Storrs McCall

David Lewis, following in the tradition of Broad, Quine and Goodman, says that change in an object X consists in X's being temporally extended and having qualitatively different temporal parts. Analogously, change in a spatially extended object such as a road consists in its having different spatial parts . The alternative to this view is that ordinary objects undergo temporal change in virtue of having different intrinsic non-relational properties at different times. They endure, remaining the same object throughout change, whereas Lewis's temporally extended 4D objects perdure.It is impossible to come down on one side or the other of the endurance/perdurance debate without a clear and unambiguous understanding of what ‘endurance’ is. ‘Perdurance’ is clear enough. Every 4D object of non-zero temporal thickness perdures simply by having temporal extension, i.e. by having different temporal parts, or stages, at different times. But Lewis muddies the waters by giving a confused and ultimately untenable definition of endurance.His first step is to cover both perduring and enduring by offering the neutral word persist. ‘Let us say that something persists iff, somehow or other, it exists at various times’ . Something then perdures if it persists by having different temporal parts at different times, no one part being wholly present at more than one time. In contrast, a thing endures if it persists by being wholly present at more than one …

Over the last 25 years, experimental findings published by Benjamin Libet have indicated that conscious acts of will are preceded by a characteristic kind of brain event of which the agent is not conscious. It, Libet says, rather than the will, is what causes actions. His discoveries, if correct, would seem to imply that the notion of a free, conscious will is an illusion, and that actions are initiated by neural processes not under conscious control. In what follows it is argued that Libet’s conclusion is incorrect, and that other evidence points to the essential causal role of consciousness in voluntary action.

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Relative to any point in time, how many possible futures are there? For example, it may rain tomorrow, or again it may not. So it would appear that relative to today, there are at least two possible futures, one involving rain tomorrow and the other not. Of course only one of these two future states of affairs will take place, and in that sense there is only one actual future, though there may be many possible futures. The only hypothesis under which there is, for every instant in time, only one possible future, is the hypothesis of universal Laplacean determinism, and this hypothesis has had little to recommend it since the advent of quantum physics. Furthermore, although among the many possible futures relative to any given moment in time there is only one which will become actual, no distinguishing mark separates this one from its fellows at the given moment. So it would appear that what confronts the world at each moment in time is an undifferentiated multiplicity of possible futures. But this multiplicity, though at first sight admittedly frightening in its implications, may be put to good philosophical use: as will be seen it yields natural and convincing definitions of the notions of physical necessity and possibility. On the other hand, alternative definitions of these notions are obtainable which do not make use of the manifold of possible futures, and these also will be presented. The paper will be in two parts, the first dealing with the concepts of physical possibility and necessity, and the second presenting a formal calculus of necessary and sufficient conditions in which the physical modalities find their place.

A theory of temporal passage is put forward which is "objective" in the sense that time flow characterizes the universe independently of the existence of conscious beings. The theory differs from Grunbaum's "mind-dependence" theory, and is designed to avoid Grunbaum's criticisms of an earlier theory of Reichenbach's. The representation of temporal becoming is accomplished by the introduction of indeterministic universe-models; each model representing the universe at a time. The models depict the past as a single four-dimensional manifold, and the future as a branched structure of such manifolds. Time flow is relativistic in that it manifests itself in a frame-dependent (but not observer-dependent) way. The indeterministic character of the universe-models is mirrored in a "temporal" theory of truth which rejects the principle of bivalence, and suitable semantics are provided for this theory. Finally, an account of physical law is given which defines it in terms of physical possibility, rather than vice versa

The evolution of a single trapped ion exhibiting intermittent fluorescence and dark periods may be described either as a continuous process, using differential rate equations, or discretely, as a Markov process. The latter models the atom as making instantaneous transitions from one energy eigenstate to another, and is open to the objection that superpositions of energy states will form which are not covered by the Markov process. The superposition objection is replied to, and two new mathematical elements, Markov vectors and Markov matrices, are proposed as additions to quantum theory. The paper concludes by attributing the cause of dark periods in the ion's history to instantaneous transitions in the ion itself, rather than to photon detection or other components of measurement.

Combining quantum mechanics with special relativity requires (i) that a spacetime representation of quantum states be found; (ii) that such states, represented as extended along equal-time hyperplanes, be invariant when transformed from one frame to another; and (iii) that collapses of states be instantaneous in every frame. These requirements are met using branching spacetime, in which probabilities of outcomes are represented by the numerical proportions of branches on which the outcomes occur. Quantum states of systems are then identified with the probability values, built into spacetime along spacelike hypersurfaces, of all possible outcomes of all possible tests to which the systems can be subjected

A common criticism of free will or origination theories is that if what we do is not the result of an unbroken sequence of causes and effects, then it must to some degree be the product of chance. But in what sense can a chance act be intentional or deliberate, in what sense can it be based on reasons, and in what sense can a person be held responsible for it? If free and responsible action is incompatible with determinism, must it not equally well be incompatible with indeterminism? Professor McCall says no. He argues that a new idea, that of a controlled indeterministic process, resolves a variety of classical dilemmas and opens the way to a new understanding of the relationship between actions, reasons, causes, and responsibility. Does he succeed? All of this, like a related line of argument by Professor McCann to which you can turn, is a long way from what seems to me the continuing arguableness of determinism and the unavoidableness of the proposition that both incompatibilism and compatibilism about freedom are false. But we all need to remember, with Cromwell, in our own bowels if not by those of Christ, that we may be mistaken. I guess that given the proportion of false to true views in the world, we need to remember it is arguable that we are more likely to be mistaken.

Any "classical" theory of truth will satisfy tarski's criterion ("p" is true if and only if p), And the principle of bivalence (every proposition is either true or false). A non-Classical theory may be obtained by rejecting these principles: - in fact it is shown that rejection of the second entails rejection of the first. If the resulting non-Classical theory is formalized, A system structurally isomorphic to either s4 or s5 is obtained. An attempt is made to show that the essential insights of intuitionist logic may be preserved if we replace their complex and in many respects "unintuitive" propositional logic by a theory of truth which is non-Classical in the sense described above