Dear gang, Some nice exchanges with various students (Erica was especially helpful here) have got me psyched for tomorrow's section. Come prepared to discuss the modal, set-theoretic arguments broached in lecture today. Here are some questions/comments, to serve as a rough agenda. Please print out this email (or otherwise bring it to class tomorrow). (1) Proper names of concrete particulars are (often) taken to be rigid designators: that is, they pick-out the same particulars in different possible worlds (to put things roughly). For instance, when we say: "Branden might have had more hairs on his head than he in fact does." if we take "Branden" to denote the same individual across possible worlds, then the name "Branden" is a rigid designator in this context. (2) It seems that the realist would want to say something similar about abstract singular terms: that they (often, at least) rigidly designate. But, in this case, things are significantly different, since it's not as if (from a realist perspective, here!) there are "attributes" that the property Courage can have in some possible worlds but not in others. It seems silly to say: "Courage might not have been a virtue." Nonetheless, I do think it is plausible that "Courage" should rigidly designate, from the point of view of a realist - even though it's tough to think of such modal statements involving abstract singular terms that would allow us to "test" this hypothesis on a non-trivial case. Be that as it may, I suggest that the main reason that we want "Courage" to be rigid is that we want claims like "Courage is a virtue" to come out *necessarily* true. If "courage" and "virtue" are rigid, and "courage is a virtue" is *actually* true, then it will also be *necessarily* true. Keep this in mind -- I will return to this point, below. Note: Despite the fact that "Courage" rigidly designates on a realist account, it is still a contingent matter which particulars exemplify courage (in which worlds, and at which times, etc.), which is also good. I claim we can have this "best of both worlds" as trope theorists too. (3) For a trope theorist, it's not as clear what one should say about abstract singular terms. Consider the trope theorist's account of what "Courage" denotes: "Courage = the set of courage tropes." There are at least two ways to read this. (i) One could say that there is a SPECIFIC set of tropes (whose membership is pre-determined), and THAT set is what courage is. On this view, "Courage" rigidly designates THAT VERY SET across all possible worlds. So, in this sense, at least "Courage" is one and the same thing in all possible worlds (and so is "virtue"), which is what realist intuitions seem to recommend. However, on this view, it does seem to follow that there could not have been more or fewer courageous people than there in fact are, which seems patently false. But, (ii) one could say that "the set of courage tropes" picks out different sets of tropes in different possible worlds (or at different times, etc.). This avoids the problem of it being impossible for there to have been more or fewer courageous people than there in fact are. But, it does so at the expense of making the denoting phrase "the set of courage tropes" a non-rigid designator, since it will denote a different set of tropes in different worlds (even at different times, etc.), just like "the number of planets" does. HOWEVER, it is unclear why this should be such a deep problem. This NEED NOT imply that what MAKES courage tropes COURAGE tropes (as opposed, say, to color tropes) varies from world to world. And, THIS may be enough to preserve the key intuitions we wanted in the first place (which, it seems to me, are logically orthogonal to the rigidity/non-rigidity issue). For instance, why couldn't the following claim be a NECESSARY TRUTH, EVEN on the account just sketched? Is there are ARGUMENT against this? "Courage is a virtue." I see no reason why this is not possible. You may think this ad hoc, but LOUX CANNOT claim this, I reckon. After all, he says that: One objection that might be raised against the account is that it explains one case of subject-predicate truth only by invoking another. Thus, we explain the truth of 'Socrates is wise' by appealing to a trope that Socrates has; but clearly the trope can do its explanatoy job only if it is the right kind of trope. It cannot, for example, be a color trope or a shape trope. It must be a wisdom. But, then, how do trope theorists explain the fact that the relevant trope is a wisdom? They invoke a strategy we have met repeatedly in our discussion of the different forms of nominalism: they insist that a trope's being what it is, being the sort of thing it is, represents a basic, unanalyzable, primitive fact. Tropes just are what they are - wisdoms, rednesses, and circularities; their being such things is not susceptible of any analysis, explanation, or reduction; but because they are what they are, the concrete objects that have them are how they are, are what they are, and are related to each other in all the ways they are. This, as far as I can tell, leaves the door wide open to my suggestion, and to the possibility that BOTH "the set of courage tropes" is not a rigid designator, AND (nonetheless) what MAKES courage tropes COURAGE tropes IS "rigid" in this sense. Since this is a primitive for the trope theorist anyway, why can't they just build the requisite rigidity into the account HERE? Nothing Loux says rules this out, does it? It seems to me that this is an independent way to preserve the realist intuitions in question WITHOUT making "the set of courage tropes" rigid. Perhaps, this gives us "the best of both worlds"? Anyway, it's a thought. (4) Finally, what about the bundle theory for PARTICULARS? This (either in realist or trope-theorist flavors) will be similar to the trope theory account of abstract singular terms. In this case, we have a collection of compresent attributes (properties or tropes, as the case may be). Here's a more precise rendition of how this might go: "Branden is the set of compresent attributes in slice R of space-time" Here, R is some spatio-temporal "slice". Now, once again, we have choices here. We can say that "Branden" is a CERTAIN set of compresent attributes, or we can say that the referent of "the set of compresent attributes in slice R of space-time" varies from world to world. Either way, things are a bit strange. If we say the former, than we are always referring to the ACTUAL Branden, whenever we say "Branden" (and in whichever world we say it!). On the latter, we'd be talking about wildly different sets of attributes from world to world. But, in any case, it seems that bundle theory countenances lots of different distinct individuals, where intuition might suggest there is but one. There are very deep problems all around here, which I will not say much more about here. I want to conclude by saying something about the sense in which "particulars have their attributes necessarily" on this kind of account. As above, I just don't see why this follows. Why can't "Branden" have his properties contingently (taking the non-rigid route), EVEN on this kind of bundle view? I grant that we end-up with a rather weird "Branden" (not very common sensical). But, I don't see why bundle theorists MUST have the view that things have their properties necessarily. Van Cleve and Loux seem to think this for reasons very similar (the same?) as those which led them to conclude that trope theory was committed to the view that there couldn't have been more or fewer courageous people than there in fact are. And, I don't see why this argument is compelling in either case. See you tomorrow. Best, Branden PS. Did you buy Wolterstorff's argument THAT sets have their members necessarily? Why not just make the argument that I did today, that the claim "1 is an element of {1,2,3}" is a mathematical truth, and be done with it? I found this, too, a strange argument, but I believe the conclusion for the same reasons that I believe "9 > 4" is a necessary truth.