Online research in philosophy

An alternative to the standard endurance/perdurance accounts of persistence has recently been developed: the stage theory (Sider, T. Four-Dimensionalism: an Ontology of Persistence and Time. Oxford: Oxford University Press, 2001; Hawley, K. How Things Persist. Oxford: Oxford University Press, 2001). According to this theory, a persisting object is identical with an instantaneous stage (temporal part). On the basis of Leibniz's Law, I argue that stage theorists either have to deny the alleged identity (i.e., give up their central thesis) or hold that stages are both instantaneous and continuants. I subsequently show that, although stage theory is flexible enough to accommodate the latter claim, the cost for accommodating it is an excessive proliferation of persistence concepts.

An alternative to the standard endurance/perdurance accounts of persistence has recently been developed: the stage theory (Sider, T. Four-Dimensionalism: an Ontology of Persistence and Time. Oxford: Oxford University Press, 2001; Hawley, K. How Things Persist. Oxford: Oxford University Press, 2001). According to this theory, a persisting object is identical with an instantaneous stage (temporal part). On the basis of Leibniz's Law, I argue that stage theorists either have to deny the alleged identity (i.e., give up their central thesis) or hold that stages are both instantaneous and continuants. I subsequently show that, although stage theory is flexible enough to accommodate the latter claim, the cost for accommodating it is an excessive proliferation of persistence concepts.

The rotating discs argument (RDA) against perdurantism has been mostly discussed by metaphysicians, though the argument of course appeals to ideas from classical mechanics, especially about rotation. In contrast, I assess the RDA from the perspective of the philosophy of physics. I argue for three main conclusions. The first conclusion is that the RDA can be formulated more strongly than is usually recognized: it is not necessary to ‘imagine away’ the dynamical effects of rotation. The second is that in general relativity, the RDA fails because of frame-dragging. The third conclusion is that even setting aside general relativity, the strong formulation of the RDA can after all be defeated, namely, by the perdurantist taking objects in classical mechanics (whether point-particles or continuous bodies) to have only temporally extended (i.e. non-instantaneous) temporal parts, which immediately blocks the RDA. Admittedly, this version of perdurantism defines persistence in a weaker sense of ‘definition’ than pointilliste versions that aim to define persistence assuming only instantaneous temporal parts. But I argue that temporally extended temporal parts (i) can do the jobs within the endurantism–perdurantism debate that the perdurantist wants temporal parts to do and (ii) are supported by both classical and quantum mechanics. Introduction The story so far 2.1 The RDA 2.2 Intrinsic properties and the idea of velocity 2.2.1 The intrinsic–extrinsic distinction 2.2.2 Velocity to the rescue? 2.3 ‘Naturalism’ 2.4 The accompaniments of rotation 2.5 Two kinds of reply: against the consensus Describing rotation 3.1 Rotation is kinematic 3.2 Beware of rigidity 3.3 An improved RDA: allowing the actual accompaniments 3.4 The RDA fails in general relativity Perdurantism without tears: the classical case 4.1 Rejecting instantaneous temporal parts 4.2 Replying to the RDA 4.2.1 ‘Kinematics’ 4.2.2 ‘Dynamics’ 4.2.3 An ‘anti-pointilliste’ objection and reply 4.3 Intrinsic properties of non-instantaneous temporal parts 4.3.1 Can the perdurantist appeal to them? 4.3.2 Temporal intrinsicality at an instant is rare 4.3.3 A better reason for temporal intrinsicality 4.4 Non-instantaneous parts can do the jobs 4.4.1 Humean supervenience revisited 4.4.2 The problem of change 4.4.3 Puzzles of coincidence 4.5 Instantaneous velocity is hardly extrinsic Support from decoherence in quantum theory 5.1 Classical and quantum: relativizing the intrinsic–extrinsic distinction 5.1.1 Unitarity: momentum as temporally intrinsic 5.2 Position and existence as nomically extrinsic.

Extending on an earlier paper [Found. Phys. Ltt., 16(4) 343–355, (2003)], it is argued that instants of time and the instantaneous (including instantaneous relative position) do not actually exist. This conclusion, one which is also argued to represent the correct solution to Zeno’s motion paradoxes, has several implications for modern physics and for our philosophical view of time, including that time and space cannot be quantized; that contrary to common interpretation, motion and change are compatible with the “block” universe and relativity; and that time, space, and space-time too, cannot exist. Instead, motion and change become the major players.

There is a longstanding definition of instantaneous velocity. It saysthat the velocity at t 0 of an object moving along a coordinate line is r if and only if the value of the first derivative of the object's position function at t 0 is r. The goal of this paper is to determine to what extent this definition successfully underpins a standard account of motion at an instant. Counterexamples proposed by Michael Tooley (1988) and also by John Bigelow and Robert Pargetter (1990) are reinforced and illuminated by considering the presence or absence of changes to the object's motion.

This paper will argue that the puzzles about instantaneous velocity, and rates of change more generally, are the result of a failure to recognize an ambiguity in the concept of an instant, and therefore of an instantaneous state. We will conclude that there are two distinct conceptions of a temporal instant: (i) instants conceived as fundamentally distinct zero-duration temporal atoms and (ii) instants conceived as the boundary of, or between,temporally extended durations. Since the concept of classical instantaneous velocity is well- defined only on the second conception of instants, we will conclude that this distinction allows us to avoid the above dilemma. If instantaneous velocity is well-defined then the states of a system at various instants are not logically distinct and thus we cannot generate Zeno’s paradox. However, if we assume that the instants are metaphysically distinct, then instantaneous velocity is not well-defined and thus the second horn of the dilemma about the causal-explanatory role of instantaneous velocity cannot be generated.