Logical determinism

Logical determinism is an old philosophical position that holds that "because propositions about future events are true or false even before the events occur, the events that the true propositions refer to must happen necessarily." Events can cause events (and even that sometimes is questioned), but statements cannot. It seems absurd to think that the truth of a statement could entail future events, but nailing down exactly what is wrong with logical determinism has occupied much discussion. This topic can be formally studied using the modern field of temporal logic, the approach to representation and reasoning about time and temporal information within a logical framework.

The complexity of these issues has been outlined:

"The philosophical and logical challenge to which the future contingency discussion gives rise is two-fold. First of all, anyone who wants to maintain some kind of indeterminism regarding the future, may be confronted with some standard arguments in favor of logical determinism, i.e., arguments designed to demonstrate that there are no future contingents at all [that is, the future is fixed]. In addition, anyone who holds that there are future contingents can be challenged to establish a reasonable truth-theory compatible with the idea of an open future. Such a theory should provide answers to questions like: Can one meaningfully regard future contingents as true or false now, if the future is open? And if so, how? Can assertions about the contingent future make any sense at all? And if so, how? Some logicians have held that no future contingent is true. However, other logicians have found that this is unacceptable. Instead, they have looked for a theoretical basis on which we might hold that a future contingent is true (or false)."

—Peter Øhrstrøm, Per Hasle: Future Contingents

Analysis

An extended analysis was made by Freddoso in 1983. Freddoso provides an analysis of the example statement about the future that "Katie will wash her car at time T". Several preliminaries are needed. One is the description of the truth of historical fact. After the event, such a statement refers to things that cannot be changed, but are only accidentally true, that is, might not have been true, and in fact were not true at some earlier time. An example is a statement made today that Socrates drank hemlock, which is true today and in fact has been true ever after the event, but was a false statement when Socrates was a boy. This kind of truth that applies to a statement about the past after an event happens is called accidentally necessary, or is said to example necessity per accidens. The truth of such statements is temporally contingent, that is, the truth of the statement depends upon the time frame under discussion. The unalterable nature of the truth of an historical statement following a contingency (after the event it refers to) is generalized formally to arbitrary times t as statement C below:

(C) If p is true at t (for example, some past time t), then the proposition that p was the case is necessary per accidens at every moment after t, and the proposition that p was never the case is impossible per accidens at every moment after t.

This statement about p can be extended to statements q that are implied by p, as expressed formally below:

(B) If p entails q, and p is necessary per accidens at t, then no one has the power at or after t to bring it about that q is or will be false.

The argument for determinism then runs as follows:

(P1) The proposition: "Katie will wash her car at T" is true now, a time long before T. (assumption)

(P2) So the proposition: "Katie will wash her car at T" will be necessary per accidens at every future moment, including every moment subsequent to now that precedes or is identical with T. (from (P1)and (C))

(P3) The truth of the proposition: "Katie will wash her car at T" entails that if the time is T, then Katie is washing her car. (assumption)

(P4) Therefore, no one (including Katie) will have the power at or before T to bring it about that it is or will be false that if T is present, then Katie is washing her car. That is, no one will have the power at or before T to bring it about that it is or will be true that Katie is not washing her car when T is present. (from (P2), (P3), and (B))

Freddoso then examines challenges to the various propositions above. He attributes to Aristotle the view that truth or falsity is not even a property of contingent statements about the future, which neither are true nor false before the event. However, Freddoso supports as most plausible the objection, called the Ockhamistic objection, that the truth of p before an event occurs is established only after the event occurs, and while the early future tense statement can be true, that truth is only back-propagated from the time of the event. Backmann calls this the Ockhamist's claim of primacy of the present. Consequently, the truth of the statement: "Katie will wash her car at T" cannot be assigned before Katie washes her car, and her act of washing the car does not depend upon the truth of this statement.

Different objections have been raised. In contrast with Freddoso, Swartz argues that it is difficult to assign a particular instant when the truth value of a contingent statement changes, and finds it unpalatable that the truth of an abstraction like a proposition about the future should be mired in such minutiae. Avoiding an argument over when "truth" is applied, Backmann suggests that Swartz and also Keil think logical determinism simply confuses semantic and linguistic matters with issues governed by nature's laws. Of course, such a clean separation of language from what we call 'nature' is debatable, at least according to enactivists.

Temporal logic

Aristotle's example of two mutually exclusive statements about the future:

There will be a sea battle tomorrow

There will not be a sea battle tomorrow

have been much discussed in terms of whether they can be assigned as true or false, and what is their relation to the possible and the necessary. For example, if the second statement is true, is it impossible today for a battle to happen tomorrow? And if the first is true, is it necessary that there be a battle tomorrow? There is debate over Aristotle's thought on the matter, but the logician Lukasiewicz proposed a three-valued logic in which, before the time set for the battle, the truth value of these statements is undetermined. However, Prior pointed out that the statement "Either there will be a battle tomorrow, or there will not" is true before the time set for the battle, despite the undecided truth of its constituent parts, posing some difficulties for a three-valued logic based upon true, false or undetermined classifications. Prior developed a temporal logic that addressed such issues. Prior was of the view that the truth value of these statements about tomorrow cannot be known today; there are no true statements about future contingents.

"...nothing can be said to be truly 'going to happen' until it is so 'present in its causes' as to be beyond stopping; until that happens neither 'It will be the case that p ' nor 'It will not be the case that p ' is strictly speaking true."

—AN Prior: Papers on Time and Tense p. 52

Much more detailed analysis using symbolic logic can be found in the references.

Further development of temporal logic, originally introduced by Prior in response to his curiosity about free will and God's omniscience, has found application in computer science and temporal search queries for databases. The ways that languages express temporal matters has proved amazingly complex and context dependent.

Summary

Whatever is taken to be the truth of contingent future statements, Swartz' summation of his deliberations is: "[The] argument that a proposition's being true prior to the occurrence of the event it describes causes the future event to occur turns on a confusion (i) of the truth-making (semantic) relation between an event and its description with (ii) the causal relation between two events." Whatever one thinks about the causal implications of statements about the future, debate about the meaning of such statements has led to profound considerations about reasoning and our understanding of how language employs the concept of time.