Think by Simon Blackburn. Chapter 6b Reasoning

Transcription

1 Think by Simon Blackburn Chapter 6b Reasoning

2 According to Kant, a sentence like: Sisters are female is A. a synthetic truth B. an analytic truth C. an ethical truth D. a metaphysical truth

3 If you reach into a jar and pull out a red jelly bean you get 10 dollars. Which of the following jars would you like to choose from:? A. Jar A: contains 1 red bean and 9 black beans. B. Jar B: contains 10 red beans and 100 black ones.

4 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.

5 How much more likely? It is worth it to remember that the likelihood of sequential occurrences of random events like coin tosses is an exponential function. The likelihood of a certain sequence of 5 coin tosses in a row is 1/2 5 = 1/32 The likelihood of a certain sequence of 10 coin tosses in a row is 1/2 10 = 1/1024 The likelihood of a certain sequence of 20 tosses in a row is 1/2 20 = 1/1,048,576

6 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 does not support the inference that the world must continue according to this pattern. 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.

7 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.

8 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: Cleanthes: The winning number is called out, to the growing amazement of both of you: and then the radio dies.

9 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 won 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 probably the 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.

10 Which of the following results is the most likely? A. Result 1: Tossing a fair coin 10 times in a row and landing heads each time. B. Result 2: Tossing a coin one time and landing heads, given that it has just landed heads on all of the previous 9 tosses. C. These two results are equally likely.

11 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.

12 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.

13 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.

14 Hume s problem of induction establishes that A. we can not prove the existence of an external world. B. we can not prove that nature is uniform. C. we can not prove that statistics are always right. D. we can not prove the Gambler s Fallacy.

15 The best response to Hume s problem of induction is that: A. there is no way to prove anything, so this is not a serious problem. B. God would not make us believe that nature is uniform if it were not uniform. C. the fact that we can not prove it, does not mean that we ought to doubt it for practical purposes. D. It can not be proven that we will never have an answer to the problem of induction, so it is ok to believe that one day we will.

16 If you reach into a jar and pull out a red jelly bean you get 10 dollars. From which of the following jars are you most likely to get a red bean. A. Jar A: contains 1 red bean and 10 black beans. B. Jar B: contains 10 red beans and 100 black ones. C. The likelihood of drawing a red bean is the same for each.

17 Which of the following statements about coin tosses is false? A. 10 heads in a row is just as likely as 5 heads followed by 5 tails. B. 10 heads in a row is less likely than some combination of 5 heads and 5 tails. C. 5 heads in a row is twice as likely as 10 heads in a row.