The Future and the Past: Is Time Real?

Core idea

We reason about time constantly, and some inferences about it feel elementary. To make that reasoning precise, logic introduces tense operators. Write P for "it was the case that" and F for "it will be the case that"; then a past-tense sentence becomes P s and a future-tense one F s. Two more operators complete the set: G ("it is always going to be the case that") and H ("it has always been the case that").

These operators attach to whole sentences and, crucially, are not truth functions — "It is 4 p.m." and "It is 4 p.m. on 2nd August 1999" can share a truth value while their F-versions diverge. Tense operators can also be iterated into compound tenses like F P s ("it will have been the case") or P P s ("it had been the case").

Priest's argument: Every situation comes equipped with a collection of earlier and later situations; P a is true now if a holds in some earlier situation, F a if a holds in some later one.

Why it matters

McTaggart's argument that time is unreal

The philosopher J. M. E. McTaggart argued that there could be no time without past and future, yet that pastness and futurity are inherently contradictory. Every event is both past and future — future before it happens, past afterwards — so each event seemingly bears incompatible properties. Reply that an event has them at different times, and McTaggart pushes to compound tenses: the event was future (P F h) and was past (P P h), which are again incompatible yet again both true. Every escape uses tenses that are themselves contradictory, so the contradiction never goes away.

The tense-logic answer

The semantics dissolves the threat. Lay the situations out on a line — earlier to the left, later to the right. If h is true at exactly one situation, every compound tense of h is simply true somewhere on the line. F P P F h, for instance, is true at some situation two steps back. The infinitude of distinct situations lets h carry all its compound tenses in different places without ever forcing F h and P h into the same situation. No contradiction arises.

Key takeaways

Mental model

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Practical application

When a puzzle seems to generate a contradiction, try building a model that satisfies every constraint at once. If the model can be built, the specification is consistent.

Example

Suppose a comet is visible at exactly one moment, midnight. Place that moment on the line. A child born the next morning can truly say "the comet was visible" (P); an astronomer a decade earlier could truly have said "the comet will be visible" (F); and a historian centuries later can truly say "it had been the case that the comet would be visible" (P P F-style talk). Every one of those tensed claims is true — each at its own situation on the line. No single situation is ever asked to host both "the comet is future" and "the comet is past." The apparent paradox of time's flow turns out to be a failure to keep track of which situation a tensed claim is evaluated at.

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