Holy Cyclops

I’m afraid it’s easy for me to let this blog slide, so now I want to do a little catching up.

Thursday night (the eighteenth) was chess club night.  The West Chester Chess Club was co-founded by two of my old friends way back when I was still in high school, and it has always been a friendly little club.  We only have one master, and our expert doesn’t usually show up; at about 1815 USCF, I’m the third-highest-rated regularly attending player.  (If you don’t know what “1815 USCF” means:  By playing in tournaments sanctioned by the United States Chess Federation [USCF], a player gets a rating, based on his results, that gives a rough idea of his playing strength relative to other USCF tournament players.  1815 is low Class A, and is somewhere around the seventy-fifth or eightieth percentile of all tournament players.  Good, but not really  good.)  Anyway, I played a considerably lower-rated player on Thursday night—we play USCF-rated games most Thursday nights—and managed to win, but it was a tough game, as usual against that particular opponent.  I took what looked like a possibly-poisoned b2-pawn in a line of the Pirc Defense’s Austrian Attack that turned into something close to an f4 Sicilian Defense after trading pawns on d4, and then defended too passively and got into trouble.  (”b2,” “f4,” “d4,” and so on, refer to squares on the chessboard, using the algebraic system of notation.  See, for example, http://www.uschess.org/beginners/read/ .)  The game became really tough, and I thought I was done for, but I managed to make a good move when he threatened to trap my queen that won another pawn, and I survived very  severe time pressure to win the game.

The last few days have been very warm—in the 80’s Fahrenheit—and my nephews and I have gone to the park, a five-minute walk from here, to shoot baskets.  My younger, ten-year-old nephew, who is a little on the short side, finally learned how to keep himself going on a swing—I observed his technique and then corrected it, telling him that he had to sit up and pull his legs back just at the highest point in his forward swing, and then sit back and point his legs forward just at the highest point in his backswing.  It worked!  He still needs a push from me to get started, but he can keep going now; he was happy.

On the way to the park, we saw a butterfly (or, possibly, moth) depositing eggs with its ovidepositor on a branch.  It had the ragged wings and light yellowish stripe around the edge of the undersides of its wings that a mourning cloak has—mourning cloaks are really gorgeous butterflies—but it had its wings folded, so I couldn’t tell what the tops of its wings looked like.  And while we were at the park, we saw a pair of hawks soaring overhead, riding the thermals.  We didn’t used to see hawks often at all, but last summer we saw them often, and now we’re seeing them again this summer.

Alas, one thing we’re not seeing are red squirrels.  A couple of summers ago, we saw several of them; it was a thrill, as I had never before seen them.  But last summer, we didn’t see them at all, and we haven’t seen them yet this year.

Later, my younger nephew and I went for bicycle rides.  He loves going for bike rides, and he likes having me go along.  (His mother requires that an adult go with him, anyway.)  On Friday, we left out Heartbreak Hill, but on Saturday, he was ready for it.  (”Heartbreak Hill” refers, naturally enough, to a long hill that steepens toward the top and is difficult to climb all at once.  I got the name from the Boston Marathon’s Heartbreak Hill.)  Both nephews and I tossed around a baseball, and on Saturday, their father and I took turns pitching, fielding, and batting with my younger nephew.  (My younger nephew has more desire to get out and do things.  My older nephew, who is thirteen years old, has Asberger’s syndrome, and he tends to keep to himself.  He does seem to be becoming more sociable than he used to be, though.) 

My younger nephew also woke up in the wee hours of Saturday morning with a sore arm.  He was very upset, and was crying.  I reassured him and, after asking a few questions about what sort of pain it was, told him that he had probably just slept on it wrongly, and that although it might hurt for a while, he’d be fine.  Then we read one of his Magic Tree House books.  (He loves the Magic Tree House series.  The characters of Jack and Annie, a pair of kids, go on adventures to different times and places, and the books are actually educational—but it’s their entertainment value that is the reason my nephew likes them!  Mary Pope Osborne writes them, and Sal Murdocca illustrates them.  The fortieth book in the series will be available this September.  See, for example, http://www.marypopeosborne.com .)  After that, he went back to sleep.

Meanwhile, I’m trying to figure out how to put advertising on my Web page and on my blog, and how to customize my blog’s display page; I installed the blog using Fantastico, via HostMonster.com, but it’s version 2.3.3, and I’m not sure how I can update to version 2.5 when the blog’s files are on HostMonster instead of on my computer.  The same problem—that the files are on HostMonster instead of on my computer—is making it difficult for me to customize this blog’s display page.  I might just uninstall this blog and then go to the WordPress Web site and set it up there.  We’ll see.  If I do that, I’ll have to save these posts!

When she was in her late teens, my sister, who is several years younger than I, converted to Islam after closely examining the merits of Christianity and rejecting it.  The fact that her then-boyfriend and soon-to-be first husband was Moslem might have had something to do with it, too; in any event, she remains Moslem, twenty years later.  For the last couple of years, I have lived with her and her second husband, a recently-naturalized American citizen from Pakistan, and their two children (my nephews), in the house my parents used to own, so I’ve had the opportunity to see, to a certain extent, how their religion affects them.  (I say, “to a certain extent,” because I do not attend their religious services and only see the effects of their Islamic belief in small ways.) 

Both my sister and my brother-in-law are good people.  When I—an avowed nontheist—tell my nephews that the most important thing in life is to be good and kind to other people, my brother-in-law tells them to listen to their Uncle Keith.  I certainly hope and expect that if my sister and brother-in-law were not Moslem, they would still be good, kind people, but in any event, it seems that they use their religious belief to reinforce such qualities and to promote such qualities in my nephews.  (I take it that most Moslems are essentially this way:  People who want to get along with each other and who mainly try to use their religious belief to reinforce their commitments to treating other people well, rather than to justify treating other people badly.  However, I confess that I do not know what percentage do use Islam to justify treating other people badly, and of course we know that some Moslems in positions of authority in other countries have done so; and I don’t know how much of that is attributable to their religion and how much is attributable to their culture.  Because many Moslems do not believe in the separation of church and state, but rather suffuse their daily lives with their religion, it’s hard to tell how to make such attributions.)

So, what differences are there between how they behave as Moslems and how they would behave if they weren’t Moslem?  Obviously, since that is a counterfactual question, I’m limited in the conclusions I can draw; but my sister probably wouldn’t keep her head covered, as she does most of the time, and they probably wouldn’t kneel on their holy rugs, turn toward the east, and pray five times each day, and they probably wouldn’t keep several copies of the Koran around the house, and they probably wouldn’t be careful to eat only halal  (Islamically approved) food, and they probably wouldn’t have art depicting mosques or a calendar with the sayings of the Islamic cleric M.R. Bawa Muhaiyaddeen hanging on their walls, and they probably wouldn’t fast in the daylight hours during Ramadan.  Perhaps my brother-in-law would drink alcohol, or womanize, were he not Moslem, although I’m inclined to doubt that he would do the former to excess or that he would do the latter at all.  He’s simply a good person.  (I don’t think my sister has ever been inclined to drink, religious belief or no religious belief.) 

The main effect, one that I deplore, is that my nephews are being raised Moslem—that is to say, they are being indoctrinated with religious belief.  I object to such indoctrination, and it’s fortunate for family harmony that my sister and brother-in-law seem to espouse a very moderate brand of Islam, so that I don’t feel compelled to loudly object to my nephews’ being taught religion.  At some point, they will ask me what I believe and why, and then I will tell them that although many very smart people do believe in God, I see insufficiently strong evidence or rational argumentation from acceptable premisses to justify such belief, and therefore withhold belief—as I think other people should, too.  For now, though, I don’t see a whole lot of ill effects from their teaching—particularly not drastic ones—and they’re even learning a foreign language as a result of it (Moslems do not think that you’re really reading the Koran unless you’re reading it in Arabic), which can only help them later in life.  The values they are learning are values of love and kindness and respect—ones I approve of; and they do not limit themselves in their social circle to other Moslem children.  They are growing up to be good people.

Modal logics dealing with possibility and necessity have sometimes been used to provide purported proofs of God’s existence, starting with some definition or characterization of God.  These, along with arguments like St. Anselm’s and Descartes’s, are classified as ontological arguments, as they attempt to argue from what it would mean to be God to the existence of God.  They use the modal operators “necessarily” and “possibly,” which are usually symbolized using a square and a diamond, respectively; but I’m going to use “N” and “P,” since they’re easier to type and since they have more mnemonic value for those of you who are not already very familiar with modal logic.  Thus, “Np” will mean, “necessarily p,” or, “p is necessarily true,” and “Pp” will mean, “possibly p,” or, “p is possibly true.” 

There are various versions of modal logic dealing with metaphysical necessity and metaphysical possibility—other modal logics have to do with other modalities, like moral obligation and moral permissibility, temporal necessity and temporal possibility, or epistemic necessity and epistemic possibility, but modal ontological arguments for the existence of God are concerned with metaphysical necessity and metaphysical possibility—and not everyone agrees on which version is the appropriate one for discussing necessity and possibility; but while there might be some question as to which modal logic is the appropriate one for discussing necessity and possibility, and while I have seen modal ontological arguments for God’s existence formulated using different modal logics (in particular, I’ve seen them using the widely accepted modal logic S5 and have also seen at least one using the modal logic KB), I will not be concerned with the somewhat technical question of whether to accept or reject any particular modal logic.  I can make my point no matter which version of modal logic is used.  (I will note that what is true in K or in KB is also true in S5.) 

The modal arguments I’m addressing in this post make these two assumptions:  First, if God exists, then his existence is not merely metaphysically contingent (possible but not necessary) but is metaphysically necessary; second, it is possible that God exists.  The idea behind the first premiss is that the world around us is merely contingent—its existence was not necessary; it could have failed to exist—and that the merely contingently existing—that which could have failed to exist—requires a necessarily existing entity either (i) to explain why it exists instead of failing to exist or (ii) to bring it into existence and to maintain its existence.  Personally, I don’t see the need for (ii)—I don’t see why, if it’s possible for something to exist, it nevertheless needs something more to make  it exist; it could exist, and it does, so what’s the problem?  Metaphysical possibility doesn’t say, “Possibly p only if something else exists”; it simply says, “Possibly p.”  As for (i), I’m not convinced that existence is the sort of thing that has an explanation; why the state of the universe is what it is at a particular time may have an explanation in terms of its state at an earlier time, for any time after time t=0, but asking for an explanation of why the universe exists at all might be pushing the notion of explanation beyond its appropriate limits.  However, such doubts are irrelevant to the point I want to make here, so let me simply grant the first premiss—i.e., let me grant that if God exists, he exists necessarily.

The problem—you knew I’d get to it eventually, didn’t you?—is that for non-contingent entities, the assumption of possible existence is tantamount to the assumption of necessary existence, while the assumption of possible nonexistence is tantamount to the assumption of necessary nonexistence.  It seems innocuous to assume that God possibly exists; assuming mere possibility isn’t assuming very much, is it?  But for an entity defined as non-contingent, assuming possibility is  assuming a lot—just as assuming the possibility of its nonexistence would be assuming a lot.  If one accepts the premiss of God’s non-contingency and also accepts the possibility that God exists, then one is forced to conclude that God necessarily exists (and, therefore, that God exists).  But if one accepts the premiss of God’s non-contingency and also accepts the possibility that God doesn’t  exist, then one is forced to conclude that it is impossible  that God exists (and, therefore, that God doesn’t exist).  The premisses (1) God’s existence would be non-contingent, (2) it’s possible that God exists, and (3) it’s possible that God doesn’t exist, are mutually inconsistent.  One may assume (1) and (2), or one may assume (1) and (3), but one may not assume all three.  Given that we are accepting (1) (i.e., that God’s existence would be non-contingent), then when a theist, in writing out a modal ontological “proof” of God’s existence, assumes (2) instead of (3), he is implicitly assuming God’s necessary existence (and, therefore, his existence); and when a nontheist, in writing out an analogous modal ontological “disproof” of God’s existence, assumes (3) instead of (2), he is implicitly assuming God’s necessary nonexistence (and, therefore, his nonexistence).  Accepting (1) and (2) instead of (1) and (3), or accepting (1) and (3) instead of (1) and (2), amounts to assuming the conclusion one wants to get in the first place.  For entities defined as non-contingent, “possibly” and “possibly not” collapse to “necessarily” and “necessarily not.”

That’s it for the basic argument.  Now, for those who would like to see a bit more technical detail….

I’ll use “&” for the conjunction ”and,” “v” for the disjunction “or,” “~” for the negation “not,” and “->” for the material conditional “if…then” (or “only if”).   Then we have (see Dan Quattrone’s post in “Doing Things with Words,” at http://dtww.blogspot.com/2005/03/logic-is-for-tricking-people.html ), using “g” to mean “God exists,” 

1.  N(g->Ng)-> (Pg->PNg)          (A theorem of the modal logic K)
2.  [N(g->Ng) & Pg]->PNg          (1, exportation)
3.  PNg->g                               (Modal axiom B [which, along with modal axiom M {a.k.a. T}, extends K to KB], written in its dual form)
4.  [N(g->Ng) & Pg]->g         (2, 3, hypothetical syllogism [propositional logic])
5.  N(g->Ng)                       (Premiss:  The non-contingency of God’s existence, if he exists)
6.  Pg                                   (Premiss:  It is possible that God exists)
7.  N(g->Ng) & Pg                 (5, 6, conjunction)
8.  g                                     (4, 7, modus ponens)

But one might equally well argue

6*.  P(~g)                     (Premiss:  It is possible that God does not exist)
7*.  ~Ng                        (6, duality)
8*.  N(g->Ng)->(g->Ng)        (substitution instance of the modal axiom M [a.k.a. T], which is part of KB [and therefore also of S5]:  Np->p)
9*.  g->Ng                     (8*, 5, modus ponens)
10*.  ~g                        (9*, 7*, modus tollens)

One is reduced to asking which he finds more likely:  That it is possible that God exists, or that it is possible that God does not exist; or that it is necessary that God exists, or that it is impossible that God exists.  But that decision must be made entirely independently of the modal ontological argument itself.  Thus, unsurprisingly, this sort of modal ontological argument, trying to define God into existence, won’t help decide whether or not God actually exists.  
 

St. Anselm of Canterbury (1033-1109) was a monk and theologian who, in his Proslogion, gave an argument for the existence of God on the basis of the definition of God—i.e., on the basis of what it would mean to be  God.  The argument is fatally flawed and should convince no one, but, somewhat surprisingly, it has supporters even to this day.  St. Anselm’s ontological argument for the existence of God runs about like this:  (1)  God is that greater than which none can be conceived; (2)  an existent God would be greater than a nonexistent God; (3) if God did not exist, then something greater could be conceived—namely, a God that did exist; (4)  therefore, God exists.

Although it is possible to analyze this argument in some detail, I’ll just give the main problem here.  The argument fails to distinguish between an object or entity  and the mental conception of an object or entity.  (A lion wandering the African savannah isn’t the same as my mental conception of it; the former is a solid object, while the latter is only an idea.)  It might be that an object God would be greater than its mental conception, or that it would be greater for both the object God to exist and the mental conception of God to be conceived than it would be for the mental conception of God to be conceived without the object God’s existing; but the conception of God may be the greatest conceivable either way.  The object God’s existence or nonexistence doesn’t affect its mental conception’s being the greatest possible mental conception.  (Had St. Anselm argued that the conception of God is the greatest conceivable mental conception, and that the conception of God as existent would be greater than the conception of God as nonexistent, so that the conception of God must be conceived as existent, I’d've had no problem with the argument—but it wouldn’t have established God’s existence.  I conceive of Pegasus as winged, as maned, as white, as solid, as physical—as existent—but I do not thereby bring Pegasus into existence; and I may conceive of Pegasus as giving a ride to my nephew instead of to Bellerophon—I may conceive of Pegasus as nonfictional rather than as fictional—but, again, I do not thereby bring Pegasus into existence.  Conceiving of God as existent is not the same as affirming God’s existence; neither being conceived of as having existence-implying properties nor being conceived of as nonfictional implies actual existence.)

Even the language of the argument is deceptive.  One conceives  mental conceptions, but conceives of  objects; as phrased, the argument has the object God conceived.  Paying proper attention to the difference between existing  and being conceived of  makes that problem go away, but it also completely nullifies the argument.  “God is that entity whose mental conception is the greatest possible,” together with, “An existent God is greater than its mental conception,” doesn’t lead to a contradiction if God is assumed not to exist. 

war

the moon all misty white—cold;
the sky all dark, the stars dull shadows.
holy cyclops licks white bones,
     belly full, marches off content,
          crimson footprints staining the ground—
and the silent shiver of the trees;
the silent shiver of the trees.

(copyright 1977)

This is the source of the name “holy cyclops.”  In the poem, it was supposed to symbolize the military-industrial complex, with its monstrous, single-minded pursuit of war, apparently heedless of the carnage thereof; but I’m using it for my Web site (www.holycyclops.com) and for this blog just because I needed a name and “holy cyclops” seemed as though it might stand out more than would “the rational nontheist.” 

If I am in single-minded pursuit of anything, it is the truth.  Whatever is known to be true should be believed; whatever is thought to be true, with justification reaching or surpassing some threshold level, should be believed; whatever is false should not be believed.  And whatever is not known to be true and is not known to be false but lacks sufficient justification to compel rational belief should not be believed.  One should simply withhold belief from that which is insufficiently well justified.  Since I see insufficiently good reason to compel rational belief in God, I do not believe in God—and unless you possess better reason than I have, I think you shouldn’t believe in God, either.  (Or in ghosts, or in telepathy, or in astrology, or in reiki, or in tarot reading, or in crystal power, or in any of a number of other things, for that matter.)  It is simply an epistemic mistake–or perhaps a doxastic one–to believe in that which is rationally unsupported or poorly supported.