No doubt the reader will be astonished to find reflections on the calculus of probabilities in such a volume as this. What has that calculus to do with physical science?
Henri Poincaré, Science and Hypothesis (1905)
Pure chance and indeterminism were discussed by Aristotle, Lucretius, and Aquinas, but were relegated to illusion and ignorance in modern times. Yet when they reappeared in contemporary physics, they found the way prepared—in the interval, through that very connection with ignorance, they had become conceptually tractable.
Let us say that the present and past are settled fact, a system X has evolved up to time t = now along its state-space trajectory u(t), and many possible futures stretch out before it. Is this world-picture unintelligible? 1 Not at all; as soon as we have a precise conception of determinism, we have one ipso facto of its opposite. As we found in the preceding chapter, we can imagine our ignorance of what the future will bring to be irremediable. Nature may lack those hidden factors needed to extend the true history of the phenomena into a deterministic story.
There may still be limits on that future. All possible trajectories which agree with u(t) up to t = now may lead the system eventually into region S of the state-space. This might be just the set of states in which observable m has value in E: the ones which, in our previous symbolism, make the proposition [m, E] true. In that case we say, equivalently:
All possible futures of X are such that [m, E] will be true.
It is necessary that [m, E] will be true.