Bill's Notes

Welcome back, Chris. Where have you been?

Well, yes, salvation and algebra may not have much to do with each other. Perhaps knowledge of algebra helps lead to knowledge of God. You never know.

Paul

Actually, mathematics is the one field of human study in which God is completely and utterly irrelevant; quaternions and Cayley numbers would be exactly the same with God, the two Gods of Zoroastrianism, the thirty some-odd gods of the greek pantheon, the everything-God-kind-of-sort-of of hinduism, or the no-God of budhism (or materialism).

Anyhow, this sort of reveling in ignorance is a very natural reaction to the sort of elitism of Bill's post: "If you can't do math, you can't reason." Socrates had no great mathematical ability — at least it was never documented that he could do algebra — but he was quite capable of reasoning.

Chris, with all due respect, I disagree with you. Very sharply. God created all things, and he saw that they were good.

The problem with the scholarship of the scribes and the Pharisees is that it was distorted by human pride and sin. The problem was not that there was anything wrong with God's good and righteous Law; only with those who arrogantly and sinfully bent the Law to their own ends.

The way to deal with sinful or prideful or "elitist" mathematicians or musicians or geologists is to call them out for their sin; not to urinate upon mathematics or music or geology.

Anyone who knows me well knows that I'm the last person in the world who could be considered an elitist— I also hold popular culture in high regard, I think it has entirely valid excellence of its own. I mean, I hold in high regard many things that elitists also hold in high regard: mathematics and sonnets and classic literature and symphonies and whatnot. But I also hold in high regard B movies and comic books and science fiction and the like. Each has an entirely valid excellence of its own, and if narrow cultural elitists have made a mistake (beyond taking arrogant and prideful attitudes on behalf of their "high cultural" bailiwicks), it is in missing and overlooking the distinctive but valid excellence which inheres in popular culture. As C.S. Lewis once put it, "The high does not stand without the low."

(Yes, I know, Lewis also wrote an essay— I believe entitled "Lilies That Fester"?— in which he pointed out that the Bible displays little if any regard for high culture. Lewis himself, FWIW, had (as I do) regard for both high culture and popular culture.)

What troubles me is not elitism or anti-elitism, though I definitely tend to take a broader view of things than either of them. What troubles me (as I've already said above) is the philistinism, the cynicism, the nihilism, which are so prevalent and so casually adopted in today's culture. In other words, what bothers me is the dismissive, "dissing" attitude of elitist and anti-elitist alike, toward that genuine excellence which happens to fall beyond the bounds of their own (elitist or anti-elitist) bailiwick. When I get into the pulpit on Sunday morning, it is quite enough for me to preach the Gospel of Jesus Christ, calling people to confess their sins against God and their neighbor, and receive in faith the forgiveness that is available through the cross of Christ. There is no calling for me to lambaste them for their often genuine liking or disliking of Shakespeare or the Star Wars movies. Except insofar as that liking or disliking is driven by sinful attitudes such as pride, arrogance, etc.

Paul,

I likewise respectfully disagree with you: God created all that is, but mathematics doesn't actually exist; it's the study of what might exist. In short, God is bound by logic just as much as we are; we're bound by it because we are images of God, and he, being a rational intelligence, is bound by logic.

And you're right that the right way to deal with elitist intellectuals is to criticize what's actually wrong with them, not to criticize ancillaries to it. Still, not everyone is a philosopher, and if we're going to deal with the least philosophical 99% of the population, we're going to have to reconcile ourselves to dealing with (sometimes extreme) inexactitude of expression. These people don't really mean to urinate on the subjects themselves; only the human practice of these subjects. Most people just don't what they mean — they say something kind of like it. On the plus side, it means that they don't really mean what they're saying.

Those of us who have studied a field in depth and made progress can easily separate the field from the human practice of the field. We know that algebra's heart and sole is not questions that pretend to be relevant by asking how much fence is needed to enclose an area, as if fencing in areas was a common activity. But people who have not progressed have a very difficult time separating out the shit that beginners have to suffer through, which is largely the accretions of the last 200 years worst practice, from the actual subject. Perspective requires at least the beginnings of mastery, so it's unreasonable to expect perspective from people who never had any mastery of a subject. Now, they should be humble enough to recognize that they won't have perspective on the subject until they have actually attained some mastery, but humility is the most difficult virtue. That doesn't make it any less important, but it does make it less reasonable to expect (in the probabalistic sense).

By the way, when I said "in the gospels Jesus didn't demonstrate a whole lot of respect for scholarship", I meant that very literally. While he had a lot to say of the scribes and pharisees, he said nearly nothing, one way or another, on the worth of scholarship. It's almost like Jesus regarded scholarship as just another profession — like carpentry or farming — rather than as some sort of spiritual endeavor akin to hindu yogis. Jesus did, after all, live among and preach to people who by modern standards were extremely uneducated.

And this is the heart of the matter, to me. Our modern age has a very strong prejudice in it to associate education with moral worth. It's a natural enough error, I guess, since knowledge is good, but it's a dangerous error, because it strikes very close to pride. In my experience, it often strikes very close to pride. And what makes it dangerous is that it's one of the vices sanctioned by our culture. As Lewis (or was it Chesteron) observed, every age has its tendencies to vice, and typically thinks that its vices are exactly the opposite of the ones that it has. Our time's vices certainly include pride — it's remarkably common for people to think ourselves the pinnacal of human history in terms of morals, knowledge, love — indeed, in every virtue. And since we have the most knowledge — we could bearly help it, coming after the people who did so much of the investigation, and with the people who will know more than us not being around yet — it's natural to laud scholarship as next to Godliness, because it allows us to boast most reasonably of our extreme worth.

And such boasts will always strike the uneducated as a statement that the educated person is worth more. Is it really strange that uneducated people will respond in anger and defiance that education isn't worth a dram?

Between the two — the elitists and the anti-elitists — I tend to side with the anti-elitists. Both groups are wrong. Education is worth something, but it's far from the most important thing. The most important thing is reconciling ourselves to God — getting into heaven — and between the two groups, the anti-elitists are less dangerously wrong.

But no, you don't need to know algebra to be saved.

Bill,

Please don't misunderstand me. I don't think that you're an elitist at all. I just meant that there is that element to your post — "If you can't do math, you can't reason".

Say what you like about Paul and math, but Cohen is still an elitist.

Dissin' algebra teachers and claiming writing is the ultimate form of reasoning makes him sound like he's a bit insecure about the size of his writing pen.

If you know what I mean.

Algebra and reason? I thought algebra was the mathematical theory of calculation.

For analogues one looks to information theory, cybernetics, &biology, at their various depths of sunkenness into that which the shadows flitting around so smugly call "the real world." Algebra, coding, translation, interpretation. I suppose that one could call this sort of thing "inference to a conception." But sweet reason? Inference to a judgment? By Crom, that's a fiction or Sherlock Holmes didn't snort coke.

Ordered structures, conditions for applicability of mathematical induction, aren't things like that the pure math of reason, at least reason of the kind to be studied in a pure-math context? Its analogues leading to our world's degenerate cinder of the mathematical light are Deductive Theory of Logic, ageless Philosophy, not to mention the Psych and Soc of rational beasts. Behold the Sciences of Reason, and of Reason's Crackups, and every such Science cracked up into schools! I rest my case, for just a moment. Okay, long enough.

Of course, pure math is about such wild pure possibilities running off in all directions, that only by the shadow &prospect of the interruptive glove of Deductive Logic, and sometimes its young siblings, Probability Theory and Deductive Maths of Info, can we form it into sound classical sense, the sense of stately alternatives in a bounded universe, alternatives in a quantum many worlds kind of way perhaps, but nevertheless, they themselves but a Vestibule to the Sciences of Phenomena in General -- such as Statistics, Cybernetics, and Philosophy, those are where the parti-wave finally hits the screen, the rubber actually hits the road, etc., that zone of qualities, samples, packet-ripped sweets &teasing tastes and wicked delicious crests of news, the culminations, which ain't enough since they need verification, along the way to the confirmed, solid haecceitous world of facts, anchors, concrete foundations, all inter-wedded, so now they're waitin' for the end of time, dynamic, material, biological, and human, reactive, nitty-gritty, &far from the madding crowd of wigged-out Platonian possibilia and phantastic equivalences which the aetherials flitting around so smugly call "the real world."

Seriously, I don't know what I regard as the realest world. This horse is real (Concretia). This horse is really tan (Apparitia). This horse really probably doesn't win races (Alternatia). This horse is really another than this hound (Platonia). Don't blame me for my post, blame Paul Burgess, whose blog's link I followed hither.

PS: Bill, does this thread get listed under your "Best Discussions"? Or should I duck when I ask you that??! ;-)

Shoot. I meant, "is roughly the same thing as saying that the a man's grandfather is the father of that man's father."

Paul,

So you hold that the lines in the word "dog" actually refers to something, quite independently of our definition of the thing? That in fact it might refer to a squirrel, and all of us english speakers has it wrong? And of all of the languages on the earth, who use different words to signify the same thing, which one of us is right? What about when a word changes meaning? For example, awesome used to mean fearsome, and now is means extremely good. Does that mean that at least some group of English speakers is just outright wrong? Supposing us to be right and our forebears to be wrong, when one of them said, "The fire in the theater was an awesome sight", and the guy standing next to him understood him perfectly, they were misusing language?

And what about the constant human habit of inventing words? We need a word to refer a particular polycarbonate polymer, so the word Lexan comes about. Should people naming things stand in fear and dread that they might be picking the wrong word, and misnaming the thing?

I'm having a difficult time understanding your position. If I say to you, hold up one light if the british are coming by land and two lights if they're coming by sea, how is this communication not purely a human invention? Is there an eternal platonic form of british-light-counts somewhere? Had Paul Reverse &co reversed the meaning of the count, would disaster have struck, or what?

Please explain, for I find this claim highly perplexing. In particular, how does it mesh with the fact that people can agree to use any sound or symbol (that they can produce) to signify some idea to another person. If I tell you that by flithblatter, I mean a dog, and that my wife's flithblatter is in need of a bath, you'll understand me perfectly. How is the mutual understanding that "flithblatter" signify's a dog not a construct of ours? Since I can do this with any noise or squiggle, it seems that they're all infinitely flexible about what they're willing to mean.

Even more, the meaning of a word, as we use it, depends largely on context. If I talk about "tip", that collection of squiggles can mean either giving a waiter money or pushing him over. The collection of squiggles can't inherently mean both, but I can easily mean both by it, and be understood in both meanings. Is the permission of a squiggle, which I can rely upon always being given, even worth talking about? It's not like the squiggle "tip" has the power to stop me from using it to mean anything that I like it to mean.

Chris, no, you're completely misreading what I'm trying to say: you're talking as if it's all completely arbitrary, and as if there were some insuperable discontinuity between the Platonic forms and us. That's not at all what I'm saying, and that's not at all how I view realism, or signs, or language.

Not at all. Not at all. Not at all.

Nor do I think that "language is useless to describe reality." Not at all. Far from it!

And since I'm very busy today, I'll simply have to ask you to re-read, and to re-think, what I've already written. Or else just let it go; but in that case, please don't substitute a straw man in my place. :-)

If you want to know who stands behind much of my thinking on signs, realism, etc., it would be the late 19th and early 20th century American logician and philosopher of science Charles Sanders Peirce. Though don't hold Peirce responsible for everything I've written here, I know I've said things here that he would have disagreed with.

And now back to work on a busy, busy day. Best regards!