Answer any 3 out of the 8 questions below. Each question requires some thought, and reasonable effort to engage. Answers should be coherent and insightful.
1)The ancient Greek philosopher and sophist Protagoras agreed to teach law to an impoverished student Euathlus, with the firm understanding that Euathlus would pay Protagoras his teaching fee after Euathlus had won his first case in court. After completing his education, Euathlus decided not to to pursue a career in law, in favor of entering politics. After a long time had elapsed, Protagoras became impatient and asked for his fee. Euathlus refused, stating that according to their agreement, he was obligated to pay his fee only after he had won his first case, and that this condition had not yet been fulfilled. Thereupon Protagoras sued Euathlus for payment; both argued their own cases in court.
Taking into account the terms of the agreement between Protagoras and Euathlus, and the fact that this case is in fact the first Euathlus is arguing in court, sketch (utilizing the kind of reasoning involved in Russell’s Paradox and the Liar’s Paradox as your model)
a)an argument that Euathlus — both in the event he wins the case and in the event he doesn’t — is not legally obligated to pay the amount of the agreed fee to Protagoras
b)an argument that Euathlus — both in the event he wins the case and in the event he doesn’t — is legally obligated to pay the amount of the agreed fee to Protagoras.
2)Suppose that a set of examination questions are sent to a class of 40 students, the responses to which are due a couple of weeks thereafter. Among the submitted responses, there is a subset of more than 20 submissions that exhibit a striking similarity of content and verbal formulation, a similarity all the more remarkable given the fact that most of the answers are incorrect, some incorrect in a quite bizarre way . Some flavor of two of the most egregious of these answers are captured by the following illustration, carefully crafted to give an indication of the various dimensions along which the responses go radically wrong: Question: “Pick a prime number between 100 and 1,000, and, using the method discussed in class, calculate its square root to three decimal places”. In response, 20 students select the number 64, and all 20 give the number 9.32184 as its square root.
Approaching this puzzle in accordance with the mode of analysis embodied in Bayes’ Theorem, how would one go about evaluating the relative probabilities of hypotheses such as H1)Each student selected the number and derived this answer independently of the others; H2)The students worked together to gain an understanding of the indicated method of extracting square roots, and then each proceeded independently to select a number and work out its square root; H3)The students all utilized a uniquely easily accessible source to understand the method for the extraction of roots, but then fell into the same natural mistake in calculating the square root.
Discuss whether any of these hypotheses provide plausible explanations of these responses. Are there other a priori plausible hypotheses that might account for this response? For each of the hypotheses H1, H2, and H3, construct a (less extreme) variant of this illustration that makes that hypothesis plausible.
3)Summarize the argument developed in Sections 1-5 of Carl Hempel’s Studies in the Logic of Confirmation, specifically that part of the paper than deals with Nicod’s characterization of the confirmation relation and the example of the Ravens that undermines it. Discuss the following situations:
a)The urn in front of you either contains 100 white balls (H1), or 75 white balls and 25 black balls (H2). Assume that these are the only two hypotheses that are at play. Does the blind extraction of a white ball confirm H1? H1 and H2? Neither? Discuss.
b)Granted the logical equivalence of “All ravens are black” and “All non-black objects are non-ravens”, what accounts for our intuition (or illusion) that the observation of a white piece of chalk, or a green leaf, or a blue pen, confirms the latter but not the former statement?
c)Granted that any observation that confirms one of the two universal generalizations must confirm the other, why is it that the observation of a white piece of chalk confirms (or perhaps just seems to confirm) the two logically equivalent generalizations to a lesser degree than does the observation of a black raven? Can you define a universe in which the observation of a white piece of chalk confirms “All ravens are black” to a greater degree than does the observation of a black raven?
4)Summarize (using your own words) Keynes’ analysis of the conditions under which it is appropriate to attribute the occurrence of an event to chance. Consider, in particular, the difference between the way we think of the problem of pre
