Whither Fractional Objects?

To me,

(1) There is at most one half of an apple in the fruit bowl

sounds fine, but

(2) There is at most one half of an object[1] in the fruit bowl

sounds odd. (I trust that others will think the same, but feel free to correct me if I’m wrong!) Surely, if an apple is an object, half an apple is half an object? But if (1) makes sense and (2) doesn’t, does that mean a half of an apple is not half an object? Perhaps the thought which drives the sense of oddness is that nothing is a half simpliciter, it is always a half of some sort of thing: One mile is half of two miles, and if we dropped the term "mile" and started calling two mile intervals “stretches”, one mile could simply be called “half a stretch”. Yet this “halfness” is nothing ontically basic; one and the same thing is half a stretch, one mile, two half-miles, and five thousand two hundred and eighty feet.

Even so, why couldn’t we have at most half of an object in the fruit bowl if “object” picks out a genuine category? If we can eat half an apple and drive half a mile, what prevents us from throwing half an object across the room? We could certainly throw half a football. The answer to these queries might be that a given entity which is a fraction of one thing is always a whole (and thus one) of something else. E.g., one slice of a pizza is also one eighth of the whole pie. We can also note that if there is at most half of an object in the fruit bowl, it cannot be the case that there is at least one, and if the bowl is not empty that is impossible. Thus we cannot say there is at most half an object in the fruit bowl; wherever we have a fraction of one sort of object there is always at least one of different sort. All this goes to show that "object" picks out a very special category if it picks out any at all.

The above reflections seem to commit us to a Fregean view in which nothing is intrinsically one or many. This view is not without its problems: Does it make good metaphysical sense to hold that how many things there are depends on what category we apply to them? Aren’t we contradicting ourselves if we say that one thing can be identical to many? After all, one deck of cards cannot be identical to two decks, why should it be any more possible for it to be identical to fifty two cards? Yet if we do not embrace the Fregean view, how else might we explain (or explain away) the strangeness of (2)? These are difficult issues, but hopefully with your input we can get a clearer view of the matter.


[1] “Object” being construed broadly as covering anything that exists.

A Coherent Account of Libertarian Free Will

Free will, it seems, requires the ability to do otherwise than one does, via the Kantian doctrine that “ought” implies “can”. If the hungry ought to be fed, for example, it seems this depends not a whit on whether they are actually fed or not. If the hungry could not have been fed, their being fed is impossible; to say they nevertheless ought to be fed is like saying someone ought to take a block of wood and carve it into a square circle. However, there is a powerful objection to the idea that free will even compatibile with indeterminism, which called the Mind Argument. Basically, it goes like this: If a given act R is contingent but uncaused, then, since it is contingent, nothing determines whether or not R occurs, and a fortiori I do not determine whether it occurs either. So if R were contingent and uncaused, it would not be under my control. Thus it appears that if my actions are undetermined I do not have free will. Nor, it seems, can we resolve the issue by holding that I will to will to will R, and so on to infinity. My mind surely does not encompass an infinite number of mental acts. But if the regress of willings terminates, there will be at least one member of the series which is uncaused. And so we're right back where we started.

In consequence of the above, we have the following criteria for a free act: In order to be free, it must be contingent, yet it must also be something I bring about. For each act of will, I must have brought it about by freely willing it, yet we must not launch ourselves on an infinite regress. My solution is something I will call the Closed Causal Loop theory of free will. There must be at least two acts of will which cause each other. The reason we need two acts is this: If there were only one act, it could not “cause itself” in any non-redundant sense, because any entity E is conditionally necessary given E no matter what E is. It would thus not be distinguished from any other act as far as "self causation" is concerned. If there are at least two acts, however, each can cause the other in the ordinary sense because they are distinct. According to this theory, a primary act of will A causes a secondary act of will B and has both B and the action chosen as its objects. B in its turn causes A and has A as its object[1]. A and B jointly cause the action to be performed, since if either A or B had not occurred then neither would the other, and if both had not occurred then neither would the action.

Is this view defensible? The following sort of objection could be raised. Since A causes B and B causes A, each will occur if the other does. So either both occur or neither occur. Call the mereological fusion of A and B ‘S’. Since my acts of will are supposed to be free and hence contingent, it is also contingent whether or not S, their fusion, occurs. So if S occurs, then by hypothesis I cause A in virtue of causing B and B in virtue of causing A, but I do not cause S, because if something is contingent it cannot “cause itself” in any non-vacuous sense, and there is nothing besides S in virtue of which I could cause it. But now the proponent of libertarian free will faces the same problem as before: If I do not cause S then its occurrence or non-occurrence is not in my control, so I am not responsible for it. By the principle that I am responsible for x and I am responsible for y if and only if I am responsible for the mereological fusion of x and y, if I am not responsible for S I cannot be responsible for A or B either.

But I think there is an easy reply: It is primarily actions, including acts of will, for which we are held responsible. However, the mereological fusion of two acts of will is not itself an act of will, any more than a mereological fusion of two ants is an ant. It is not the sort of thing I could be responsible for, for it is neither a willing nor an action of mine. It is only willings, actions of mine, or consequences of those actions for which I can be held responsible, and the fusion of two willings is none of these. It is therefore no defect that I do not bring it about. All that is required is that I be responsible for each act individually, not the conjunctive state of affairs that both obtain.

I have, of course, done nothing to show that this account is true, nor even that it is in the least compatible with what psychology and neuroscience have revealed about the mind (as, indeed, it very probably is not). Nevertheless, it seems at least conceptually coherent, and so I conclude that a coherent account of libertarian free will is possible. Irrespective of its truth or falsity, this account provides a counterexample to the Mind Argument as given above. There may be sound arguments for the incompatibility of free will and indeterminism, but the Mind Argument is not one of them.

[1] I hold that B does not have the action chosen as one of its objects, otherwise it is not clear to me that it would be distinct from A.