Because you are highly unlikely to cast the deciding vote in the next elections, it is often said that you don’t have a reason to vote in order to change the outcomes. In a recent paper, however, Zach Barnett forcefully argues that this is a mistake. He shows how it follows, from rather conservative assumptions, that in many real-life cases the expected social value of voting is higher than its cost. Barnett is successful, we believe, in showing that the commonly (...) held belief – that voters do not have a reason to vote in order to change the outcomes – is way too hasty. However, Barnett is – we argue in this paper – too quick on one key premise, and once this is noticed, it becomes unclear how often Barnett’s reasoning can point to a justification of voting to change the outcomes. Barnett’s reasoning, we conclude, may apply to significantly less real-life scenarios than he suggests. (shrink)

Many efforts have been made in recent years to construct formal systems for mechanizing general mathematical reasoning. Most of these systems are based on logics which are stronger than first-order logic. However, there are good reasons to avoid using full second-order logic for this task. In this work we investigate a logic which is intermediate between FOL and SOL, and seems to be a particularly attractive alternative to both: ancestral logic. This is the logic which is obtained from FOL by (...) augmenting it with the transitive closure operator. While the study of this logic has so far been mostly model-theoretical, this work is devoted to its proof theory. Two natural Gentzen-style proof systems for ancestral logic are presented: one for the reflexive transitive closure, and one for the non-reflexive one. We show that these systems are sound for ancestral logic and provide evidence that they indeed encompass all forms of reasoning for this logic that are used in practice. The two systems are shown to be equivalent by providing translation algorithms between them. We end with an investigation of two main proof-theoretical properties: cut elimination and constructive consistency proof. (shrink)

We present a new justification for methodological triangulation (MT), the practice of using different methods to support the same scientific claim. Unlike existing accounts, our account captures cases in which the different methods in question are associated with, and rely on, incommensurable theories. Using a nonstandard Bayesian model, we show that even in such cases, a commitment to the minimal form of epistemic conservatism, captured by the rigidity condition that stands at the basis of Jeffrey’s conditionalization, supports the practice of (...) MT. (shrink)

The purpose of the paper is to defend a modified version of the report given by Strabo about the transmission of the writings of Aristotle during the Hellenistic period. The basic dilemma was pointed out by Dom Jean Liron in 1717: The existence of our Corpus Aristotelicum entails that Strabo must be exaggerating either in assuming that the manuscripts brought by Neleus to Scepsis were the only manuscripts of the Aristotelian and Theophrastean writings, or in asserting that these manuscripts (...) were severely damaged. Many writings of our Corpus are missing in the Hellenistic catalogue of Aristotle's works while they are listed in the later catalogue of Ptolemy al-Gharïb; furthermore, the single books of the transmitted treatises are labelled by means of the pre-Hellenistic system of 24 letter labels, whereas in the Hellenistic catalogue the single books are numbered by means of the Hellenistic system of 27 alphabetic numerals. This suggests that the treatises missing in the Hellenistic catalogue formed part of a collection which was inaccessible in Hellenistic times and which, therefore, preserved the pre-Hellenistic system of book-labelling. After the rediscovery of the collection its system of book-labelling was maintained by the editors who laid the foundations of our Corpus. The same criterion reveals the Eudemian Ethics in eight books to be a later compilation. (shrink)