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Saturday, June 26, 2010

A Difficulty With Haecceity Properties

imported from http://maverickphilosopher.typepad.com/maverick_philosopher/2010/06/my-difficulty-with-haecceity-properties.html

By popular demand, here is revised version of a post that first appeared on the old blog in July of 2005.

Introduction. I find haecceity properties hard to accept, although I grant they they would do various useful jobs if they existed. ('Haecceity' from the Latin haecceitas, thisness.) In this post I explain one or two of my reasons for nonacceptance. If you know your Plantinga, you will know that he is my primary target in these notes. This post is not about Duns Scotus or any medieval.

Definition. Suppose we take on board for the space of this post the assumptions that (i) properties are abstract objects, that (ii) they can exist unexemplified, and that (iii) they are necessary beings. We may then define the subclass of haecceity properties as follows.

A haecceity is a property H of x such that: (i) H is essential to x; (ii) nothing distinct from x exemplifies H in the actual world; (iii) nothing distinct from x exemplifies H in any metaphysically possible world.

So if there is a property of Socrates that is his haecceity, then there is a property that individuates him, and indeed individuates him across all times and worlds at which he exists: it is a property that he must have, that nothing distinct from him has, and that nothing distinct from him could have. Call this property Socrateity. Being abstract and necessary, Socrateity is obviously distinct from Socrates, who is concrete and contingent. Socrateity exists in every world, but is exemplified (instantiated) in only some worlds. What's more, Socrateity exists at every time in every world that is temporally qualified, whereas Socrates exist in only some worlds and only at some times in the worlds in which he exists. Haecceity properties have various uses. I'll mention just one.

Use. Suppose I need to analyze 'Socrates might not have existed.' I start with the rewrite, 'Possibly, Socrates does not exist' which features a modal operator operating upon an unmodalized proposition. But 'Socrates does not exist,' being a negative existential proposition, gives rise to an ancient puzzle dating back to Plato. How is reference to the nonexistent possible? The sentence 'Socrates does not exist' is apparently about Socrates, but how so given that he does not exist? If the meaning of 'Socrates' is the name's referent, and nothing can be a referent of a term unless it exists, then Socrates must exist if he is to have nonexistence predicated of him. But the whole point of the sentence is to say that our man does not exist. How can one say of a thing that it does not exist without presupposing that it exists? Haecceities provide a solution. We can understand 'Socrates does not exist' to be about Socrateity rather than about Socrates, and to predicate of Socrateity the property of being exemplified. Recall that Socrateity, unlike Socrates, exists at every time and in every world. So this property, unlike Socrates, is always and necessarily available. Accordingly, we analyze 'Possibly, Socrates does not exist' as 'Possibly, Socrateity is not exemplified.' Socrates' possible nonexistence boils down to Socrateity's possible nonexemplification. It is a nice, elegant solution to the puzzle --assuming that there are haecceity properties.

Problem. One of the stumbling blocks for me, however, is the notion that the thisness of an individual could exist even if the individual whose thisness it is does not exist. Consider the time before Socrates existed. During that time, Socrateity existed. But what content could that property have during that time (or in those possible worlds) in which Socrates does not exist? Socrateity is identity-with-Socrates. Presumably, then, the property has two constituents: identity, a property had by everything, and Socrates. Now if Socrates is a constituent of identity-with-Socrates, then it seems quite obvious that Socrateity can exist only at those times and in those worlds at which Socrates exists. Socrateity would then be like Socrates' singleton, the set consisting of Socrates and Socrates alone: {Socrates}. Clearly, this set cannot exist unless Socrates exists. It is ontologically dependent on him. The same would be true of identity-with-Socrates if Socrates were a constituent of this property.

Problem Exacerbated. If, on the other hand, Socrates is not a constituent of Socrateity, then what gives identity-with-Socrates the individuating content that distinguishes it from identity-with-Plato and identity-with-Pegasus? Consider a possible world W in which Socrates, Plato, and Pegasus do not exist. In W, their haecceities exist since haecceities ex hypothesi exist in every world. What distinguishes these haecceities in W? Nothing that I can see. The only things that could distinguish them would be Socrates, Plato, and Pegasus; but these individuals do not exist in W. It might be said that haecceity properties are simple: identity-with-Socrates is not compounded of identity and Socrates, or of anything else. Different haecceities just differ and they have the content they do in an unanalyzable way. But on this suggestion haecceities seem wholly ungraspable or inconceivable or ineffable, and this militates against thinking of them as properties. I have no problem with the notion of a property that only one thing has, nor do I have a problem with a property that only one thing can have; but a property that I cannot grasp or understand or conceive or bring before my mind -- such an item does not count as a property in my book. It would be more like a bare particular and inherit mutatis mutandis the unintelligibility of bare particulars.

Haecceities must be nonqualitative. Consider a conjunctive property the conjuncts of which are all the mutiply exemplifiable properties a thing has in the actual world. Such a property would individuate its possessor in the actual world: it would be a property that its possessor and only its possessor would have in the actual world. Such a property is graspable in that I can grasp its components (say, being barefooted, being snubnosed, being married, etc.) and I can grasp its construction inasmuch as I understand property conjunction. But the only way I can grasp Socrateity is by grasping is as a compound of identity and Socrates -- which it cannot be for reasons given above.

Note that Socrateity is not equivalent to the big conjunctive property just mentioned. Take the conjunction of all of Socrates' properties in the actual world and call it K. In the actual world, Socrates has K. But there are possible worlds in which he exists but does not exemplify K. And there are possible worlds in which K is exemplified by someone distinct from him. So Socrateity and K are logically nonequivalent. What we need, then, if we are to construct a qualitative thisness or haecceity of Socrates is a monstrous disjunctive property D[soc] the disjuncts of which are all the K's Socrates has in all the possible worlds in which he exists. This monstrous disjunction of conjunctions is graspable, not in person so to speak, but via our grasp of the operations of conjunction and disjunction and in virtue of the fact that each component property is graspable. But D[soc] is not identical to Socrateity. The former is a qualitative thisness whereas the latter is a nonqualitative thisness. Unless the Identity of Indiscernibles is true, these two thisnesses are nonequivalent. And there are good reasons to think that the Identity of Indiscernibles is not true. (Max Black's iron spheres, etc.) So D[Soc] is not identical to Socrateity.

Conclusion. To compress my main point into one sentence: identity-with-Socrates is graspable only as a compound of identity and Socrates; but then this property cannot exist unexemplified. Hence haecceity properties as defined above do not exist.

COMMENT

Scotus actually says

...sensus non cognoscit obiectum in quantum est distinctum a quolibet quod non est unum ista unitate numerali; quod patet, quia nullus sensus distinguit hunc radium Solis differre numeraliter ab illo radio, cum tamen sint diversi per motum Solis, si circumscribantur omnia sensibilia communia, puta diversitas loci vel situs; et si ponerentur duo quanta simul omnino per potentiam divinam, quae essent omnino similia et aequalia in albedine et quantitate, visus non distingueret ibi esse duo alba; si tamen cognosceret alterum istorum, in quantum est unum unitate numerali, cognosceret ipsum in quantum distinctum numeraliter a quolibet alio

"...sense does not know an object insofar as it is distinct from whatever is not one by that numerical unity, which is clear, because no sense distinguishes this ray of the sun to differ numerically from that ray, even though they are diverse through the motion of the sun, if all common sensibilia are set aside (such as diversity of place or position). And if two quanta were supposed to be exactly together by divine power, which were entirely similar and equal in whiteness and quantity, sight would not distinguish two white things to be there. If nevertheless it were to know one or the other of those, insofar as it is one by numerical unity, it would know it insofar as [it is] distinct numerically from any other". (Super distinctione III. libri II. sententiarum
quaestio i)

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