The insoluble problem of future tense statements

Vallicella finally addresses the problem of Excluded Middle and Future-Tensed Sentences.  A prediction in 1996 that the FTSE would reach 10,000 by 2011 would have been wrong at the time the prediction was made.  As he points out (using the US Dow index as his example), subsequent events merely made it evident that the content of the prediction was false, rather than bring it about that the prediction had a truth-value.  Not even God can restore virginity*.

This suggests that the Law of Excluded Middle applies to future tense statements, but this causes him puzzlement, expressed in the following 'aporetic triad'.

1. Law of Excluded applies unrestrictedly to all declarative sentences, whatever their tense.
2. Presentism: Only what exists at present exists.
3. Truth-Maker Principle: Every contingent truth has a truth-maker.

They can't all be true, according to him, because the conjunction of any two implies the negation of the third. So here is a genuine insoluble problem. Each has a strong claim to our acceptance, but all of them cannot be true together.

Is that right? First, I don't see why the three statements are logically inconsistent.  Why can't the truthmaker for a future tense statement exist now, in the present? However, presumably Maverick buys the argument I gave here.  If the truthmaker exists now, and given that we cannot change the immediate present or the past, we cannot change the truthmaker’s existence. So we cannot change the future, for the truthmaker that exists now makes the future true, but we can change the future, ergo etc.  So we can assume the additional premise

4. The truthmaker for any contingently true proposition exists only at the time for which the proposition is true.

By the expression 'time for which' a proposition is true, I am attempting to translating the medieval Latin pro tempore, meaning, roughly, any time at which any present tense statement corresponding to a non present tense statement is true. For example, if I truly say 'it will rain next week', when today is 3 December 2011, the time for which my statement is true = any day next week, i.e. the week commencing Monday 5 December.  The corresponding present tense statements are 'it is raining today', uttered on Monday, or on Tuesday, Wednesday etc.

But statements 1-4 above cannot all be true.  If only things in the present exist, future truthmakers do not exist. It may be that they will exist, but they don't now.  So the statement 'it will rain next week' has no truthmaker (although, if it does rain, it may be that it will have one).  And yet law of excluded middle surely applies to any statement whatever.  If it does rain next week, and I say that it will rain next week, then surely we can say next week that 'Edward was right'.

Which of the four statements above is incorrect?  (Rhetorical question, for those who read my blog regularly).

*Pace Peter Damian.

There was no eclipse yesterday

There was in fact no eclipse yesterday, as I predicted two days ago.  Hence my prediction was right.

Snow in London

Alan Rhoda has been defending the idea that there must be some necessary connection between the present and the future in order for propositions about the future to be true or false. I restate his argument as follows. A true proposition depends on what exists - a 'state of affairs' - for its being true. The state of affairs that makes the proposition true at some particular time must exist also at the same time. Accordingly, it cannot be true now that there will be snow in London tomorrow, unless this truth 'supervenes upon present reality', i.e. there is some existing state of affairs which makes this proposition about the future true. Which is absurd. Why should snowing in London tomorrow be logically connected with any state of affairs existing today?

The mistake lies in his assumption that what makes a proposition true at some time must exist at that same time. Certainly there is a connection between truth and existence. This was recognised by the scholastic philosophers of language. Unumquodque sicut habet esse, ita et veritatem "As each thing is in respect of being, so it is in respect of truth", taken from Aristotle Metaphysics book 2 (993b 31). A proposition signifying that some state of affairs exists, is true or false depending on whether that state of affairs exists or not.

A corollary of this is what I shall call the Adequacy Principle: that the state of affairs signified to exist by the proposition can be no more (and no less) than what makes the proposition true. Otherwise, suppose a proposition signifies the existence of more than what is required to make it true, e.g. suppose that it signifies the existence of X and Y, but Y alone is sufficient to make it true. Then so long as Y exists, the proposition will be true, even if X does not exist, and even though the proposition signifies that X does exist. This is impossible, therefore a proposition can signify the existence of absolutely no more than what is sufficient to make it true. (A similar argument proves that a proposition can signify the existence of no less than what is necessary to make it true, but that is not relevant here).

From the Adequacy Principle it follows that a proposition in the future tense, signifying that some state of affairs Y will exist, depends for its truth on the future existence of Y, and nothing else, particularly nothing else in the present. The proposition 'It will snow in London' can be analysed as

* Snowing in London will be the case

which signifies that the future state of affairs 'snowing in London' will exist. It signifies no more than that, in particular, it does not signify that some state of affairs X exists now. Why should it? It may be that some present state of affairs (large cold front sweeping in from Siberia) will be the cause of the snow. But the proposition in the future tense has nothing to say about cold fronts.

Scotus on future contingency

I mentioned in this post last year that I was working on Scotus' discussion of the problem of future contingents, in his Questions on the Perihermenias, and I said I would discuss it in the future. Alan Rhoda's post on 'alethic openness' has finally got me round to doing so. Alan writes:

For a proposition to be true, what it represents as being the case must
correspond to reality, to what is the case. Likewise, for a proposition to be
true now, what it represents as being the case must correspond to present
reality, to what is the case now. [my emphasis]

Scotus discusses a claim very similar to this in Book I of the Questions, qq 7-9. He disputes the claim apparently made by Rhoda above, namely that the truth of a proposition about the future must correspond in some way to 'present reality'. He writes:

It must be understood that a proposition about the future can be understood to
signify something in the future in two ways. So that the proposition about the
future signifies it to be true now that something in the future will have to be
true [verum esse habebit] (for example, that ‘you will be white at a’ signifies
it now to be in reality so that at time a you will be white). Or it can be
understood that it signifies now that you will be white then: not that it
signifies that it is now such that then you ought to be white, but that it
signifies now that then you will be white. For to signify it to be [the case]
now that you will be white at a, signifies more than to signify that you will be
white at a.

It rather hangs upon what Rhoda means by 'true now'. Scotus argues for something like a redundancy theory of future truth. A proposition that says that S will be P so is (now) true iff it will be P, and false if it will not be P. If you mean by 'is now true' something like 'something exists now in reality that makes the proposition true' then Scotus would disagree (and so probably would I). If you mean that 'now' simply indicates the present tense of the 'is' in 'is true', then this is harmless and trivially true.

I think Scotus puts this very neatly, and we do have to take seriously his claim that "to signify it to be [the case] now that you will be white at a, signifies more than to signify that you will be white at a."

See also my discussion of rain tomorrow.