It doesn't make sense to say that you don't like math. Math is simply a tool, an alphabet—if not a language*—which we use to convey our theories on the nature of the physical world in the most precise way we can. It isn't actually a thing that bears liking or disliking, except that one may like the skilful manipulation of the tool itself, or the beauty of the resulting theorems. One normally would not do the opposite, that is, dislike handling the tool badly, because if one is bad at wielding a tool one either learns quickly how to wield it well, or goes on to something one finds easier to do. Myself, I blame school for this irrational hatred of mathematics. It is one of those few environments where one may be forced to consistently do a job one is bad at, and therefore, one of the few places that one can learn to hate a means of communication.
Sunday, May 31, 2009
Wednesday, May 27, 2009
Sorites Paradox refutation
I was recently introduced to something called the Sorites Paradox. The person explaining it to me also referred to it as 'the vagueness paradox'. My response, before hearing its explanation, was that perhaps if one is more precise, the paradox ceases to exist. The Sorites paradox can be explained as follows:
Imagine a heap of sand. Take one grain away. Is it still a heap? Presumably so. Now remove another, and another, and another, and... at what point does it cease to be a heap?
However, a heap is an imprecise idea. It is an approximate, not a specific, measure. It makes no sense to talk of heaps in terms of the number of grains of sand; grains of sand are a very precise numerical measure. The paradox arises only when this precise measure is applied to this imprecise concept.
One ought to use only the degree of precision in one's language that is correct to the problem. This is because seeking appropriate degrees of precision helps to solve problems most efficiently. There will be some problems that do not require more than a certain degree of precision in the definition of their terms, and insisting on seeking further precision is unnecessary and, in fact, would just distract from solving the actual problem.
Indeed, it seems that this paradox does not take into account that a heap is an imprecise concept. It assumes that a precise definition of a heap must be necessary in order for it to be meaningful, and that a paradox arises when it is not. The value of having terms like 'heap' or 'pile' is in fact that they are vague. We need not measure them precisely and can use approximations. This is very useful in one's day-to-day existence and does not benefit from being defined more precisely.
This is apparently a paradox that confounds many an Oxford philosophy student, and presumably their professors as well since the solution has not been explained to them to resolve their confusion. I must say that I was very unimpressed.
Imagine a heap of sand. Take one grain away. Is it still a heap? Presumably so. Now remove another, and another, and another, and... at what point does it cease to be a heap?
However, a heap is an imprecise idea. It is an approximate, not a specific, measure. It makes no sense to talk of heaps in terms of the number of grains of sand; grains of sand are a very precise numerical measure. The paradox arises only when this precise measure is applied to this imprecise concept.
One ought to use only the degree of precision in one's language that is correct to the problem. This is because seeking appropriate degrees of precision helps to solve problems most efficiently. There will be some problems that do not require more than a certain degree of precision in the definition of their terms, and insisting on seeking further precision is unnecessary and, in fact, would just distract from solving the actual problem.
Indeed, it seems that this paradox does not take into account that a heap is an imprecise concept. It assumes that a precise definition of a heap must be necessary in order for it to be meaningful, and that a paradox arises when it is not. The value of having terms like 'heap' or 'pile' is in fact that they are vague. We need not measure them precisely and can use approximations. This is very useful in one's day-to-day existence and does not benefit from being defined more precisely.
This is apparently a paradox that confounds many an Oxford philosophy student, and presumably their professors as well since the solution has not been explained to them to resolve their confusion. I must say that I was very unimpressed.
Saturday, May 16, 2009
Paris Freedom Fest
A heads-up: I've been invited to speak at the Paris Freedom Fest this September. I'm thinking of focusing the talk on something relating to the Enlightenment, possibly America. A little pro-Americanism wouldn't go amiss, I'm sure. However, if there are things other than that that people would like me to deliver a talk on, mention them! I'd like to have suggestions as there might have been something I didn't think of.
Wednesday, May 6, 2009
Common misconceptions, Rand, and reasonableness
A little while ago, I was asked by a person of the internet why I liked Rand. My response was as follows:
My interlocutor—in interests of privacy I won't say where this conversation took place, but I will say that the man was purporting to be a philosopher—responded thus:
Hum, and he says he values being intellectually serious. Actually, that's a significant part of how bad that was as a response. The addition of that little phrase, "if you're going to be intellectually serious", is very telling. It's blatant argument by authority. Amongst philosophers (admittedly, in the conversation in question, I was half-purporting to be one too—though far more humbly than he!) one's intellectual integrity is basically one's currency. This man says he likes reason, but then in the very next sentence he threatens my claim to my own intellectual integrity if I don't go back on my previous post, and agree with him that Rand does not believe that human acheivement is joyful. Removing that sentence would not have changed the meaning of his argument; it is superfluous meta. Evidently he doesn't think enough of his arguments to believe that he can rely on them to persuade me, and adds in a bit of bullying just in case.
I didn't mention the above in my response, however, to avoid getting into a pointless meta-discussion with the man. Instead I wrote this:
It was afterwards pointed out to me that of course, as false is the "privileged" claim is of The Fountainhead and Atlas Shrugged, it is even more false of Anthem and We The Living. The main characters of those books aren't even privileged enough to live in free societies.
It's interesting to note that a lot of the very best ideas seem to be subject to the most misconceptions. I hear people getting Rand wrong much more often than I hear them getting Marx wrong. Same goes for, say, Popper vis a vis Nietzche. Thinking about it briefly, I imagine this might have something to do with the fact that there are reasons for the bad ideas being bad. A common one is that they are indistinct or imprecise. This would contribute to people saying things indistinguishable from what the originator said, although each may be subtly different even if only in the speaker's head. On the other hand, the better (and more precise) ideas take more work to understand, so less people understand them and there are more misconceptions.
I'm not sure about this theory though. Antirational memes seem to have a lot to do with it too, especially with regards to Rand. Hum.
Another thought; reasonableness. When people say "please be reasonable" or "I'm not being unreasonable", I think this seems to have definite connotations of compromise. Insistently pursuing your own principles in an argument might prompt one's interlocutor to say, "Rihatsu, please be reasonable!" Qualifying one's argument with the words, "now I'm not being unreasonable here," has implications of, "I'm not unwilling to slightly compromise with you on this matter". It's not the direct meaning of the phrase, but I think there are some definite connotations. This may be worth either pursuing, or at least bearing in mind.
I like her insistence that we have to use reason to get anything done (even if she doesn't always stick to it herself [ie, romance]), and her stress on absolute individual sovereignty/liberty, and most of all I like how utterly joyful she is about human acheivement. Advocating taking joy in truly magnificent things is one of the best aspects of her worldview imo. :)
My interlocutor—in interests of privacy I won't say where this conversation took place, but I will say that the man was purporting to be a philosopher—responded thus:
Ok, celebrating our use of reason is definitely a cool thing. But a lot of the Rand stuff I read, if you are going to be intellectually serious, really didn't give a joyful picture of human achievement per se, it was much more a celebration of luck + ability + fuck everyone else. And that is much less cool. Taking joy in truly magnificent things is as well and good, of course, but doing that by ignoring all the shit in the world is simply the unjustified province of the privileged.
Hum, and he says he values being intellectually serious. Actually, that's a significant part of how bad that was as a response. The addition of that little phrase, "if you're going to be intellectually serious", is very telling. It's blatant argument by authority. Amongst philosophers (admittedly, in the conversation in question, I was half-purporting to be one too—though far more humbly than he!) one's intellectual integrity is basically one's currency. This man says he likes reason, but then in the very next sentence he threatens my claim to my own intellectual integrity if I don't go back on my previous post, and agree with him that Rand does not believe that human acheivement is joyful. Removing that sentence would not have changed the meaning of his argument; it is superfluous meta. Evidently he doesn't think enough of his arguments to believe that he can rely on them to persuade me, and adds in a bit of bullying just in case.
I didn't mention the above in my response, however, to avoid getting into a pointless meta-discussion with the man. Instead I wrote this:
Which Rand did you read? I think that's a wilfully negative interpretation of what she advocates. For example in Atlas Shrugged, she tells the reader that Dagny was determined since age 12 to run the railroad, to the degree that it didn't even occur to her that it might be socially unacceptable until age 15, whereupon she dismissed that as unimportant. If that's what you mean by "fuck everyone else", I think that's most unfair. Many, many novels have the theme of "following what you think is right contrary to social stricture".
However it is true that she does not actually tell us where Dagny's determination/enthusiasm comes from. I think that that part just wasn't relevant to the point of the novel, and in order to explain it properly the book would have had to have been about half as long again, rendering it completely unreadable. ;) But there are lots of ways we can easily figure out where it might come from. If you'd like to go into these, we can. :)
I'm not entirely sure what you mean by privileged? Do you mean rich? If so I would point out that the idea that "Rand hates the poor!" is quite misguided. In The Fountainhead, Roark spent most of the novel in dire poverty, and never actually became massively rich. Wealth wasn't his reward. Wynand, however, the billionaire that made the most money, was cast in a light less good than Roark's. He was one of the flawed characters, and his money had a lot to do with that (I'm thinking of the scene in which he says something like, 'the priest in the cloister gives up worldly possessions and retains his soul; I have given up my soul and my compensation is cars and yachts and money'. He says outright in this scene that the priest's position is preferable). Also there's Cherryl, in AS, who is only virtuous so long as she is poor-but-hardworking, and the moment James Taggart impresses her and marries her, and she sells out to his values—again taking money in exchange for the loss of personal integrity—she's doomed. So by privilege you can't possibly mean wealth, but I'm not sure what you do mean, exactly?
Note, by the way, that as an advocate of laissez-faire, Rand couldn't possibly advocate 'fuck everyone else' seriously. You have to cooperate with people in order to participate in free trade, otherwise you won't make a trade agreement. Perhaps you confuse the idea of staying true to your own personal integrity and not compromising what you think is right, with the idea of giving everyone else the finger? If so, I'd point out that through finding mutual preferences, it is not hard to separate cooperation and sacrifice. In other words, when interacting and trading with others (I mean trade in the less vernacular sense of, 'swapping ideas'—since this is what all trade technically constitutes, though I'm aware that's a disingenuous usage—so this would include things like having conversations as well as standard trade), you don't have to lose out or compromise your morality.
What do you include under truly magnificent things, and why doesn't the invention/realization of the skyscraper or the construction of the railroad fall under this category?
It was afterwards pointed out to me that of course, as false is the "privileged" claim is of The Fountainhead and Atlas Shrugged, it is even more false of Anthem and We The Living. The main characters of those books aren't even privileged enough to live in free societies.
It's interesting to note that a lot of the very best ideas seem to be subject to the most misconceptions. I hear people getting Rand wrong much more often than I hear them getting Marx wrong. Same goes for, say, Popper vis a vis Nietzche. Thinking about it briefly, I imagine this might have something to do with the fact that there are reasons for the bad ideas being bad. A common one is that they are indistinct or imprecise. This would contribute to people saying things indistinguishable from what the originator said, although each may be subtly different even if only in the speaker's head. On the other hand, the better (and more precise) ideas take more work to understand, so less people understand them and there are more misconceptions.
I'm not sure about this theory though. Antirational memes seem to have a lot to do with it too, especially with regards to Rand. Hum.
Another thought; reasonableness. When people say "please be reasonable" or "I'm not being unreasonable", I think this seems to have definite connotations of compromise. Insistently pursuing your own principles in an argument might prompt one's interlocutor to say, "Rihatsu, please be reasonable!" Qualifying one's argument with the words, "now I'm not being unreasonable here," has implications of, "I'm not unwilling to slightly compromise with you on this matter". It's not the direct meaning of the phrase, but I think there are some definite connotations. This may be worth either pursuing, or at least bearing in mind.
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