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!
