Think by Simon Blackburn Chapter 6a Reasoning
Introduction Philosophers attach enormous significance to our capacity to reason, and for this reason the study of reasoning itself is the most fundamental of all philosophical endeavors. This chapter lays out some of the fundamental aspects of the study of reasoning, and some of the perennial philosophical problems about the nature of reasoning. However, we will be focusing only on the problem of induction.
Circular reasoning Do you recall the problem of the Cartesian Circle? It involved Descartes claim that we can trust our clear and distinct ideas of the world. Descartes argued that we could trust our clear and distinct ideas because God gave them to us, and that since God is not a deceiver, he would not have given us clear and distinct ideas if they could not be trusted. The problem was that Descartes actually needed to use and trust the criterion of clarity and distinctness to prove God s existence in the first place.
The problem of induction There is another famous reasoning circle involved in the attempt to prove that we can trust our reasoning about nature. It s called the problem of induction. The problem is that all of our beliefs about the way the world is are based on things we have experienced in the past. For example, if you think that eating will satisfy your hunger, this is just because in the past eating has satisfied your hunger. if you think the ball will fall and bounce when you drop it, this is just because the ball has always done this in the past.
The uniformity of nature The question is: how do we know that the past is a reliable guide to the future? (p.212) Suppose we tried to establish this by some kind of argument. For example we might say that we know that the past is a reliable guide to the future because in the past, the past has been a pretty reliable guide to the future. You can see the problem. When we argue this way, we are just assuming that our past experiences with respect to using the past as a guide to the future are a reliable guide to our future experiences with using the past as a guide to the future. Just like the Cartesian Circle, we find that we have assumed the very point at issue.
The problem of induction is best captured by the question: A. How do we know the future is real? B. How do we know that past is a reliable guide to the future? C. How do we know the future is a reliable indicator of the past? D. How is God s existence provable on the basis of inductive evidence?
The problem of induction is similar to the problem of the Cartesian Circle because A. Both involve circular reasoning. B. Both use the criterion of clarity and distinctness. C. Both are committed in Descartes Meditations. D. Both are fundamentally analogical arguments.
The laws of the universe. This problem is much deeper than it may at first appear, and it has serious practical consequences as well. One way to show this is to begin with the fact that whenever we observe patterns in nature, we tend to assume that they must have some discernible cause. This is basically just a way of stating Leibniz s principle of sufficient reason. The problem with this view, however, is that patterns can in fact be produced by random processes. The failure to appreciate this fact is at the heart of a lot of confusion about how the world works, and it is known as The Gambler s Fallacy.
The Gambler s Fallacy The Gambler s Fallacy basically involves believing that there is such a thing as being hot or cold when you are playing a game of chance, like roulette, craps, or a slot machine. For example, people who have been having a good night at the table have a hard time quitting because they think they are hot. Specifically, they think that the fact that they have had a series of winning bets means that they will continue to have winning bets. Of course, this belief is what makes casino owners very wealthy people. People who run casinos know that there is no such thing as being hot or cold. When you are dealing with random games, the past results, not only does not guarantee, but actually has nothing whatsoever to do with the future.
The Gambler s Fallacy 2 Another manifestation of the gambler s fallacy is the belief that as a certain kind of result accumulates, the pressure builds up for it to change. This is what people sometimes call The Law of Averages. (In fact there is no such thing.) So, for example, people who have been cold at the tables will often convince themselves that this recent history means the odds have to shift back in their favor at some point. Or, people who have been pulling a slot machine all night and getting no payout often feel that it would be foolish to quit, since the odds are now so much in favor of a jackpot. This is the same kind of mistake: basically games of chance have no memory whatsoever.
Randomly produced patterns Many people have a hard time believing all this, and if they believe it they still have a hard time processing it s implications. For example, suppose you were to start flipping a perfectly ordinary nickel and recording whether it comes up heads or tails each time. Ask yourself this, which of the following patterns is more likely to come up? HHHHHHHHHHHHHHHHHHHHHHHHHHHHHH HTHTHTHTHTHTHTHTHTHTHTHTHTHTHTHT HTTHHTTTHTHTTTTHHTTHTHHHHTTTHHTH The answer is that they are all equally likely. In fact, every single pattern is just a likely as any other.
Basics of probability It s pretty easy to understand why this is. Consider just one toss of a coin. As you know, there is a 50% chance of getting heads and a 50% chance of getting tails. This is simply because there are only two possibilities and they are both equally likely. Now consider two tosses in a row. There are four different results that can occur here. HH TT HT TH All of these are equally likely too. In particular, HH is no more or less likely than HT. There is a 25% chance of either one. Now consider three tosses. There are now eight possible results. HHH HHT HTT HTH TTT TTH THH THT These, too, are all equally likely. There is a.125% chance of every sequence. We can do this forever. The result is that 100 heads in a row, or a perfectly alternating sequence of heads and tails has exactly the same probability as any other one that actually appears to be perfectly random.
If I flip a fair coin five times in a row and each time it comes up heads, then the next time I flip the coin is more likely to be tails than heads. A. True B. False
What does randomness look like? Lots of people think that random processes can t produce patterns, but this is simply untrue. A funny example of this is the ipod Shuffle. When Apple first made the Shuffle the songs were actually generated randomly. Of course, this means that sometimes the same song might be played two or more times in a row. When people noticed this happenig, they assumed the Shuffle was not random and that Apple was trying to promote certain songs. So Apple actually had to change it to a non random program, just to satisfy most people s uninformed views about what randomness really is.
Applications to physics An Austrian philosopher and physicist named Ludwig Boltzmann applied these basic insights to physical systems. Essentially he pointed out that if we think of a container filled with a gas, we will tend to assume that the gas, which is just a collection of molecules, will tend to be spread out more or less evenly within the box. If we then ask ourselves which of the following is more likely: (1) a configuration of molecules that corresponds to our expectation that the molecules will be spread out more or less evenly, or (2) a configuration in which every molecule in the box is in one half of the box, we will naturally say that the spread out configuration is more likely. In fact, however we will be wrong. Just as with coin tossing, all configurations of molecules are equally likely.
Applications to physics 2 But we are not as confused as it seems. The truth is that it is still far more likely that the molecules will be spread out evenly throughout the box. But this is not because one distribution is more likely than another. It is just because there are more- orders of magnitude more- ways to spread the molecules throughout the box, than for them to be bunched up in one half of the box. The point is that nothing physically prevents this. The reason we never encounter it is strictly a statistical phenomenon, not a matter of physical impossibility. This is what is going on with coin-tossing as well. Our sense that a random-looking distribution is more likely than a perfect run of heads or tails has a basis in statistics. The fact is that there are many, many more ways to make sequences that look random to us, than sequences that look ordered. But again, there is nothing more physically likely about any given sequence.
Which of the following statements about coin tosses is true? A. 10 heads in a row is just as likely as 5 heads followed by 5 tails. B. 10 heads in a row is just as likely as a combination of 5 heads and 5 tails. C. 10 heads in a row is just as likely as 5 heads in a row.
Which of the 10 BB s in a box is more likely to have been produced by a random process? A. 1 B. 2 C. They are both equally likely. 1 2
What all this means What all this means is that there is no way to prove that a particular pattern we observe is not simply a statistical phenomenon, one that gives no reason whatsoever to suppose that the observed pattern must, or is even likely to continue in this way. If you really grasp what is being said here this should be quite disturbing. It means that all of the order that we now call the universe could, in fact, be the result of purely random processes.
What all this means 2 If, for example, you think of tossing a coin an infinite number of times, you will realize that you can imagine absolutely any sequence you like, and at some point in the series you will be able to find it. In fact, if it is truly an infinite series, you will be able to find that sequence, along with every other sequence, an infinite number of times. Similarly, if you imagine the universe as simply a collection of molecules banging around in a box forever, every single sequence of collisions, including the one that corresponds to the highly ordered universe we now observe, will be found. And yet it will all be perfectly random.
The lottery for the golden harp So now the point of Blackburn s story about the lottery for the golden harp should be clear. The lottery for the golden harp is really not much different than the California State Lottery. The odds of winning the lotto are a little worse (1 in 16 million) than the odds of winning the golden harp (1 in 10 million). But both are incredibly low. Also, in Blackburn s lottery, one of the spirits is guaranteed to have the winning number, which is not the case with the lotto. Applying golden harp reasoning to the lotto, Blackburn asks you to imagine that you and your friend Philo both have lotto tickets, and are sitting next to the radio on Saturday night as they call out the winning number. Your numbers differ only in the last digit as follows. Philo: 1 2 3 4 5 6 Cleanthes: 1 2 3 4 5 27 The winning number is called out, to the growing amazement of both of you: 1 2 3 4 5 and then the radio dies.
The lottery for the golden harp 2 To this point, both of you are equally in the running to become multi-millionaires. You both have already defied the odds by getting the first 5 numbers right ( 1 in 450,000). The question is who is most likely to have one the whole thing? Of course, because we understand the randomness of the lotto, most of us will at least say that there is no guarantee that either of us has won. But even though we know the numbers are generated by a random process, Blackburn s point is that most of us will still tend to think Philo is the likely winner. The pattern is just so obvious. The problem, of course, is that there is no pattern. At this point you both have exactly the same chance (1/45) of being the winner.
Responding to Hume How do we respond to Hume s point that there is no way to prove that nature is uniform? Some people have responded that this shows that the uniformity of nature is an article of faith, and that in the end science requires faith just as much as religion does. This point can not be simply dismissed, but it is a bit of an overstatement. Many people disagree on whether one should have faith in, say, the miracle of Christ s resurrection. But no sane person really thinks it makes sense to conduct our daily business without considering our past experience.
Descartes Redux The more traditional response to Hume is actually to reject the requirement of proof. Try to recall how Hume criticized Descartes attempt to prove the existence of the external world. He said that if you doubt everything, then you have taken away the very tools by which you would prove the existence of the external world.
The practicality of rationality This is the proper response to Hume as well, and in fact it is really Hume s fundamental point. There is no non circular way to prove that the past is a reliable guide to the future. But we do not actually need to prove it in order for it to be a reasonable assumption. Just as we can not practically doubt our own existence or the existence of an external world, we also can not practically doubt the uniformity of nature.