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- David S. Oderberg, Instantaneous Change Without Instants.In this essay, I first set out the principles of change, paying particular attention to the need for a support for all changes and to the need for prime matter. I then discuss the nature of time, arguing that time is not actually composed of durationless instants but that instants can be understood as limits to an infinite process of potential division. I then give a definition of instants in terms of intervals and propose a way of modeling them. In the next section I bring together the two previous sections by explaining change as an instantaneous process that does not involve actual instants. In the final section I draw out a larger metaphysical moral that emphasizes the role of potentiality and sees the potentiality in change and the potentiality in time as but different aspects of the same radical potentiality in nature.
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Four principles about Time have the consequence that God must be everlasting, and not timeless. These are 1) events occur over periods of time, never at instants, 2) Time has a metric if and only if there is a unified system of laws of nature, 3) The past is the realm of the causally unaffectible, the future of the causally affectible, 4) Some truths can only be known at certain periods. Yet God is not Time’s prisoner’, for the unwelcome features of Time--the increase of unaffectible events, the cosmic clock’ ticking away--only occur if God so chooses.
Introduction -- The common hellenic meaning of "genus" -- The Pollaxos legomena or things said in many ways -- Genus in the explanation of change : the subject and substratum principles -- To what is Aristotle's theory of change a response? : the pre-socratic and platonic background -- Change : the principles of nature in physics I -- A first mention of matter and form -- Genus in the explanation of change : the definition of change -- Aristotle's definition of change : physics III -- The circularity objections -- The advantages of Aristotle's theory -- The use of genus in change -- Genus in the explanation of change generation, "for man begets man" (1032-24) -- Generation -- Change and genus -- The generation of animals as organic substances -- Animal generation and the mule -- Genus in definitions : the Aristotelian and platonic division of a genus -- "What is definition?" -- Platonic division and definition -- Aristotle's use of genus and animal taxonomy -- The use of "genus" in Pa I -- Analogy vs. the more and the less -- Taxonomy : the megista gene -- Genus in definitions : why Aristotle was a realist -- Division and definition in Aristotle -- Causal definitions , substantial definitions, and definitions by matter and form -- The unity of definition and division -- The use of genus in definition -- Case study I : the definition of the psyche -- On matter as substratum -- On matter : the domain problem -- On matter : is it substance? -- On matter : potentiality -- The elements : is ontological reduction possible? -- Proper matter and generation revisited -- The indeterminacy vs. nature problem -- On genus as matter -- The analogy interpretation : Aristotle's mention of genus as matter -- The literal interpretation : Aristotle's use of genus as matter -- The principal unity of Aristotle's thought.
On stage theory, ordinary continuants are instantaneous stages which persist by exduring—by bearing temporal counterpart relations to other such stages. Exduring objects lack temporal extension and there is a sense in which they are wholly present at multiple instants. How then is exdurance different from endurance? I offer a definition of ‚exdurance’ that clearly sets it apart from other modes of persistence.
This article analyzes the status of passive potentiality of prime matter and sensible objects in Plotinus' Enneads . In particular, it will focus on Enneads II 5 [25] and confront it with other treatises, specifically Enneads III 6 [26]; II 6 [17]; VI 2 [43] and VI 3 [44]. It aims at offering a new interpretation of treatise 25 and at proposing a reconstruction of Plotinus' notion of change in the sensible realm that illustrates both his critique of Aristotle's notion of substantial change and his acceptance of Aristotle's view of qualitative change.
We propose a modular ontology of the dynamic features of reality. This amounts, on the one hand, to a purely spatial ontology supporting snapshot views of the world at successive instants of time and, on the other hand, to a purely spatiotemporal ontology of change and process. We argue that dynamic spatial ontology must combine these two distinct types of inventory of the entities and relationships in reality, and we provide characterizations of spatiotemporal reasoning in the light of the interconnections between them.
Aristotle's conception of being is dynamic. He believes that a thing is most itself when engaged in its proper activities, governed by its nature. This paper explores this idea by focusing on Metaphysics , a text that continues the investigation of substantial being initiated inMetaphysics Z. Q.1 claims that there are two potentiality-actuality distinctions, one concerned with potentiality in the strict sense, which is involved in change, the other concerned with potentiality in another sense, which he says is more useful for the present project. His present project is the investigation of substantial being, and the relevant potentiality is the potentiality for activity, the full manifestation of what a thing is. I explore Aristotle's two potentiality-actuality distinctions AND argue that the second distinction is modeled on the first, with one crucial modification. Whereas a change is brought about by something other than the object or by the object itself considered as other (as when a doctor cures himself), an activity is brought about byte object itself considered as itself. This single modification yields an important difference: whereas a change leads to a state other than the one an object was previously in, an activity maintains or develops what an object already is.
Dummett in his recent paper in Philosophy replies in the negative to the question, “Is time a continuum of instants?” But Dummett seems to think that this negative reply entails giving an alternative theoretical account; he nowhere canvasses the possibility that there is something amiss with the question. In other words, Dummett thinks that he still has to reply to the question, “What (then) is time?” I offer no answer whatsover to such ‘questions’. Rather, I ask what it could possibly mean to say that time is (e.g.) a continuum of instants (and by extension, whether it can mean anything at all to assert that it isn't). In the course of doing so, I suggest that Dummett's ‘Anti-Realism’ is invariably a form of Realism, just a subtly inconsistent form. Anti-Realism keeps the fundamental metaphysical picture of Realism intact. Anti-Realism still thinks that there is a Reality...settling whether Realism or Anti-Realism is correct! ‘Anti-Realism’ is never anti-Realist enough.
Our model of time is the classical continuum of real numbers, and our model of other measurable quantities that change over time is that of functions defined on real numbers with real numbers as values. This model is not derived from reality or from our experience of it, but imposed on reality; and the fit is very imperfect. In classical mathematics, the value of a function for any real number as argument is independent of its value for any other argument: the analogue is Hume's doctrine that events are loose and separate. This makes continuity in the change of any quantity a contingent law of physica, rather than a conceptual necessity. The article explores alternatives to this classical model.
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.
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.
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