The master argument and branching time

Lars Gundersen



It is argued that reconstructions of the so-called ‘Master Argument’ of Dideros Cronos to the effect that possibility should be understood as present or future truth, essentially relies on two axioms: i) that every true proposition concerning the past is necessary, and ii) that it follows necessarily from a proposition being true that it always has been the case that it would be true. It is furthermore argued that these two axioms are inconsistent in the sense that any tense/modal semantics which incorporates both collapses either modally (fails to distinguish between truth simpliciter and modalised truth) or temporally (fails to offer a plausible semantical account for propositions about the future). This finding is, furthermore, taken as indicator for the more generel claim that there are principled difficulties involved in construing semantics for combined tense/modal logical systems.

Full Text:



Aristotle, The Works, (W. D. Ross trans.), Oxford, 1908.

Kneale, W. & M., The Development of Logic, Oxford, 1962.

Michael, F. S., “What is the Master Argument of Diodorus Cronos?”, American Philosophical Quarterly, 1976.

Prior, A., Past, Present and Future, Oxford, 1967.

Rescher, N., “On the logic of chronological propositions”, Mind, 1966.

Thomason, R., “Indeterminist truth and truth-value gaps”, Theoria, vol. 36, 1970.

White, M., “Necessity of the past and modal-tense logic incompleteness”, Notre Dame Journal of Formal Logic, vol. 25, 1984.

ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

Partnerzy platformy czasopism