Wolfgang Schwarz

Fundamental properties have no intrinsic nature

Let F be a fundamental property, understood as a maximal class of possible things that are perfectly similar in one respect. (This is one of Lewis's four proposed definitions of fundamental properties, and I think the best one.) And suppose I have F. What would it take to know that I have F?

Given that F is some class { Wo, Fred, ... }, and given that having F means being a member of F, it might seem puzzling how I can be ignorant about whether or not I'm F: how could I fail to know that I am a member of { I, Fred, ... }? But here we are substituting corefering expressions in a (hyper)intensional context, which is illegitimate. If I knew that F = { I, Fred, ... }, then I probably ought to know that I am F. So if I don't know that I am F, that's because I don't know that F = { I, Fred, ... }.

This ignorance could have two (non-exclusive) explanations. First, I might only know the class F under some opaque mode of presentation that doesn't give me access to its members. For instance, I might know F only as the property that plays such-and-such a role in our world, without knowing which property (i.e. class) it actually is that plays the role. Among the possibilities I can't rule out are possible worlds in which, say, G = { Mary, George, ... } plays the F-role. And G doesn't contain me. That's why I don't know whether I have the property that plays the F-role.

This is the kind of quiddistic ignorance Russell, Maxwell, Langton, Lewis and others have argued for, except that fully knowing, or identifying a property, on the present account, is not being acquainted with a universal, but knowing exactly which possible things have it and which don't.

Things, too, can be known under various modes of presentation. Hence I might know that F = { Wo, Fred, ... }, without knowing that F = { I, Fred, ... } because I don't realize that I = Wo. So under what mode should one know the instances of F in order to identify F? If haecceitism were true, we could say that one has to know exactly which haecceities (at which worlds and times) are coinstantiated with F. The haecceities would have to be picked out by their essence, not by some contingent aspect, of course. It is mysterious to me how we could ever identify a haecceity in this way. So on this view, it is probably impossible to identify any fundamental property.

Modes of presentations for individuals provide the other explanation of how I might fail to know that I am F, even when I know what class F is: I could fail to recognize myself as a member of that class, for instance by failing to know my haecceity.

Now let's set aside haecceitism and think of individuals as completely characterized by their qualitative properties. More precisely, assume a world can be completely characterized by giving a distribution of fundamental properties over existentially quantified individuals: "there are x,y,z such that Fx, ~Fy, Fz, Gx, Gy, Gz, Hxy, ~Hxz etc.". Let's also assume a principle of recombination: any statement of this kind describes a possible world (or a centered world if we leave one variable free).

(Simple monadic) properties all look very similar now. Within a given world, there can be substantial differences between F and G: F may be rare and G common, F may bring about H and G may not, etc. But for each such world, there will always be a mirror world where G is rare and F common, where F brings about H and G does not, etc. In the description of the whole pluriverse, uniformly swapping "F" and "G" changes nothing. On haecceitism, by constrast, swapping makes a difference: when before we had Fa somewhere in logical space and Ga nowhere, we afterwards have Ga somewhere and Fa nowhere.

It is tempting to think of fundamental properties as sui generis entities with their own peculiar natures. Then F and G could differ in such natures -- some kind of qualitative higher-order properties --, even if they don't differ in their pluriverse distribution. But if we replace primitive universals with primitive plural similarity, so that fundamental properties are maximal classes of things that are perfectly similar in one respect, that makes littles sense. From the point of view of the pluriverse, the difference between two such classes F and G is mere numerical distinctness: there is no substantial difference in distribution (as there would be on haecceitism), nor in any other higher-order properties; F is a maximal class of fundamentally similar things, and G is a maximal class of fundamentally similar things, and that's it. Fundamental properties, therefore, have no intrinsic nature. (Even with universals, one can say that fundamental properties are merely numerically distinct. Armstrong does that. Without universals, however, and without haecceitism, this conclusion seems inevitable.)

There are, of course, lots of things to know about F: that it's instantiated in our world, that it interacts with other properties in such-and-such a way in our world, that I have it, etc. But these are contingent and external properties of F. In another world, F has none of that, while G has it all. And in a sense, these two worlds are merely numerically distinct.

Since fundamental properties have no nature, there can be no real ignorance about their nature -- as Russell and Maxwell and Langton have claimed there is. Where there is nothing to know, there is nothing to be ignorant of.

(Is this Lewis's view? I think so. But (as Dave Chalmers pointed out in our quidditism reading group) some of Lewis's remarks in "Ramseyan Humility" don't quite fit the picture: that acquaintance could in principle give us the knowledge of fundamental properties that we lack, and that God could possess this knowledge.)