Tuesday, February 15, 2011

"A sailor went to sea sea sea…

…to see what he could see see see
But all that he could see see see
Was the bottom of the deep blue sea sea sea"

One of the most famous arguments in Aristotle's corpus is found in De Interpretatione 9, and it concerns the logical status of future contingents (C•f) and fatalism in general. Fatalism is the doctrine that whatever happens, happens necessarily (not, mind you, the more bland idea that whatever happens necessarily happens). Aristotle draws upon the Greek-Persian battle of Salamis (20 September 480 BC) to mount his discussion of fatalism.

A month or so ago I read Richard Sorabji's rich book, Necessity, Cause and Blame, which refreshed my engagement with the famous "sea-battle" discussion (SBD). Today I was reading Robert Nozick's Invariances and he also discusses the SBD, though only in passing. Meanwhile, of course, for the past month or so, I have been worrying the freewill and determinism debate (FDD) more than usual. This afternoon a few ideas came together.

Prior to the sea-battle, on 19 September, say, as the Persian ships converge and the Greek ships secure defensive positions, two citizens of Salamis make a bet. X says that B* the battle might not happen (due to contrary winds, acts of the gods, a change of the Persian heart, etc.), while Z says that B the battle will take place. Night falls and the next day the battle does take place. Z collects his winnings.

Aristotle's question is, "Since B is true, and since truth is by definition incorrigible (i.e. unchangeable), was it necessary that Z would win? Was it even possible for X to win?" For, if B is unconditionally true, then B* is unconditionally false, viz., ⊃ ⊤B ∴ ⊥B*. The opposite logical content of B and B* entail that their truth values entail the necessary falsity of each other.

This was troublesome to Aristotle, since he realized that if all C•f are necessarily true, even before they happen, then everything necessarily happens. Aristotle challenges this fatalist logic by denying all C•f have truth value at all. It was, therefore, possible for B* to be true prior to the battle, even though it is necessarily false once the battle takes place. Since B, prior to SB, had no truth value at all, its truth could not be used to defeat the possible truth of B*. There is no shortage of discussion of this topic, so I will limit myself to remarks about how this scenario relates to the FDD and, as you might have guessed, how Aristotle's point undermines determinism.

The crux of the matter is this: what about the world in which B was true made it the case that B was in fact true? What were the grounding conditions (C•g) for the truth of B (B•T)? On the day of SB and afterward, the C•g for B•T were simply the fact that the battle took place. B could not possibly be false in correspondence with a world in which SB actually happened. At time tSB, and at all times tSB+, therefore, ⊤B. Aristotle grants all this.

But what about at a time prior to SB (tSB-)? What about or in the world made it the case that ⊤B? Here is where determinism comes into the picture, even if the determinist were willing to jettison fatalism. For the determinist might grant that SB did not have to happen unconditionally (i.e. he might grant ~⊤B). There is nothing unconditionally necessary about B, rather, for the determinist, B is only conditionally necessarily true. The conditions for the truth of B (i.e. C•(B•T)) are simply the prior causal factors that led to SB (i.e. C•SB-). Presumably those C•SB- need not have happened unconditionally; after all, suppose the universe had never existed, or had existed with very different physical laws.

Hence, the determinist can agree with Aristotle that fatalism is false by granting that ◊~⊤B ∴ ~⊤B (i.e. since B is possibly only conditionally true, B is not unconditionally true). Instead, argues the determinist, ◊~⊤B ∧ ◊□​B ∴ □B (i.e. since B is not unconditionally true but is contingently necessary, therefore B is conditionally necessarily true). Further, since C•SB- grounds B•T, then, given ◊C•SB-, □B•T ∴ □B (i.e. the absolute contingency of C•SB- still entails the necessity of B•T, the latter which entails that B is true). If (…yes, if only…) we had adequate knowledge of C•SB-, asserts (…asserts…) the determinist, we could have predicted B––nay, we could have seen its truth as a necessary consequence of C•SB-.

Here's the problem, though: if the C•g for B just are C•SB-, then C•SB- just is the complete description of SB (i.e., C•SB-C•T). This is absurd, however, since numerous other C•g are required for B•T, namely, the fact that the battle and the events in the battle actually take place! C•SB- may be the case, but they do not of themselves entail B•T, since B cannot be true if not a single arrow were fired, if not a single sword was swung, if not a single command was given, if not a drop of blood was spilt on 20 September 480 BC. So, while C•SB- grounds (B ∨ B*)•T (i.e. the truth of the disjunctive between B and B* prior to SB), it is only SB which grounds B•T.

A truly complete account of the C•g for SB will necessarily include the things in which a battle actually consists, things, crucially, which could not possibly fall under C•SB-. The problem for the determinist is that he believes C•SB- is 'already' an adequate account of C•g for B (i.e. C•SB-B•T). If determinism is true, there can be nothing which adds to the causal efficacy of C•SB- to bring about SB. For if any other causal factors were needed for C•SB- to entail SB, then C•SB– are not of themselves C•(B•T), and SB does not necessarily and wholly follow from C•SB-, which means that determinism is false.

I tried to make a similar point a couple years ago in my postling about "the steps taking you", but I have been horribly remiss in not expanding that post to make the full anti-determinist point. This post is meant to redress my negligence, though that other post intends to discuss the problems determinism creates for scientific explanation. In a nutshell, if it is a necessary result of the physical features of, say, your left foot at time-place t•plf that you end up at, say, Marston's Deli, then a proper scientific account of the physical features of your foot would have to include reference to Marston's Deli. The same theoretic gerrymandering effect would apply to all objects of scientific study and scientists would not be able to do that most essential operation for formulating scientific laws, namely, abstracting the ideal ratio from particular deviations and data. To say more, I shall have to live to codgitate another day.

1 comment:

djr said...

You might enjoy Roderick Long's dissertation, 'Free Choice and Indeterminism in Aristotle and Later Antiquity': http://proquest.umi.com/pqdlink?Ver=1&Exp=02-16-2016&FMT=7&DID=744423351&RQT=309&attempt=1&cfc=1

Unfortunately, it now costs money to read it, but it's pretty cool stuff. Rod is the coolest anarcho-libertarian I've ever read. Helps that he's an Aristotelian. But, unlike everything else of his I've encountered, his dissertation has nothing to do with anarcho-libertarianism -- except, of course, insofar as metaphysical liberatianism is a supposition of political libertarianism (which probably isn't true anyway).

I, in my naive ignorance, wonder whether determinism only becomes a serious worry when we make the mistake of thinking of causation as a necessitating relation between events, rather than primarily a matter of natural agents of various kinds exercising their causal powers. But like I said, I'm naive.