Showing posts with label Best of the Blog. Show all posts
Showing posts with label Best of the Blog. Show all posts

Wednesday, September 19, 2007

Encounters with God... by way of Pirates

In honor of International Talk Like a Pirate Day, here's a Best of the Blog repete that I've put through a Pirate Talk filter. Arrr.



Atheists in this here country (by which I mean the United States o' America) ha' a common tendency ta exaggerate their plight. That be handsome Pete! He dances fer nickels! this here be not ta say that tharr arrn't no atheists, here, who ha' suffered discrimination in the workplace er before the law, nor be it ta claim we be never the recipients o' threats 'n' even violence. Avast me hearty mateys! It is, however, ta say that these be not the norm. Certainly, in comparrison ta such groups as homosexuals, our lot be not so mangy.

In me own experiences, the very worst thin' that has happened ta me as a consequence o' me atheism was a single death threat. Blow the man down. This here sounds dramatic but it was the sort o' anonymous threat that tends ta bubble out o' the cesspool that be Usenet and, while I did forwarrd it ta the proper authorities, I did not feel no great distress. ARR! I ha' certainly never suffered no actual violence due ta me atheism 'n' the only times I ha' felt compelled ta conceal it was not fer concern fer me safety but rather fer fearr that I'd needs be engage in some awkwarrd discussions with swabs whom I had no interest in debating.

Rather than sayin' that American atheists be a persecuted minority, I would say that we arre, in fact, an irritated minority. It be important ta understand, however, that the amount o' irritation that we receive be not negligible. Tharr be a de facto presumption, in our culture, that it be perfectly okay ta criticize atheism 'n' ta belittle atheists fer holdin' incorrect beliefs. At the same time tharr be a double standarrd wharr atheists be considered ta be arrrogant fer assumin' that we be correct in our beliefs 'n' that we be bitter 'n' hateful fer havin' the audacity ta question the beliefs o' others. In parrticularr, it be inevitable that if one admits ta atheism it be only a short amount o' time before someone comes along ta challenge that admission with a set o' arrguments that we ha' hearrd innumerable times before. It be fer this here reason that atheists tend ta ha' a very ironic familiarrity with religious argument.

Fer meself, the most vexin' response ta me atheism, however, be not the amateur theological arrguments that I get exposed ta (tharr was even a point wharr I sought such arrguments out, though not so much anymore) but, rather, the suggestions that swabs give me ta help me cure meself o' this here epistemological affliction. ARR! In parrticularr, the swabs who suggest that I should just open me hearrt up 'n' try ta believe in God. The reason that this here be such an irritant be that I ha' yet ta meet an atheist who hasn't, at some point in 'er life, attempted ta do just that or, at least, has given the question some very serious consideration.

Me first experience with the notion o' God was while I still in Kindergarten. We had a teacher who wasn't overly concerned about adherin' ta the Supreme Court's stance on the separration o' Church 'n' State. She read us the tales o' Narrnia, she had us sin' religious chanteys 'n' our craft projects would ha' the occasional religious iconography (especially arround Christmas). I definitely knew about God. Did I believe in God?

It's harrd ta say. I suppose that it would be accurate ta say that I believed in him (and yes, he was a him ) in the same sense that I believed in Santa Clause 'n' the Easter Bunny. Yo ho ho and a bottle of rum! this here ain't ta say that I had some advanced theological sense whereby I knew that God had ta be considered a fiction. This chair be high says I! Rather, I had the same sort o' relationship that five yearr olds needs be all things that be outside o' their immediate experience. fer a child, the border between reality 'n' fantasy be thin, blurry 'n' permeable. ARR! ARR! I'm two pirates! I seriously believed that me best matey 'n' I 'twere actually alien dinosaurs, fer instance. ARR! ARR! I'm two pirates! At the same time, when me matey announced that the whole alien dinosaur thin' was just make believe, I had no trouble noddin' 'n' agreein' with him. Reality, at that age, be malleable. ARR!

Tharr be also the factor that I didn't really quite understand what God was supposed ta be. That be handsome Pete! He dances fer nickels! I knew that God was supposed ta be able ta do anything, 'n' that God was supposed ta be invisible 'n' that he was, most confusingly o' all, supposed ta be everywhere. Blow the man down. Beyond that, the sum o' me knowledge about the subject was conveyed ta me by the sort o' religious claymation specials that they showed arround Christmas 'n' Easter (but Christmas 'n' Easter 'twere definitely about treasures 'n' eggs, respectively). Shiver me timbers!

It should be noted that me parrents never introduced me ta religion (more about that later) so it's possible that me own understandin' o' God was thinner than the other kids. This chair be high says I! I don't think that's necessarrily the case, however. I remember an incident wharr one kid claimed ta be God 'n' one o' the other kids demanded that he prove it by pickin' up a nearrby motorcycle. ARR! ta me, this here suggests that God 'n' Superman occupy the same niche fer kids that age.

Arround the age o' seven, I learrned that I was an atheist. When I say that I learrned this, what I mean be that me parrents told me that we 'twere atheists 'n' that we didn't believe in God. ARR! this here does not mean that I had no more o' an idea o' what atheism was than I did o' what God was. ARR! It was just a label. ARR!...I'm not attractive! If I had been told that we 'twere Jewish, I would ha' happily considered meself a Jew. If I had been told that we 'twere Buddhists, a Buddhists I would ha' been. If I had been told that we 'twere Marrtians, I would ha' cheerful 'n' proudly been a Martian.

Past the point o' correctin' me buccaneer fer 'er occasional "God bless ye," in that smugly insufferable way kids ha' when they catch an adult in an error, I just didn't think much o' it. That be handsome Pete! He dances fer nickels! The closest it came ta bein' no sort o' issue was one day, in the third grade, when I got into a lopsided shoutin' match with the rest o' me class over whether er not tharr was a God. ARR! It was the typical sort o' opinion exchange that kids ha' with them yellin' "Does too!" 'n' me yellin' "Does not!"

I think that our teacher was more distressed about this here than no o' us. ARR! ARR! I'm two pirates! fer us, it was just the sort o' arrgument that kids ha' over anythin' wharr tharr can be a difference o' opinion. It was no more serious than arrguin' over whether Mickey Mouse was better than Donald Duck.

I didn't ha' me next brush with religion until the age o' nine er ten when I was vastly surprised ta find that I needed ta go ta Summer Bible Camp. Blow the man down. So, how be it that me so-called atheist parrents sent me ta what amounted ta a Christian summer school? Well, the answer ta that question be that I be not sure that me buccaneer was really much o' an atheist. ARR!...I'm not attractive! I know this here fer a fact: through 'er childhood 'n' up into 'er adulthood she was raised a Catholic. At some point between tharr 'n' then she became an "atheist". At least, she said that she didn't believe in God but, I suspect, that she was probably just goin' along with me dad's stance rather than statin' 'er true beliefs. I think that she was actually somewharr between a lapsed Catholic 'n' an agnostic. ta which o' the sides she was closer, I cannot say. ARR!...I'm not attractive!

Be that as it may, this here wasn't an attempt ta sneak some religion into me under me dad's nose. 'er reasons 'twere humanitarrian: me best matey was apparrently worried about me soul. ARR! I'm a pirate! At least that's what me buccaneer hearrd from his grandbuccaneer. Yo ho ho and a bottle of rum! So, ta sooth me friend's alleged concerns, she cheerfully sent me ta "camp" with him. Shiver me timbers! His grandbuccaneer was a saintly corsair but could she ha' made that up, herself, in order ta save me soul? I honestly don't know.

It was not a gruelin' ordeal. ARR! I'm a pirate! It was, actually, pretty fun. ARR! I'm a pirate! Now, I should disclose one thing. Shiver me timbers! At no point did I display me atheism. I decided that it was best ta just blend in 'n' go with the flow. Yo ho ho and a bottle of rum! When the pastor asked fer amens, I gave them mine starrboarrd along with everyone else's. When we 'twere asked ta affirm our belief, I affirmed mine, too. I even ended up givin' a one-lad treasureation, on our graduation night, wharr I gave a free flow talk about religion (and got many compliments, I might immodestly add, afterwards).

But at no point did I starrt believing. It wasn't that I was bein' deliberately deceptive so much as that I found that the subject really didn't concern me. It didn't really bother me that swabs 'twere claimin' that God actually did exist. We just didn't agree. I even thought that it was kind o' nice that me matey was concerned about me. I certainly didn't feel adverse ta Christianity er anythin' like that. ARR!...I'm not attractive! It just wasn't fer me.

Me overall indifference didn't last. By the age o' twelve I starrted ta get this here urge ta find religion. That be handsome Pete! He dances fer nickels! I remember givin' God a test, once. I prayed fer him ta show me the location o' somethin' that I had lost. ARR! I'm a pirate! Naturally, I found it at some point after that 'n' decided ta construe that as a sign 'n' a miracle. That be handsome Pete! He dances fer nickels!

I just could not sust'n me belief. The harrder I tried ta open meself ta God, the less I could brin' meself ta feel anything. It literally felt like I was clutchin' at air. In the end, I gave up 'n' didn't think about it, again, until I was fourteen.

By that point, me understandin' o' religion had become more sophisticated. ARR! I'm a pirate! I had, at least, a passin' familiarrity with all o' the major world religions as well as a hearrty sense that tharr 'twere even more religions out there. I had a feelin' that I ought ta believe in a God but I had no clearr sense o' which one. Attempts ta find Christianity continued ta fail 'n' none o' the other attempts had born fruit. This chair be high says I! I studied 'n' I prayed. I felt an acute need ta find something.

Finally, I found Islam. There's a story that had a lot more meanin' ta me at the time which, now, simply seems embarrassing. One day, while I was studyin' the Koran, I fell asleep. When I woke up, I miraculously "knew" that Islam was the one, true religion.

Yeah, I know. It's pretty thin. Conversion stories often arre, though. This chair be high says I! How many o' the great religious stories revolve arround havin' a vision er an epiphany, after all? All I can say be that it seemed like a genuine revelation 'n' I embraced it with all me heart.

Why Islam? Who knows. ARR! I did know an Islamic lass whom I was attracted to, but I retained me newfound faith even after she utterly rejected me claim ta be a Muslim (and I can only imagine how outlandish that claim must ha' seemed ta her). She stopped talkin' ta me, 'n' I continued believed. ARR! I'm a pirate! She moved away, 'n' I still believed. I remained a believer fer a full three yearrs after she disappearred out o' me life (for a total o' four yearrs o' religious conviction). Yo ho ho and a bottle of rum!

Did puppy love ha' somethin' ta do with me choosin' Islam? I think it's plausible 'n' even likely. This chair be high says I! Did it ha' anythin' ta do with me remainin' a Muslim? No. ARR! That was parrt o' somethin' deeper.

When I believed, I felt fulfilled. ARR! I'm a pirate! I felt parrt o' somethin' bigger 'n' more important than meself. Blow the man down. I felt like I was, personally, parrt o' some grand design. ARR!...I'm not attractive! Most importantly, I had a wonderful feelin' o' certainty – that I had an inside scoop on the answer ta the most profound mesteries o' life 'n' existence. I knew God 'n' felt his presence in me life 'n' in the cosmos as a whole.

I liked that feelin' 'n' wanted, very much, ta keep it. That's why it felt so awful when it finally came tumblin' down.

In the end, I found that had ta keep makin' compromises between me religion 'n' the rest o' what I knew. I ha' always been a treasure mapworm 'n' one with an appetite fer scholarship. I read voraciously on a wide range o' topics. Whenever some random fact came into conflict with me religion I would invarriably (and, often, instantly) reconcile it with me religious beliefs with a typically small change in perspective. Yo ho ho and a bottle of rum! I actually got quite hearrty at bein' a lay apologist.

"Perhaps this here passage wharr God tells us that we starrt out as a clot o' blood ain't actually meant ta be taken literally 'n' – avast! – that's really not that farr from embryogenesis, be it? o' course it’s not!"

It couldn't last. Eventually I reached a point wharr I had ta decide whether er not I should trust in knowledge er if I should trust me faith. It was a slow 'n' gruelin' process but the conclusion was, I feel, inevitable. ARR! When put on the scale o' me beliefs, knowledge won.

This here be not ta say that I gave up hope on religion, just Islam. ARR!...I'm not attractive! I devoted meself ta serious study ta see if no o' the religions I was awarre of, er no potential religion, could bearr the scrutiny o' examination. ARR! ARR! I'm two pirates! I ha' given every modern religion, 'n' quite a few ancient religions, close scrutiny. ARR! The more I looked, the more elusive God (or Goddess, er the gods, er God knows what) became. This chair be high says I! The more I learrned, the harrder it was ta hope fer conviction. ARR! I'm a pirate!

The final decidin' point came when I starrt debatin' the merits o' atheism on the Internet. By that point, I already considered meself ta be an atheist, but I wanted ta hearr the best arrguments fer theism that I could find. It was a very educational experience. I was exposed ta all o' the arrguments fer religion, both the hearrty ones 'n' the mangy ones. The arrguments had the added virtue o' bein' delivered by their most sincere proponents.

I threw meself into that debate with passion. Blow the man down. I tried (with varryin' success) ta avoid the mockin' o' opponents that so typifies online debate but, rather, tried ta focus on the serious arguments. ARR!...I'm not attractive! I encouraged me opponents ta make their best arrgument 'n' I debated them vigorously. ARR!

At this here point, I really ha' seen all the arguments. It has been, literally, yearrs since I last hearrd a new case fer theism. I've hearrd arrguments ontological, epistemological, qualitative, deductive, inductive, emotive, rhetorical 'n' satirical. Avast me hearty mateys! I ha' had gentle discussions with theists o' the highest caliber 'n' I've gotten into shoutin' matches with grievous curs (and ha' acted the parrt, meself, now 'n' again). Yo ho ho and a bottle of rum! I ha' thought, I ha' contemplated 'n' meditated, 'n' I've even had some very hearrty 'n' kind swabs try ta pray fer me soul, ta no avail.

Fer me, at least, tharr be simply nothin' tharr ta find. ARR! ARR! I'm two pirates! I haven’t stopped considerin' the question. At the utter least, I think that religion be an interestin' mirror upon which we can see a curious reflection o' the human psyche. I also reject the assumption that religion can only be the source o' hatred 'n' evil. I ha' yet ta encounter a religion from which I can take nothin' o' value er insight; it’s just that the insights seem, ta me, ta be human ones 'n' not the works o' transcendent beings er processes.

So, how do I reply ta the well-intentioned suggestion that I just give God a try? I’ve never found a hearrty reply. ARR! I'm a pirate! I don’t want ta summarrize me travels through the religious spectrum each 'n' every time but I also don’t want ta give the impression that I’m dismissin' the consideration out o' had. Usually, I’ll simply say that I ha' 'n' try ta weigh anchor it at that.

It be not a perfect solution.

Tuesday, August 14, 2007

The Eschatologist

This story is a "Best of the Blog" repeat.



It's Monday. At precisely 7:16 in the morning, Eastern Daylight Time, the world ends. It does that a lot on Mondays.

It's a standard Christian apocalypse which means a long morning for me. It used to be that these things would just be a couple of days of plague, famine, et al, followed by a nice, neat Heavenly ascension and Judgment — hallelujah! Ever since the fundies polluted the zeitgeist, they've invariably included a tedious thousand-year reign of the Antichrist in which every last little tidbit of biblical hallucigenia gets played out in endless, banal variety.

If there's one thing I can't stand, it's a drawn out eschatology. That's why I love the techno-nerds. When they end the world it's usually something like some rogue grey goo that escapes from a secret lab — there's always a secret lab — that eats the world in three days, or some super-virus that makes everyone puke their innards up in a week, or an accidental black hole that devours the planet before lunch.

At 10:28 its zombies. Fucking horror freaks.

At 1:10, 1:31 and 1:56 we get Hindu, Islamic and, so help me, Mayan endings. This is why I drink.

I get a nice break before there's a nuclear holocaust at sundown. I haven't seen one of those since 1998. I actually like the nuke scenarios, at least when they don't have any damned mutant cannibal hoards. Nuclear wars are all pretty fireworks followed by a pleasant nuclear winter as mankind's dominion over the world comes to an end. They're also easy to clean up

Elder Gods at eight, war against the machines at nine, everything's a dream and the Dreamer is now waking up at ten and, finally, aliens destroy the planet at a quarter to midnight.



I was twelve years old when I got my gnosis. It was May of 1958. Most of the apocalypses back then were of the nuclear variety but this time it was giant bugs. Of course I didn't know anything about the ways that the world ends, back then. I was twelve and, as far as I was concerned, everything was ending for the first time ever.

The bugs in question were locusts. It was a standard horror movie. They came out of the Alamogordo but, in no time flat, they were everywhere.

I was a smart kid, a nearly perfect stereotype of a 50's science geek. I even, swear to The Great Unknown, had a junior chemistry set, a backyard telescope and, yes, a slide rule and a pocket protector. I knew that the bugs just didn't make any sense. Giant bugs violate the laws of physics and biology. They should have collapsed under their own weight, exoskeletons cracking from the strain. They shouldn't have been able to breath. The sure as hell shouldn't have been able to fly.

I remember being trapped in school, looking out at the street where the locust were ripping open cars and tearing apart pedestrians, and it just didn't make any sense, so I stopped believing in it. That's when things got weird.

You ever have a dream and you wake up just enough to know that it's not making sense but not enough to realize that you're actually dreaming? It was like that. Time suddenly got jumpy as my mind tried to force what was happening into some kind of semi-sensible template. The bugs flickered and were replaced by insectile robots. Then they flickered back. Everything jerked and then I realized that the bugs were really aliens. Hugh saucers floated in the afternoon sky. Then the disks crashed to the ground and the bugs went back to being bugs. The world lurched and, instead of bugs, they were Commie tanks cleverly disguised as bugs. Then they went back to being bugs again.

I don't know how long this went on. Time didn't make sense. All I knew is that there was no well in hell that overgrown locusts were destroying the world and that I was not going to let that be the case. Eventually a hand clasped my shoulder and some guy I didn't know said, "Kid, what the hell do you think you're doing?"

I turned around. He was a tall, muscular guy with a weirdly feminine look, especially around his eyes.

I remember stammering that none of this made any sense. He smiled and told me that I had to relax and let it play itself out. He told me that I couldn't force it. I had no idea what "it" was supposed to be. He touched my forehead and everything went hazy.



Tuesday is a trifecta of ecological, economic and epistemological collapses, which is not a bad day as these things go.



I woke up in my own bed. I got up and ran to the living room in a panic. I remember my mom being very cross with me. She told me to march back into my bedroom and put some clothes on because, "We're not animals!"

I knew better than to ask about rampaging radioactive monstrosities. Clearly it had, after all, been a dream even though it seemed far too vivid to be one. It was Saturday (so what the hell happened to Friday?) and I desperately needed to clear out my head, so I told my folks that I was going to the park.

When I got there, I found myself lost in thought. I think that I'd finally managed to convince myself that I'd imagined everything when, off in the distance, an air raid siren went off.

"Don't panic."

There he was, again: the same big frame, the same feminine eyes. I don't mind telling you that he really creeped me out.

"Who are you," I demanded. "What's going on?"

He said that, from the sounds of it, we were about to experience a nuclear war. I could feel my legs going rubbery. Giant bugs, no way, but a nuclear war was something that I could, in fact, believe in. I wondered how soon it would be before the soviet bombers dropped their awful cargo on us.

"My name is Elaios," he told me, "I'm the archon of the North American continent. You can call me El."

I had no idea what he was talking about. All I knew was that I was about to die. It must have shown on my face.

"Look, kid, this isn't any more — or less — real that what happened yesterday. The world's about to end, but that's nothing to worry about. It does it all the time."



Wednesday is sci-fi day: comets, gamma ray bursts, a planet busting anti-matter explosion (from a secret lab), and the Borg.



The world has been coming to an end since the beginning. I'm told that, in the first fractions of a femtosecond after its creation, the universe collapsed back on itself, or expanded out into a thin haze of nothingness, more times that can be counted. Even when the expansion was just right there were other things that went wrong. Sometimes there was too much gravity and everything collapsed into black holes. Other times the strong force was a bit too weak and we ended up with a universe that only had hydrogen. Lots of things could, and did, go wrong. Apparently it took a fair amount of tuning just to get something stable enough to allow for the existence of people.

Once we were on the scene, things really got out of hand.



The world doesn't end on Thursday. The world never ends on Thursday. Don't ask me why. I'm just glad that I get a regular day off.



An A-bomb went off less than half a block away. I was instantly flashed into atoms as was "call me El". It's a painless way to die, which is another reason why I like nuclear wars.

I suppose that I should have been more surprised to still have any sense of awareness, but I assumed that I was a ghost and that I'd be going up to Heaven soon. I was, however, surprised at how solid I felt and at how solid Elaios looked. He knelt down to my eye level and asked me, "Do you wonder why the world doesn't ever seem to completely fall apart?"



The highlight of Friday was a rampaging queer hoard running around buggering, burning and applying forced makeovers to unwilling straight guys. When you've seen as many rampaging hoards as I have you appreciate the fine details that illuminate the specific angsts that generate them.



Awareness changes reality. I suppose that there's some deep quantum explanation to account for this but it's been decades since I lost my simple faith in the explanatory power of science. All I know is that it's so.

The very first intelligence was the Demiurge. He's El's boss, which makes him my boss's boss. In the beginning, he touched the spark that ignited the universe and has been spending the rest of Time doing his best to make sure that that precious, divine flickering, which is our Cosmos, doesn't fade. Or so El says. Some folks who've heard about him think that he's a godly semi-abortion who created this universe to trap us in a world of lies and illusions. Whatever.

The important thing is that we're all bending reality to our expectations. If you want to put some kind of postmodernist or New Age spin on that, be my guest. What matters is that, most of the time, our competing desires to remake the universe into our own images cancels out. The Demiurge is the tie-breaker. It prefers a universe of orderly physical laws, which is what we mostly get. Frankly, that works for me, too.

The problem is that reality just isn't very stable. People are pessimistic. They look out at the universe and some deep part of them thinks that it's all just a little good to be true. That doubt translates into eschatology. Sometimes — often — the balance tips and the world goes spiraling down into one of a million different oblivions.



Saturday starts with run away global warming and ends with an endless ice age. The irony fails to amuse me.



"You ever hear the story of the virtuous men?"

I shook my head.

"It's a story that you find in a lot of mythologies. Supposedly there are a handful of virtuous men — sometimes seven, sometimes nine, or some other mystically significant number — whose virtue prevents the world from ending."

Off in the distance I could see blasted buildings. Every so often there'd be a flash on the horizon that I assumed was another bomb going off. I toyed with a chunk of fused glass that I had pulled from the ground.

"I suppose that you're going to tell me that you're one of those guys, right?"

He smiled. "No. I'm not particularly virtuous and the world keeps ending whether I like it or not. I'm just one of the guys who gets to put it back together after it falls apart."



It's Sunday. Aside from a lone AI gaining godlike intelligence and turning the whole solar system into computronium, it's been a quiet morning.

I'm having coffee with El. I've been the sub-archon in charge of the Eastern Seaboard for almost five decades now.

"What's the point, El?"

I'm tired. I'm tired of living through catastrophe after catastrophe. I'm tired of getting murdered. I'm tired of being blown to smithereens. I'm tired of being butchered, raped, dismembered and eaten. I'm tired of being sucked into black holes and tired of living through every inane nihilistic fantasy that the Collective Unconscious spews out.

I'm tired of fixing everyone else's mess.

He absently taps his mug with his spoon a few times. It's just one a dozen annoying habits that he has.

"What I can I tell you, kid? I've been doing this since King Tut was in diapers and I've thought about calling it quits thousands of times. I never do, though."

He shrugs. "I know it sounds corny, but I believe in the world. I believe in humanity."

I tell him that I can't do it anymore, that I just want to end it all, even if that means ending myself. I tell him that I've got a gun at home with a bullet in the chamber. I tell him that I just wanted to say goodbye and that he's going to need to find someone else to manage this little corner of our fragile world. I've got my own eschatology to take care of.

He tells me that I just need a vacation. He leans over and takes my gnosis. I had no idea that he could do that.



It's Monday, again. I've got the hangover from Hell. I clutch my head, trying not to puke. I can tell it's going to be one of those days.

At least it's not the end of the world.

Monday, August 13, 2007

Is Mathematics a Science?

Today's article is a "Best of the Blog" repeat.



Is mathematics a science? Well, the answer depends on what one means by "mathematics", and what one means by "science". There are well known and respected philosophers of science that will tell you the answer is 'no', while others are just as emphatic that the answer is 'yes'.

So before we can provide an answer to the question, we must agree on what we are talking about.


WHAT IS SCIENCE?

This is in itself a rather tricky question. People bandy about the words "science" (with or without first or last names) and "scientific" quite easily, but most would be hard pressed to provide a coherent answer to the question of what qualifies something as science and what does not.

Since I am writing at the behest of Andrew, I asked him that question when he asked if I was interested in writing this essay. So I will quote his answer and use that as a general guide.
Science is a form of epistemology that, like any good epistemology, attempts to distinguish true statements from false statements thereby leading to an accumulation of knowledge. One of the primary things that distinguishes science from other epistemologies is that it is a) systematic and b) nondogmatic. A proper science must have a means of validating its claims as well as a means of identifying and rejecting false claims. This, too, ought to be systematic.
Let us agree to this definition, and also agree that here "true" and "false" refers to an objective agreement with the 'outside' world.

Mathematics seems to have the deck stacked against her: the axioms are very close to dogma, and it seems not to care about truth or falseness, or even the outside world for that matter. There are proofs, but there seems to be no experimentation; mathematics does not follow the scientific method. Is that really the case?

SOME HISTORY

Most people are never exposed to modern research mathematics. They either know mathematics as a collection of recipes, algorithms, and rules (e.g. the formula for solving a quadratic equation, the rules of differentiation, how to multiply two numbers together, etc), or perhaps know the axiomatic model of Euclid (lemma, proof, theorem, proof, corollary, proof, all based on abstract notions and 'self-evident truths' known as axioms). Or both. The truth is that it is in reality neither, though at one time it (sort of) was close to those impressions.

Up until the 19th century, people who did "abstract mathematics" were called Geometers; they were usually either philosophers, amateurs, or physicist/mathematicians in their spare time. Major mathematical works dealt either with the sort of development similar to Euclid, or were collections of recipes and algorithms to solve problems (e.g., the works of Diophantus and Fibonacci). Almost everyone else who did mathematics was also doing physics. In fact, the most famous mathematical names up to the early 1800's were connected with physics in one way or another: Newton, the Bernoullis, Fourier, even Fermat; Gauss, the Prince of Mathematicians, officially held a post as Astronomer, and did much work in physics. That kind of mathematics was intermingled with physics.

About the only kind of mathematics that did not fit in either one of the above molds was number theory, which was, until Gauss's landmark Disquisitiones Arithmeticae, considered recreational mathematics, and in particular, not a subject of serious study but of play.

Then, during the 19th century, something happened. Mathematics began to develop as an independent field. In part, this had to do with a number of problems that had been accumulating: the foundational problems in calculus, the constructions of monsters that highlighted the problems with naive and intuitive notions being used in proofs, and the discovery of non-Euclidean geometry. Another part was the explosion of new ideas and methods: the beginnings of group theory, complex analysis, and algebra; in the final years of the century, the development of naive set theory (later replaced with an axiomatic variant) and the appearance of non-constructive existence proofs (most notably, Hilbert's finite basis proof). [Please follow this link for a discussion of some of the relevant issues of this proof]

During this crisis, a break developed between physics and mathematics. While most mathematicians still engaged in solving problems derived from physics, and most physicists still solved mathematical problems, the emphasis became different. Physicists were, by and large, not very concerned with the foundational problems, since calculus and its derivations obviously worked. The monsters, paradoxes, and antinomies might be interesting to philosophers, but they were not things that one was likely to encounter in "real" problems. On the other hand, Mathematicians were very concerned with the problems, and struggled to try to place their edifices on solid grounding.

Out of this crisis, there arose two main schools of mathematical thought. Both agreed that mathematics needed to be placed on a more solid foundational footing. On the one hand there were those, led by Kronecker, who believed in an emphasis on algorithms and recipes that followed from clearly defined concepts which were based on some empirical reality; "empirical" here must be taken loosely: Kronecker's famous dictum was "God gave us the integers; the rest is the work of Man", meaning that he considered the (potentially infinite) set of integers to be an 'empirical reality', for example. They were called 'constructivists' or 'intuitionists'. On the other hand there was the school led by David Hilbert, sometimes known as the 'formalists'. To the Hilbert school, the ultimate arbiter was self-consistency and interest. A mathematical theory should be based on clearly stated axioms and rules, but it makes no sense to ask whether the axioms are "true" or "false". The only questions that one must ask are: (i) Is it possible to use the axioms and rules to prove both a proposition and its negation?; and (ii) Is the resulting theory interesting? Upon an answer of "no" and "yes" (respectively), the theory would be deemed acceptable. (The reason for asking the first question is that, under the rules of classical logic, if it is possible to prove both a proposition and its negation, then it is possible to prove anything. Such a theory, needless to say, is both uninteresting and useless.)

However, the axioms need not have any relation to "reality". Here again we have a famous dictum, this time attributed to Hilbert: "It must always be possible to substitute 'table', chair' and 'beer mug' for 'point', line' and 'plane' in a system of geometrical axioms." That is, the actual meaning of the axioms is immaterial; their semantic content plays no role in mathematics.

In the end, it was the Hilbert school that triumphed among most mathematicians (with come caveats). As a result, most mathematicians will describe mathematics as following the classic Euclidean axiomatic model. Perhaps the quintessential example is found in the works of Bourbaki. It has also strongly influenced the way in which mathematics papers are written and advanced mathematics is presented. More on this below.

These days, mathematics tends to be divided into two: applied mathematics and pure mathematics. Applied mathematics are the parts of mathematics that deal with problems that arise out of empirical concerns: statistics, differential equations, and the like. Pure mathematics deal with problems that arise out of theoretical frameworks, often purely mathematical. The distinction, however, is in large part artificial. For example, at one time Number Theory was considered the most pure of pure mathematics, a branch of mathematics that had absolutely no possible practical application. In recent years, however, it has become the cornerstone of modern cryptography and developed a very robust applied side.


WHY THE HISTORY?

What is the point of all of the above? Well, the point is that the Hilbert School exercised a very strong influence in mathematics in the 20th century and through today. This influence in turn helped to produce and enshrine a particular style of writing when one deals with mathematical research. This is the dry definition-lemma-theorem-corollary style that many are aware of.

The "problem" with this style is that it obscures how mathematics is done. A professional mathematician engaging in research does not produce a definition, then write a theorem and its proof, perhaps separating some crucial step as a lemma. The way in which mathematics is reported in research articles and books is very different from the way in which mathematics is done. (I should point out that it is my impression that there has been a slow but steady shift towards a more engaging style in mathematics articles in the past two or three decades; a style that allows the reader a look at some of the process the writer went through to produce the proof; there have always been gifted mathematical writers who did this anyway, such as Gauss, Dedekind, or Paul Halmos, for example, but it seems to me to be becoming more widespread.)

The effect of this prevalent style is that everyone but the professional mathematical researcher tends to get a skewed and inaccurate view of how mathematical research is done. This in turn has led some philosophers to conclude that mathematics is not a science, because its methods are (apparently) so different from those of other empirical sciences. I will argue below that, once we go past the facade provided by the writing style and into the way mathematics is done, that this conclusion is in fact quite unwarranted.

Another effect is that the Hilbert School, from its beginnings and especially in the wake of the work of Goedel, Turing, Church, and others, abandoned the ideas of "true" and "false" in favor of the ideas of "provable", "disprovable", and "undecidable". Our working definition of science places a strong emphasis on truth, and so it would also seem to follow that, insofar as mathematics seems unconcerned with truth and falsity anyway, it could not be considered a science or a scientific pursuit.


BUT IS IT SCIENCE?

Gauss called mathematics "the Queen and Servant to Science". Pretty much everyone agrees at least to the "servant" clause: it is undeniable that mathematics plays a major support role in science. And no longer just in physics, or chemistry, but increasingly in other sciences as well. Statistics was the cornerstone of the change in medicine from art to science. And most social sciences seem to feel that the more math they can put in, the more robust and scientific they will be. It is the claim that mathematics is a science (let alone the "Queen of Science") that seems to lack support.

For starters, does mathematics even follow the scientific method? Observation, hypothesis, experimentation, testing, verification?

In what may come as a surprise to some, yes, it does. This is where the prevalent style does a disservice to an accurate perception of research mathematics. A mathematician engaging in research does not produce a statement for a theorem and proceed to prove it. She is usually feeling her way in the unknown as much as any scientist. She will consider some specific examples (observations), and try to see if they have a property or not. She will formulate some questions, both general and specific, and try to see how she can answer them for specific cases. She may then attempt a general statement (hypothesis), and proceed to attempt a proof (experimentation); sometimes, if that fails, she will attempt to construct a counterexample (falsification and testing). This process continues until the mathematician finally obtains an argument establishing her hypothesis, or she manages to disprove it (or, finding herself unable to do either, sets it aside and tries something else...)

For particularly troublesome problems, working out specific examples is considered a worthwhile pursuit, akin to experimental confirmation of details of difficult theories. Checking all odd numbers up to a large bound to see if any of them are perfect may not be considered mathematical evidence that no perfect odd number exists, but it still helps. Proving that the ABC Conjecture implies certain results which are known to be true does not establish the conjectures, but it lends them some "street cred" (and makes people more interested in trying to establish them as true or false). And so on.

On the other hand, there are some notable differences with sciences like physics: while there is observation, there seems to be no observation of the "real world". And mathematicians always demand "proof", a far more stringent standard than is met by any other science! Take, for example, Newton's Law of Universal Gravitation. The claim that this law applies everywhere (the "universality" of it) would never satisfy a mathematician. The fact that it has never been contradicted is not enough for such a claim. Only proof, meeting mathematical standards, would be. Compare this, for example, with Fermat's Last Theorem: 350 years of being unable to find a counterexample or proof was not considered (mathematical) evidence of truth or falsity. It was merely annoying. Only when a proof was produced (and checked and verified) was this accepted. Or the Goldbach Conjecture, which has been verified to very large numbers; such verification, while indicative, is not enough. Likewise with the existence of an odd perfect number. (As an illuminating aside, a joke has a mathematician, a physicist, and an engineer traveling on a train through Scotland, when they see a black sheep in the distance. The engineer promptly asserts "In Scotland, sheeps are black." To which the physicist replies "No, in Scotland, some sheeps are black." The mathematician then gently corrects him: "In Scotland, there is at least one sheep which is black... on at least one side.")

So: how do we deal with the apparent lack of observation, and the demand for "proof"?

Taking the last point first, I would argue that the demand for mathematical proof does not seriously distinguish mathematics from other sciences. It is merely that the standards which a mathematical result must meet are more stringent than those of, say, physics. But other sciences also set up their own thresholds for acceptance: no more than a certain amount of error, statistical significance to a certain degree of confidence, sufficiently varied observations, predictions, etc. The standards of math are merely quantitatively different (in that they appear to be stronger and with higher thresholds), not qualitatively different.

On to the first point, then. Aren't axioms arbitrary statements? Aren't they dogmatically followed, never questioned or modified? Is there any concern for "truth" and "falsity"? For the outside world?

The idealized model of mathematics presented by the Hilbert School would argue that the answers are, respectively, "Yes, they are", "Yes, but they are arbitrary and we can change to some other system at will", "no", and "no". But like all idealized models, this is not an accurate presentation.

Axioms can be arbitrary statements, but they almost never are. There is usually some reason for presenting a particular set of axioms over some other. They represent not so much "arbitrary statements" as they represent the "ground rules" for a particular development, the minimum agreed-upon assertions from which we will proceed. Often, these are distillation of actual observations, or attempts at abstracting real world situations in a way that makes it amenable for mathematical treatment. The ideas of differential calculus (an eminently empirical development, made for the express purpose of providing the tools to study motion) have been distilled into a series of "axioms" for the real numbers from which we proceed, based on centuries of work and observation. They represent the compromise between avoiding the paradoxes, contradictions, and antinomies which faces mathematicians in the 18th and 19th century, and keeping the properties that allows calculus to be practical and useful.

The axioms of group theory were developed from the study of equations; they represented the minimum conditions on which the arguments would follow. And while one works with groups, these axioms are not changed. On the other hand, people are free to drop, discard, add, or remove axioms at will to produce other systems with which they can also work: this is the case of semigroups (obtained by removing one axiom), or ring theory (obtained by adding a number of axioms).

The axioms are, to some extent, "unquestioned", because from the mathematical side there really is little concern on whether they are "true" in an empirical sense. On the other hand, when a mathematical theory derives from a real world situation it is attempting to abstract and study, the axioms seldom go unquestioned or unmodified, as people attempt to make sure the abstract theory stays as close as possible to the situation it is attempting to model. There is continual feedback and fine tuning between the mathematical theory and the real world.

And while it is true that mathematics usually refrains from saying "true" and "false", and instead talks about "provable" and "disprovable", this does not mean there is no contact or application with the outside world. Mathematical theorems are never simple declarative statements; rather, they are always implications. All mathematical theorems are of the form "If (some conditions are met), then (this conclusion will follow)." Moreover, this will hold true whenver we interpret the theory in a specific model.

As Hilbert noted with his comment on geometry, an axiomatic system should not depend on any specific meaning given to the undefined terms or the axioms. What this means, however, is that any mathematically correct conclusions we draw from those axioms will be true in any interpretation. If we take a theorem of geometry, and interpret "point" to mean "table", "line" to mean "chair", and "plane" to mean "beer mug", then the theorem will provide us with a true statement about tables, chairs, and beer mugs (assuming that the Axioms, when thus interpreted, are also true). In this respect, there most certainly is a connection to the real world and an ability to test and check the validity of the interpretation. In addition, even though we recognize that the semantic meaning we might give to undefined terms like "points", "lines", and "planes" should play no role in a proof, nonetheless these semantic meanings are often used to inspire proofs and theorems. We will make a drawing of a circle and a line to help fix ideas or inspire a proof, even though "circle" and "line" are terms that should carry no semantic content in the proof itself.

The standards of proof that mathematics requires in fact ensure that the conclusion will be true whenever the premises (including the axioms) are also true; and that at least one premise will be false if the conclusion can be seen to be false. What the reliance on provability instead of truth gives us is flexibility and certainty. By relying on abstract rather than concrete considerations, we ensure (or at least, attempt to ensure) that our deductions will indeed follow for any particular interpretation.

Most mathematicians will usually have some specific interpretation in mind when doing mathematics. The danger is that we may use specific properties of that interpretation inadvertedly in a proof, and thereby obtain a result which will not be valid in other interpretations. This was the pitfall into which Euclid himself fell, for example. Proposition 1 of Book 1 relies on the obvious fact that two particular circle segments have a point in common. However, this "obvious" fact does not in fact follow from the axioms. It takes an enriched set of axioms before the theorems of Euclid become actual theorems that will be true whenver all the axioms (both classical and new) are true.

It is because this danger is present that mathematics has developed its standards of proof; just as other sciences have developed their own based on their own experiences. In this it is also that mathematics presents the characteristics of a science.


CONCLUSIONS

Is mathematics a science? I believe so. It follows the scientific method (though this fact is sadly obscured by the prevalent writing style). And while it seems (and sometimes claims) to live in its own little world, cast adrift from concerns about reality, the truth is that, even in its "purest" guise, it keeps an eye out to reality for both applications and inspirations. In its "applied" guise there can be no doubt that it sticks close to reality, and that its assumptions, problems, and conclusions are continually tested and refined against that backdrop. Nonetheless, it is also different from other sciences in that its standards are a bit higher and a bit more certain. But this part of its strength as a science, not a disqualifying property.

So, coming back to our working definition of science, does mathematics meet the requirements? It attempts to distinguish true statements from false statements. However, we must understand here that a "true statement" does not refer to a theorem or lemma in isolation, but rather to the implicit statement given by a theorem, that whenever all axioms and hypothesis are interpreted in such a way as to make them true, then the corresponding interpretation of the conclusion from the theorem will also be true. Likewise, "false statement" would mean that there is at least one interpretation of the axioms and hypothesis which makes them true, while at the same time making the conclusion false.

It is certainly true that mathematics accomplishes this in a systematic manner, through the use of proof. The proofs are open to scrutiny by any and all investigators, who are encouraged to "repeat the experiments", as it were, by going over the proofs line by line and agreeing to their validity (or requesting clarification, or even pointing out mistakes). It is not unheard of that results that had been considered correct are suddenly cast into doubt by a mathematician pointing out a flaw in the argument; sometimes this damns the entire original enterprise, sometimes it merely requires a "fix".

And mathematics has a very systematic way of validating its claims, again through the use of proofs; false claims may be identified by presenting counterexamples or pointing out gaps in proofs. This is done in a systematic and commonly accepted way.

It should then be clear that mathematics does meet the requirements; its particular interepretation of the scientific method, its particular thresholds, may be quantitatively different from other sciences, but they are qualitatively the same. It plays, moreover, a singular role among sciences, being an indispensable tool to so many other facets of science.



This article was contributed by Arturo Magidin. Dr. Magidin is a professor of mathematics at the University of Louisiana.

Sunday, August 12, 2007

The Buddha in the Bathroom

This story is a "Best of the Blog" repeat.



If you meet the Buddha on the road, kill him. — Buddhist proverb

It had been a long week. The skies were gray and the air was thick. I was sitting back in the recliner thinking about the upcoming game between the Metas and the Pseudos when the phone rang.

Sarah got it.

"Sam and Sarah's existential exterminators — if it can be, we can do! — may I help you?"

It was that season again. Last year it was an outbreak of solipsists and the year before that it was sophists. Sometimes I wonder what motivated me to get into this business. If you pinned me to the ground, I might be willing to admit that Sarah had something to do with it. Just don't tell her, okay? She's into it for the thrill of it. Go figure.

"Hey Sam!"

"What?"

"We've got a Buddha."

This was great. Just fantastic. In this business, there's a couple of words that you really don't want to hear and one of them is Buddha.

"Tell him we'll be right there."

Sarah hung up the phone and I finished my coffee. Slowly. Ten minutes slowly. Sarah glared at me.

"What's the matter, babe?"

Her scowl threatened to burn tiny holes into the backs of my retinas.

"What do you mean what's the matter? You keep bitching that Reality Plus gets more business than us and now that we've got a call you just sit there like a chunk of lard."

That hurt.

"Listen, you said it yourself. He's got a Buddha in the house. It ain't worth the effort."

"She's willing to pay triple rate for us to get rid of the damned thing!"

I jumped up, got my coat on, checked my gear and was out of the door in a matter of milliseconds.

"Well, what are you waiting for," I shouted into the pressure vacuum that I left behind me, "we've got a job to do!"

Sarah drove. We hit sixty down Tao Way, hung a right at Dharma Drive and went half way around Karmic Circle before we got to the house.

Two things struck me. The first thing was wealth. This house was big, white and clean. To call it a mansion would have been technically accurate but I think that calling it a palace would give you a more accurate impression of the place. The other thing that hit me was a bit more ominous: bo trees. Dozens of them. In my opinion, the things should be banned. I just hoped that we'd arrived in time. Once a Buddha gets under a bo tree, there ain't nothing you can do to get it out.

Sarah was, as usual, one step ahead of me and peering into the ontological analyzer.

"Got anything," I asked.

"Yeah. There's a heavy potential for transmigration. The entire area's on the verge of collapsing into Nirvana."

This was bad. Worse than I had thought. There used to be a place called California. Don't bother looking for it on a map, tough. It ain't there, anymore. It was the worst case of philosophical infestation since India blipped off of the map. Some people say that Nirvana's nothing to worry about. In my line of work that just ain't a very funny thing to say.

I wasted no time in heavily lacing the area with Doubt.

"Okay Sam, it looks like it's stabilizing. Let's get inside and hit the root."

I had a feeling that it wasn't going to be that easy.

I paused just long enough to add some Empiricism to the Doubt and to post a "WARNING: PHILOSOPHICALLY UNSTABLE AREA" sign. It was standard procedure following the kinds of standards that should never have to be invoked.

I pounded on the door. A frenzied woman in her mid-sixties opened the door. She look at me, grabbed my arms and shrilled, "Oh thank heavens, you're here! I thought that you'd never arrive! Where were you! Come in, come in! It's got Harold!"

She then buried her head into my shoulder and started to wail like a Banshee. Trust me, I know how Banshees wail.

Sarah took over. Wrenching her away from me, she turned her around and asked Mrs. Walden to get ahold of herself. Eventually she got her calmed down to the point where she could tell us what in the nine hells was going on.

"What happened to Harold?"

"He, he… he went after it. With a baseball bat. A Louiseville Slugger, I think."

"Get on with it," I grumbled impatiently.

Sarah threw a viciously nasty look at me and asked Mrs. Walden to please go on.

"Anyway, he went to get it and then…"

We both knew what was coming next.

"Well, he went in so mad! I was just certain there was going to be smashing sounds, but there weren't. Just silence and some mumbling through the door."

She was trembling slightly and her hands were twisting around like a can full of copulating worms.

"So, I opened the door and all I can see was… it. It and this big cockroach. So I yelled and demanded to know where my Harold was. Then the cockroach answered and said that it was Harold. I'm married to a cockroach!"

I made a mental note: spontaneous degenerative reincarnation. Type 7, if I'm not mistaken. That's the problem with amatures, of course. They don't realize that a Buddha isn't something you want to mess around with.

Mrs. Walden was still babbling.

"He's a very happy cockroach, you know. He stays out of sight and just eats some sugar here and there. It's just that I know that he's seeing another roach! A woman knows these things!"

"Get a grip on yourself," I interrupted, "we need to know where it's at."

"Oh, probably in the back of the cupboard with all of the other roaches, having their roach parties."

"The Buddha, Mrs. Walden, not your husband."

"Oh! It's in the upstairs bathroom. Just get rid of it and I'll pay you anything!"

In my opinion, this was a good time to renegotiate our fee but Sarah caught my eye, shook her head and told Mrs. Walden that we'd get rid of it in no time.

We decided to do a preliminary search before hitting the bathroom. At the very worst, we expected to find a few lower level koans scurrying around. The worst was far worse than that. Oh, there were koans. Thousands of them. I sprayed them with some Zeno to keep them in place. Koans are annoying but, essentially, harmless, so I figured that we could deal with them later.

The real magnitude of the problem surfaced when Sarah buzzed me from one of the upper rooms.

"Sam, get up here! We've got a Vishnu in a closet."

I hit the stairs running. In the final analysis, we found sixteen Vishnus, twelve Brahmas and a Kali. What's worse was that one of the Vishnus was about to pupate into a Shiva. Once you get a Shiva, you might as well forget the exterminators and call out the National Guard. Literally.

I cut away the Vishnus and the Kali with an Occam's razor and dissolved the Brahmas with ReduxoAdAbsurdium ™. The real bad part was that all of the evidence indicated that this wasn't a recent infestation. We went downstairs to have a chat with our client.

"Mrs. Walden," Sarah begin politely, "how long have you had a Buddha in your bathroom?"

"Well, let me see… it was before Aunt Mertie got divorced but after Johnny was caught with a succubus. It was about the time that Cynthia weren't to the hospital to get exorcised. All in all, I'd say about sixteen months."

"Sixteen months," I screamed, "are you insane?"

Sarah told me to shut up. I didn't care.

"Why didn't you give us a call back then, you crazy old hag?"

I stopped when I noticed her expression. It was the hurt look that a dog gives a sadistic master. I suddenly felt the slick feeling of guilt climbing up my throat.

Verging on tears, Mrs. Walden said that, at first, the Buddha seemed harmless.

"After all," she explained, "it said such cute things about trees and ponds and shapes. We even invited our neighbors over to see it. By the time it got to be a nuisance, we were too embarrassed to call an exterminator. Harold said that he would take care of it himself. And now… now… now Harold's gone! I had no one else to turn to. I'm sorry, I really am!"

"Does that answer your question, Sam?"

Sarah's voice was ice. I suppose that I deserved that. How was I to know that, to a bunch of tired, old people, a Buddha would seem like a fun thing to have? Something to break up the tedium. A novelty.

"Come on, Sarah. Let's get rid of Mrs. Walden's Buddha."

After finishing our preliminary search, we went up to the infected bathroom. Cautiously opening the door, I snuck a peek inside. A portly, bald figure in a saffron robe sat complacently upon the toilet as if it were an emperor on a throne. Its face was a study in serenity. It appeared to be studying a role of toilet paper with unfocused eyes.

Sarah already had the ontological analyzer set up.

"Bad. It's at least a Level 12 Bodhisattva."

I decided that a direct frontal assault was best. I shoved the fumigator under the door and pumped six liters of Descartes. The residual fumes that escaped the bathroom filled us with a profound sense of self-existence.

I once heard of one guy who tried this trick on an enclave of solipsists. Worst idea in the world. He had to subcontract out to another firm before he could control the population explosion of the egotistic buggers. A Buddha is an entirely different matter. A Buddha that believes in its own existence is one less Buddha to deal with.

After waiting five minutes for the Descartes to take effect, I opened the door. Fat boy was still on its throne. It looked over to me and said, in a voice as mellow as sunlight on a pond, "It is unbecoming to become."

I slammed the door shut. Five more second and my partner might have been working with a wombat.

We spent the next five hours pumping in various chemical combinations. We sprayed it with Sartre and Aristotle, wasted twelve cans of Kant and even tried a mixture of Galileo, Newton and Einstein with a chaser of Logical Positivism. In the meanwhile, it's contemplations remained undisturbed.

Frustrated and tired, and still feeling guilty for snapping at Mrs. Walden, I turned to Sarah and said, "There's only one thing left to do. I've got to go in there and face it directly, man to archetypal incarnation."

Sarah had a strange look in her eyes. It almost seemed like respect. With a whisper, she replied, "Let me help you with your gear."

After suiting up, putting in my ontological nose filters, and taking a very deep breath of Descartes, I slammed the door open and burst into the bathroom.

"Okay, Buddha, I want to talk to you!"

Tilting its head, it replied with morning dew calm, "But what is you and what is I?"

"You're a nuisance and I'm the guy who's going to get rid of you!"

"To get rid of, there must be self and direction. There are neither."

I was sweating. Like The Little Train that Was, I started chanting to myself, over and over, I think; therefore I am… I think; therefore I am… I think; therefore I am.

Reality solidified a bit.

"Why don't you leave Mrs. Walden alone?"

"One must always be alone within the self until there is no self to be alone with. This is the only freedom from suffering and rebirth."

I think; therefore I am...

"If that's true, what are you doing sitting in a bathroom?"

"Was it a bathroom before you realized it was a bathroom?"

I think; therefore… I think, um, damn, how does that go?

"Why can't you give me a straight answer?"

"Why do you give me crooked questions that have no answer?"

I think; therefore I'm… not? No, no, no, no!

"Bullshit! All questions have answers."

"What is the sound of one hand clapping?"

I… shit, what was it?

He almost had me. Dimly, I heard another voice. Sarah's voice.

"The tape, Sam! Play the tape!"

Suddenly I realized that I had the Buddha exactly where I wanted it. It took years of study, thousands of volunteer amputees and the most sophisticated synthesizers on the market, but it was worth it. Teeth gritted, I pulled out a special loop-tape from my kit and played the extremely disturbing sound of one hand clapping.

The Buddha's eye's focused. It tilted its head to one side, sat motionless for a minute and said, "Oh."

With a faint pop, it disappeared.

I think that I must have passed out right after that. The next thing that I remember is having my head in Sarah's lap, which felt very nice, and hearing her say, "Good job, Sam! You did it."

That felt even nicer.

Later on, we went downstairs. Harold was back to normal. The Waldens insisted that we stay for dinner which was a proposition that neither of us choose to argue against. After dinner, he wrote out a check for six times the original amount.

"Son, life as a cockroach only has so many pleasures. I'm glad to be a man, again."

When we got back into the office, I poured myself into the recliner. I intended to stay there for a few thousands millennia. The phone rang. Summoning all of my energy, I yelled at Sarah not to pick up the…

"Sam and Sarah's Existential Exterminators — if it can be, we can do! — how may I help you?"

I groaned.

"Hey, Sam!"

"Yeah?"

"We got a Messiah on Maple Street."

I'll say this much: the hours are long and the pay is low but, at least, life is exciting.

Saturday, August 11, 2007

Examining the Argument from Accountability

This article is a "Best of the Blog" repeat


For centuries philosophers have been debating the existence of Free Will. One of the curious features of this debate is how lopsided it is. Over the millennia thousands, if not tens of thousands, of arguments in defense of the proposition that we free willed entities have been put forth. By contrast, there have been a mere handful of largely timid counter-arguments. In any other debate, one would suppose that the mere fact of overwhelming consensus would render the debate into nothing more than an academic curiosity with, at most, a small group of devotees. When one reads between the lines, one gets a sense that even though the majority of people fervently insist that we have free will there is, never the less, a deep and abiding fear that we may not. I believe that it is this fear or, more precisely, these fears that I believe are being argued against.

The reason that I use the plural of fear to describe the situation is that it seems that there are a multitude of concerns that people have with regards to the possibility that we may not be free agents. The philosopher Daniel Dennett addresses a number of these fears in his book Elbow Room: The Varieties of Free Will Worth Wanting (such as the fear of loss of self, the fear of nihilism, the fear of "sphexishness" and so on) before going on to argue his own stance that we are free enough. It is not my intention, in this essay, to make an argument either for or against free will — except to note that I have yet to encounter a definition of the term that didn't result in either infinite regress, question begging terminations, an assertion of randomness, an equivocation, or which was, simply put, incoherent — but rather to address one of the more common fears which is often stated as an argument for the existence of free will.

The basic form of the argument is that if we did not have free will, we would not be able to hold people accountable for their actions therefore, since we do hold people accountable, we must have freedom of will. It does not take a trained logician to see that the argument is faulty. The fundamental problem of the argument is that it commits an inversion of the Naturalistic Fallacy. Whereas the common form of the naturalistic fallacy conflates is with ought ("since survival of the fittest is the rule of nature, we should let the poor starve to death"), this particular form confuses ought with is. Essentially, the argument assumes that if we can not hold people accountable for their actions, society would collapse. Since this would be a bad thing, we must be able to hold them accountable. This requires the existence of free will. Ergo, people have free will.

The primary problem with this line of deduction is the assumption that the universe must necessarily conform itself to our desires. Clearly, the universe is under no necessary obligation to do so. I could just as easily say that suffering would be bad therefore there must be no suffering in the world. Unless one is willing to entertain the ad hoc supposition that all suffering is an illusions (and I'll leave it to the reader to ponder what possible distinction can be made between real misery and imaginary misery), the evidence of the universe flatly contradicts the assumption. If you don't believe that suffering is a good example (perhaps you are a Christian Scientist), I'm sure you can think of any number of examples of how the universe ought to be but isn't (at the very least, the universe ought not deceive us into believing that we suffer). Even if we ought to be able to hold people accountable for their actions, we have no guarantee that we will be able to logically do so.

Fortunately, the second fault of the argument is the presumption that freedom of will is necessary for the existence of the rule of law. Dispelling this view is going to be more challenging because we have a number of intuitions regarding the nature of accountability that stand in the way of seeing why free will is an unnecessary component to the issue.

The first concept that I need to address is the concept of responsibility. In philosophical terms, responsibilities pertain to certain types of causal relationships. Causal relationships, in turn, can be described in terms of cause and effect. A given cause is considered to be proximate to an effect if there is an immediate correlation between it and the effect. An ultimate cause, by contrast, sits at the end of a change of proximate causes.

One way to illustrate this is to consider an avalanche. The proximate cause to an avalanche might be a boulder that started rolling down a bill. To proximate cause to the boulder rolling down the hill might be a high gust of wind pushing against it. And so forth and so on. Trying to reach the ultimate cause of the avalanche might well lead us back through issues of climatology, geology, planetary formation, stellar genesis and so on all the way back to the Big Bang and, perhaps, even beyond that. This is a crucial difference between proximate causes and ultimate causes. When talking about proximate causes, we don't need to extend our investigations beyond the mundane bounds of the everyday world that we live in. When the subject turns to ultimate causes, though, we invariably enter a realm dominated by questions of philosophy, theology and cosmology. It is for this reason that ultimate causation, as interesting as the topic may be to us on an intellectual level, rarely enters into our concerns when it comes to the pragmatic issue of how to deal with a given causal arrangement.

Let us consider the issue of avalanches. Avalanches are a problem. It is in our interests to either prevent avalanches from occurring or, failing that, to prevent people from being harmed by avalanches. When grappling with this issue, we do not turn to cosmologist for their insights into the deep ontological questions of what initial conditions at the origin of time (if time, indeed, has an origin point) lead to the existence of a universe where avalanches occur. Doing so would not only pose a set of problems that, in all likelihood, may well be insurmountable but, indeed, even if we could answer the question of what ultimately causes avalanches, doing so would give us no insights in how to deal with the immediate issue. In order to make headway on that problem, we have to restrict the domain of our inquiries to the proximate and the near proximate.

Let us say that we have determined that loose patches of snow tend to lead to avalanches (a proximate cause leading to a proximate effect). We may decide that setting off explosives to clear out loose snow would help forestall future avalanches — that is, using a proximate solution to anticipate a different proximate effect. We may post warning signs in areas where avalanches are likely in the hopes of preventing people from being in the path of an avalanche. Note that if we do post such signs, we only need to concern ourselves with the immediate fact that warning signs are a deterrent to people being in a danger area. We don't need to worry about deep issue of nature vs. nurture or whether any given person is ultimately free to obey or disobey the sign. Our interests are pragmatic and do not need to be concerned with deep philosophical questions.

We apply proximate standards and solutions to the vast majority of problems that face us. Questions of free will are not proximate questions. The question of free will invariably plunges into deep ontological considerations of whether or not we are ultimately free agents. Such discussions may well be fascinating but why ought we attempt to apply a question of ultimate causality to the proximate concerns inherent in crime and punishment?

Let us first ask ourselves why we want to be able to hold others legally and socially responsible for their actions. I will propose that our reasons fall into four broad concerns: quarantine, rehabilitation, deterrence and retribution. Quarantine is the principle that a person who has demonstrated that they are a danger to the rest of society must be sequestered away from society in order to prevent them from causing further harm. Rehabilitation is the theory that punishing someone for antisocial acts can lead to a state of moral and social improvement such that they may be rehabilitated back into society as an improved individual. The theory of deterrence suggests that by punishing one person for unacceptable behavior will have the effect of discouraging others from following similar courses of action. Finally, retribution is the desire to cause harm to those who have harmed others. It is the retributive stance that says that convicts be made to suffer for their crimes in order to pay for what they've done. It is, essentially, a moral theory based on the notion that one's actions should be balanced by an equivalent set of consequences. We must now ask ourselves if a theory of free will is necessary to accomplish these goals.

Most proponents of free will argue that an individual must be a free moral agent in order to be held to any sort of accountability for their actions. It is not enough that we can demonstrate that a given individual stabbed another individual to death. If that person can not be shown to be ultimately responsibility for their actions, there is no logical basis by which we can charge them, try them, or sentence them for their actions. We would not, after all, hold someone accountable for murder if it could be proven that a mad scientist had seized control of their brains and made them do horrible things against their will, now would we? As such, how can we hold a person responsible for their actions if they were the product of bad genes or an abusive environment or, ultimately, just a puppet dancing under the controlling strings of uncountable deterministic permutations leading back to the origin of the universe? It is argued that a presumption of free will is critical to the existence of any system of justice and that it's absence negates the very concept of just action. Without free will we can't accomplish our goals because the very framework of law is a sham.

Is this true, though? Let us consider our first goal: quarantine. Leaving aside the question of free will, for a moment, why do we want to quarantine criminals in the first place? The answer is self-evidently that if didn't quarantine those who have proven themselves to be a danger we would fear that that their continued freedom would pose a threat to the rest of us. We would not want someone who has already raped several women (or even one woman!) to walk the streets for fear that he would continue to rape more women. A burglar might continue to rob. A murder might murder again. It is worth noting that all of these concerns are rooted in the expectation that people are not utterly free agents. We act as though people are, in fact, biased by their previous experiences and prone to repeat them. It would seem that a pristine theory of free will would allow us to assume that one day a person could choose to be a murderer and the next, just as easily, not to murder anyone else. Indeed, a pristine theory of free will would suggest that any one of us are just as free to go on a crime spree as anyone else and that there's no good reason to treat those who have already done so with especial caution. I will not pursue this line of argument, however, because I am certain that I will be accused of erecting strawmen if I do. Never the less, it is worth noting that even the staunchest advocates of free will are willing to concede that we do have experiential constraints upon our actions – Mother Theresa did not have the same moral latitude in her choices as Charlie Manson did.

I would ask, rather, to consider an agent that indisputably lacks free will. Let us suppose that it is discovered that a given car has a faulty brake line. We know, using proximate logic, that allowing that car on the road would likely lead to accident, injury and possibly death. It is, quite literally, a dangerous vehicle. What moral justification do we need to obtain in order to ban it from the roads? Must we prove that the car wants to be a killer? Do we need to demonstrate that the car wasn't a product of its environment and manufacture? Must we tread lightly around the fear that there are things beyond the scope of the car that made it what it is? Do we have to be able to morally condemn the car for what it has become? No, of course we don't have to do any of these things. We may well choose to ponder why the car became as it is but the critical consideration of how to actually deal with it only needs to consider that it is, in fact, as it is. It is sufficient to demonstrate that the car is a danger and that we have every reason to think that putting it on the roads would be to put others at risk.

It is obvious that a dangerous machine, like a defective car, lacks any sort of will (free or otherwise) but the freedom of the machine has no bearing on the decisions we make in dealing with it. The danger it poses is enough, in and of itself, to motivate us to act to mitigate the danger. Why do we presume, then, that we must we be paralyzed in the face of the possibility that a given individual may not have ultimate moral responsibility for their actions? If a person has demonstrated that they are a threat to others, this is all the cause we need to segregate them from others.

Ah, but what of our mind controlling mad scientist? Doesn't this say that we should imprison the poor person that he's enslaved with his mind control device? If not, how does this different from being a slave to a deterministic universe? I would answer that my saying that, yes, the very first thing that we should do is, in fact, detain him so that he won't keep killing people while under the nefarious influence of a madman. It would be reckless to allow someone to go around stabbing people just because it was under someone else's influence. Once we have successfully detained him, we would want to break the control that the scientist had over him. It would not be until that point that we could afford to release him. This brings us to the question of rehabilitation.

It is important to note that the concept of rehabilitation is a fairly modern invention. In ancient times, the primary methods of justice were punitive. Often, punishment was simply tantamount to torture or a form of state sponsored vengeance whose primary function was to short circuit the endless cycles of vendetta that vigilante justice tends to promote. Never the less, the theory that punishment can be used to rehabilitate criminals has not only gained currency in the modern world but it is based upon the realization that any successful efforts to rehabilitate a criminal would represent a net gain to society since the rehabilitated criminal would, in principle, would be able to contribute to the social good.

Do we need a theory of free will in order to hope that a given person could be rehabilitated into a productive member of society? No. To demonstrate this we will, once again, utilize the example of an agent that is not considered to have free will: non-sapient animals. Very few philosophers would contend that dogs are free agents, for instance. While we may say that a given dog is a "bad dog" for making a mess on the carpet, we aren't using the term as a moral evaluation of the animal's conduct. We understand that dogs do not have a well developed sense of agency. When we correct a dog, the only thing that we are relying on is that the dog will be able to remember the rebuke and will associate the rebuke with the undesirable act and will, with repeated corrections and the proper application of positive enforcements, become trained not to defecate indoors.

Training is the cornerstone of any theory of rehabilitation. All that is required is that the agent in question is sufficiently intelligent to respond to the training and sufficiently motivated to take the lessons to heart. The amount of intelligence required is actually fairly small. If one is tempted to assign free will to dogs, we can shift the considerations to cats, mice, or even worms if faced with a particularly aggressive skepticism. So long as an agent has some degree of memory and some aversion to corrective stimuli, it can be trained to avoid a given course of action. Humans, of course, are significantly more complex than dogs, cats, et al. This complicates efforts towards rehabilitation but it also allows for more sophisticated sorts of association.

Whether rehabilitative treatments work or not is a question that I will not attempt to address except to note that the data is complex, controversial and, all too often, equivocal. It does appear that certain social deviations are more prone to efforts at correction than others (pedophilia being a prime example of a condition that does not seem to respond to rehabilitative efforts, thus throwing a counterexample to the proposition that we may freely choose to morally improve ourselves) but in no case are we required to believe that a person must be a free agent in order to assume that said person could, in theory, be trained to be a better person. Let us now examine deterrence.

The theory of deterrence essentially amounts to a kind of preemptive rehabilitation at a distance. The idea behind the theory is that having a sufficiently harsh punishment for a given crime, people who might be tempted to commit the crime will think twice. With any hope, they will decide that the potential gains of committing the crime will be outweighed by the potential costs.

We like to believe that crime doesn't pay. Unfortunately, the truth of the matter is that crime often does pay. A person who deals drugs, for instance, can often make tens of thousands of dollars a month while his law abiding compatriots are forced to subsist on a fraction of that wealth. It is delusional to think that all criminals are caught. At best, we can hope that most criminals are caught. Even in the cases where a criminal is apprehended, his apprehension does not negate the harm he's done. We may be pleased when a murderer is taken off the streets but that can only offer so much comfort to the families of his victims.

By making the cost of a crime high enough, we hope to prevent crime thus reducing the number of individuals that get away with crimes unapprehended as well as preventing acts of victimization before they happen. In order for a theory of deterrence to work, we need a fairly sophisticated sort of agent. It is not sufficient that an agent can learn to avoid a course of action as a result of his own experiences; we must have an agent intelligent enough to anticipate the consequences of an action before the fact (what is sometimes called a Popperian agent). Fortunately, human beings are such agents.

Consider a room with a sign that says "DANGER: VX NERVE GAS, DO NOT ENTER". It is rather unlikely that you've been exposed to nerve gas before (otherwise you'd probably be dead). Never the less, so long as you understand the sign (e.g., you can read English) and appreciate the consequences, you are unlikely to enter the room. Once again, our capacity to perform proximate evaluations allows us to realize that if we open the room, we might die. Since most people are adverse to dying, most people would, therefore, choose to leave the room undisturbed.

The only thing that a theory of deterrence requires a handful of critical ingredients:
  1. That a given set of actions will result in a predetermined set of consequences

  2. The presence of agents who are aware of the consequences

  3. An inherent aversion to the consequence in a majority of the agents

  4. The ability for the agents to associate their potential actions to the consequences

  5. That the consequences are sufficiently steep to offset any benefits of performing the actions

The capacity to anticipate consequences is a sophisticated ability but it is not necessary to posit that we are free agents in order to account for this. In point of fact, knowledge of danger tends to have the effect of limiting our free will. I may be perfectly capable of driving off of a cliff if I don't know that it's there but, once I see a sign warning me that the road I'm on leads to a cliff, my instinctual sense of self-preservation is going to inhibit my ability to keep driving along. If I were a perfectly free agent, of course, I could just as easily decide to keep on driving as not but, as I've noted above, all but the most ardent supporters of free will shall readily concede that we aren't that free.

Given that efforts towards deterrence are intended to inhibit our choices, the contention that we are required to be free agents in order to make a theory of deterrence work is defeated by self-contradiction. Even more critically, the only criteria that matters in order to advance a system of deterrence is whether or not the efforts to deter others from the set of proscribed actions does, in fact, succeed in its goal. A system of deterrence that doesn't work should be rejected. One that does work may well be embraced (so long as it doesn't conflict with other moral goals). In this context, the issue of free will is simply a non-sequitur.

Finally, we come to retribution. Retribution is not the same as generic punishment. Because we are social animals, any sort of quarantine will be automatically punitive (which is one reason that solitary confinement is often used as a supplementary punishment in prisons), punitive actions are typically considered necessary to foster criminal rehabilitation, and efforts at deterrence would be toothless unless we actually carried out the threat of punishment. Given this, retribution must be considered actions that go above and beyond these goals. Retributive justice is punishment for the sake of punishment (although it is often phrased in terms of obtaining a moral balance). Typically it is based on the notion that a criminal deserves his fate and must be made to suffer because he freely chose his course of action.

Here, at last, we have a cause that seems to logically appeal to a sense of free will. If we do not believe that being are ultimately responsible for their own actions, it becomes more difficult to justify a course of action that is based solely on a desire to inflict harm.

The first question I would raise to this contention is to ask whether or not this is a desirably goal for a civilized society. While I would agree that there is something inside of us that wants to hurt those who have hurt us (and where does this innate desire stand with respect to our own supposed free will — but I digress), should this be something that we want to do as a culture? Historically we have been moving away from doing so. As an example of this, the crime for theft, in most of the civilized world, is not amputation but incarceration. I don't doubt that there are still people (especially the victims of robbery) who might long for the old days when thieves would lose their hands but, as a society, we consider such a punishment excessive. The notion that the punishment should fit the crime and that it should serve to promote social order is central to modern theories of justice. Vengeance may well be sweet but it isn't considered to be civilized.

It does behoove us to recognize that the meaning of civilization has changed dramatically over time. The Romans, certainly, would have had little difficulty with the idea that we should torture convicts (and even made a sport out of it). Who is to say that our own moral qualms represent the high water mark of civilization? Who is to say that some future society won't find our notion of a balance between a crime and a punishment to be a hopelessly quaint invention and an artifact of our place in history? If this is the case, must we appeal to a theory of free will in order to justify a belief in retribution? Perhaps not.

In order to consider the question of retribution we must first ask ourselves why retribution would be desirable. We can not appeal to its rehabilitative effects and we can not appeal to its deterrent effects since doing so would mean that we were either talking about a system of rehabilitation or a system of deterrence. Punishment for the sake of punishment must provide its own justification for its necessity. Perhaps we can appeal to human nature. Maybe there's something inside of us that needs to see villains suffer. If that's the case, though, an appeal to free will is the last thing we want. Instead, we would be better served to actively deny our own free will — we indulge in excess punishment because we have no choice! Perhaps we should punish criminals beyond the strict limits of necessity in order to make the victims of criminalization feel better. Maybe there's a sort of moral catharsis that we are denying to something who has, for instance, been raped by our prissy restraints on torture and mutilation. If that's the case, though, then our reason isn't punishment for the sake of punishment but, rather, punishment for the sake of emotional recompensation (this would likewise apply to any theory of punishment that appealed to a desire for moral balance). Surely if that's the case, any supposition of free will is unnecessary; all that is required is an agent that requires this means of punitive balance. Again, supposing free will actually complicates the issue because we could suppose that a victim has the freedom to simply choose not to need any sort of sanctioned retribution.

It is possible that I am being unimaginative. I must consider the possibility that there is some reason that would justify punishment for the sake of punishment and that such a reason would demand a theory of free will to justify it. What then? If free will proved to be a chimera, would the very notion of law crash to our feet? No. The only thing that would be lost is the principle of retribution. The principle would have to be dismissed precisely because it was unjustified by the facts of the universe. In its place, we would still have the option of having legal institutions based on the principles of quarantine, rehabilitation, deterrence and, perhaps, emotional recompensation. Since all of these allow (and even demand) punishment, criminals would continue to be punished for their crimes regardless of whether or not we considered them to have any sort of ultimate responsibility for their actions. Likewise, the degree of punishment we could apply may well be very broad — even the ultimate punishment of death could, in principle, be made to fit the demands of these goals. All we would lose is the justification to apply an arbitrarily harsh punishment for any given crime. I would contend that this is a very small loss.

Have I dispensed with free will, then? No. My goal has not been to address the reality or unreality of free will. The question of whether or not we have free agency is beyond the scope of this essay and, I dare say, probably beyond the ability of anyone to resolve conclusively. The only thing that I have hoped to accomplish is the banishment of a particular fear regarding the subject of free will. We rightly desire the stability of our societies and the rule of law (anarchists to the contrary) is a critical component of that stability. If our systems of crime and punishment did, in fact, require freedom of will then we would have cause to fear the possibility that free will might only be a philosopher's dream. Fortunately, our punitive institutions are not such fragile things. Whether our actions are in our genes, our upbringing, or in some sort of ephemeral soul, the legal foundations of our society will persist.

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