In a post the point of which was merely to underscore the difference between absolute and necessary truth, I wrote, somewhat incautiously:

Let our example be the proposition p expressed by 'Julius Caesar crossed the Rubicon in 44 B.C.' Given that p is true, it is true in all actual circumstances. That is, its truth-value does not vary from time to time, place to place, person to person, or relative to any other parameter in the actual world. P is true now, was true yesterday, and will be true tomorrow. P is true in Los Angeles, in Bangkok, and on Alpha Centauri. It is true whether Joe Blow affirms it, denies it, or has never even thought about it. And what goes for Blow goes for Jane Schmoe.

As a couple of astute readers have pointed out, the usual date given for Caesar's crossing of the river Rubicon is January 10, 49 B.C. and not 44 B. C. as stated above. If only the detection and correction of philosophical erors were as easy as this!

The erudite proprietor of Finem Respicem, who calls herself 'Equity Private' and describes herself as a "Armchair Philosophy Fangirl and Failed Theoretical Physicist Turned Finance Troublemaker," writes, "Caesar crossed the Rubicon on January 10, 49 B.C., reportedly (though perhaps fancifully) prompting Gaius Suetonius Tranquillus to comment *Alea iacta est* ('The die is cast.')" And Philoponus the Erudite has this to say:

I'm not sure whether you are deliberately testing the faithful readers of The Maverick, but the accepted date for Caesar and Legio XIII Gem. wading across fl. Rubico is 49 BCE, on or about Jan 10th. That's what is inferred from Suetonius' acct of Divus Caesar at the beginning of **De Vita Caesarum **(written 160 years after the fact) and some other latter sources like Plutarch.

So I stand corrected on the factual point. Both correspondents go on to raise philosophical points. I have space to respond to only one of them.

Equity Private asks, concerning the proposition expressed by 'Caesar crosses the Rubicon in 49 B.C.,' "But is it true in 50 BC? In a deterministic universe, I think it is. In a non-deterministic universe I think it isn't. Are you a determinist?"

To discuss this properly we need to back up a bit. I distinguish declarative sentences from the propositions they are used to express, and in the post in question I was construing propositions along the lines of Gottlob Frege's *Gedanken*. Accordingly, a proposition is the sense of a context-free declarative sentence. A context-free sentence is one from which all indexical elements have been extruded, including verb tenses. Propositions so construed are a species of abstract object. This will elicit howls of outrage from some, but it is a view that is quite defensible. If you accept this (and if you don't I will ask what your theory of the proposition is), then the proposition expressed by 'Caesar crosses the Rubicon in 49 B.C.' exists at all times and is true at all times. (Bear in mind that, given the extrusion of all indexical elements, including verb tenses, the occurrence of 'crosses' is not present-tensed but tenseless.) From this it follows that the truth-value of the proposition does not vary with one's temporal perspective. So, to answer my correspondent's question, the proposition is true in 50 B.C. and is thus true before the fateful crossing occurred!

I am assuming both Bivalence and Excluded Middle. Bivalence says that there are exactly two truth-values, true and false, as opposed to three or more. If Bivalence holds, then 'not true' is logically equivalent to 'false.' Excluded Middle says that, for every proposition p, either p is true or it is not the case that p is true. Note that Bivalence and Excluded Middle are not the same. Suppose that Bivalence is false and that there are three truth-values. It could still be the case that every proposition is either true or not true. (In a 3-valued logic, 'not true' is not the same as 'false.') So Excluded Middle does not entail Bivalence. Therefore Excluded Middle is not the same as Bivalence. Bivalence does, however, entail Excluded Middle.

Here is a simpler and more direct way to answer my correspondent's question. Suppose some prescient Roman utters in 50 B.C. the Latin equivalent of 'Julius Caesar will cross the Rubicon next year.' Given Bivalence and Excluded Middle, what the Roman says is either true, or if not true, then false. Given that Caesar did cross in 49 B.C., what the prescient Roman said was true. Hence it was true before the crossing occurred.

Let's now consider how this relates to the determinism question. Determinism is the view that whatever happens in nature is determined by antecedent causal conditions under the aegis of the laws of nature. Equivalently, past facts, together with the laws of nature, entail all future facts. It follows that facts before one's birth, via the laws of nature, necessitate what one does now. The necessitation here is conditional, not absolute. It is conditional upon the laws of nature (which might have been otherwise) and the prior causal conditions (which might have been otherwise).

If determinism is true, then Caesar could not have done otherwise than cross the Rubicon when he did *given* the (logically contingent) laws of nature and the (logically contingent) conditions antecedent to his crossing. If determinism is not true, then the laws plus the prior causal conditions did not necessitate his crossing. Equity Private says that the Caesar proposition is not true in 50 B.C. in a non-deterministic universe. But I don't think this is right. For there are at least two other ways the proposition might be true before the crossing occurred, two other ways which reflect two other forms of determination. Besides causal determination (determination via the laws of nature and the antecedent causal conditions), there is also theological determination (determination via divine foreknowledge) and logical determination (determination via the law of excluded middle in conjunction with a certain view of propositions). Logical determinism is called fatalism. (See the earlier post on the difference between determinism and fatalism.)

Someone who is both a fatalist and an indeterminist could easily hold that the Caesar proposition is true at times before the crossing. Equity Private asked whether I am a determinist. She should have asked me whether I am a fatalist. For it looks as if I have supplied the materials for a fatalist argument. Here is a quick and dirty version of an ancient argument known as 'the idle argument' or 'the lazy argument':

1. Either I will be killed tomorrow or I will not.

2. If I will be killed, I will be killed no matter what precautions I take.

3. If I will not be killed, then I will be killed no matter what precautions I neglect.

Therefore

4. It is pointless to take precautions.

This certainly smacks of sophistry! But where exactly does the argument go wrong? The first premise is an instance of LEM on the assumption of Bivalence. (2) looks to be a tautology of the form* p --> (q -->p)*, and (3) appears to be a tautology of the form *~p -->(q -->~p)*. Or think of it this way. If it is true that I will killed tomorrow, then this is true regardless of what other propositions are true. And similarly for (3).

Some will say that the mistake is to think that LEM applies to propositions about future events: in advance of an event's occurrence it is neither true nor not true that it will occur. This way out is problematic, however. 'JFK was assassinated in 1963' is true now. How then can the prediction, made in 1962, 'JFK will be assassinated in 1963,' lack a truth-value? Had someone made that prediction in 1962, he would have made a true prediction, not a prediction lacking a truth-value. Indeed, the past-tensed and the future tensed sentences express the same proposition, a proposition that could be put using the tenseless sentence 'JFK is assassinated in 1963.' Of course, no one could know in 1962 the truth-value of this proposition, but that is not to say that it did not have a truth-value in 1962. Don't confuse the knowledge of truth with truth.

Suppose I predict today that such-and-such will happen next year, and what I predict comes to pass. You would say to me, "You were right!" You would not say to me, "What you predicted has acquired the truth-value, true." I can be proven right in my prediction only if I *was* right, i.e., only if my prediction was true in advance of the event's occurrence.

So the facile restriction of LEM to present and past is a dubious move. And yet the 'lazy argument' is surely invalid!

Thank you for the post.

Can we not, however, deny the validity of the lazy argument by denying that the LEM yields (1)? To illustrate my point, let "Tp" signify "It will be the case tomorrow that p," "Apq" the disjunction of p and q, and "Np" the negation of p. Given this notation, we easily see that (1) can be read either as (TApNp) or as (ATpNTp). LEM, however, yields only the latter and not the former, which is the interpretation required for the conclusion to follow.

As for the problem of correct predictions, why can't we say that they only become true once whatever they predicted comes to pass, just as Michel's lacing Antoine's coffee with arsenic only becomes the cause of his death after Antoine has consumed the beverage? That way, no prediction will ever be true while it still refers to a future time.

Posted by: Leo Carton Mollica | Tuesday, November 29, 2011 at 06:00 PM

Hi Leo,

I take it you are saying that (1) is ambiguous as between

a. It will be the case that (I will be killed or I will not be killed)

and

b. Either it will be case that I will be killed or it will not be the case that I will be killed.

First of all, as I see it, (1) is not ambiguous. What it means is (b). And (b), as you suggest, follows from LEM.

So I am not following you.

We colloquially say things like, 'Her prediction came true,' but all this means is that what was predicted is now known to be true. It needn't be taken to me that the content of the prediction was without a truth-value and then acquired a truth-value. Truth and the knowledge of truth are easily confused.

Arguably, if no prediction concerning a future contingent is true at the time it is made, then no such prediction can be fulfilled. For a prediction is fulfilled when the event predicted happens.

Tricky stuff, eh?

The relevance of the arsenic comparison escapes me.

Posted by: Bill Vallicella | Wednesday, November 30, 2011 at 05:18 AM

Can we add premises for a different conclusion?

1. Either I will be killed tomorrow or I will not.

2. If I take precautions I will not be killed tomorrow.

3. If I will be killed, I will not have taken precautions.

4. If I will not be killed, then I will have neglected precautions.

Therefore

5. It is useful to take precautions.

Same logic (use of LEM), just more complicated premises. In real life, premises multiply beyond our ken.

Posted by: Bill | Wednesday, November 30, 2011 at 10:13 AM

sorry, "NOT" neglected on #4.

Posted by: Bill | Wednesday, November 30, 2011 at 12:30 PM

I misspoke in my original comment: (1) is ambiguous between

1'. "Either tomorrow it will be the case that (it is not the case that I am killed) or tomorrow it will be the case that (I am killed)" and

1''. "Either it is not the case that tomorrow it will be the case that (I am killed) or tomorrow it will be the case that (I am killed)."

Only (1''), as far as I can see, follows from LEM, because it is the disjunct of two contradictories. In order for the lazy argument to go through, however, the stronger claim (1'), it would seem, is needed, for only (1') yields the conclusion that future truths are fixed.

I brought up the arsenic example to illustrate how an event or action (such as poisoning coffee) can acquire a feature after it has passed. Similarly, I was suggesting, a prediction could become accurate after it has been made and what it predicted has come to pass.

My reason for being suspicious about predictions of future contingents being correct when they are made is that, if we suppose as much, then what is being predicted would seem to already be "fixed" regarding its truth value, and thus not really a future contingent. It has nothing to do with considerations of colloquialisms or knowledge.

Am I making more sense?

Posted by: Leo Carton Mollica | Thursday, December 01, 2011 at 05:01 AM

Sorry, Leo, but I can't quite wrap my mind around the ambiguity you are claiming.

Posted by: Bill Vallicella | Thursday, December 01, 2011 at 11:47 AM

Consider an analogy with belief, letting Dp stand for "Socrates believes that p". Now, clearly, we can distinguish

5. (D(~p))∨(Dp) from

5'. (~Dp)∨(Dp),

and, indeed, the latter is true while the former is false: Socrates may, for some propositions, simply have no opinion as to whether they are true or false. Similarly, I am suggesting, (1) can be interpreted as

1'. (T(~p))∨(Tp) or as

1''. (~Tp)∨(Tp),

where Tp stands for "Tomorrow it will be the case that". Now, only (1'') is yielded by the law of the excluded middle, for only in it are the two disjuncts contradictories. Since (~Tp) does not on its own entail (T(~p)), the two interpretations of (1) are not equivalent. But it is (1') that the lazy argument requires, because only (Tp) or (T(~p)) can be taken as immediately implying that whether p does or does not obtain tomorrow is already a settled matter.

My inspiration for this argument comes from A. N. Prior's

Time and Modality, Ch. X, which is no doubt far clearer.Posted by: Leo Carton Mollica | Thursday, December 01, 2011 at 04:15 PM

You are right that (5) and (5') are different. And yes, the latter is true. But the former could also be true. Let one of the disjuncts be true, then by Addition one can infer the disjunction. This is valid: p; therefore p v q.

So you are making a Prioresque move. Now I see what you are getting at.

Posted by: Bill Vallicella | Friday, December 02, 2011 at 05:25 AM

Biil, you say "(2) looks to be a tautology of the form

A corollary of (3*) is and this is to deny the pointlessness of taking precautions. The fatalistic argument gets its strength by glossing the modal character of the problem.p --> (q -->p)," and we can think of this as saying "If it is true that I will [be] killed tomorrow, then this is true regardless of what other propositions are true." I think (2), and your latter explication of it, are both modal in character. The force of 'no matter what precautions I take' is a universal quantification over sets of precautions. We can express this asBut suppose I am wrong about this. And suppose you are right about the tenseless nature of propositions. Then we can rerun the argument the day after tomorrow as follows,

But now the 'no matter what precautions I took' makes no universal claim. It merely says And now there is no pressure to infer that precautions are pointless.without any change of truth-values:Posted by: David Brightly | Friday, December 02, 2011 at 06:01 AM