Wednesday, December 9, 2009

Reporting live...

Is there ever a wholly determined and complete "way the world is"? Determinism entails that there is such a "report" on all things at every instant, since at every instant the world necessarily is the way it is without an indeterminate remainder. If there is a complete and fully determinate way the world is, it would include a complete "report" of that state of affairs.

However, if the way the world is necessarily entails a report on all things, then the way the world is at any instant would have to include a report about the way of the world just subsequent to the report's existence. On determinism, ex hypothesi, at time t1 the existentiation of the report is either wholly determined to obtain or not to obtain. If at t1 the world is of W(x,y,...n) characteristics, the report R about W(x,y...n), coherent and complete only at time t2, would add a new fact to W(x,y...n), namely R(W(x,y...n)), which is in principle not included in W(x,y...n) prior to t2. If R(W(x,y...n)) is included in R(W(x,y...n)), then the way the world actually is would not be W(x,y...n), but rather W(R(W(x,y...n))), in which case any report about the world as a fully determinate state of affairs would be undecidable--indeterminate--between W(x,y...n) and W(R(W(x,y...n)), which, in turn, of course means the world is never actually wholly determinate. If it is determined to be that R(W(x,y...n)) will come to be, then, if R(W(x,y...n)) is determined to be the true statement of the way the world is at t1, then R(W(x,y...n)) necessarily includes R(W(x,y...n)) itself as already being included in W(x,y...n). Yet, R(W(x,y...n)) is false if it does not include its own existence and its existence as a true meta-statement is only true on the exclusion of its existence in W(x,y...n)), for R(W(x,y...n)) is true in reference to W(x,y...n)), not W(R(W(x,y...n))).

On a more specific level, if at any time t I am wholly determined to be of P(W(x,y...n)) character, then my character (or action) at time t+1 is strictly and wholly predictable. Now, my strictly and wholly predictable character at t+1 could be a state of affairs in which either I correctly predict my next action or I don't. In that case, however, if my character at t already deterministically includes my correct or incorrect prediction of my next action, then P(W(x,y...n)) includes an indeterminate element which can only be true (or determinate) at t+1, in which case P(W(x,y...n)) at t is in principle not fully determined. As such, neither I nor the world are wholly determined. For the very factuality of the truth-content about such determinateness requires a meta-determination of its determinateness at a time subsequent to its alleged determinateness. The world may be determinate at t, but that can't be a coherent and complete truth at t, since the true, complete proposition-set about the world-at-t must, at t+1, propositionally "bracket" and enclose the world-at-t, even though the world-at-t does not include the determinate truth of its meta-description until t+1. As such, the fully dterminate description of the world-at-t is only true at t+1, at which time, of course, it becomes evident that the world-at-t was indeterminate with respect to the reported world at t+1.

[ADDENDUM on 10.12.09:

Someone may object that this only proves a pseudo-indeterminacy, in which truth-conditions spiral recursively towards infinity--viz., "It is true that it is true that it is true that it is true that... R(W(x,y...n))--without altering the fact that such an infinite pseudo-indeterminacy resolves into the one deterministic state of affairs, namely W(x,y...n). All recursive meta-Rs are true only as logical "emanations" of the one deterministic W(x,y...n); as such, they don't conflict with the actual, singular determinacy of W(x,y...n).

The problem is, however, that W(x,y...n) is only possible as a propositional truth-- viz., "The world is wholly determinate now at time t and at all times"--if R(W(x,y...n)) actually exists as the truth about W(x,y...n). The propositionally coherent determinism of W(x,y...n) requires R(W(x,y...n))'s veracity about W(x,y...n). If a meta-observer stepped back from W(x,y...n) and said, "It might be true that R(W(x,y...n)) or that R(W(x,y...(n-1))) is." But then, the truth of R(W(...)) would be indeterminate with respect to the a posteriori correctness of the meta-observer's decision for R(W(x,y...n)) or R(W(x,y...(n-1))). As J. R. Lucas says in The Freedom of the Will, albeit with a slightly different emphasis, "Truth outruns provability."

We can't assert that W(x,y...n) is the fact of the matter until R(W(x,y...n)) is a coherent proposition; and it can only be coherent if W(x,y...n) is the fact of the matter. (By analogy, "Quags are blath" is not a coherent, assertable proposition unless quags exist blathly as a determinate matter of fact.) Once, however, R(W(x,y...n)) exists in W, W(x,y...n) is no longer the fact of the matter: in fact W(R(W(x,y...n))) is. There is an inherent indeterminacy between the allegedly determinate completeness of W(x,y...n) and its completeness being assertably true in R(W(x,y...n)). Is it the truth that R(W(x,y...n)) or R(W(R(W(x,y...n))))? R(W(x,y...n)) doesn't include itself (yet) as a true state of affairs, since it is necessarily a subsequent, novel fact added to W(x,y...n). Once, however, R(W(x,y...n)) is true, it is actually a truth-maker for R(W(R(W(x,y...n)))), and R(W(x,y...n) no longer true: in fact R(W(R(W(x,y...n)))) is. In that case, "the actual world" is necessarily indeterminate between, at least, W(x,y...n) and W(R(W(x,y...n))). Only if R(W(x,y...n)) is true is it true that W(x,y...n). Once R(W(x,y...n)) actually exists as the truth, however, W(x,y...n) must immediately become W(R(W(x,y...n))), otherwise it would lack at least one determinate state of affairs (viz., R(W(x,y...n))). Lacking all determinate states of affairs, W(x,y...n) would therefore not be truly and wholly determinate in itself, whereupon determinism in the actual world is would be false.

We can easily spin this inherent indeterminacy to infinity, but in that case we have a W which is indeterminately true not in just two ways, but in an infinitude of possible states of affairs. Consequence for determinism? A state of affairs comprised of an infinite number of possible states of affairs is indeterminate in potentially infinite ways. So determinism is false in the actual world. It can't be a determinately true R in W that R(W(x,y...n)), since R(W(x,y...n) would have to include itself as a determinate truth in W(x,y...n), whereupon W(x,y...n) is no longer determinately and singularly W(x,y...n), but is W(R(W(x,y...n))).]

[ADDENDUM on 11.12.09:

The world in which R(W(x,y...n)) is true is not the world about which R(W(x,y...n)) is asserted. R(W(x,y...n)) is only true if W(R(W(x,y...n))) is the fact of the matter. Then, however, W(x,y...n) is not the fact of the matter: W(R(W(x,y...n))) is.


I don't think time-indexing will help either. A critic might say that R(W(x,y...n)) is true at t2 of W(x,y...n) at t1, and therefore (t2(R(W(x,y...n))) cannot impinge on the determinateness of W(t1((x,y...n)). But if A at t1 predicts (asserts) R(W(x,y...n)) then at t2 W(R(W(x,y...n))). Now, if A at t1 predicts (asserts) wrongly R(W(t1(x,y...n))), then at t2 W(¬R(W(x,y...n))). Alternately, if A at t1 predicts (asserts) correctly R(W(x,y...n)), then at t2 W(R(W(x,y...n))). Either way, at t1, W, as a singular necessary grounding condition for its effects, is indeterminate between W(t2(R(W(x,y...n)))) and W(t2(¬R(W(x,y...n)))) as its true effects. At t1 it can be true either that R(W(x,y...n)) or ¬R(W(x,y...n)), and therefore at t1 either W(R(W(x,y...n))) or W(¬R(W(x,y...n))), in which case ¬(□W(x,y...n)). So determinism is false.]

1 comment:

Convenor said...

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