Archive for May 14th, 2008

The Brilliancy That Wasn’t

Wednesday, May 14th, 2008

I don’t think I reported on last Thursday night’s game at the West Chester Chess Club.  I played a boy, P.D.—perhaps ten years old—and won, but I had a chess hallucination and made the win more difficult than it should have been.  I had White, and the game began 1 e4 c5 2 Nc3 e6 3 Nf3 Nc6 4 d4 cxd4 5 Nxd4 Bb4  (I wasn’t really familiar with this variation, but the way I handled it worked out well.)  6 Qd3 Ne5 7 Qg3 Ng6 8 Nb5 d6  (I was expecting 8 … e5, after which might have followed 9 Bg5 Nf6 10 O-O-O) 9 a3 Bxc3+ (9 … Ba5 Nxd6+; 9 … Bc5 10 b4 Bb6 11 Nxd6+) 10 Qxc3 Kf8 11 Be3 a6 12 Nxd6 Qf6 (12 … Qxd6 Bc5) 13 Qc5 N8e7 14 O-O-O Ne5 (It’s here that I hallucinated.  I thought I could play 15 Nxc8 Rxc8 16 Bg5 Qg6 [16 … Rxc5 Rd8#] 17 Qxc8+ Nxc8 18 Rd8#, winning brilliantly.  Unfortunately, the e5-knight now blocks my queen’s coverage of the square g5.)  15 Nxc8 (I should just have played Bd4, winning the e5-knight) Rxc8 16 Qc7 g5 (A good response.) 17 Rd8+ Rxd8 18 Qxd8+ Kg7 19 Qd2 (I wanted to keep pressure on him and not let him attack my king along the c-file.) h6 20 Be2 N7c6 21 Rf1 Rd8 22 Qc3 Ng6 (I thought his letting me trade queens was a mistake, since I could win the pawn-up, two-bishops-for-two-knights ending; I thought he needed to try to generate pressure against my king) 23 Qxf6+ Kxf6 24 Rd1 Rxd1+ 25 Kxd1 e5 26 c3 (taking away Nd4) Nf4 27 Bf1 (preserving the two bishops; a question I’ll try to remember to ask the club master is whether I should have done so or whether I should have played 27 Bxf4, reducing the number of pieces on the board) Ke7 28 Bc5+ Kd7 29 g3 Ne6 30 Be3 Ke7 31 Kc2 Kf6 32 Kd3 Kg6 33 a4 Ne7 34 b4 f5 35 exf5+ Kxf5 36 Bg2 Nd8 37 Bc5 Nec6 38 Bb6 h5? (permitting me to win a piece) 39 b5 axb5 40 axb5 Nf7 41 bxc6 bxc6 42 Bxc6 Kg4 43 Bd7+ Kf3 44 Be8 Nd6 45 Bxh5+ Kg2 46 Bc7 e4+ 47 Ke3 Nc4+ 48 Kxe4 Kxf2 49 h4 Black resigns.  So, I thought I would win brilliantly, and then had to grind it out.  15 Bd4 would have been much better than 15 Nxc8 was!

I don’t know what causes chess hallucinations.  I’ve miscalculated combinations by looking at a bishop sacrifice and then, later in the combination, foreseeing myself using that same bishop.  This time, I missed that his e5-knight blocked my queen’s coverage of g5—I had been eyeing Bg5 for a while, and didn’t notice that it was impossible.  It would have been really lovely had it worked!

Meanwhile, I’ve been adding to my Web site ( www.holycyclops.com ).  I now have five “little lessons” on my site—Playing for the Endgame, Building Walls, Tempo Moves, Outflanking, and Entombed Pieces.  And I’ve just learned how to make the squares different colors!  Maybe I’ll go back and do a little tinkering with diagrams. 

On Fatalism

Wednesday, May 14th, 2008

When we think about past events, we normally think of them as “written in metaphysical stone.”  Nothing we could do could make an event E that has already happened at time t fail to happen at time t, and nothing we could do could make an event E that has already failed to happen at time t happen at time t.  I express this by saying that E has an occurrence-value O(E).  Even if one countenances time travel to the past, it seems as though one cannot make an event E which has already happened unhappen, or make an event E which has already failed to occur happen; all one can do is to create a second time-stream in which E’s occurrence-value is different than it was in the first time-stream.  E’s occurrence or non-occurrence at t—O(E)—is fixed for any particular time-stream.  And most of us do not countenance time travel to the past, and therefore take O(E) to be fixed, for any past event E.

By contrast, we tend to think of the future as open.  A future event E might happen or might not happen in this time-stream; its occurrence-value O(E) is not fixed, even in this time-stream.  We take there to be a fundamental disanalogy, in this regard, between past events and future events.  The fatalist argument attempts to undercut this disanalogy.  Reiterating that “O(E)” means “E has an occurrence-value,” and taking p to be the proposition “E occurs at time t,” I give a simple version here:

1.  p v ~p      (Premiss, by the Law of the Excluded Middle)
2.  p—>O(E)    (Premiss:  If it is true that E occurs at time t, then E has an occurrence-value)
3.  ~p—>O(E)   (Premiss:  If it is true that E fails to occur at time t, then E has an occurrence-value)
4.  O(E)        (1, 2 ,3, Constructive Dilemma)

Note that this argument seems to hold both for past events and for future events.  Also note that it says nothing about human freedom.  If p is now true, it may very well be via human choice that E occurs, and that the present truth of p is attributable to a freely made choice; and similarly if p is now false.  The argument ascribes to E a present occurrence-value, but it does not say why E has that present occurrence-value.

However….

The argument rests on the Law of the Excluded Middle, so one may deny that the Law of the Excluded Middle applies to future events; this seems to be Steven Cahn’s suggestion in Fate, Logic, and Time.  One might claim that for future events, neither p nor ~p is true.  And this seems reasonable to me.  I have written premisses (2) and (3) as conditionals, but the biconditionals p<—>O(E) and ~p<—>O(E) really hold, if one holds any sort of correspondence theory of truth.  To say that the proposition “E occurs at time t” is true is just to say that E occurs at time t, and to say that E occurs at time t is to say that the proposition “E occurs at time t” is true.  Thus, to say p v ~p is to say that either E occurs at time t or else E does not occur at time t, and to take p v ~p as saying that either “E will occur at time t” is now true or else “E will not occur at time t” is now true is to take it as saying that either E’s occurrence at time t is now the case or else  E’s nonoccurrence at time t is now the case.  But this, it can reasonably be claimed, is to assume the truth of the fatalistic doctrine itself, for what the non-fatalist wants to say is that neither E’s occurrence at future time t nor E’s nonoccurrence at future time t is “written in metaphysical stone”—that future event E’s occurrence or nonoccurrence won’t be decided, not only epistemically but also metaphysically, until future time t, and therefore that it is not now true that E will happen and it is also not now true that E will not happen. 

The non-fatalist would want to read the argument, for future events, as

1.  p will be true or p will be false
2.  If p will be true, then E will have occurrence-value.
3.  If p will be false, then E will have occurrence-value.
4.  Therefore, E will have occurrence-value.

Such a reading, taking p to have a future truth-value but not a present truth-value, doesn’t imply that E already has an occurrence-value; only that it will have one.  Alternatively, the non-fatalist could construct an anti-fatalist argument, for future events:

1.  p is not now true and p is not now false.     (Anti-fatalist premiss)
2.  E now has occurrence-value if and only if either p is now true or p is now false.  (Premiss)
3.  It is not the case that either p is now true or p is now false.   (1, de Morgan’s Law)
4.  Therefore, it is not the case that E now has occurrence-value.  (2, 3, Modus Tollens)

Of course, the anti-fatalist argument assumes its conclusion just as much as the fatalist argument assumes its conclusion.  Where the fatalist argument assumes that propositions about the occurrence of future events already have truth values and therefore, via the correspondence of a proposition’s truth and the content expressed by the proposition’s being the case, assumes that future events have occurrence-values, the anti-fatalist argument assumes that propositions about the occurrence of future events now lack truth-values and therefore, again via the correspondence between truth and content, assumes that future events lack occurrence-values.  Both the fatalist and the anti-fatalist argument really fail to be arguments at all, but are simply choices of how to view the metaphysical nature of future events.  And that may very well depend on one’s view of time.  One who models spacetime according to Einstein’s “block universe,” for example, might very well make the fatalist choice.  But it looks to me as though the difference between the fatalist and the anti-fatalist is simply one of differing intuitions.