Online research in philosophy

It is widely believed that shapes are intrinsic properties. But this claim is hard to defend. I survey all known theories of shape properties, and argue that each theory is either incompatible with the claim that shapes are intrinsic, or can be shown to be false.

Four-dimensionalism, or perdurantism, the view that temporally extended objects persist through time by having (spatio-)temporal parts or stages, includes two varieties, the worm theory and the stage theory. According to the worm theory, perduring objects are four-dimensional wholes occupying determinate regions of spacetime and having temporal parts, or stages, each of them confined to a particular time. The stage theorist, however, claims, not that perduring objects have stages, but that the fundamental entities of the perdurantist ontology are stages. I argue that considerations of special relativity favor the worm theory over the stage theory.

Christensen [Philosophy of Science, 50: 471–481, 1983] and [Philosophy of Science, 57: 644–662, 1990] provides two sets of counter-examples to the versions of bootstrap confirmation for standard first-order languages presented in Glymour [Theory and Evidence, Princeton University Press, Princeton, 1980] and [Philosophy of Science, 50: 626–629, 1983]. This paper responds to the counter-examples of Christensen [Philosophy of Science, 50: 471–481, 1983] by utilizing a new notion of content introduced in Gemes [Journal of Philosophical Logic, 26, 449–476, 1997]. It is claimed that this response is better motivated and more effective than that presented in Glymour [Philosophy of Science, 50: 626–629, 1983]. It is then argued that while this response meets some of the counter-examples of Christensen [Philosophy of Science, 57: 644–662, 1990] two of those counter-examples, though not unanswerable, suggest the need for a substantial reformulation of the formal versions of bootstrapping. The essay proceeds with such a reformulation, arguing that this new formulation better fits the philosophical insights that originally motivated bootstrapping than do Glymour’s earlier formulations. In the concluding sections some alternative solutions to the problem posed by the Christensen counter-examples are discussed.

Ignoring the temporal dimension, an object such as a railway tunnel or a human body is a three-dimensional whole composed of three-dimensional parts. The four-dimensionalist holds that a physical object exhibiting identity across time—Descartes, for example—is a four-dimensional whole composed of 'briefer' four-dimensional objects, its temporal parts. Peter van Inwagen (1990) has argued that four-dimensionalism cannot be sustained, or at best can be sustained only by a counterpart theorist. We argue that different schemes of individuation of temporal parts are available, which undermines van Inwagen's argument.

In an earlier work I developed an argument favoring one view of persistence (viz., perdurance) over its rivals, based on considerations of the relativity of three-dimensional spatial shapes of physical objects in Minkowski spacetime. The argument has since come under criticism (in the works of Theodore Sider, Kristie Miller, Ian Gibson, Oliver Pooley, and Thomas Sattig). Two related topics, explanatory virtues and explanatory relevance, are central to these critical discussions. In this paper I deal with these topics directly and respond to my critics by offering a new perspective on the issue.

Background and assumptions. Persistence and philosophy of time ; Atomism and composition ; Scope ; Some matters of methodology -- Persistence, location, and multilocation in spacetime. Endurance, perdurance, exdurance : some pictures ; More pictures ; Temporal modification and the "problem of temporary intrinsics" ; Persistence, location and multilocation in generic spacetime ; An alternative classification -- Classical and relativistic spacetime. Newtonian spacetime ; Neo-Newtonian (Galilean) spacetime ; Reference frames and coordinate systems ; Galilean transformations in spacetime ; Special relativistic spacetime ; Length contraction and time dilation ; Invariant properties of special relativistic spacetime -- Persisting objects in classical spacetime. Enduring, perduring, and exduring objects in Galilean spacetime ; The argument from vagueness ; From minimal D-fusions to temporal parts ; Motivating a sharp cutoff ; Some objections and replies ; Implications -- Persisting objects in Minkowski spacetime. Enduring, perduring, and exduring objects in Minkowski spacetime ; Flat and curved achronal regions in Minkowski spacetime ; Early reflections on persisting objects in Minkowski spacetime : Quine and Smart ; "Profligate ontology"? ; Is achronal universalism tenable in Minkowski spacetime? ; "Crisscrossing" and immanent causation -- Coexistence in spacetime. The notion of coexistence ; Desiderata ; Coexistence in Galilean spacetime ; Coexistence in Minkowski spacetime : CASH ; Alexandrov-Stein present and Alexandrov-Stein coexistence ; AS-Coexistence v. CASH : symmetry, multigrade, and objectivity ; As-coexistence v. CASH : relevance ; The mixed past of coexistence ; No need in the extended now -- Strange coexistence? Coexistence and existence@ ; The asymmetry thesis ; The absurdity thesis ; Collective CASH value of coexistence ; Collective existence@ and coexistence in classical spacetime ; Collective existence@ and coexistence in Minkowski spacetime ; Contextuality ; Chronological incoherence ; Some objections -- Shapes and other arrangements in Minkowski spacetime. How rigid is a granite block? ; Perspectives in space ; Perspectives in spacetime ; Are shapes intrinsic to objects? ; The causal objection ; The micro-reductive objection ; Pegs, boards, and shapes ; Perduring objects exist.

The nature of persistence of physical objects over time has been intensely debated in contemporary metaphysics. The two opposite views are widely known as "endurantism" (or "three-dimensionalism") and "perdurantism" ("four-dimensionalism"). According to the former, objects are extended in three spatial dimensions and persist through time by being wholly present at any moment at which they exist. On the rival account, objects are extended both in space and time and persist by having "temporal parts," no part being present at more than one time. Relativistic considerations seem highly relevant to this debate. But they have played little role in it so far. This paper seeks to remedy that situation. I argue that considerations based on the special theory of relativity and the notion of coexistence favor perdurantism over endurantism.

Although considerations based on contemporary space-time theories, such as special and general relativity, seem highly relevant to the debate about persistence, their significance has not been duly appreciated. My goal in the paper is twofold: (1) to reformulate the rival positions in the debate (i.e., endurantism (three-dimensionalism) and perdurantism (four-dimensionalism, the doctrine of temporal parts)) in the framework of special relativistic space-time; and (2) to argue that, when so reformulated, perdurantism exhibits explanatory advantages over endurantism. The argument builds on the fact that four-dimensional entities extended in space as well as time are relativistically invariant in a way three-dimensional entities are not.

Visual objects can be represented by their similarities to a small number of reference shapes or prototypes. This method yields low-dimensional (and therefore computationally tractable) representations, which support both the recognition of familiar shapes and the categorization of novel ones. In this note, we show how such representations can be used in a variety of tasks involving novel objects: viewpoint-invariant recognition, recovery of a canonical view, estimation of pose, and prediction of an arbitrary view. The unifying principle in all these cases is the representation of the view space of the novel object as an interpolation of the view spaces of the reference shapes.

I offer an argument in defense of four-dimensionalism, the view that objects are temporally, as well as spatially extended. The argument is of the inference-to-the-best-explanation variety and is based on relativistic considerations. It deals with the situation in which one and the same object has different three-dimensional shapes at the same time and proceeds by asking what sort of thing it must be in order to present itself in such different ways in various "perspectives" (associated with moving reference frames) without being different from itself. I argue that the best answer is that the object must be four-dimensional. It will then have differing 3D shapes in different perspectives because such shapes are intrinsic properties of its 3D parts.