Monday, December 31, 2007

Knowledge is value.

As it’s the last day of the year I’ll allow myself a glimpse at the big picture. I started my second wave of philosophy with the intention of exploring the dual nature of the mad. I had seen at first hand the brilliant yet unpredictable thought processes of certified schizophrenics and manic depressives. Among the great thinkers and artists to whom we owe so much there are to be found a high density of mad men and women. Often their madness goes unmentioned in deference to their achievements. The summation is that creative minds seems to be capable of great folly and great wisdom. The rest of us look on in terror and pity.

My idea was that the mad know things that are beyond the reach of the sane. On a similar vein, the mad see the value in things that the sane overlook. The problem is that this is hard to even state, partly because the mad are seen by certain officious types as ill, their beliefs as “delusions”, or “symptoms”, their political rights as suspended and their condition one of suffering. But the real reason is that in philosophy, analytic philosophy at least, “S knows that p” is considered to be factive, so: “Einstein knows that time is relative” is only true if time is relative. Since the sane believe that a lot of what mad people believe is false, calling these things “knowledge” is against the rules, even if the mad person claims to know what he believes and we don’t claim to know that the mad person’s beliefs are false .

So I am under pressure to rephrase my initial thought as that the mad “believe” things that are beyond the reach of the sane. Now I can say that mad people believe things that are more likely to be false. This looks very promising indeed since we can explain the mad genius. If the mad believe what is more likely to be false, then they are higher risk believers. A Wall Street slogan is “the higher the risk the higher the return". When in the jungle of improbable beliefs the mad man stumbles across a true proposition, as long as he can tame it and bring back to the suburbs of probable beliefs alive, he will have found something of great value. Whereas the sane, who get their beliefs second hand from text books and TV, are scarcely likely to believe anything of any value. Of course, there is exchange value and use value. Second hand ideas can be very useful, and you can always hawk them to children or students. But beliefs that no one else have are for that reason worth a great deal. Of course this is only if they are true! But they appear to the believer just as valuable whether they are true or not, since to believe something is the same thing as believing it to be true.

But now enter the complication. Value and belief are the subject matter of decision theory. If something is improbable in decision theory, it is less valuable not more valuable. I put £36 on double six at even odds I have an improbable belief that the dice will come up two sixes. My speculation is worth £1 to anybody who knows the ways of dice. This is because out of 36 possible futures, only in one do I win. Yet if I believe it, in the sense that I know it, then my speculation would be worth £72. This is because there is only one possible future, and in that future the dice come up double six. So from my perspective I do not have an improbable belief at all. From my perspective, if I am certain the dice will come up double six, my belief is not just highly probable, it is true. So we have a pair of perspectives, from one of which my belief is improbable and from the other it is certain. Which perspective is right? The problem here is that this depends on no fact in the world!! Of course if the dice comes up snake eyes, then my belief was improbable and false. But if it comes up two sixes, those who valued my punt at £1 are still right. Their assessment of the situation is un-falsifiable in the face of experience.
The thoughts of the creative genius are clearly not of this kind. It is not as if when Einstein came up with Special Relativity it was clear to everybody else that the theory had only a 1/36 chance of being correct, and Einstein just got lucky. No one had even been able to conceive of it. A recent Lakatos award winner suggests that the pieces were all there and if Einstein hadn’t come up with it, some one else would have. It is easy to think up ideas that have already been thought up. Stephen Tiley came up with Hook’s law, I’ve come up with binomial probability distributions, “Bad News” came up with “A stairway to Heaven” by Lead Zeppelin, and a tax collector named Saul came up with Christianity, adding in his own homophobic twist.
Likewise with Darwin. The theory of evolution is, in its essence, very easy to understand. But it wasn’t a low probability hypothesis that no one but Darwin had the craziness to back. It wasn’t a hypothesis at all. Of all the people in the world, only one came up with evolution. The beliefs involved were highly improbable in this sense, they were one in a million. I am not implying that Darwin was mad incidentally, there are enough idiots who would love to go back in time and put him in a strait jacket as it is without me adding to their number.
So the decision theoretic model of improbable beliefs is not what I am after. Making wild guesses doesn’t count. One man’s wild guess is another man’s low probability hypothesis. What I am after is risky knowledge. This is not the same as betting on the thin end of the odds.
So now we have some highly philosophically interesting concepts in the pot. Knowledge, value, probability, belief contents. It seems like the value of knowledge increases in inverse proportion to its probability. But that knowledge is only knowledge if its probability is 1.
Let us look at the great mathematicians of value. They are no longer working in the abstract but are now in the stables of the super rich, hedging their wealth. Wealth does not stand still, but is alive. Leave it unattended and it will dwindle, tend to it and it will grow. The price of a stock now is an indicator of the price of the stock in the future. We can project the price into the future by seeing the range of future prices as a probability distribution. We can calculate a single value from this distribution and call that the expected value, or utility of the stock. But there is another dimension that is a little more mathematically slippery. The expected value of two stocks can be the same while the risk can be different. Black and Scholes came up with a measure of Risk in terms of variance. This can be thought of in terms of standard deviations from the mean. This again can be given a value and in derivative markets risk can be bought and sold like anything else. Here we have a mathematical equivalent of the creative genius idea. It has a probability of 1, but a high risk. However, the problem is that variance doesn’t work for probability 1. When a proposition has a probability of 1 of being true, there is no probability distribution.

Lets just try equating knowledge with value. How so? What is the value of a bet that pays £67 if p is true given that you know that p is true? Answer £67. In general the value given knowledge equals the value. Compare with probability. What is the value of an outcome with a probability of ½. Answer, ½ of the value of that outcome if it were known. Truth = probability times value. Knowledge = Value.

A contemporary question in epistemology is “what is the value of knowledge”. The answer here is that the value of knowledge is the value of the truth. Whereas the value of a partial belief is the value of the truth times the probability. What should we find out? What should be the subject of our inquiry? Which of the myriad facts that lie just beyond our reach should we step forward and grasp? The answer is, those that are of value, since the value of knowledge just is the value of the truth. It is the love of the good that should guide us through life.

Wednesday, December 05, 2007

Jonny versus John Wright on Freewill

Tonight I’m not going to post about Ted Honderich’s talk on his new theory of consciousness, interesting though it was, but rather about John Wright’s exemplary talk about Freedom and Determinism. The reason for this is that in my mysterious past I carved out a thesis on freedom and determinism under the tutelage of Professor Honderich himself. It has been established by science that I have got a learning difficulty, which was given to Honderich’s consciousness as a teaching difficulty. Consequently my views on freedom and determinism may be negatively defined by Ted’s views. So in reading my views on J.Ws talk, you might be able to deduce T.Hs views on determinism. Two birds with one stone.

John Wright’s talk was exemplary in my view since he laid out the whole debate very clearly and not only presented his argument, but the whole logical space in which his argument worked. Consequently, (perhaps aided by my learning difficulty) I was able to see with great clarity where the argument went wrong.

John’s argument was what he called a barrel argument, meaning that you partition up the logical, or conceptual space into mutually exclusive and jointly exhaustive alternatives and eliminate each alternative. Usually the alternatives are that “e”, some event was either caused, or not caused. If it was caused, so the argument goes, it was not an act of free will, but if it was not caused then it was also not an act of free will. Therefore there are no acts of free will. Boom! Boom! both barrels.

Fast forward a few possible libertarian responses, including “Pink’s magic barrel”, and we get to the really interesting part of John’s talk. He tries to run the barrel argument by partitioning the logical space into 5 broadly speaking modal alternatives. The five alternatives were 1. Metaphysically impossible, 2. Contingent Random. 3. Contingent probabilistic. 4. Contingent historically/physically determined. 5. Metaphysically necessary. The argument goes that these categories are mutually exclusive and exhaustive in that for all e, if e is an event, (I’m a little weak on this, perhaps it shouldn’t be event, but proposition) then it falls into one and only one of these categories. The twist is that these categories don’t mention causation, explicitly anyway, since the libertarian justly accuses the original barrel argument of ruling out free acts from the start by implicitly assuming that free choices aren’t causes, and that the only powers are causal powers.

It is clear that we can rule out 1 and 5 straight away. If “e” is metaphysically necessary or impossible, then “e” is not an act of free will. Boom! Boom! So now it looks like if John can rule out 2, 3 and 4 then he has ruled out acts of free will without mentioning cause. He then says that 2, if an event is random then it is not an act of free will Boom! 3, If an event is probabilistic it is not an act of free will Boom! 4. If an event is historically/physically determined then it is not an act of free will Boom! Therefore there is no act of freewill.

Dirty Harry: “I know what you're thinking. Did he fire six shots or only five? Well, to tell you the truth, in all this excitement, I've kinda lost track myself. But being as this is a .44 Magnum, the most powerful handgun in the world, and would blow your head clean off, you've got to ask yourself one question: Do I feel lucky? Well, do ya punk?"

So John seemed to think that the libertarian would be forced to find a sixth barrel but that there is no conceptual space left for a sixth alternative.. All in all, a great talk which provoked a lot of interesting discussion.

But I wonder why a determined event is not an act of freewill? The idea is immediately appealing and needs no sophisticated argument. “Determined” can be substituted with “couldn’t have been otherwise”. A free choice necessarily could have been otherwise. Therefore free choices are not determined, and determined events are not free choices.

Given this, why is it that a contingent yet historically/physically determined event couldn’t have been otherwise? What ever your views about time, it is now determined that the allies won world war 2. But could it have been otherwise? Yes. The allies could have lost WWII. What is the probability that the allies won WWII? Well, call me anti revisionist, but I would say the probability that the allies won is 1. But what was the probability in 1940? Considerably less than 1. Or might it not be the case that it was completely random that the allies won? Suppose aliens observing earth in the early forties tried to predict who would win using incredibly sophisticated science of human behaviour. Might they not conclude that it was random what the outcome would be? My point here is these categories: determined, random, probabilistic, aren’t mutually exclusive. The same event could be random, historically determined and probabilistic relative to different times and theories and information states. So the five barrel argument fails, not because there is a sixth barrel, but because the five barrels aren’t mutually exclusive.

To freely choose that F through action A it must be the case that P(F A) – P(F ~A) > 0. As P(F A) – P(F ~A) tends to 1, the greater the freedom of the choice. If P(F A) = P(F ~A), then F is not freely chosen at all, whatever value for P(F A). What is not clear to me is why John thinks that this equality must hold in all cases. Surely even in the most determined of cases we want to say that things would have gone differently counterfactually. Whatever the probability that I wrote this blog post, counterfactually, if I hadn’t freely chosen to have done so, then it wouldn’t have been written. Therefore it was a consequence of my free choice.

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