The medieval theory of consequence

The recovery of Aristotle??s logic during the twelfth century was a great stimulus to medieval thinkers. Among their own theories developed to explain Aristotle??s theories of valid and invalid reasoning was a theory of consequence, of what arguments were valid, and why. By the fourteenth century, two main lines of thought had developed, one at Oxford, the other at Paris. Both schools distinguished formal from material consequence, but in very different ways. In Buridan and his followers in Paris, formal consequence was that preserved under uniform substitution. In Oxford, in contrast, formal consequence included analytic consequences such as ??If it??s a man, then it??s an animal??. Aristotle??s notion of syllogistic consequence was subsumed under the treatment of formal consequence. Buridan developed a general theory embracing the assertoric syllogism, the modal syllogism and syllogisms with oblique terms. The result was a thoroughly systematic and extensive treatment of logical theory and logical consequence which repays investigation.     

Intersecting Identities as a Source of Religious Incongruence

Chaves (2010) argues that much of the work in the sociology of religion is susceptible to the religious congruence fallacy—the tendency to assume consistency between religious beliefs and one's attitudes and behaviors across situations when they are in fact highly variable. We build on and extend this argument by focusing on intersecting group identities as a mechanism for identifying such incongruence, not only within religious contexts, but also at the intersection of categories such as gender and race. To illustrate this argument, the analysis draws on data from the 2006 Panel Study of American Religion and Ethnicity (PS‐ARE) to assess how race, gender, and religion interact to produce different levels of attitude and behavior incongruencies on key issues of the day, specifically conservative social values and voting behaviors. The results find marked differences and inconsistent relationships between attitudes and behaviors across racial‐gender groups. We use the analysis to highlight the conditions that result in incongruence at the intersections of identity categories and pinpoint where social scientists are most vulnerable to committing the congruence fallacy.     

Plural signification and the Liar paradox

In recent years, speech-act theory has mooted the possibility that one utterance can signify a number of different things. This pluralist conception of signification lies at the heart of Thomas Bradwardine’s solution to the insolubles, logical puzzles such as the semantic paradoxes, presented in Oxford in the early 1320s. His leading assumption was that signification is closed under consequence, that is, that a proposition signifies everything which follows from what it signifies. Then any proposition signifying its own falsity, he showed, also signifies its own truth and so, since it signifies things which cannot both obtain, it is simply false. Bradwardine himself, and his contemporaries, did not elaborate this pluralist theory, or say much in its defence. It can be shown to accord closely, however, with the prevailing conception of logical consequence in England in the fourteenth century. Recent pluralist theories of signification, such as Grice’s, also endorse Bradwardine’s closure postulate as a plausible constraint on signification, and so his analysis of the semantic paradoxes is seen to be both well-grounded and plausible.

The probability of a given 1-choice structure

A 1-choice structure arises whenever each person in a group chooses exactly one other person according to some criterion. Our purpose is to study the situation in which these choices are made at random. As noted in Harary, Norman and Cartwright [2], such a structure can be represented by a directed graph in which the points represent people and the directed lines their choices. We first describe the shape of such a 1-choice structure, and define its symmetry number. With the help of these properties we are then able to develop and prove a formula which gives a probability of obtaining a given structure in the random choice situation. In order to supply data for these results, we include in the Appendix the diagrams of all 1-choice structures with at most 7 points and the probability of each.The preparation of this article was supported by Grant MH 10834 from the National Institute of Mental Health and Grant 1026-66 from the U. S. Air Force Office of Scientific Research.