I present a puzzle which seems simple, but is found to have interesting implications for confirmation. Its dissolution also helps us to throw light on the relationship between first- and second-order probabilities construed as rational degrees of belief.

By a `denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phrase is denoting solely in virtue of its form. We may distinguish (...) three cases: (1) A phrase may be denoting, and yet not denote anything; e.g., `the present King of France'. (2) A phrase may denote one definite object; e.g., `the present King of England' denotes a certain man. (3) A phrase may denote ambiguously; e.g. `a man' denotes not many men, but an ambiguous man. The interpretation of such phrases is a matter of considerably difficulty; indeed, it is very hard to frame any theory not susceptible of formal refutation. All the difficulties with which I am acquainted are met, so far as I can discover, by the theory which I am about to explain. (shrink)

Professor Copi provides us with the following example:Remove all cards except aces and kings from a deck, so that only eight cards remain, of which four are aces and four are kings. From this abbreviated deck, deal two cards to a friend. If he looks at his cards and announces that his hand contains an ace, what is the probability that both his cards are aces? If he announces instead that one of his cards is the ace of spades, what (...) is the probability then that both his cards are aces? (shrink)

At least one of these conceptions of probability underlies any theory of statistical inference (or, to use Neyman's phrase, 'inductive behavior'). ...

Definite descriptions, I shall argue, have two possible functions. 1] They are used to refer to what a speaker wishes to talk about, but they are also used quite differently. Moreover, a definite description occurring in one and the same sentence may, on different occasions of its use, function in either way. The failure to deal with this duality of function obscures the genuine referring use of definite descriptions. The best known theories of definite descriptions, those of Russell and Strawson, (...) I shall suggest, are both guilty of this. Before discussing this distinction in use, I will mention some features of these theories to which it is especially relevant. (shrink)

In an article “Countering a Counter-intuitive Probability” [4], Lynn E. Rose discusses a question in conditional probability, claiming that the following problem posed by Copi [1] is usually incorrectly solved:Remove all cards except aces and kings from a deck, so that only eight cards remain, of which four are aces and four are kings. From this abbreviated deck, deal two cards to a friend. If he looks at his cards and announces that his hand contains an ace, what is the (...) probability that both his cards are aces? If he announces instead that one of his cards is the ace of spades, what is the probability then that both his cards are aces? (shrink)

There are obvious benefits to be gained from the study of logic: heightened ability to express ideas clearly and concisely, increased skill in defining one's terms, enlarged capacity to formulate arguments rigorously and to analyze them critically. But the greatest benefit, in my judgment, is the recognition that reason can be applied in every aspect of human affairs.

This is an illustrated guide to a wonderland of reason where nothing is as it seems, through a maze of mental curiosities and contradictions. It discusses paradoxes of all types--mathematical, logical, scientific, philosophical and more. Though many involve sophisticated concepts and logical reasoning, none requires a highly technical background-knowledge of ordinary language and simple arithmetic will do. Twenty-five stand-alone chapters each present and discuss a different paradox, including: the Barber Paradox; the Crocodile's Dilemma, M. C. Escher's Paradoxes, the Liar Paradox, (...) the Prisoner's Dilemma, the Raven Paradox, Zeno's Paradox, and many others. Each chapter features an end note indicating related paradoxes elsewhere in the book. Includes 118 mind-boggling illustrations, optical illusions and visual acrobatics. (shrink)