Doris Olin
Pages: 233
https://www.jstor.org/stable/j.cttq4946

1. Front Matter
(pp. i-vi)
(pp. vii-viii)
3. Preface
(pp. ix-x)
4. 1 The nature of paradox
(pp. 1-20)

Paradoxes can be fun. They can also be instructive, for the unravelling of a paradox may lead to increased philosophical knowledge and understanding. The paradoxes studied in this work offer promise of both these features. But paradoxes may be also disturbing; their study may reveal inadequacies, confusion or incoherence in some of our most deeply entrenched principles and beliefs. The reader is forewarned: some of the material that follows may prove unsettling.

It seems wise to begin at the beginning, with the questions “What is a paradox?” and “How does one resolve a paradox?” But first we need some examples...

(pp. 21-36)

Paradoxes are baffling. Faced with an apparently impeccable argument that leads to an apparently outrageous conclusion, we are confused and confounded. On the one hand, the conclusion appears false; on the other hand, it apparently must be true. What appears to be cannot be, we assume. This is the source of our fascination; this is why there is a problem.

Recently, impressive arguments have been advanced that this underlying assumption is mistaken. A statement can beboth true and false,it is maintained; further, it can be rational to believe that a given statement and its negation are both true....

6. 3 Believing in surprises: the prediction paradox
(pp. 37-60)

A teacher announces to her student S that she will give him exactly one examination during the next week, and it will be a surprise: S will not be able to predict, prior to the day of the examination, on which day it will be held.² The student, a star logician, objects that this is impossible. He argues as follows. “If the exam were held on Friday, then on Thursday evening, realizing that no examination had yet been given, I would reasonably expect it on Friday; hence a Friday examination would not be a surprise. But, if the examination were...

7. 4 The preface paradox, fallibility and probability
(pp. 61-78)

Is consistency always an epistemic virtue?¹ The traditional view has been that consistency is essential to rationality, that it is something to be aimed at in all our beliefs.² Inconsistent beliefs, it is maintained, are always unreasonable. Call this “the conservative position”. The central issue of this and the following chapter is whether conservative stance on consistency is correct.

First, some terminology. A set of statements is inconsistent if it is logically impossible for all the statements in the set to be true. For instance, the statements

(i) Pierre is a politician.

(ii) All politicians sometimes lie.

(iii) Pierre never...

(pp. 79-104)

The lottery paradox is the most powerful of the consistency paradoxes, and the greatest threat to the traditional view of consistency. It draws us into a tangle of thorny issues in epistemology, in particular, issues concerning knowledge and justified belief. But the paradox itself is simple and elegant. It depends on one key philosophical premise, the principle of high probability, which can be stated as:

(HP) There is a number$n\left({1.5such that ifPhas probabilitynforS, thenSis justified in believingP. (HP) is motivated largely by the threat of scepticism. The moral many... 9. 6 Newcomb’s problem (pp. 105-136) You have been presented with an exciting opportunity.¹ Before you on the table are two boxes,B1and22.B1is transparent; you can see tha it contains$1,000.B2, which is opaque, contains either $1,000,000 or nothing. B1:$1,000B2: \$1,000,000 or nothing

You have a choice between two actions: taking what is in both boxes or taking only what is in the second box. Before you make your choice, the following background information is carefully explained. The content of the second box is determined by a superlative predictor who has successfully predicted the choice of all (almost all)...

10. 7 The prisoner’s dilemma
(pp. 137-166)

You and a colleague have been arrested and charged with committing a crime. You are isolated in separate cells, unable to communicate. The prosecutor, aware of the shakiness of his case, offers a deal in order to elicit a confession. If you both remain silent, he informs you, there is enough evidence to convict you of a lesser charge, and you will consequently each receive a year in prison. However, if you provide details of the crime and your partner remains silent, you will get off scot-free and he will face a sentence of ten years. Similarly if he confesses...