The hidden assumption in MacKay's logical paradox concerning free will

In a series of recent publications, MacKay has proposed what can only be called a paradox, concerning the notion of free will. (Cf. MacKay [1960], [1965], [1966], [1967], [1969], [197I].) MacKay purports to show that it is in some sense impossible to deny the validity of the belief in a free will (at least for the actor in question). At the outset we must distinguish two forms of the question of free will. One form, the traditional version, which MacKay's arguments do not establish, and a second, weaker version, which MacKay seeks to prove. Historically the claim for a free will was the claim that one's actions or decisions were outside the scope of ordinary physical determinism. That is, arguing for the validity of free will was seeking to establish that one's actions or decisions were not the result of causes but rather that they arose, to some extent, de vacuo. This is what is usually meant by the notion of free will and MacKay's proposals do not establish this sense of the term. What MacKay purports to establish is a weaker version of the concept in which one's actions or decisions can be completely causally determined in the strong sense for external observers but logically undetermined for the actor in question. MacKay conceives this situation as one of philosophical relativism in that one's actions can be both determined (from another's point of view) and undetermined from one's own point of view. This then is the crux of the issue; in order to examine MacKay's thesis we must examine the question of how it can be possible for an action to be both determined and undetermined simultaneously depending upon the point of view from which the situation is discussed. We must also examine what it means to say that something is logically undetermined and to ascertain how this differs from ordinary physical indeterminism. First let us consider the logically indeterminate situation of an actor (A). Assume that we wish to predict the future states of A's brain. Any complete prediction must consider those states of A's brain dealing with what A believes. The question is whether or not A believes our prediction. If A believes it then the prediction could not be correct both before and after his believing it, for if correct before then it describes A as not believing it and if correct after A comes to believe it then it could not have been correct before. That is, our prediction becomes a variable effecting A's brain states thus making our prediction forever recursively incomplete. Furthermore, MacKay has argued rather cogently that the gambit of withholding our prediction from A will not allow us to escape from our dilemma. For if our prediction were a complete and binding one it would merit universal assent, logically, by all participants including A. However, A would be manifestly in error were he to believe our prediction for by that very act our prediction would be falsified. Thus there exists no determinate specification of A's future beliefs which is binding on everyone, including A, before he decides. It is in this sense that MacKay would say that A's decision is logically indeterminate. Contrast this situation with the completely determinate one, a complete prediction of which would merit universal assent by all observers. MacKay