, the particularity of
this apple and
that apple so as to be able to speak of them as particular apples at all.
Or another way to put this is that particularity itself is already a 'type'
qua particular. This was, by the way, Hegel's point
viz his critique of 'sense-certainty' that opens up the
Phenomenology - that every attempt to capture singularity by means of speaking about a 'this' is already implicated in the universal. But - and this is the crucial point - the implication of the particular in the universal cuts both ways: apple
qua type is, in equal measure, a 'particular type': we can see this if we subsume 'apple' as a token of the type 'fruit'. At no point in this whole dialectic do you end up with 'real singulars'; instead all you have are types and tokens whose roles are
reversable depending on the point of view one takes.
There is no ground-level of real singulars from which the type-token distinction builds itself off from: the whole conceptual machinery is realized 'in one fell swoop', as it were. As soon as you have tokens, you have types. And, worse, types and tokens are
promiscuous in the sense that one can be transformed into the other: a token is always-already a type by virtue of it belonging to the type 'token' ('cuts both ways'). So the question is: given this promiscuity, what, at the end of the day, indexes tokens as tokens and types and types, if not some God-given ontological scaffolding
qua Great Chain of Being? And the answer can only be: whatever it is 'we' are trying to do with them. This is why I think rejecting the reality of types also entails rejecting the reality of particulars, insofar as even particulars already belong to the order of types (and vice versa!).
--
Another way to make the above point is by recourse to Jacques Lacan's dictum that 'there is no metalanguage': no matter how long you spend going up 'up a level', from token to type to next-level type, you will
never arrive at some final Capital-T Type which accounts for the distribution of tokens and types among the lower-levels. This is, among other things, an anti-theological point, or, to put it more positively, a naturalist one in which types and and tokens are
made and
produced and not 'given'.