Chrysippus’ counterargument against the Master Argument: a reappraisal

It is widely held that as a nego suppositum, Chrysippus’ response to Diodorus Cronus’ Master Argument is that the impossible “this man has died” follows from the possible “Dio has died”. A principal claim of this article is that Chrysippus was not actually committed, against Diodorus, to the tenet that there are deductions and conditionals whereby from the possible the impossible follows. I argue that this is most likely part of a Chrysippean exemplum fictum of a real dialectical discussion and it merely reflects a Chrysippean dialectical strategy, a merely instrumental agreement (συγχώρησις) with Diodorus on the admissibility of some single-premised arguments. As historical evidence for my conjecture I highlight two key passages by Sextus Empiricus which help to understand that Chrysippus’ real tenet was an ancient implicational counterpart of a deictic version of the Identity-Elimination Rule, whereas most likely, according to Diodorus the identitarian major premiss of this rule is redundant, so that it must be eliminated.

Hamesucken and the Major Premiss in the Libel, 1672–1770: Criminal Law in the Age of Enlightenment

This chapter examines prosecutions for hamesucken between 1672 and 1770, the first date being that of the establishment of the refounded Court of Justiciary. One of John Millar's last surviving letters is to John Wilde, the Professor of Civil Law in Edinburgh, discussing a recent conviction for the crime, expressing his view that hamesucken had fallen into disuse. The chapter considers how arguments were developed in framing the major premiss in the libel from the law of nature and nations, a practice which also allowed influence from English criminal law. It begins with a discussion of procedure in criminal trials during the period, followed by an analysis of the law of hamesucken as found in treatises and the practice of the Justiciary Court. It also looks at the 1752 trial of James Macgregor before concluding with some remarks on marital rape.

NORMAL DERIVABILITY IN CLASSICAL NATURAL DEDUCTION

A normalization procedure is given for classical natural deduction with the standard rule of indirect proof applied to arbitrary formulas. For normal derivability and the subformula property, it is sufficient to permute down instances of indirect proof whenever they have been used for concluding a major premiss of an elimination rule. The result applies even to natural deduction for classical modal logic.

Are "Gap-Fillers" Missing Premisses?

Identifying the missing or unstated premisses of arguments is important, because their logical quality depends on them. Textbook authors regard enthymematic syllogisms (e.g., "Elvis is a man, so Elvis is mortal") as having an unstated premiss - the major premiss (e.g., "All men are mortal"). They are said to be such because these syllogisms become formally valid when the major premiss is added (i.e., it is a gap-filler). I argue that unstated major premises are not gap-fillers: they support a part of the argument that is already given implicitly - the inference claim ("If the premisses are true then the conclusion is true"). As such, their logical status is the same as that of an unstated proposition that supports the minor premiss, which is not part of the argument. Therefore, the so-called "major premiss" is not an unstated premiss of the enthymeme.

The Inarticulate Premiss

What follows purports to give the opinions of three judges of the highest court of appeal in Newstate, Africa. The title is taken from a pregnant phrase of O. W. Holmes, an American writer on jurisprudence. He held that the result of a case depended upon ‘the inarticulate major premiss’ of the judge (or the unstated assumption which most influenced his judgement), at least in matters of first impression—i.e. cases in which the judges must determine for the first time what is the operative rule (‘norm’) of law. He urged this proposition in sharp opposition to the popular notion that a judge merely applied to the ascertained facts clear rules of law, which he found in earlier cases or in statutes.