Abstract
A set of axioms implicitly defining the standard, though not instant-based but interval-based, time topology is used as a basis to build a temporal modal logic of events. The whole apparatus contains neither past, present, and future operators nor indexicals, but only B-series relations and modal operators interpreted in the standard way. Determinism and indeterminism are then introduced into the logic of events via corresponding axioms. It is shown that, if “determinism” and “indeterminism” are understood in accordance with their “core” meaning, the way in which they are formally introduced here represents the only right way to do this, given that we restrict ourselves to one real world and make no use of the many real worlds assumption. But then the result is that the very truth conditions for sentences about indeterministic events imply the existence of tensed truths, in spite of the fact that these conditions are formulated (in the indeterministic axiom) in terms of tenseless language. The tenseless theory of time implies determinism, while indeterminism requires the flow of time assumption.
Similar content being viewed by others
REFERENCES
Arsenijević, M.: 1992, ‘Eine aristotelsche Logik der Intervalle, die Cantorsche Logik der Punkte und die physikalischen und kinematischen Prädikate: I–II’, Philosophia naturalis 29, 1992/2.
Beer, M.: 1994, ‘Temporal Indexicals and the Passage of Time’, in L. N. Oaklander and Q. Smith (eds), The New Theory of Time, Yale University Press.
Belnap, N.: 1992, ‘Branching Space-Time’, Synthese 92.
Bochman, A.: 1990, ‘Concerted Instant-Interval Semantics: I–II’, Notre Dame Journal of Formal Logic 31.
Burggess, J. P.: 1982,‘Axioms for Tense Logic. II: Time Periods’, Notre Dame Journal of Formal Logic 23.
Cantor, G.: 1962, Gesammelte Abhandlungen, Hildesheim.
Deutsch, H.: 1990, ‘Real Possibility’, Nous 24.
Grünbaum, A.: 1973, Philosophical Problems of Space and Time, Reidel.
Hamblin, C. L.: 1969, ‘Starting and Stopping’, The Monist 24.
Hamblin, C. L.: 1971, ‘Instants and Intervals’, Studium generale 24.
Le Poidevein, R.: 1991, Chance, Cause and Contradiction: A Defence of the Tenseless Theory of Time, St. Martin Press, NY.
Leibniz, G. W.: 1956, Leibniz-Clarke Correspondence (trans. and ed. H. G. Alexander), Manchester University Press.
Lewis, D. K.: 1973, Counterfactuals, Harvard University Press.
Lewis, D. K.: 1986, On the Plurality of Worlds, Basil Blackwell.
Lukasiewicz, J.: 1920, O determinizmie, Z zogadnien logiki i filozofii, Warszawa.
Mellor, D. H.: 1998, Real Time II, Routledge.
Needham, P. (1981), ‘Temporal Intervals and Temporal Order’, Logique et Analyse 24.
Newton-Smith, W. H.: 1980, The Structure of Time, Routledge and Kegan Paul.
Oaklander, L. N.: 1994, ‘Thank Goodness It's Over’, in L. N. Oaklander and Q. Smith (eds), The New Theory of Time, Yale University Press.
Paul, L.: 1997, ‘Truth Conditions of Tensed Sentence Types’, Synthese 111.
Rescher, N.: 1968, ‘Truth and Necessity in Temporal Perspective’, in R. Gale (ed.), The Philosophy of Time, Humanities Press, New Jersey.
Smart, J. J. C.: 1980, ‘Time and Becoming’, in Peter van Inwagen (ed.), Time and Cause, Reidel.
Smith, Q.: 1993, Language and Time, Oxford University Press.
Stalnaker, R.: 1976, ‘Possible Worlds’, Nous 10.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Arsenijević, M. Determinism, Indeterminism And The Flow Of Time. Erkenntnis 56, 123–150 (2002). https://doi.org/10.1023/A:1015646303123
Issue Date:
DOI: https://doi.org/10.1023/A:1015646303123