Holy Cyclops

In Paul Boghossian’s Fear of Knowledge:  Against Relativism and Constructivism, a book I’ve recently started reading and am enjoying, he presents an argument against what he calls “cookie-cutter fact-constructivism.”  He is arguing against the sort of view advocated by Nelson Goodman and Hilary Putnam, and illustrated by Goodman’s “constellation” example:  We draw the lines around groups of stars and call them “constellations”; the groups of stars aren’t constellations until we notice them as such.  There is no such fact as “The Big Dipper is a constellation” until we say there is.  That fact is socially constructed.  Moreover, all such facts are socially constructed:  We use our concepts to “carve up” reality, just as a cookie cutter cuts up dough into shaped pieces, and since this “carving up” isn’t done until we do it, we construct the facts about reality; moreover, no way of conceptually “carving up” reality is closer to the way things really are than any other, for there is no way things really are.

Boghossian argues that this “cookie-cutter” view contradicts itself, because even if one says that constellations are delineated by human concepts, and that their constituent stars are similarly delineated by human concepts, and that their molecules (well, plasma, but I don’t think that’s important here) are similarly delineated by human concepts, and so on, one still requires, at some basic level, a “dough” which our concepts can operate on, and there has to be a way that that “dough” really is, unless one wants to insist that the “carving up” goes on infinitely, level after level, which clearly seems absurd.

The problem I see is that this argument only works on the reality-objectivist fact-constructivist—the one who says that there really is an objectively existing reality, and whose fact-constructivism consists of applying human concepts to that reality.  That is to say, his argument only works to establish the reality of an underlying objectively real “dough” against those fact-constructivists who already agree that there is one.  (Such fact-constructivists might then have to agree that there is a way things are at the fundamental level—the level of the “dough”—and simply reserve their fact-constructivism for all higher levels of fact; they might also adopt the view I’m about to describe for everything except the “dough.”)  The reality-subjectivist fact-constructivist, on the other hand, may simply insist that concepts do not apply to objectively existing reality (or to elements of it), but instead apply to one’s own mental life (or to elements of it)—that, for example, my concept of stripedness is not applicable to objectively real tigers but is instead applicable to my ideas of tigers.  (He might or might not agree that if there happened to actually be objectively existing tigers, then my application of the concept of stripedness to my ideas of tigers could be extended, so that the concept of stripedness would then be applicable to actual tigers.)  As long as it is not agreed that there are actual tigers, and as long as it is maintained that the concept of stripedness applies to my ideas of tigers rather than to actual tigers, the only “dough” the reality-nonobjectivist fact-constructivist is committed to is the “dough” of his own ideas—his own thoughts and mental images and the like. 

Perhaps Boghossian will address that sort of position later in his book.  I’ll find out.  

My father has Alzeimer’s disease, and my Mother’s Day present to my mother is to spend some time visiting them at their retirement community so that I can care for him while she does other things for a few days.  I did this once before, for a week, when she visited my brother in Florida, and I didn’t find it nearly as hard as my mother had led me to believe it would be.  In fact, it was easy.  My father is at the stage where he asks a question, and you answer it, and two minutes later he asks the same question, and you answer it again, and two minutes later, he asks the same question.  But I’m patient, and I just answer the question each time it’s asked.  And it does seem to me that information sinks in; it just takes lots of repetition for it to do so.  I remember once in the car he asked my mother what they were doing that day, and she told him they were going to see the doctor (for what purpose, I don’t remember, but she included that information in her answer to his question).  Two minutes later, he again asked what they were doing that day, and again she told him they were going to see the doctor and why.  Two minutes later he asked her not what they were going to do that day, but rather why they were going to see the doctor.  And he doesn’t ask the same question over and over all day long; he asks it two or three times. 

Anyway, I’m patient, and it doesn’t particularly bother me to have to repeat my answers, or to ask him a couple of times if he has enough shampoo while he’s showering (so as to jog his memory and make sure he uses the shampoo).  But then, he’s not my spouse of over fifty years.

I’ve brought along a few books I’m reading:  an Erma Bombeck book I bought my mother for her upcoming birthday and want to finish before giving to her; the philosopher Paul Boghossian’s Fear of Knowledge:  Against Relativism and Constructivism, which I’ll be commenting on in the philosophy section of this blog; Bertrand Russell’s History of Western Philosophy, which I recently stumbled upon in the local library; and The Encyclopedia of Chess Middlegames:  Combinations, a great book filled with chess problems and solutions.  I didn’t bring The Poincaré Conjecture, about the shape of the universe, or the Samuel Reshevsky chess book I just bought but whose title I forget. I hope to get some reading done while I’m here, but there’s a computer here, and I tend to lose a lot of time reading and writing online!

Thursday night, as usual, was my night for going to chess club.  I played a slightly weaker player, but, with Black, I got a really bad position out of the opening.  He should probably have crushed me.  But I defended, and he missed his best moves, and I wound up a piece and three pawns ahead in material before doing something I only rarely do these days:  Blundered away a piece.  It was in time pressure, so I have some small excuse, but still—leaving a knight where it can be taken for nothing is not good.

But sometimes it’s better to be lucky than to be good, and after blundering away the piece, I was still up three pawns, with a killer central passed pawn.  Once I got through time pressure, the win was easy.

Back on my Web site, I’ve been adding color to my chess diagrams.  (I’ve also fixed a little bad analysis in my Playing for the Endgame “little lesson.”)  It looks great!  And I discovered that I can print out those diagrams after all—I had thought that although the diagrams displayed well, the bits of HTML code that call the program that makes them display as diagrams would just show up as gibberish when I printed the page.  But no—they print beautifully.  (But my printer needs new cartridges, both color and black-and-white, and my sister’s printer now needs a new black-and-white cartridge, so I’m temporarily not printing anything—an inconvenience, since I wrote a poem for tonight’s “poetry slam” that I’m now going to have to copy by hand in order to take with me.)

My nephews decided that they wanted to play a little baseball today, so we went out and played with a plastic ball and plastic bats.  One of them had drawn home plate and three other bases, along with baselines and a pitching rubber, on the driveway, in chalk.  I pitched what was essentially batting practice to them, but when they hit fair balls they ran around the bases.  They seem to really enjoy it.

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. 

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.

God is sometimes characterized as omniscient, and his omniscience is sometimes taken to include knowledge of the future–of all future events.  But his foreknowledge of events, it is sometimes argued, is logically inconsistent with human beings’ having freedom of the will.  After all, if God already knows what will happen, how can we have any real choice in the matter?  We must choose exactly in accordance with God’s foreknowledge.   

The simple argument for the incompatibility of God’s foreknowledge with human freedom of the will, using “Np” to represent “metaphysically necessarily p,” “Pp” to represent “metaphysically possibly p,” “x” to represent “x occurs at time t,” and “Kx” to represent “it is known that x occurs at time t,” is

1.  N(Kx—>x)  (Premiss—to know that x will occur at t requires that x will occur at t)
2.  Kx—>x        (1, modal axiom M [or T], i.e., Np—>p)
3.  Kx                  (Premiss—it is known that x occurs at t [since God has complete foreknowledge])
4.  x                     (2, 3, modus ponens)

Hence, if we assume that event x at t is foreknown, we know that event x at t occurs—and, therefore, not event not-x at t.  But where is human freedom if what is foreknown dictates what occurs?

The problem with this can be shown if we simply take “Kx” to denote postknowledge instead of foreknowledge.  The same argument works just as well, and yet we don’t think that postknowledge dictates the event x’s occurrence at t.  Rather, we think that event x’s occurrence at t dictates which of “x occurs at t” and “not-x occurs at t” is known.  For an omniscient postknowing being, x dictates Kx, and not-x dictates K(not-x).  We might similarly say that for an omniscient foreknowing being, x dictates Kx, and not-x dictates K(not-x)—i.e., that whether x or not-x happens at time t determines whether x is known or not-x is known, even if the knowledge is foreknowledge instead of postknowledge.

Yet, there’s a clear asymmetry between the cases of foreknowledge and postknowledge.  If a person A makes the choice between x and not-x at time t, and if, at some later time, a postknower tells person A which choice he made, we see nothing strange about it, and it certainly doesn’t affect how we think of person A’s freedom to choose.  On the other hand, if a foreknower tells person A which choice he will make, there is a problem:  Why can’t person A just be contrary and choose to act otherwise than he has been told he will?  If he can do so, then he has the power to render foreknowledge false, which surely can’t be done; if he cannot do so, then he doesn’t seem to be choosing freely. 

It seems that if foreknowledge is to be compatible with freedom of the will, any foreknower is limited in what he can do between the moment of his first attaining foreknowledge and the time t when x is chosen.  In particular, he cannot initiate a chain of events that might lead person A to do what he otherwise would not do.  The simplest way to ensure this would be for the foreknower to remain passive.

Do we, then, limit God, so that although his omniscience extends to complete foreknowledge of events, he does not exercise any power he might have over the course of human events?  (While this might be a stronger restriction than really necessary, it seems like an aesthetically pleasing choice.)  Do we instead say that God’s omniscience does not extend to knowledge of future events? 

My younger nephew and I went for one of our frequent bike rides today, and we spotted a red squirrel!  We first saw one around here two summers ago—it was, in fact, the first time in my life that I had seen a red squirrel—and saw them throughout that summer, in the trees and on the fence lining our driveway and also in the trees and on the fence lining one side of the local park, where we shoot baskets.  But we didn’t see any last year, and I was afraid they were gone from this area. 

Riding our bicycles today, however, we saw one, again running along a fence and climbing a tree, next to a farmlike property with a pair of horses and, recently, some Canada geese (I counted seven today).  I’ve enjoyed seeing the purple tulips around the neighborhood, but seeing the red squirrel was the high point of our ride! 

Saturday, I played in the West Chester Chess Club’s First Saturday of the Month Quads.  Normally, we have around thirty-two to thirty-six players, but we only had twenty-two players this time.  Maybe people were staying home so that they could watch the Kentucky Derby, which the pre-race favorite Big Brown won.  But sacrificing a whole day’s worth of chess for two minutes of horse racing seems unlikely.  Whatever the reason, turnout was down, and I, with my low Class A rating, played in the second quad.

For those who are unfamiliar with how quads are run, and perhaps even with chess, I’ll note that when someone plays in a USCF-sanctioned tournament (”USCF”=”United States Chess Federation”), he gets a rating—a measure of playing strength—based on his results and on the strengths of his opponents.  The more rated games one plays, the more accurate his rating becomes.  In quads, the four highest-rated players are grouped together, and the four highest-rated players below them are grouped together, and so on, and each player plays one game against each of the other three players in his quad.  (If the number of players isn’t even, the tournament director plays, making it even; and if the number of players still isn’t a multiple of four, the bottom group is a six-person section in which each person still plays three games but in which the pairings are handled by something called the “Swiss system,” a well-established system for pairing players, round after round, in a tournament.)  My rating (1815, but now probably up to about 1830) is in the top fourth or fifth of tournament players; I had the seventh-highest rating among the twenty-two players.  USCF classes include Senior Master (2400+), National Master (2200-2399), Expert (2000-2199), Class A (1800-1999), Class B (1600-1799), Class C (1400-1599), Class D (1200-1399),  and Class E (1000-1199); few adults are lower-rated than 1000, although many kids are.  (The local chess club only has one master and one expert.) 

I had a strange quad.  I won my first game, when I should have lost—I got into a very inferior position straight out of the opening, struggled to come up with active play, and held on, only to reach a middlegame position in which I was sure I was lost.  But my opponent didn’t make the moves I thought he’d make, and I wound up trading down into a favorable endgame, which I then won.  In the second round, I played a very drawish game, only to stumble into a lost ending!  <Sigh>  Then, in the third round, my opponent handed me an Exchange (a rook for either knight or bishop—in this case, a knight) by letting me fork his queen and rook with my knight, and after many more moves, I forced his resignation.  So, it wasn’t a bad quad, measured by results—I scored 2-1—but it wasn’t a quad in which I played the way I want to. 

Now that I have the use of ChessImager (see previous post), I’ve been able to put a few “little lessons” in the chess section of my Web site with diagrams.  I have sections on playing for the endgame, on building walls, and on tempo moves, and a couple of other sections are planned.  I’m delighted!

I played Black against the club master last night, and although I lost, I’m happy, overall, with the game I played.  I played a Caro-Kann, he played his 1 e4 c6 2 Nc3 d5 3 Qf3 line–the one that caught me off-guard once before when we played–and I completely neutralized his advantage.  We wound up in an endgame with two bishops each and pawns on both sides of the board in a nearly symmetrical position, but somehow he managed to win.  I suppose that’s why he’s a master.  Of course, I missed a couple of his moves, including the one that won a pawn for him.

Tomorrow, I play in the First Saturday of the Month quads.