Thursday, December 16, 2010

Coincident objects

In an earlier post I said that I did not think it strictly correct to say that persons are or identical to their functional brains (more specifically, their cerebrums). My reasoning is as follows:

There is a principle of metaphysics that seems correct and I think most metaphysicians would agree. It is Liebniz's law of identity or the indiscernibility of identicals. Expressed in 2nd order logic, it says

Basically, it just says that an object has all the properties it has. That seems so true to be trivial and it is. There is a stronger principle of identity that is the converse of that principle which says that if objects a and b has all (both genuine and "mere-cambridge") properties in common then they are identical. This later principle is a little more controversial as a famous paper by Max Black but this last principle is not relevant to this case.

Since the first principle thus cannot be faulted. But consider this example by Gibbard: Let's say that there is a lump of clay called "Lumpl" which is created at exactly the same time as a statue which is made out of that clay. We will call this statue "Goliath." They are also destroyed at a same later time. Now both the statue and the lump of clay exists at exactly the same time and occupy the same region of space. Thus are they the very same object or alternatively, does Lumpl=Goliath?

If you say "yes" then there seems to be properties which each has that the other does not have. Lumpl, for example, has the modal property that it can survive being stepped on but if Goliath is stepped on, he will be destroyed. Goliath has the property that it can survive the loss of one of its arms but Lumpl will not survive that loss of clay. Thus this seems to be a case where we either say that they are not the same object even though they occupy the same region of space and time or we say that the Leibniz's principle is false, i.e., that something can have properties it does not have. I think the later is nonsensical and so we should accept the former.

For similar considerations, I think persons are coincident with their functional cerebrums but are not strictly speaking, identical with them much as Goliath is coincident with Lumpl but not strictly speaking identical with it. There seems to me to be good metaphysical and practical ethical reasons not to identify persons with their brains but to see them as coincident together.

But it has occurred to me that one possible way to flesh this out better is to view Lumpl and Goliath (or other coincident objects) as having different essential properties. We know that one can have different inessential properties and still be the same thing. You may have been taller or shorter than you are in some possible scenario and still be you. You might have liked the color blue instead of hating it and you'd still be you. But your essential properties will remain. Changing them will change the truth of the identity conditions.

Thus for Lumpl, called it now "l," it may have a set of essential conditions which we can express as a conjunction of sentences ascribing its essential properties: [P1(l) & P2(l) & P3(l)...] with P1, P2, P3... all being essential properties of Lumpl. This conjunction we can call "E." It will include the property of survival after being stepped on among one of its conjuncts. E will be disjunctive with some string of sentences call it "In" with In itself just a string of disjunctive sentences of its inessential properties, Q1, Q2, Q3.... Thus In=[(Q1(l) v Q2(l) v Q3(l)...]. Thus E v In will be all the properties, essential and inessential, Lumpl has and will identify it in this world and all possible worlds (complete description of Lumpl) while E by itself will identify it in all possible worlds (essential description). Some properties may be indefinite whether it is or is not essential, however.

When we look at it like this, coincident objects don't seem to be that counter-intuitive and odd. Two coincident objects have different essential properties so for Lumpl, the property of survival after getting stepped on will be in its essential sentential conjunctive string but for Goliath, it will not be. Descriptively, they are thus different. I don't see there to be any more difficulties when viewed this way than mereological objects. A car's tires are part of the car but the tires are not identical with the whole car. They share overlapping regions of space. The only difference in coincident objects is that they share all their occupied space instead of partially as in mereological objects.


  1. This makes sense to me and would also be useful for explaining intensional identities. For example, someone might know who Barack Obama is and understand the phrase "44th President of the United States" without knowing that the two are identical. But they're definitely not identical in all possible worlds, just this one. On the other hand, there isn't some obvious property we can use to separate the two out, since they refer to the same object.

  2. It has occurred to me that it might be far better to use modal logic so that the first string of sentences describing its essential properties ascribe necessity to each sentence while the last string of disjunctive ones are of possibility.