I've seen it claimed that Theists and scientists alike work off Revelation, requiring things to be revealed. Forgive me if I'm leery of sentences that use a word once (especially a Capitalized One), and then essentially (re)define it in a later clause, but I've seen many trains driven through the logical holes created by such sentences.
The revelations (I'll use small 'r' here) that scientists require are of a rather particular and restricted nature which, because of its restrictions, benefits from a relevance not shared by personal, divine, transcendentally introspective, or Theistic Revelation (big 'R'). Big-R Revelation can be privately accessible to only those special few to whom it is Revealed. Big-R Revelation can be contingent on holding certain beliefs, conducting your life in certain ways, or somehow getting yourself into the appropriate relationship with the appropriate supernatural entities. Big-R Revelations can be incorrect (as you say: there can certainly be "false revelations"). There's a lot of things that are able to be big-R Revelations, and the more different things something can be, the less you can say about it.
Small-r revelation... the stuff which scientists depend upon to be revealed in the course of their inquiries... is terribly constrained by comparison. Small-r revelations cannot depend on your beliefs or supernatural relationships. Small-r revelations must be publicly accessible, in the sense that any criteria one must satisfy to observe the revelation are objectively verifiable ("you must have access to a 520nm laser" is ok, "you must be in a truly prayerful state of mind" is not).
There's a lot of things that aren't able to be small-r revelations, which means there's more that can be said about them. In particular, by virtue of their publicness, we can distinguish whether something is a true revelation or a false Revelation (i.e. "Yes, yes, we're sure that it has been Revealed to you that by mixing soap and ballpoint pens with a potato masher, you initiated Cold Fusion. Please forgive us for not funding your research after it turned out your discovery could not be repeated when anyone aside from yourself was able to observe the process.")
In that regard, at least, I agree with the point that "it is not impossible to distinguish between one revelation or the other as being true or false." That only holds for small-r revelations, though... the kind that, yes, scientists work off.
Big-R Revelation, though, the kind that scientists don't use (except in the same manner as daydreams, science fiction, and off-the-wall questions from their occasionally surprising mother-in-law: as inspiration for a direction of inquiry) and which a number of Theistic positions depend upon, does not have the benefit of having a way that one can distinguish between true ones and false ones.
Or, rather, there are Revealed ways to make such distinctions, and naturally those Revealed ways confirm themselves to be true Revelations, but they also are confirmed to be false Revelations by other such Revealed ways. If, contrary to what I suspect you believe, the ways which had been Revealed to you (or those whose authority you submit to) for distinguishing between true and false Revelations were actually false... how would you discern that? How could you discern that?
This also relates to moral relativism or "agreeing-to-disagree". Consider yourself fortunate if you haven't heard anyone say something like "well, there's what's true (Revealed) for me, and what's true (Revealed) for you, and they're not the same thing, so the best we can do is live and let live, and agree to disagree." Statements like that can only be based on big-R Revelations, which can differ from person to person, and without any non-Revealed means for anyone to discern the truth or falsity of a Revelation, you really are stuck treating them all on equal footing.
Well, except for things that have been Revealed to you, of course, because even though those may be false Revelations, it's been Revealed to you that they aren't. And, even though that may have been a false Revelation, it's been Revealed to you that it isn't. And, even though that may have been a false Revelation, it's been Revealed to you that it isn't. And, even though that may have been a false Revelation, it's been Revealed to you that it isn't. And even though it's clear that you never actually can get into the clear with this line of reasoning, most people will stop after finitely many steps and conclude that, yep, their Revelations really are true and are have been adequately confirmed.
Being stuck treating almost all Relevations on equal footing is where one becomes mired in the neighborhood moral relativism, since you're stuck dealing with the situation that, even if not all claims are true, most claims are equally true, and that's a bad place to be in and a hard one to get out of.
But that's the price of giving big-R Revelation a role in arbitrating truth.
Comments to the effect of "one can similarly point to Theists in regards to the truth of an immaterial reality", are not unwelcome comment, because it's a false similarity that runs afoul of the difference between little-r revelation and big-R Revelation.
Scientists, confined to little-r revelation, have a limited ability to disagree. Now, I'm not saying they don't disagree! I wouldn't deny some of the terrible and unfortunate rows in the history of science, nor would I sweep under the rug the incidents where conflicting positions benefited from a dialectic resolution that led to understanding superior to either initial point of view. That said, the publicness and commonality of little-r revelations does put a severe damper on the extent to which honest scientists (be they be Muslim or Infidel) can disagree.
Theists, on the other hand, manage to generate more and more disagreements as time goes on, thanks to their centering on big-R Revelations. Whether it's how the Catholic church isn't orthodox while the Orthodox church isn't catholic and the Mormons are Christians who aren't Christian (depends on which Christian Theists with sufficient training and experience you ask), or it's how the truth of immaterial reality that the sufficiently trained and experienced Hindus have a consensus on fails to match up with the truth of immaterial reality that the sufficiently trained and experienced Jews have a consensus on, it's decidedly not the case that there is consensus among all trained and experienced Theists as to the truth of immaterial realities.
So, mentions of consensus, Theists, and immaterial realness do well to highlight a corollary to my objection to big-R Revelation: while small informed consensus can be useful for approaching truth in the context of little-r revelation, it becomes useless in the context of big-R Revelation. Since, as I said before, searching for truth is important to me both in itself and as a necessary path to discerning "The Good", I'm loathe to see potentially useful truth-seeking tules rendered useless!
Shifting gears.
In bringing up trustworthyness, I admit that irrationality does not prevent someone from holding a true position: there's an... interesting... character in this area who is known for ranting down streets spouting general nonsense punctuated by the occasional exclamation of "...and therefore Lincoln is DEAD!" It's a rather disconcerting tirade but, all other things aside, I can't fault the correctness of his conclusion.
In his public proclamations, at least, the guy is certainly irrational. With the exception of loaning him money (you can't give him money unless you're ready to avoid him henceforth, he WILL remember you and eventually return anything you send his way), it's pretty safe to not consider him trustworthy... at least as far as communication goes. I'm not under the impression that his irrationality or the untrustworthiness of his reasoning are grounds to claim that Lincoln is still alive and well, and that neither age nor gunshot wounds have slowed him down much at all.
All that said, if he exclaimed about one of those American presidents that most Americans never learn about (let's say Wuggie, for example) and you were an American like most, I think you'd be wise to take the position: "I don't know who Wuggie is, whether Wuggie even exists or not, and given existence, whether Wuggie is dead or not... and a proclamation that Wuggie is real and really dead that comes from an irrational and factually untrustworthy person does not serve to persuade me of any such things."
In discussions about atheists accusing Theists of irrationality, it seems that sometimes the concerns is less with how Theists related to what they thought was true, and more with how atheists relate to what theists think is true. As such, while irrationality and untrustworthiness would not preclude a Theist from having randomly stumbled upon the truth, such conditions would preclude other people from taking them seriously. Not knowing whether they've actually got the truth or not, and knowing that a broken clock is more than twenty thousand times more likely to be wrong than to be right, if you're going to leap to any conclusion other than "I don't know", it's wiser to conclude that the irrational person is wrong, rather than right.
Changing gears again.
Stage magic such as sawing lovely assistants in half, which step far outside the constraints that reason imposes on truth, can be properly distinguished from the truth. For those not steeped in Revelations of the truth of ESP, mind-reading tricks can be distinguished from truth as well, despite the senses and intuition continuing to insist that there's not room for other explanations. Hidden-information legerdemain tricks, however, can only be properly distinguished from the truth by A> cracking the trick, or B> running it enough times in a controlled manner to demonstrate that the appropriate statistics are wrong. A> is obstructed by taking advantage of known unreliabilities in perceptions, and B> isn't relevant to this issue. Unless I've accidentally constructed a false dichotomy, this is a setting where, no, you can't properly distinguish the illusion from the truth.
Gear shift.
What is entailed by 'falsifiability'? 'The truth' is, unless you subscribe to irrationality, necessarily not falsifiable. There aren't just certain truths about the world which are not falsifiable: if you think you can find a truth which is falsifiable, I'll show you that what you've got isn't a truth.
No, it's not truths which anyone ought to try to falsify. That's a fool's errand. It's assertions of truth. It's claims of truth. There are certain claims which are not falsifiable. Lots of them, actually. Solipsism's a perennially annoying one. Claims that the world came into existence half a second ago, and everything burst into being in such a way that there appears to be a historical record and memories and, in general, a "past". Assertions that every time someone pats a kitten, four invisible intangible green monkeys who are powerless to interact with anything in any way spring into existence. These are claims about what is true, and they're not falsifiable.
Yes, of course the monkey thing could be true and, if that were the case, you couldn't prove otherwise. That's not the complaint, though. The issue is that we have no way (not even in principle) of knowing whether the monkey-claim is correct or not.
One can certainly say something doesn't have to be falsifiable in order to be true... and that's weaker than could be said. One can even say that something must not be falsifiable in order to be true, since what is true is (to those indulging in rationality) not false. If you want to say that a claim doesn't have to be falsifiable in order for the claim to be correct... yeah, you can have that one too. The negation of the kitten-monkey claim is equally unfalsifiable, and that doesn't mean that such monkeys do spontaneously manifest, any more than the original claim's unfalsifiability means they don't.
The problem is that whenever you have a position which depends on the truth or falseness of the content of a claim, and that claim's correctness with respect to the world cannot, even in principle, be established, then you're saddled with a position whose relevance to the world cannot, even in principle, be established. You can claim it's relevant until the cows come home, but there's no possible way to demonstrate that it actually is, because such a demonstration would serve to confirm or falsify the unfalsifiable claim, and that's not an option (it violates the assumption that the claim is unfalsifiable, and unless you're irrational, that's not a tenable situation.)
In other words, if unfalsifiable claims form part of a foundation, then everything that truly depends on them for support can have no impact on any aspect of the world, in any way, whatsoever. They cannot make anyone's lives better, or make anyone happier, or lead to more peace, or endow every young girl with a kitten that she wouldn't get anyhow, because if they did, those differences would serve to make the unfalsifiable claims falsifiable.
In short: Unfalsifiable claims can't help to justify a set of beliefs, because the truth or falsity of what they assert is necessarily irrelevant.
Showing posts with label essays. Show all posts
Showing posts with label essays. Show all posts
2.27.2008
4.03.2007
Apologia pro apologia
I am, to a limited degree, a Twelve Tribes apologist. I'm not a member, but I'll stand up and offer some defense on their behalf on some issues. This post is intended to clarify my qualifications to do so, make clear ways I'm not qualified to do so, explain my motivations for doing so, and make it clear that I see issues they're not defendable in.
First, an item of 'lack of qualifications'. I'm not a member. I've never been a member. Despite what I'm sure they hope, I'm not going to be a member unless the entire organization changes in some pretty fundamental ways. More on that later. I can't offer the insider perspective of an accepted member, and I'm quite aware that there are things I haven't been told.
Next, some degree of qualifications. My information regarding the Twelve Tribes does not come predominantly from the web (I've read a lot of what's available on the web, and I'll say more about such material soon.) I've spent a large amount of time in a small handful of their locations. I've spent some time at one of their businesses. I've spent some time at one of their houses. I've visited a couple of their other houses and businesses. I've had extensive conversations with a number of men, women, and children. I've had some of them over to my house on a number of occasions. I've attended a few of their regularly scheduled ceremonies, and a couple of the sporadic ones. In short, I have interacted extensively with some members of the Twelve Tribes on a personal level.
Another degree of qualification: Communication is one of my particular fields of study. For anyone with some personal experience of these folks and some reading of what's available on the web (including their own internal publications), there seems to be a vast disconnect between what they say about some subjects and what they actually do. A lot of that (not all, but a lot) is due to the Twelve Tribes as a group having some remarkably bad communication skills in some areas. When I say 'remarkably bad', I mean it the same way I would accuse someone who said "Let's go forth and pillage that village!" when they meant "It's time to harvest the apple crop" as having some remarkably bad communication skills. I have at my disposal some tools and skills which make it easier for me to understand what they mean (despite what they say), and I count this as a qualification.
Time for a disqualification: My ability to translate is limited by my ability to observe what they do as individual people. If there are areas where information is being deliberately held back from me, that'll result in inaccurate translations. Any argument I make has to be qualified with "Assuming what I've seen has been accurately representative". This isn't much of a drawback, though, since the same applies to any source of information, and I do have the advantage of having a more reliable source.
Qualification: I do have first-hand information. Aside being an International House of Porn, the Web is a great source of information, but it's not a great source of reliably reliable information. Any dork with a keyboard can contribute a Wikipedia article, and unless the number of people who really know what they're talking about is larger than the number of people who think they know what they're talking about (but don't), what you're going to see will be, effectively, worthless garbage. Emotionally charged, rabble-rousing, call-to-arms garbage, but garbage nonetheless. If you pick a random topic, and think about how many people really have good, reliable, well-researched information on it, you should come up with a pretty small number. If you look at the same topic and imagine all the schmucks who think they know more than they really do, you should come up with a larger number. Information on the web about the Twelve Tribes -could- be accurate, but most of it is exceedingly unreliable, and much of it is distressingly second-hand.
So, while my first-hand information -may be- deliberately compromised by the agendas of the people in the Twelve Tribes that I interact with, keep in mind that stuff on the web is -probably- compromised by the agendas of the people writing it. Really, I suggest you actually drop your assumptions and biases and try to dig up information for yourself, but that's usually asking too much.
Qualification: I'm not a member, and I'm not going to be a member. I realize this is, in some regards, a disqualification, but it cuts both ways. I'm not subject to their indoctrination, I've got no pressure to keep certain things secret, and I've got reasons for not being a member. I see that they have some real issues, and I'm not interested in ignoring those points. Not in order to join them, and not in order to make them sound better than they are to anyone else. Moreover, my objections are based on a decent amount of first-hand, personal information, not on the shallow knee-jerking that comprises most of what's on the web.
And that leads into my motivations. There are bad things... really bad... about the Twelve Tribes. There are good things... really good... about the Twelve Tribes. I'm aware of some stuff in each of these categories. I would very much like to see them abandon the bad stuff and do something fantastically great with the good stuff, but that requires that they realize the bad stuff is actually bad. So, I'm motivated to affect the situation so they're more likely to be able to see what they're doing wrong.
There's a problem, though. Well, a bunch of them, but the first is this: It's hard to see what you're doing wrong unless someone else you trust can point it out to you. Individually, the Twelve Tribes have got this point figured out and use it heavily, and generally use it well. (That's one of thier good things.) As a group, however, they don't trust anyone but themselves, and so as a group, they're not in a good position to overcome their blind spots and be able to see the things they're collectively doing wrong. So, I'm motivated to affect the situation so they (as a group) might be able to trust some other source to help them identify bad things in themselves.
That raises another problem: There's got to be a trustworthy entity to give trust to, otherwise you're just setting yourself up to get screwed. To a certain degree, you can base trust on the benefit of the doubt, but if you've already observed that someone isn't trustworthy, you'd be an idiot to trust them... and the Twelve Tribes are largely in this situation. They get attacked, over and over, for things they don't believe and things they don't do... largely because the attackers are ignorant of what's actually going on, and too lazy to find out (aside from reading what's available on the web, which I've already lamented.) If I had a drinking problem, but was very good at never injuring anyone (drunk or not) and always paying all my bills (drunk or not), then someone who came up and attacked me on the grounds that I hospitalized folks and never paid my dues would be... something less than credible. I wouldn't be interested in seeking their help with my drinking problem, that's for sure. In a similar manner, the Twelve Tribes are quite justified in not listening to external criticisms, even the few that are relevant, because as a general rule, external criticisms are wildly untrustworthy. So, I'm motivated to affect the situation so that there are some trustworthy outside sources that could help the Twelve Tribes identify bad things in themselves.
And that leads to why I'd be, to a limited degree, a Twelve Tribes apologist. If you'll allow me to indulge in some hyperbole, I'd like to ride forth and vanquish all the criticism, venom, and moral indignation that's born of ignorance and misunderstanding... and I want to do so in order to clear the field for criticism born of good, accurate, trustworthy information. I want to take down people's inappropriate attacks on the Twelve Tribes and divert those energies to appropriate attacks. I want to stop people from reinforcing the currently established fact that the Twelve Tribes can't trust outside perspectives, because if they don't have outside perspectives they can trust they won't be able to overcome and clean themselves of the truly bad elements hiding in their collective blind spots.
First, an item of 'lack of qualifications'. I'm not a member. I've never been a member. Despite what I'm sure they hope, I'm not going to be a member unless the entire organization changes in some pretty fundamental ways. More on that later. I can't offer the insider perspective of an accepted member, and I'm quite aware that there are things I haven't been told.
Next, some degree of qualifications. My information regarding the Twelve Tribes does not come predominantly from the web (I've read a lot of what's available on the web, and I'll say more about such material soon.) I've spent a large amount of time in a small handful of their locations. I've spent some time at one of their businesses. I've spent some time at one of their houses. I've visited a couple of their other houses and businesses. I've had extensive conversations with a number of men, women, and children. I've had some of them over to my house on a number of occasions. I've attended a few of their regularly scheduled ceremonies, and a couple of the sporadic ones. In short, I have interacted extensively with some members of the Twelve Tribes on a personal level.
Another degree of qualification: Communication is one of my particular fields of study. For anyone with some personal experience of these folks and some reading of what's available on the web (including their own internal publications), there seems to be a vast disconnect between what they say about some subjects and what they actually do. A lot of that (not all, but a lot) is due to the Twelve Tribes as a group having some remarkably bad communication skills in some areas. When I say 'remarkably bad', I mean it the same way I would accuse someone who said "Let's go forth and pillage that village!" when they meant "It's time to harvest the apple crop" as having some remarkably bad communication skills. I have at my disposal some tools and skills which make it easier for me to understand what they mean (despite what they say), and I count this as a qualification.
Time for a disqualification: My ability to translate is limited by my ability to observe what they do as individual people. If there are areas where information is being deliberately held back from me, that'll result in inaccurate translations. Any argument I make has to be qualified with "Assuming what I've seen has been accurately representative". This isn't much of a drawback, though, since the same applies to any source of information, and I do have the advantage of having a more reliable source.
Qualification: I do have first-hand information. Aside being an International House of Porn, the Web is a great source of information, but it's not a great source of reliably reliable information. Any dork with a keyboard can contribute a Wikipedia article, and unless the number of people who really know what they're talking about is larger than the number of people who think they know what they're talking about (but don't), what you're going to see will be, effectively, worthless garbage. Emotionally charged, rabble-rousing, call-to-arms garbage, but garbage nonetheless. If you pick a random topic, and think about how many people really have good, reliable, well-researched information on it, you should come up with a pretty small number. If you look at the same topic and imagine all the schmucks who think they know more than they really do, you should come up with a larger number. Information on the web about the Twelve Tribes -could- be accurate, but most of it is exceedingly unreliable, and much of it is distressingly second-hand.
So, while my first-hand information -may be- deliberately compromised by the agendas of the people in the Twelve Tribes that I interact with, keep in mind that stuff on the web is -probably- compromised by the agendas of the people writing it. Really, I suggest you actually drop your assumptions and biases and try to dig up information for yourself, but that's usually asking too much.
Qualification: I'm not a member, and I'm not going to be a member. I realize this is, in some regards, a disqualification, but it cuts both ways. I'm not subject to their indoctrination, I've got no pressure to keep certain things secret, and I've got reasons for not being a member. I see that they have some real issues, and I'm not interested in ignoring those points. Not in order to join them, and not in order to make them sound better than they are to anyone else. Moreover, my objections are based on a decent amount of first-hand, personal information, not on the shallow knee-jerking that comprises most of what's on the web.
And that leads into my motivations. There are bad things... really bad... about the Twelve Tribes. There are good things... really good... about the Twelve Tribes. I'm aware of some stuff in each of these categories. I would very much like to see them abandon the bad stuff and do something fantastically great with the good stuff, but that requires that they realize the bad stuff is actually bad. So, I'm motivated to affect the situation so they're more likely to be able to see what they're doing wrong.
There's a problem, though. Well, a bunch of them, but the first is this: It's hard to see what you're doing wrong unless someone else you trust can point it out to you. Individually, the Twelve Tribes have got this point figured out and use it heavily, and generally use it well. (That's one of thier good things.) As a group, however, they don't trust anyone but themselves, and so as a group, they're not in a good position to overcome their blind spots and be able to see the things they're collectively doing wrong. So, I'm motivated to affect the situation so they (as a group) might be able to trust some other source to help them identify bad things in themselves.
That raises another problem: There's got to be a trustworthy entity to give trust to, otherwise you're just setting yourself up to get screwed. To a certain degree, you can base trust on the benefit of the doubt, but if you've already observed that someone isn't trustworthy, you'd be an idiot to trust them... and the Twelve Tribes are largely in this situation. They get attacked, over and over, for things they don't believe and things they don't do... largely because the attackers are ignorant of what's actually going on, and too lazy to find out (aside from reading what's available on the web, which I've already lamented.) If I had a drinking problem, but was very good at never injuring anyone (drunk or not) and always paying all my bills (drunk or not), then someone who came up and attacked me on the grounds that I hospitalized folks and never paid my dues would be... something less than credible. I wouldn't be interested in seeking their help with my drinking problem, that's for sure. In a similar manner, the Twelve Tribes are quite justified in not listening to external criticisms, even the few that are relevant, because as a general rule, external criticisms are wildly untrustworthy. So, I'm motivated to affect the situation so that there are some trustworthy outside sources that could help the Twelve Tribes identify bad things in themselves.
And that leads to why I'd be, to a limited degree, a Twelve Tribes apologist. If you'll allow me to indulge in some hyperbole, I'd like to ride forth and vanquish all the criticism, venom, and moral indignation that's born of ignorance and misunderstanding... and I want to do so in order to clear the field for criticism born of good, accurate, trustworthy information. I want to take down people's inappropriate attacks on the Twelve Tribes and divert those energies to appropriate attacks. I want to stop people from reinforcing the currently established fact that the Twelve Tribes can't trust outside perspectives, because if they don't have outside perspectives they can trust they won't be able to overcome and clean themselves of the truly bad elements hiding in their collective blind spots.
3.27.2007
Morality Play
Why be moral? Because doing otherwise doesn't make sense. Doing otherwise doesn't work well in the long run. Doing otherwise will result in shooting yourself (and others) in the metaphorical foot. In a nutshell, not being moral is shortsightedly stupid.
I'm not talking about why just [insert group here] should be moral, here, I'm talking about why anyone should be moral, and that's because the reasons that immorality doesn't work have nothing to do with supernatural entities. Whether the universe is blamed on Brahma, Yahweh, Allah, The Force, or nothing at all, there are certain aspects that couldn't have been put together any differently (at least, not without having a meaningless, completely self-contradictory undifferentiated mass in which everything that exists does not exist, and vice versa). There are some constraints on how a natural world could be which can't be violated by the most super of supernatural forces, and morality arises from those constraints.
Concisely: Morality, coming from a source beyond any supernatural entity, and being a property of every natural system, is relevant to everyone, whether they add supernatural entities to their worldview or not.
One concern many theists have seen is that many atheists seem to think that the morality of theists is somehow inferior. At this point, perhaps it's clear why. If someone said to you (I'm temporarily assuming the reader is a theist) that morality didn't come from your god, but rather came from, say... following laws... you'd be rightly concerned. There's a misattribution going on, and worse yet there's the risk that if people run around thinking "Morality equals lawfulness" and some jerk puts a bad law on the books, people will think that following the bad law is moral. Ack! Worse yet, since the law is open to various degrees of interpretation, someone with the authority to decide on how the law is interpreted might attribute the wrong spirit to the letter, and so now everyone is compelled to follow a law ("be moral") even if it is what you know to be immoral! Double ack! You could even have people saying "Well, without the law, there'd be no reason to be moral... might as well drink and be merry, for tomorrow you die!" when you know full well there are more important reasons than the law to be moral. Triple ack! And on top of it all, you're painted as immoral for worrying about higher levels of morality than that dictated by the law. Quad overkill ack!
That's the kind of misattribution that many atheists go "Quad overkill ack!" over when they hear people claiming that morality comes from supernatural sources. There's a misattribution, there's the ability to subject morality to various biased interpretations, the bad interpretations can be handed down in some cases from a priviledged few and thus spread alarmingly quickly, people start saying things like "Sure you could be moral, but why?", and brights in general are often suspected of having an inferior class of morality simply because they're trying to get their morality from the proper source.
When atheists are saying that morality without gods is superior to a morality dictated by gods, it often comes from a similar concern to a theist saying that morality dictated by gods is superior to a morality dictated by human laws. Sure, you might get lucky and manage to keep in line with the true source, but there's far too much room for human bungling and misattribution of why things are important.
Then again, sometimes it's coming from a common combination of bitterness and pompousness. Every group has people like that, too.
There's also something similar to misattribution that's a concern, though it's not quite the same. I'm thinking of an experiment that was done at a daycare center. In a nutshell, there were often a few parents every week who picked their kids up late, which wasn't so great for the daycare workers that had to stay to watch the not-gone-yet kids. The center started charging a 'late pick-up fee', and... late pickups went up! What was a matter of being inconsiderate before was now merely a matter of a very small fee for a very convenient service. Worse yet, when the center dropped the late fee, the late pickups didn't go down. Hey, they're doing the extra service for free now! No conscience pangs AND no hit on the wallet, how great is that?
By misattributing an issue from the realm of morality to the realm of externally enforced consequences (in this case, by adding a penalty fee) people were led to ignore the moral aspect and think only of the inflicted consequences aspect and, worse yet, when the consequences were taken away, they didn't revert to moral behavior, but acted as if the action were now just fine!
Whenever I hear someone say "Sure, you could be a moral atheist, but why?" I worry that here is someone who wouldn't be moral if they weren't essentially being told to, and it's scary and sad. Perhaps there are people who couldn't be moral if they weren't told to, in which case it's a good thing someone's telling them to... but I suspect there are a lot of people who could once have been moral simply because it doesn't make sense not to, but who've been led to misattribute the source of morality and, in so doing, have lost their capacity to actually be moral, and only retain the ability to act morally.
It's also possible that there are people who believe in supernatural forces but don't mistakenly label those things as sources of morality... people who are fundamentally moral, and simply add a layer of religious decoration on top of it without mistaking the decoration for the real thing. I have not, to the best of my knowledge, ever met anyone or heard of anyone who fit this description, so it certainly seems unlikely to me, but perhaps that is more an upshot of how pervasive modern religious piekories have to be in order to survive, and less a property of religious piekories in general.
I'm not talking about why just [insert group here] should be moral, here, I'm talking about why anyone should be moral, and that's because the reasons that immorality doesn't work have nothing to do with supernatural entities. Whether the universe is blamed on Brahma, Yahweh, Allah, The Force, or nothing at all, there are certain aspects that couldn't have been put together any differently (at least, not without having a meaningless, completely self-contradictory undifferentiated mass in which everything that exists does not exist, and vice versa). There are some constraints on how a natural world could be which can't be violated by the most super of supernatural forces, and morality arises from those constraints.
Concisely: Morality, coming from a source beyond any supernatural entity, and being a property of every natural system, is relevant to everyone, whether they add supernatural entities to their worldview or not.
One concern many theists have seen is that many atheists seem to think that the morality of theists is somehow inferior. At this point, perhaps it's clear why. If someone said to you (I'm temporarily assuming the reader is a theist) that morality didn't come from your god, but rather came from, say... following laws... you'd be rightly concerned. There's a misattribution going on, and worse yet there's the risk that if people run around thinking "Morality equals lawfulness" and some jerk puts a bad law on the books, people will think that following the bad law is moral. Ack! Worse yet, since the law is open to various degrees of interpretation, someone with the authority to decide on how the law is interpreted might attribute the wrong spirit to the letter, and so now everyone is compelled to follow a law ("be moral") even if it is what you know to be immoral! Double ack! You could even have people saying "Well, without the law, there'd be no reason to be moral... might as well drink and be merry, for tomorrow you die!" when you know full well there are more important reasons than the law to be moral. Triple ack! And on top of it all, you're painted as immoral for worrying about higher levels of morality than that dictated by the law. Quad overkill ack!
That's the kind of misattribution that many atheists go "Quad overkill ack!" over when they hear people claiming that morality comes from supernatural sources. There's a misattribution, there's the ability to subject morality to various biased interpretations, the bad interpretations can be handed down in some cases from a priviledged few and thus spread alarmingly quickly, people start saying things like "Sure you could be moral, but why?", and brights in general are often suspected of having an inferior class of morality simply because they're trying to get their morality from the proper source.
When atheists are saying that morality without gods is superior to a morality dictated by gods, it often comes from a similar concern to a theist saying that morality dictated by gods is superior to a morality dictated by human laws. Sure, you might get lucky and manage to keep in line with the true source, but there's far too much room for human bungling and misattribution of why things are important.
Then again, sometimes it's coming from a common combination of bitterness and pompousness. Every group has people like that, too.
There's also something similar to misattribution that's a concern, though it's not quite the same. I'm thinking of an experiment that was done at a daycare center. In a nutshell, there were often a few parents every week who picked their kids up late, which wasn't so great for the daycare workers that had to stay to watch the not-gone-yet kids. The center started charging a 'late pick-up fee', and... late pickups went up! What was a matter of being inconsiderate before was now merely a matter of a very small fee for a very convenient service. Worse yet, when the center dropped the late fee, the late pickups didn't go down. Hey, they're doing the extra service for free now! No conscience pangs AND no hit on the wallet, how great is that?
By misattributing an issue from the realm of morality to the realm of externally enforced consequences (in this case, by adding a penalty fee) people were led to ignore the moral aspect and think only of the inflicted consequences aspect and, worse yet, when the consequences were taken away, they didn't revert to moral behavior, but acted as if the action were now just fine!
Whenever I hear someone say "Sure, you could be a moral atheist, but why?" I worry that here is someone who wouldn't be moral if they weren't essentially being told to, and it's scary and sad. Perhaps there are people who couldn't be moral if they weren't told to, in which case it's a good thing someone's telling them to... but I suspect there are a lot of people who could once have been moral simply because it doesn't make sense not to, but who've been led to misattribute the source of morality and, in so doing, have lost their capacity to actually be moral, and only retain the ability to act morally.
It's also possible that there are people who believe in supernatural forces but don't mistakenly label those things as sources of morality... people who are fundamentally moral, and simply add a layer of religious decoration on top of it without mistaking the decoration for the real thing. I have not, to the best of my knowledge, ever met anyone or heard of anyone who fit this description, so it certainly seems unlikely to me, but perhaps that is more an upshot of how pervasive modern religious piekories have to be in order to survive, and less a property of religious piekories in general.
3.22.2007
Symmetry breaking
Meet Allen Marshall and Marshall Allen.
Allen's a good person. Not perfect, but well above average. He's got a good life. Again, not perfect, but well above average. Allen knows this comes from holding A above all else. The same holds, for the most part, for Marshall. The main differences are that Marshall's good fruits come from holding M above all else, and he knows that the standard of A that allows Allen to be a good person with a good life will, eventually, run out of steam, whereas Marshall's own standard of M won't. Allen feels similarly, except he knows that M will eventually fail.
This is sad on two counts, the first being that Allen and Marshall are friends, so Allen would much prefer that Marshall realize he's headed down a dead end before running into it face-first (and vice-versa) and the second being that by holding himself to the higher standard of M, Allen would still end up meeting his original, lower standard of A as well. At least, so Marshall claims. Allen, in turn, knows that Marshall would still get M by putting in the extra work to meet the higher standard of A.
Alas, nothing Allen says or does seems to make this point. Allen's got a good life, but it's not good enough to persuade Marshall that A is more important than M. Allen's a good person, but Marshall says that's despite Allen holding A above M, not because of it, and so isn't an indicator that Allen's right. Allen may hope that Marshall will come to accept the importance of A, but as time goes on, there's less and less evidence that it'll happen. Nor does Marshall have it any better, as all of his evidence is just as unconvincing to Allen.
With such a fundamental disparity, are there any worthwhile grounds on which Allen and Marshall can be friends in a meaningful sense, or is "friendly acquaintance" the best that can be hoped for? What range of things might they be able to both improve upon together, from their separate starting points? How broad is the range of things that are between A and M which can only be reached from the 'higher' one, and not the 'lower'?
If there's a yet-'higher' standard Q which, if it were followed, would subsume both A and M, what are the chances of either Allen or Marshall being able to become aware of it? Are their chances at all improved if they have access to each other?
Allen's a good person. Not perfect, but well above average. He's got a good life. Again, not perfect, but well above average. Allen knows this comes from holding A above all else. The same holds, for the most part, for Marshall. The main differences are that Marshall's good fruits come from holding M above all else, and he knows that the standard of A that allows Allen to be a good person with a good life will, eventually, run out of steam, whereas Marshall's own standard of M won't. Allen feels similarly, except he knows that M will eventually fail.
This is sad on two counts, the first being that Allen and Marshall are friends, so Allen would much prefer that Marshall realize he's headed down a dead end before running into it face-first (and vice-versa) and the second being that by holding himself to the higher standard of M, Allen would still end up meeting his original, lower standard of A as well. At least, so Marshall claims. Allen, in turn, knows that Marshall would still get M by putting in the extra work to meet the higher standard of A.
Alas, nothing Allen says or does seems to make this point. Allen's got a good life, but it's not good enough to persuade Marshall that A is more important than M. Allen's a good person, but Marshall says that's despite Allen holding A above M, not because of it, and so isn't an indicator that Allen's right. Allen may hope that Marshall will come to accept the importance of A, but as time goes on, there's less and less evidence that it'll happen. Nor does Marshall have it any better, as all of his evidence is just as unconvincing to Allen.
With such a fundamental disparity, are there any worthwhile grounds on which Allen and Marshall can be friends in a meaningful sense, or is "friendly acquaintance" the best that can be hoped for? What range of things might they be able to both improve upon together, from their separate starting points? How broad is the range of things that are between A and M which can only be reached from the 'higher' one, and not the 'lower'?
If there's a yet-'higher' standard Q which, if it were followed, would subsume both A and M, what are the chances of either Allen or Marshall being able to become aware of it? Are their chances at all improved if they have access to each other?
3.20.2007
A Fair Share
(A) Are you dong your fair share around the house? (B) Do you think you're doing your fair share? These are, for better or worse, not the same question. To many folks, it's obvious that (A) is a different question from (C) Do other people in the house think you're doing your fair share, and that (B) and (C) are likely to be mismatched, but realizing that (A) and (B) are different often takes some practice to really get used to.
That's not to say that people don't try. I know many folks who use the rule of thumb
Since a post here wouldn't be a post here without a good digression or tangent, I'd like to take a minute to talk about cake. Cake is a classic object for "how do you fairly divide something" problem, and for a homogenous cake, the "you cut, I choose" or "I cut, you choose" strategies work just fine for two people. But what about when you've got more people? For homogenous cakes, there are similar strategies that ensure that 'fairness' is satisfied, at least in the form of "If I cut an unfairly sized piece, I'm the one who'll end up with the unfairly sized piece."
But what about a non-homogenous cake? What about a chocolate/vanilla marble cake with frosting (thick in some places, thin in other), walnuts in most of it, some pieces with strawberries on top, some pieces with candlewax drippings and a candlehole, and let's toss a lovely edible candy effigy on the top. Suddenly, the scene changes, because different pieces of the cake can be more desirable to different people. Perhaps you're allergic to walnuts: you'd probably rather have a small portion without walnuts than a large portion that's stuffed with nuts. Perhaps I reaaaaally like strawberries. I could happily pass up a large piece without fruit if it meant I could get a small piece with fruit. Some third person might have a moderate preference for chocolate to vanilla, so would be just as happy with a medium-small chocolate piece as a medium-large vanilla piece.
With a heterogeneous cake and two people, "You cut, I choose" isn't symmetric with "I cut, you choose" any more, because where that cut falls can be important! You might cut things in a way that presents me with two equally bad options from your point of view, but I might like one option far more than the other. In the sense of "You suffer if you cut unfairly", you still have that issue, but in the sense of "If you cut fairly, I don't care which piece I get either", the situation has changed! On the other hand, you might be able to cut the cake in a way that you felt one piece was better than the other, and I thought the other piece was better than the one, so unless I'm a masochist, we both end up getting more than our 'fair share' of goodness.
Reeling the tangent back in closer to reality, consider the 'cake' of housework. Pretend, for the sake of argument, that while you may not exactly enjoy mopping floors, you find it far less onerous than balancing checkbooks. For the same argument, I'll also pretend that I don't like balancing checkbooks. I don't have to pretend that I prefer that activity to mopping, because it's true. We could split up the chores by having you do the books and me do the floors. According the the rule of thumb, that would be a good solution, since I'd feel like I was doing the harder/less pleasant part, and you'd feel the same way. And, indeed, if there really were some objective way of measuring bookkeeping against cleaning, we might indeed each be doing our fair share. But, if that were the case, if we switched roles, we'd also be doing our fair share.
The rule of thumb, however, would throw a red flag. "You're doing the easier stuff!" it would say, "You're not pulling your weight!" Even if both of you were pulling your weight (with reversed roles or not), the rule of thumb would give a false negative. Lacking enough communication to get a broader picture of what's going on, this could lead to switching roles (not so great, because while still fair, everyone's stuck with more than their share instead of less), or it could lead to rule of thumb indoctrinees building up a resevoir of guilt over getting away with doing less than their fair share, or it could lead to anti-guilt defensive anticipation due to expecting the other person to eventually complain about doing more than their fair share.
So, as a second approximation... another rule of thumb that still isn't exactly on the mark but gets closer... I'd suggest the following:
That's not to say that people don't try. I know many folks who use the rule of thumb
"If it doesn't feel like you're doing more than your share, you're doing less than your share".I've used it. I think it's often appropriate. It's kept me from accidentally complaining about doing more than was fair when, in actuality, I wasn't even pulling my own weight. As a first approximation goes, I think it's a good one, but I don't think it's spot-on.
Since a post here wouldn't be a post here without a good digression or tangent, I'd like to take a minute to talk about cake. Cake is a classic object for "how do you fairly divide something" problem, and for a homogenous cake, the "you cut, I choose" or "I cut, you choose" strategies work just fine for two people. But what about when you've got more people? For homogenous cakes, there are similar strategies that ensure that 'fairness' is satisfied, at least in the form of "If I cut an unfairly sized piece, I'm the one who'll end up with the unfairly sized piece."
But what about a non-homogenous cake? What about a chocolate/vanilla marble cake with frosting (thick in some places, thin in other), walnuts in most of it, some pieces with strawberries on top, some pieces with candlewax drippings and a candlehole, and let's toss a lovely edible candy effigy on the top. Suddenly, the scene changes, because different pieces of the cake can be more desirable to different people. Perhaps you're allergic to walnuts: you'd probably rather have a small portion without walnuts than a large portion that's stuffed with nuts. Perhaps I reaaaaally like strawberries. I could happily pass up a large piece without fruit if it meant I could get a small piece with fruit. Some third person might have a moderate preference for chocolate to vanilla, so would be just as happy with a medium-small chocolate piece as a medium-large vanilla piece.
With a heterogeneous cake and two people, "You cut, I choose" isn't symmetric with "I cut, you choose" any more, because where that cut falls can be important! You might cut things in a way that presents me with two equally bad options from your point of view, but I might like one option far more than the other. In the sense of "You suffer if you cut unfairly", you still have that issue, but in the sense of "If you cut fairly, I don't care which piece I get either", the situation has changed! On the other hand, you might be able to cut the cake in a way that you felt one piece was better than the other, and I thought the other piece was better than the one, so unless I'm a masochist, we both end up getting more than our 'fair share' of goodness.
Reeling the tangent back in closer to reality, consider the 'cake' of housework. Pretend, for the sake of argument, that while you may not exactly enjoy mopping floors, you find it far less onerous than balancing checkbooks. For the same argument, I'll also pretend that I don't like balancing checkbooks. I don't have to pretend that I prefer that activity to mopping, because it's true. We could split up the chores by having you do the books and me do the floors. According the the rule of thumb, that would be a good solution, since I'd feel like I was doing the harder/less pleasant part, and you'd feel the same way. And, indeed, if there really were some objective way of measuring bookkeeping against cleaning, we might indeed each be doing our fair share. But, if that were the case, if we switched roles, we'd also be doing our fair share.
The rule of thumb, however, would throw a red flag. "You're doing the easier stuff!" it would say, "You're not pulling your weight!" Even if both of you were pulling your weight (with reversed roles or not), the rule of thumb would give a false negative. Lacking enough communication to get a broader picture of what's going on, this could lead to switching roles (not so great, because while still fair, everyone's stuck with more than their share instead of less), or it could lead to rule of thumb indoctrinees building up a resevoir of guilt over getting away with doing less than their fair share, or it could lead to anti-guilt defensive anticipation due to expecting the other person to eventually complain about doing more than their fair share.
So, as a second approximation... another rule of thumb that still isn't exactly on the mark but gets closer... I'd suggest the following:
"If nobody wants to swap workloads with you, you're not doing less than your share."Of course, this requires communicating with other people, so automatically involves more work than the first rule of thumb, but weighed against alternatives like "everyone doing one of the fair shares they dislike most" and "feeling unnecessarily guilty" and "becoming unnecessarily pre-emptively defensive", perhaps it'd be worth the extra effort sometimes.
3.15.2007
Evidence vs The Dayalektik
Intuitionistic proof
Hands up if you're aware that logicians talk about all sorts of different logics. Emphasis on the plural. If you are currently afflicted with an elevated hand, you probably have heard about intuitionistic logic, and can safely skip down a ways. And put your hand down. Unless it's enjoying the view, of course.
For all the rest of you, I'll begin by apologizing (mildly) for the name. I didn't come up with the name, so I can't apologize much for it, but given how nearly opposite its original meaning (and usage in this term) is from any of the current meanings that you may already be puzzling through... well, someone ought to apologize, and I'm not afraid to throw that first stone.
This isn't feminine intuition, it's not mathematical intuition, it doesn't have to do with intuitive people... heck, I'm not even going to explain what kind of intuition it is, because it's not really all that necessary to understanding the concept. I'll just recommend this: whenever I say "intuitionistic", pretend I instead said "evidential" or "monotonic".
If 'monotonic' makes you think of medicine taken by mononucleosis sufferers, just go with 'evidential' instead.
So, how does intuitionistic logic differ from run-of-the-mill everyday logic? In one sense, it all boils down to rejecting the law of the excluded middle. That is to say, it rejects Sherlock Holmes' maxim that "when you have excluded the impossible, whatever remains, however improbable, must be the truth." On the face of it, this might seem a disastrous thing to do (or, at least, I thought it was) but consider this not-quite-accurate-but-illuminating example:
A man is told there may be a pot of gold buried under his farmland. He goes out and digs a hole. If he finds a pot in the hole, then he has established that, yes, there is a pot of gold buried under his farmland. If, on the other hand, the hole has nothing but dirt, he hasn't proven that there's no gold under his land! He could try again, in a different spot. If he finds gold, he's proven that the statement was true, but if he fails, he has not proved it false, but again he could dig another hole. In this manner, any 'true' hole can prove the statement true, but no 'false' hole proves the statement false.
Perhaps farmlands are small enough, in your mind, to be able to dig up the whole place looking for gold, in which case I simply ask that you change 'farmland' to 'nation' and 'gold' to 'WMDs', which should be enough to convince you that there are relevant issues here.
Now, proving something doesn't exist is notoriously more difficult than proving something does exist, but even when it comes to proving that something does exist, intuitionistic logic holds more stringent standards. Here's another example which has recently entertained me:
Someone wants to know if there are any two numbers, x and y, such that both of them are irrational numbers (numbers like Pi, which can't be exactly expressed as the ratio of two whole numbers) but that x^y (x to the power y) is a rational number. Here's a non-intuitionistic proof that this is true: The square root of 2 is an irrational number, so perhaps x=sqrt(2), y=sqrt(2) satisfies the property that x^y is rational, and maybe it doesn't. If it does, well then, the claim is true. If it doesn't, that means that sqrt(2)^sqrt(2) is an irrational number... which isn't so useful, except that this in turn means that perhaps x=sqrt(2), y=sqrt(2)^sqrt(2) satisfies the property. Indeed, the value of x^y turns out to be 2, which is a rational number!
So, either x=sqrt(2), y=sqrt(2) satisfies the property, or (if that's not the case) x=sqrt(2), y=sqrt(2)^sqrt(2) satisfies the property, so the property is true. Any way you cut it, there are two numbers that satisfy the property.
There's a proof that there are such numbers, but... uh... what ARE those numbers? Is it the first pair? Is it the second pair? We've just proved that some pair of numbers exists without nailing down what the numbers actually are, and while that's allowed in everyday logic, it's not kosher by intuitionistic rules. If we want an intuitionistic proof that something exists, it's necessary to actually go out and find an actual specimen, not just show that it's impossible for one to fail to exist.
It's provable (intuitionistically and otherwise) that 'normal' (i.e. classical) logic and intuitionistic logic are equally powerful. What you can do with one, you can do with the other, so it wouldn't make sense to say that one is better than the other in terms of being able to prove more, or failing to prove less, or the suchlike. There are, however, ways in which using a different (and equally capable) system of logic can be handy.
For an example, I turn to C.S. Lewis. Mere Christianity is a fun read, and some parts of it appear tremendously persuasive. Alas, it's an excellent example of what some folks I know call "The Dayalektik" (any resemblance to 'dialectic' that your ears may detect should be ignored, as The Dayalektik is a method for obfuscating truth and making people agree with things by pushing them through a series of subtle false dichotomies, rather the opposite of the meaning of Socratic dialectic, and I'm not sure how it relates to Marxist dialectic.) Lewis sets up a series of arguments where each major step essentially ran "Either A or B or C must be true, A and B are clearly false, so C is true." Then, of course, going on with C assumed to be true, another step was taken, and so forth.
While the method of "List all the cases, eliminate the impossible ones, and say the remaining one is true" is logically impeccable, the method of "List some of the cases, eliminate all but one, and say the remaining one is true" isn't. If you haven't listed all the cases, it might be that you haven't even listed the 'true' case, so you can end up 'proving' that something false is true by elimination. It's a powerful method for clouding minds, evading the truth, and coming to unsound conclusions, and the worst part is that it's very, very, very easy to use this method completely by accident and with the best of intentions. Yes, people who want to cloud the truth have good reason to use this method, but without discipline and training, people who want to reveal the truth can blunder into it even while trying to avoid it.
I raise this example because it's a place where intuitionistic reasoning nicely fails to present a big danger. To show, intuitionistically, that C is true, it's necessary to give evidence that it is true, not simply accumulate evidence that everything else isn't true. False dichotomies aren't a big problem, because knocking out a strawman collection of opposition isn't intuitionistically enough to support a pet view... there actually has to be something substantial supporting it before you can claim victory.
Now, to those who raised their hand way back at the beginning, I am aware that there's a certain amount of proof-by-eliminating-alternatives that's still intuitionistically acceptable, but I still assert that it requires enough work to prevent the false dichotomy from being a pitfall that's excessively easy for the untrained to stumble into. And if your hand is still up at this point, you might consider giving it a rest.
So, the take-home of today is that if you're worried you're dealing with a false dichotomy, consider taking a hiatus from the law of the excluded middle and demand positive proof of an assertion, not just negative evidence against its negation.
Hands up if you're aware that logicians talk about all sorts of different logics. Emphasis on the plural. If you are currently afflicted with an elevated hand, you probably have heard about intuitionistic logic, and can safely skip down a ways. And put your hand down. Unless it's enjoying the view, of course.
For all the rest of you, I'll begin by apologizing (mildly) for the name. I didn't come up with the name, so I can't apologize much for it, but given how nearly opposite its original meaning (and usage in this term) is from any of the current meanings that you may already be puzzling through... well, someone ought to apologize, and I'm not afraid to throw that first stone.
This isn't feminine intuition, it's not mathematical intuition, it doesn't have to do with intuitive people... heck, I'm not even going to explain what kind of intuition it is, because it's not really all that necessary to understanding the concept. I'll just recommend this: whenever I say "intuitionistic", pretend I instead said "evidential" or "monotonic".
If 'monotonic' makes you think of medicine taken by mononucleosis sufferers, just go with 'evidential' instead.
So, how does intuitionistic logic differ from run-of-the-mill everyday logic? In one sense, it all boils down to rejecting the law of the excluded middle. That is to say, it rejects Sherlock Holmes' maxim that "when you have excluded the impossible, whatever remains, however improbable, must be the truth." On the face of it, this might seem a disastrous thing to do (or, at least, I thought it was) but consider this not-quite-accurate-but-illuminating example:
A man is told there may be a pot of gold buried under his farmland. He goes out and digs a hole. If he finds a pot in the hole, then he has established that, yes, there is a pot of gold buried under his farmland. If, on the other hand, the hole has nothing but dirt, he hasn't proven that there's no gold under his land! He could try again, in a different spot. If he finds gold, he's proven that the statement was true, but if he fails, he has not proved it false, but again he could dig another hole. In this manner, any 'true' hole can prove the statement true, but no 'false' hole proves the statement false.
Perhaps farmlands are small enough, in your mind, to be able to dig up the whole place looking for gold, in which case I simply ask that you change 'farmland' to 'nation' and 'gold' to 'WMDs', which should be enough to convince you that there are relevant issues here.
Now, proving something doesn't exist is notoriously more difficult than proving something does exist, but even when it comes to proving that something does exist, intuitionistic logic holds more stringent standards. Here's another example which has recently entertained me:
Someone wants to know if there are any two numbers, x and y, such that both of them are irrational numbers (numbers like Pi, which can't be exactly expressed as the ratio of two whole numbers) but that x^y (x to the power y) is a rational number. Here's a non-intuitionistic proof that this is true: The square root of 2 is an irrational number, so perhaps x=sqrt(2), y=sqrt(2) satisfies the property that x^y is rational, and maybe it doesn't. If it does, well then, the claim is true. If it doesn't, that means that sqrt(2)^sqrt(2) is an irrational number... which isn't so useful, except that this in turn means that perhaps x=sqrt(2), y=sqrt(2)^sqrt(2) satisfies the property. Indeed, the value of x^y turns out to be 2, which is a rational number!
So, either x=sqrt(2), y=sqrt(2) satisfies the property, or (if that's not the case) x=sqrt(2), y=sqrt(2)^sqrt(2) satisfies the property, so the property is true. Any way you cut it, there are two numbers that satisfy the property.
There's a proof that there are such numbers, but... uh... what ARE those numbers? Is it the first pair? Is it the second pair? We've just proved that some pair of numbers exists without nailing down what the numbers actually are, and while that's allowed in everyday logic, it's not kosher by intuitionistic rules. If we want an intuitionistic proof that something exists, it's necessary to actually go out and find an actual specimen, not just show that it's impossible for one to fail to exist.
It's provable (intuitionistically and otherwise) that 'normal' (i.e. classical) logic and intuitionistic logic are equally powerful. What you can do with one, you can do with the other, so it wouldn't make sense to say that one is better than the other in terms of being able to prove more, or failing to prove less, or the suchlike. There are, however, ways in which using a different (and equally capable) system of logic can be handy.
For an example, I turn to C.S. Lewis. Mere Christianity is a fun read, and some parts of it appear tremendously persuasive. Alas, it's an excellent example of what some folks I know call "The Dayalektik" (any resemblance to 'dialectic' that your ears may detect should be ignored, as The Dayalektik is a method for obfuscating truth and making people agree with things by pushing them through a series of subtle false dichotomies, rather the opposite of the meaning of Socratic dialectic, and I'm not sure how it relates to Marxist dialectic.) Lewis sets up a series of arguments where each major step essentially ran "Either A or B or C must be true, A and B are clearly false, so C is true." Then, of course, going on with C assumed to be true, another step was taken, and so forth.
While the method of "List all the cases, eliminate the impossible ones, and say the remaining one is true" is logically impeccable, the method of "List some of the cases, eliminate all but one, and say the remaining one is true" isn't. If you haven't listed all the cases, it might be that you haven't even listed the 'true' case, so you can end up 'proving' that something false is true by elimination. It's a powerful method for clouding minds, evading the truth, and coming to unsound conclusions, and the worst part is that it's very, very, very easy to use this method completely by accident and with the best of intentions. Yes, people who want to cloud the truth have good reason to use this method, but without discipline and training, people who want to reveal the truth can blunder into it even while trying to avoid it.
I raise this example because it's a place where intuitionistic reasoning nicely fails to present a big danger. To show, intuitionistically, that C is true, it's necessary to give evidence that it is true, not simply accumulate evidence that everything else isn't true. False dichotomies aren't a big problem, because knocking out a strawman collection of opposition isn't intuitionistically enough to support a pet view... there actually has to be something substantial supporting it before you can claim victory.
Now, to those who raised their hand way back at the beginning, I am aware that there's a certain amount of proof-by-eliminating-alternatives that's still intuitionistically acceptable, but I still assert that it requires enough work to prevent the false dichotomy from being a pitfall that's excessively easy for the untrained to stumble into. And if your hand is still up at this point, you might consider giving it a rest.
So, the take-home of today is that if you're worried you're dealing with a false dichotomy, consider taking a hiatus from the law of the excluded middle and demand positive proof of an assertion, not just negative evidence against its negation.
11.09.2006
Swallowing the implications
Fun fact: The 'big bang' theory has some significant non-secular history. Did Lemaître approach the issue as a scientist in search of truth or a priest in search of theistically supporting evidence? I don't know, and while I've got my suspicions, I haven't dug up evidence to confirm or refute them. I just think it's interesting that what may, possibly, have been a look-gods-must-exist attempt today ends up being denounced as godless 'just-theory' speculation.
That came to mind when I was thinking about the notion of 'Intelligent Design' recently. I'll admit that, to date, I haven't been presented with any arguments for ID that weren't laced with invalidating holes, so I've moved from a position of "I'm skeptical, but they claim to be doing things rigorously, so they deserve a fair hearing" to "I quort that people who profess adherence to ID will employ gaps in their reasoning." That is to say, I've become biased based on consistent experiences.
If you can't support a position without using swiss-cheesed arguments, though, how could such a position persist? Shouldn't it be shot down by now? The usual cynical replies aside, it seems there would need to be something propping up a desire to keep pushing the point.
"One acts on assumptions. What do you assume?" asked the Player in Rosencrantz and Guildenstern are Dead. If you assume that everything was created by something intelligent, then you'd know that while your current argument has problems, they're problems with the argument, not the conclusion... since you know that the conclusion is true. I won't say much about the dishonesty intrinsic a position in which "even if there's a flawless proof that something is false, it maintains that there must be a proof that the thing is true because... well... you know it's true!" beyond that it's dishonest and that if you're going to posit a universe which is inherantly contradictory, there's really no point trying to talk about it.
So, why was ID bringing the background of Big Bang theory to mind? Well, while most ID arguments I've seen are strictly flawed, I'll admit there are just some that, so far, only have holes in them. Perhaps those holes will get well and properly filled in at some point in the future, and there'll be a flawless proof that, yes indeed, everything has a designer. I'll admit, I would find that tough to swallow, and would go over the argument very carefully, but it could happen, and I'm not the type to reject it just because I know it has to be wrong, even if it isn't.
I think, though, that most theists on the planet would find it a lot tougher to swallow than I would. I expect that if people who really care about rigorous arguments start trying to make the case for ID work, it'll start to fall into the poor graces enjoyed by Evolution, Big Bang, and much of science in general. Not, however, because it would be more evidence that deities aren't necessary, but rather that it'd make mono (or even finite poly)-theism a much less tenable position.
I'm not about to go trying to lay out a rigorous argument for ID, but I'll outline why I think it'd be potentially terrifying for a lot of major religions.
Essentially, self-causality is either possible, or it's not. For an ID argument to be solid, one thing it needs to do is rule out the possibility of self-causality, since otherwise the universe could have no creator but itself, and I think that runs contrary to the point of most ID arguments. So, suppose it can be established that self-causality isn't an option. The universe, then, must certainly have a (designing) cause, which presumably is also established to be intelligent. And, self-causality not being an option you know three things: The 'designer' has a cause, that cause isn't itself, and that cause isn't the universe (this third item rests on the assumption that causation is transitive: If A causes B, and B causes C, then A can also be said to cause C). The designer's designer, similarly, has a designer (which isn't itself). In particular, there can be no ultimate designer (or 'first cause') since self-causality has been ruled out. Without the option for self-causation, the minimum count of designers designing designers is infinite, and there's no topmost one.
I imagine that accepting that gods exist at all (and that there are infinitely many of them) wouldn't be nearly as rough on me as accepting that your ultimate, highest, unsurpassed god is, necessarily, practically at the very bottom of an unending chain... far closer to you than to most designers. You don't even have the option of getting a better designer way higher up the chain, because no matter how far up you go, you're still talking about a designer who's practically at the very bottom and far closer to you than to most of the other designers.
On the one hand: "Woha, well, I guess there are gods." On the other hand: "My god is pitifully trivial and, in the grand scheme of things, infinitely unimportant."
That's gotta be rough.
One objection I can see to my prediction is that it doesn't take into account that modern ID arguments tend to be much more probabilistic in nature, and wouldn't explicitly claim that self-causation is impossible, but rather that it's only sufficiently unlikely that you shouldn't buy it, at least when talking about things so irreducibly complex that certain probabilities fall below certain arbitrary thresholds. I can see this objection because I think it's entirely possible for more complicated things to arise from less complicated ones, so I can imagine 'designers' that are far less complex than their 'designs'. The requirement of 'intelligence', however, sets some lower bounds on the allowed complexity for designers, however, and that bound is still a good deal higher than, say, the complexity of your favorite beetle organ.
Basically, if an ID argument is strong enough to demonstrate that it's probabilistically ridiculous to imagine the observable world without an intelligent designer, the argument's going to be more than strong enough to show it's at least as ridiculous to imagine that such a designer isn't, in turn, designed. While such a probabilistic argument does allow someone to say "Yes, but at -this- level, you really do have self-causation", it would also show that the most justified level to assume self-causation is the one without any designers at all. It wouldn't be necessary to start believing in an infinite stack of designers, but it would be provably worse to believe in one than to believe in none.
And now for a mathematical digression. It would seem that I'm implying that a solid probabilistic ID argument says "Belief in none is silly, believe in one is more silly, belief in two is even more silly, and so forth... but belief in infinitely many is not silly." And, indeed, that is the implication. If that seems awkward to you, I'm not going to just say "Well, that's the kind of thing that happens when you start mucking outside the finite", even though it's true. I'm going to present a similarly ackward, but hopefully much more accessible, infinite-weirdness situation.
Think about the counting numbers: 0, 1, 2, 3, 4, 5, and so forth. I'm going to define a sequence of sets to think about: The initial set, Set-1, is just {1}. One element, which is the number 'one'. The next set, Set-2, you get by adding in the two next larger elements, and taking away the smallest element. The next larger elements are one and two, and the smallest element is also the only one: zero. Thus, Set-2 is {2,3}. Set-3 is made in a similar fashion: Add the two next larger, remove the smallest, you get {3,4,5}. Set-4 works the same way, you get {4,5,6,7}. Set-5? {5,6,7,8,9}. By this point, you may have noticed that Set-N has N elements, which are {N,N+1,N+2,...,2N-1}. If so, well done. If not, it really does work that way.
So, what happens when we go infinite? What's the set you get if you repeat this process infinitely many times? How bit is it?
Given how I led into this, you might guess correctly, but pretend you didn't have any hints or foreshadowing. People tend to see that at each step, the sets get bigger, so after infinitely many steps, you must have an infinitely large set, yeah? Alas, no. You end up with a completely empty set. Nobody home at all!
Seriously. I'm not joking. Just try to name even -one- number that would be in the final set. If there's infinitely many, there should be at least one, right? But 1 isn't in it, we kicked out 1 when we went to Set-2, and we never looked back. 39 isn't in there either... we kicked it out when we went to Set-40, and we never added it back in. Pick any number (call it X), and the sad truth is, X isn't in the set, because it got kicked out in the process of going to Set-(X+1).
A sequence of increasinly large sets, when you 'go out to infinity', leads you to a completely empty set. That's mucking about outside the finite, for you. Not so different from a sequence of increasingly improbable beliefs, when you 'go out to infinity', becoming the only probably belief.
So, honestly, I expect that the whole ID thing is going to go the way of the geocentric universe and the flat world (by which I don't mean 'becoming featured in Terry Pratchett's novels'). Still, if there really is enough truth behind the idea for something solid to be proved, I think it'll end up going the way of evolution and the big bang, in terms of being thoroughly unacceptable to many religious viewpoints.
That came to mind when I was thinking about the notion of 'Intelligent Design' recently. I'll admit that, to date, I haven't been presented with any arguments for ID that weren't laced with invalidating holes, so I've moved from a position of "I'm skeptical, but they claim to be doing things rigorously, so they deserve a fair hearing" to "I quort that people who profess adherence to ID will employ gaps in their reasoning." That is to say, I've become biased based on consistent experiences.
If you can't support a position without using swiss-cheesed arguments, though, how could such a position persist? Shouldn't it be shot down by now? The usual cynical replies aside, it seems there would need to be something propping up a desire to keep pushing the point.
"One acts on assumptions. What do you assume?" asked the Player in Rosencrantz and Guildenstern are Dead. If you assume that everything was created by something intelligent, then you'd know that while your current argument has problems, they're problems with the argument, not the conclusion... since you know that the conclusion is true. I won't say much about the dishonesty intrinsic a position in which "even if there's a flawless proof that something is false, it maintains that there must be a proof that the thing is true because... well... you know it's true!" beyond that it's dishonest and that if you're going to posit a universe which is inherantly contradictory, there's really no point trying to talk about it.
So, why was ID bringing the background of Big Bang theory to mind? Well, while most ID arguments I've seen are strictly flawed, I'll admit there are just some that, so far, only have holes in them. Perhaps those holes will get well and properly filled in at some point in the future, and there'll be a flawless proof that, yes indeed, everything has a designer. I'll admit, I would find that tough to swallow, and would go over the argument very carefully, but it could happen, and I'm not the type to reject it just because I know it has to be wrong, even if it isn't.
I think, though, that most theists on the planet would find it a lot tougher to swallow than I would. I expect that if people who really care about rigorous arguments start trying to make the case for ID work, it'll start to fall into the poor graces enjoyed by Evolution, Big Bang, and much of science in general. Not, however, because it would be more evidence that deities aren't necessary, but rather that it'd make mono (or even finite poly)-theism a much less tenable position.
I'm not about to go trying to lay out a rigorous argument for ID, but I'll outline why I think it'd be potentially terrifying for a lot of major religions.
Essentially, self-causality is either possible, or it's not. For an ID argument to be solid, one thing it needs to do is rule out the possibility of self-causality, since otherwise the universe could have no creator but itself, and I think that runs contrary to the point of most ID arguments. So, suppose it can be established that self-causality isn't an option. The universe, then, must certainly have a (designing) cause, which presumably is also established to be intelligent. And, self-causality not being an option you know three things: The 'designer' has a cause, that cause isn't itself, and that cause isn't the universe (this third item rests on the assumption that causation is transitive: If A causes B, and B causes C, then A can also be said to cause C). The designer's designer, similarly, has a designer (which isn't itself). In particular, there can be no ultimate designer (or 'first cause') since self-causality has been ruled out. Without the option for self-causation, the minimum count of designers designing designers is infinite, and there's no topmost one.
I imagine that accepting that gods exist at all (and that there are infinitely many of them) wouldn't be nearly as rough on me as accepting that your ultimate, highest, unsurpassed god is, necessarily, practically at the very bottom of an unending chain... far closer to you than to most designers. You don't even have the option of getting a better designer way higher up the chain, because no matter how far up you go, you're still talking about a designer who's practically at the very bottom and far closer to you than to most of the other designers.
On the one hand: "Woha, well, I guess there are gods." On the other hand: "My god is pitifully trivial and, in the grand scheme of things, infinitely unimportant."
That's gotta be rough.
One objection I can see to my prediction is that it doesn't take into account that modern ID arguments tend to be much more probabilistic in nature, and wouldn't explicitly claim that self-causation is impossible, but rather that it's only sufficiently unlikely that you shouldn't buy it, at least when talking about things so irreducibly complex that certain probabilities fall below certain arbitrary thresholds. I can see this objection because I think it's entirely possible for more complicated things to arise from less complicated ones, so I can imagine 'designers' that are far less complex than their 'designs'. The requirement of 'intelligence', however, sets some lower bounds on the allowed complexity for designers, however, and that bound is still a good deal higher than, say, the complexity of your favorite beetle organ.
Basically, if an ID argument is strong enough to demonstrate that it's probabilistically ridiculous to imagine the observable world without an intelligent designer, the argument's going to be more than strong enough to show it's at least as ridiculous to imagine that such a designer isn't, in turn, designed. While such a probabilistic argument does allow someone to say "Yes, but at -this- level, you really do have self-causation", it would also show that the most justified level to assume self-causation is the one without any designers at all. It wouldn't be necessary to start believing in an infinite stack of designers, but it would be provably worse to believe in one than to believe in none.
And now for a mathematical digression. It would seem that I'm implying that a solid probabilistic ID argument says "Belief in none is silly, believe in one is more silly, belief in two is even more silly, and so forth... but belief in infinitely many is not silly." And, indeed, that is the implication. If that seems awkward to you, I'm not going to just say "Well, that's the kind of thing that happens when you start mucking outside the finite", even though it's true. I'm going to present a similarly ackward, but hopefully much more accessible, infinite-weirdness situation.
Think about the counting numbers: 0, 1, 2, 3, 4, 5, and so forth. I'm going to define a sequence of sets to think about: The initial set, Set-1, is just {1}. One element, which is the number 'one'. The next set, Set-2, you get by adding in the two next larger elements, and taking away the smallest element. The next larger elements are one and two, and the smallest element is also the only one: zero. Thus, Set-2 is {2,3}. Set-3 is made in a similar fashion: Add the two next larger, remove the smallest, you get {3,4,5}. Set-4 works the same way, you get {4,5,6,7}. Set-5? {5,6,7,8,9}. By this point, you may have noticed that Set-N has N elements, which are {N,N+1,N+2,...,2N-1}. If so, well done. If not, it really does work that way.
So, what happens when we go infinite? What's the set you get if you repeat this process infinitely many times? How bit is it?
Given how I led into this, you might guess correctly, but pretend you didn't have any hints or foreshadowing. People tend to see that at each step, the sets get bigger, so after infinitely many steps, you must have an infinitely large set, yeah? Alas, no. You end up with a completely empty set. Nobody home at all!
Seriously. I'm not joking. Just try to name even -one- number that would be in the final set. If there's infinitely many, there should be at least one, right? But 1 isn't in it, we kicked out 1 when we went to Set-2, and we never looked back. 39 isn't in there either... we kicked it out when we went to Set-40, and we never added it back in. Pick any number (call it X), and the sad truth is, X isn't in the set, because it got kicked out in the process of going to Set-(X+1).
A sequence of increasinly large sets, when you 'go out to infinity', leads you to a completely empty set. That's mucking about outside the finite, for you. Not so different from a sequence of increasingly improbable beliefs, when you 'go out to infinity', becoming the only probably belief.
So, honestly, I expect that the whole ID thing is going to go the way of the geocentric universe and the flat world (by which I don't mean 'becoming featured in Terry Pratchett's novels'). Still, if there really is enough truth behind the idea for something solid to be proved, I think it'll end up going the way of evolution and the big bang, in terms of being thoroughly unacceptable to many religious viewpoints.
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