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)

In the April number of the Classical Quarterly, Mr. H. J. Cunningham calls in question my interpretation of a passage in the speech of Claudius on the claims of the Gallic chieftains, which I will follow his good example by quoting in full. It forms the first legible sentence of Column II.

This old difficulty has recently received a new explanation from the pen of Dr. E. G. Hardy . Dr. Hardy believes—and his view has met with some acceptance—that the disability, under which these Gallic candidates for admission to the Senate laboured, was the want of a municipalis origo. Up to this time, he contends, only Romans who were members of a town of Roman or Latin rights were eligible for admission to the Senate. Now in the Tres Galliae there were (...) practically no such towns: these Gallic chiefs possessed the ciuitas individually by special grant and not as members of any municipality. Hence the door of the curia was closed to them while it was open to Romans from Lugdunum or Vienna. (shrink)

In the Classical Quarterly of April, 1914, I ventured to call in question the explanation of this well-known difficulty put forward by Dr. E G. Hardy in his Roman Laws and Charters. Dr. Hardy has done me the honour of replying to my article in the October Quarterly, but his lengthy argument entirely fails to convince me.

This old difficulty has recently received a new explanation from the pen of Dr. E. G. Hardy. Dr. Hardy believes—and his view has met with some acceptance—that the disability, under which these Gallic candidates for admission to the Senate laboured, was the want of a municipalis origo. Up to this time, he contends, only Romans who were members of a town of Roman or Latin rights were eligible for admission to the Senate. Now in the Tres Galliae there were practically (...) no such towns: these Gallic chiefs possessed the ciuitas individually by special grant and not as members of any municipality. Hence the door of the curia was closed to them while it was open to Romans from Lugdunum or Vienna. (shrink)

There is already a copious literature comparing Claudius' oration on the admission of the primores Galliae into the Roman Senate with Tacitus’ account of the speech and of the opposition's case in Annals 11. 23–4. Yet the Emperor's own purpose in speaking as he did still needs some illumination. Scholarly concentration on technical points about the citizenship, on Claudius’ antiquarianism and on his debt to Livy has been fruitful, but it has often distracted attention from Claudius’ immediate aim. Meanwhile, Tacitus’ (...) interpretation has been insidious in colouring our view of what course of action the imperial orator was trying to defend before the Senate. (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)