- 07/04/2019 at 6:22 am #1322962EduGorillaKeymasterSelect Question Language :
Sometimes one’s evidence for a proposition is sharp. For example, you’ve tossed a biased coin thousands of times. 83% of the tosses landed heads, and no pattern has appeared even though you’ve done a battery of statistical tests. Then it is clear that your confidence that the next toss will land heads should be very close to 83%. Sometimes one’s evidence for a proposition is sparse but with a clear upshot. For example: You have very little evidence as to whether the number of humans born in 1984 was even. But it is clear that you should be very near to 50% confident in this claim. But sometimes one’s evidence for a proposition is sparse and unspecific. For example: A stranger approaches you on the street and starts pulling out objects from a bag. The first three objects he pulls out are a regular-sized tube of toothpaste, a live jellyfish, and a travel-sized tube of toothpaste. To what degree should you believe that the next object he pulls out will be another tube of toothpaste? The answer is not clear. The contents of the bag are clearly bizarre. You have no theory of “what insane people on the street are likely to carry in their bags,” nor have you encountered any particularly relevant statistics about this. The situation doesn’t have any obvious symmetry, so principles of indifference seem to be of no help. Should your probability be 54%? 91%? 18%?
It is very natural in such cases to say: You shouldn’t have any very precise degree of confidence in the claim that the next object will be toothpaste. It is very natural to say: Your degree of belief should be indeterminate or vague or interval-valued. On this way of thinking, an appropriate response to this evidence would be a degree of confidence represented not by a single number, but rather by a range of numbers. The idea is that your probability that the next object is toothpaste should not equal 54%, 91%, 18%, or any other particular number. Instead it should span an interval of values, such as 10%, 80%.The toothpaste-in-the-bag example is artificial, but many realistic examples have been proposed. What is your confidence that “there will be a nuclear attack on an American city this century”? What is your state of opinion concerning “the price of copper and the rate of interest twenty years hence, or the obsolescence of a new invention, or the position of private wealth owners in the social system in 40 years”?
It is tempting to agree with J. M. Keynes that “About these matters there is no scientific basis on which to form any calculable probability whatever” and to think that the problem isn’t just that our computers aren’t fast enough. The idea is not that some computational or representational limitation prevents you from having a definite probability. Give an agent access to exactly your evidence relevant to the toothpaste claim, or, say, the claim that there is a God. Give her all the computers, representational tools, brain upgrades, etc. that you like. Still it seems as though the agent would go wrong to have any very precise degree of belief in the relevant claim. According to Scott Sturgeon: When evidence is essentially sharp, it warrants a sharp or exact attitude; when evidence is essentially fuzzy-as it is most of the time-it warrants at best a fuzzy attitude.In the passage, the author was concerned with which of the following?
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