Wednesday, October 15, 2008

Transworld identity without haecceities

Haecceities are individual essences, even of non-existent beings. Necessarily, entity exists iff its haecceity is instantiated. Some folks think we need haecceities to make sense of alien individuals—i.e., individuals that exist in other worlds but not in ours. We don't, as long as we are willing to be Leibnizian in denying the identity of indiscernibles. Here, then, is a simple theory of identity across worlds that entails the essentiality of origins. The theory applies both to substance-like and event-like individuals.

I will give the simplest version of the theory, for beings in an absolute time who do not engage in any time travel and without backwards causation. A general version of the theory requires the replacement of times by "causal (or maybe even explanatory) points"—points in the causal history of an entity. This is a bit tricky, and so I won't bother with it.

Let e be an entity and w a world. Say that H is a qualitative history of e up to t in w provided that e exists at t in w and H is a proposition giving an at least partial description of w such that:

  1. H is purely qualitative except respect of e and t: i.e., the only particulars that are de re involved in H are e and t;
  2. H states that e exists at t and gives a complete description of the intrinsic properties of e at t, subject to the restriction in (1);
  3. For any state of affairs reported in H, any and all the causes in w of that state of affairs are also reported in H;
  4. H reports that e exists at t;
  5. H is a minimal proposition satisfying (1)-(4).
Now, let w1 and w2 be two worlds such that e1 exists in w1 and e2 exists in w2. Then e1=e2 if and only if there are times t1 and t2 and histories H1 of e1 up to t1 in w1 and H2 of e2 up to t2 in w2, such that H1's description of e1 and t1 coincides exactly with H2's description of e2 and t2.

To put it roughly, e1 and e2 are identical if and only if there are points in the existence of each one, such that their respective histories up to these points are the same.

This view entails essentiality of origins. It also implies that there cannot be two entities which, along with their causal histories, have been indiscernible up to some time. Thus, there cannot be completely identical twins. This consequence is counterintuitive, but may be but a small price to pay for avoiding haecceities.

Given this view, we can form something like a haecceity from the disjunction of all the histories of an entity in a world.

The view can be varied by relaxing or tightening the conditions (1)-(5) on histories. I do not yet know which is the optimal version.

4 comments:

Daniel Murphy said...

Dr. Pruss,

I'm not sure I fully understand the theory, but would it be accurate to say that it seeks to provide purely qualitative essences, as opposed to essences that have to include a non-qualitative essence/haecceity as a component? You say that by the theory we can avoid haecceities, but also that an entity exists iff its haecceity is exemplified. Is the haecceity necessarily exemplified something like a qualitative one (involving its history/origins) and the one avoided an alleged non-qualitative one?

If I am understanding the theory correctly, there seems to me to be a difficulty for affirming the "if" part of the "if and only if" in "e1=e2 if and only if..." What about the case of a multiverse, say two universes, qualitatively identical up to some time t. In this case two entities e1 and e2 would exist, one in u1 and one in u2, and e1 cannot be identical with e2 since u1 and u2 are distinct. Then there are two worlds w1 and w2 (identical with each other) and times t1 and t2 (designating the same time, e.g. "10 seconds after the universe's beginning") such that a history H1 of u1 (therefore including an exhaustive description of e1) terminating at t1 will exactly match a history H2 of u2 (and hence e2) terminating at t2. So it seems that the history of e1 and e2 are the same (meeting the sufficient condition for identity on the theory), but e1 and e2 are non-identical.

This would not actually challenge the essentially of origins, but rather the idea that origins (qualitatively specified) are sufficient to constitute an essence.

Admittedly this denies the (qualitative) identity of indiscernibles, but this is due to counterexampling it, not assuming its falsity. (One thing that I don't understand is that you say at the beginning that, on the theory, we should deny the identity of indiscernibles, but at the end you seem to endorse the principle by concluding that there cannot be two non-identical indiscernible individuals - no twins)

I'm not sure of the import of "the disjunction of all the histories" bit. Wouldn't any two distinct histories of an individual in a world w* be such that one includes the other as an initial segment (i.e., one includes the individual's history up to a higher time t than the other does)? If so, is this meant to capture the idea that perhaps the history of an individual posterior to its beginning-to-exist can be essential (such that we want to include that further history as a disjunct)?

Alexander R Pruss said...

Daniel:

Good questions!

1. Yes, these are purely qualitative essences.

2. The theory denies the possibility of two things having the same history up to some point. This is a strong version of the identity of indiscernibles. (I screwed up and wrote about denying the identity of indiscernibles--I should have said, of course, that one is affirming it.) Here's where modal intuitions differ. I find the view I am defending plausible enough, that I find it easy to deny the possibility of two multiverses with a common initial segment. :-)

3. Let's say that t0 is the first time at which x exists. Then the disjunction of all the histories will be equivalent to the history up to t0 (all the other histories will be stronger than the history at t). However, suppose that there is no first time at which x exists, either because x has always existed, or because the beginning of x's existence is an interval open at the bottom end. In that case, the disjunction is a way of capturing the limiting behavior as one goes towards the beginning of x's existence, as it were.

Daniel Murphy said...

Dr. Pruss,
Thanks for the further explanation concerning the theory. I'd be interested in how you find it easy to deny the possibility of the co-existence of two universes with qualitatively identical initial-segments. Why think that God could not have created a second universe an initial segment of which was (qualitatively) just like an initial segment of our universe? Wouldn't this clash with omnipotence? I suppose the reason for denying that it clashes with omnipotence would be the same reason to hold to the relevant version of I-I, namely, that this multiverse example is a logically or metaphysically incoherent state of affairs; but why think that it is?

The scenario I proposed wouldn't jeopardize the essentiality of origins (e1 and e2 could be essentially tied to their respective histories), and so it would seem that intuitions for the essentiality of origins would not speak against this view. Further, if we added the restriction that we are only considering possible individuals in *this* universe, then essentiality of origins could, it seems, amount to essences and not just essential properties. That is, a qualitative history of origins + a universe-indexed property could amount to an essence, and it would be natural for the latter part to be tacitly assumed in many cases of talking about possible individuals. (But whether these would ultimately be qualitative essences I don't know, since it seems to me that universe-indexed properties need to be non-qualitative (because I think qualitative specifications of initial segments of universes can be multiply instantiated).)

Incidentally, I think that an anti-Molinism argument can be made by denying the qualitative I-I and arguing that creaturely essences cannot exist pre-creation (because, following Adams, there are no non-qualitative thisnesses of non-actual individuals).

Alexander R Pruss said...

Bibliographic note: a version of this theory is discussed by B. Brody, 1980, Identity and Essence, Princeton, NJ: Princeton University Press.