Free construction of time from events

Thomason, S. K.

doi:10.1007/bf00296174

Cited by 21 publications

(27 citation statements)

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“…Total precedence. The reader who is acquainted with the logical literature on time, events and "periods" (Van Benthem, 2013) might be surprised that we do not have, like (Russell, 1936;Walker, 1947;Thomason, 1984Thomason, , 1989, a primitive relation P encoding complete precedence. This choice was philosophically justified in section 2.4, but the technical justification for using primitives like R + , R − instead of precedence is, as we shall see, that they have a natural topological interpretation.…”

Section: Os Ismentioning

confidence: 99%

“…Philosophically, the problem with this axiom is that it implies the identity of events existing at exactly the same times. This is in general unacceptable, since such events might for instance occur at different places; indeed, Thomason (Thomason, 1989), Russell (Russell, 1936) and Walker (Walker, 1947) do not have such an axiom. Moreover, the axiom would seem to prevent us from expressing the simultaneity of events, since in its presence there cannot be distinct events that are simultaneous.…”

Section: Os Ismentioning

confidence: 99%

“…Of course, an answer to this problem depends on deciding what counts as a map between event structures, i.e., we must provide a category of event structures and event maps. In Thomason (1989), Thomason considers as maps those functions that preserve complete precedence. We, on the contrary, shall take as maps those functions that preserve R + , R − , O and also the operations ⊕, up to equivalence ≡.…”

Section: Representation Of Events As Intervalsmentioning

confidence: 99%

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The Logic and Topology of Kant’s Temporal Continuum

Pinosio¹,

Lambalgen²

2018

The Review of Symbolic Logic

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Abstract. In this article we provide a mathematical model of Kant?s temporal continuum that satisfies the (not obviously consistent) synthetic a priori principles for time that Kant lists in the Critique of pure Reason (CPR), the Metaphysical Foundations of Natural Science (MFNS), the Opus Postumum and the notes and fragments published after his death. The continuum so obtained has some affinities with the Brouwerian continuum, but it also has 'infinitesimal intervals' consisting of nilpotent infinitesimals, which capture Kant's theory of rest and motion in MFNS. While constructing the model, we establish a concordance between the informal notions of Kant?s theory of the temporal continuum, and formal correlates to these notions in the mathematical theory. Our mathematical reconstruction of Kant?s theory of time allows us to understand what ?faculties and functions? must be in place for time to satisfy all the synthetic a priori principles for time mentioned. We have presented here a mathematically precise account of Kant?s transcendental argument for time in the CPR and of the relation between the categories, the synthetic a priori principles for time, and the unity of apperception; the most precise account of this relation to date. We focus our exposition on a mathematical analysis of Kant's informal terminology, but for reasons of space, most theorems are explained but not formally proven; formal proofs are available in (Pinosio,

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Section: Os Ismentioning

confidence: 99%

Section: Os Ismentioning

confidence: 99%

Section: Representation Of Events As Intervalsmentioning

confidence: 99%

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The Logic and Topology of Kant’s Temporal Continuum

Pinosio¹,

Lambalgen²

2018

The Review of Symbolic Logic

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“…We start in section 2 with the use of context in Gaifman 2002 to sidestep the Sorites paradox before returning in the succeeding sections to the special case of time. A basic aim is to critically examine the intuition that the temporal extent of an event is an intervalan intuition developed in Kamp 1979, Allen 1983and Thomason 1989 A concrete linguistic question concerning intervals is brought out by (2).…”

Section: Introductionmentioning

confidence: 99%

Temporal Propositions as Vague Predicates

Fernando

2010

Logic, Language and Meaning

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Abstract. The idea that temporal propositions are vague predicates is examined with attention to the nature of the objects over which the predicates range. These objects should not, it is argued, be identified once and for all with points or intervals in the real line (or any fixed linear order). Context has an important role to play not only in sidestepping the Sorites paradox (Gaifman 2002) but also in shaping temporal moments/extent (Landman 1991). The Russell-Wiener construction of time from events (Kamp 1979) is related to a notion of context given by a string of observations, the vagueness in which is brought out by grounding the observations in the real line. With this notion of context, the context dependency functions in Gaifman 2002 are adapted to interpret temporal propositions.

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“…This treatment is echoed in various later accounts, from Whitehead [1929] and Walker [1947] to Kamp [1979] and van Benthem [1983], where events are taken as primary entities inducing periods as secondary (and instants as merely tertiary) entities. More recently, Thomason [1989] argued that the mathematical connection between the way events are perceived to be ordered and the underlying temporal dimension is essentially that of a free construction (in the category-theoretic sense) of linear orderings from event orderings, induced by the binary relation "wholly precedes". Furthermore, Forbes [1993] explored a modal account whereby the time-series of a given world w is construed as a sequence of equivalence classes of entities existing at w, the classes being determined by facts about the possible worlds that branch from w.…”

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confidence: 99%

Events, Topology and Temporal Relations

Pianesi

Varzi

1996

Monist

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We are used to regarding actions and other events, such as Brutus' stabbing of Caesar or the sinking of the Titanic, as occupying intervals of some underlying linearly ordered temporal dimension. This attitude is so natural and compelling that one is tempted to disregard the obvious difference between time periods and actual happenings in favor of the former: events become mere "intervals cum description".1 On the other hand, in ordinary circumstances the point of talking about time is to talk about what actually happens or might happen at some time or another. We talk about 'now' and 'then' in an effort to put some order in our description of what goes on. And since different events seem to overlap in so many different ways, a full account of their temporal relations seems to run afoul of a reductionist strategy.This raises two philosophical questions. The first is whether we can actually go beyond time, as it were, i.e., whether we can take events as bona fide entities and deal with them directly, just as we can deal with spatial entities such as physical bodies or masses without confining ourselves to their spatial representations. This is a controversial issue (though probably not as controversial as it used to be), and ties in with a number of unsettled problems concerning, e.g., the structure of causality or the definition of adequate identity and individuation criteria for events. 2 The second question is whether we can perhaps do without time, i.e., whether we can dispense with time points or intervals as an independent ontological category and focus only on actual or potential happenings, in opposition to the form of reductionism mentioned above-in short, whether we can account for the temporal dimension in terms of suitable relations among events. This is also a highly controversial issue, and relates to the classical dispute concerning relational vs. absolutist conceptions of (space and) time. It is this second question that we intend to focus on here. Even if the acceptance of events as part of our ontological inventory is in itself a matter of dispute, we shall assume there to be enough good arguments to justify a positive attitude in this regard: events are part of the furniture of the world, whatever their exact ontological make up. We shall actually assume that events are individuals, as opposed to, for instance, states of affairs. 4 The focus of our concern is whether this assumption allows one to answer also the second question in the af-

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Free construction of time from events

Cited by 21 publications

References 3 publications

The Logic and Topology of Kant’s Temporal Continuum

The Logic and Topology of Kant’s Temporal Continuum

Temporal Propositions as Vague Predicates

Events, Topology and Temporal Relations

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