John Venn’s opposition to probability as degree of belief

John Venn is known as one of the clearest expounders of the interpretation of probability as the frequency of a particular outcome in a potentially unlimited series of possible events. This view he held to be incompatible with the alternate interpretation of probability as a measure of the degree of belief that would rationally be held about a certain outcome based upon the reliability of testimony and other prior information. This paper explores the reasons why Venn may have been so opposed to the degree-of-belief interpretation and suggests that it may have been a way for him to resolve a conflict in his own mind between his ideas of proper scientific methods of inference and the religious beliefs that he held as a young man.     

Interpreting Aristotle on mixture: problems about elemental composition from Philoponus to Cooper

Aristotle’s On generation and corruption raises a vital question: how is mixture, or what we would now call chemical combination, possible? It also offers an outline of a solution to the problem and a set of criteria that a successful solution must meet. Understanding Aristotle’s solution and developing a viable peripatetic theory of chemical combination has been a source of controversy over the last two millennia. We describe seven criteria a peripatetic theory of mixture must satisfy: uniformity, recoverability, potentiality, equilibrium, alteration, incompleteness, and the ability to distinguish mixture from generation, corruption, juxtaposition, augmentation, and alteration. After surveying the theories of Philoponus (d. 574), Avicenna (d. 1037), Averroes (d. 1198), and John M. Cooper (fl. circa 2000), we argue for the merits of Richard Rufus of Cornwall’s theory. Rufus (fl. 1231-1256) was a little known scholastic philosopher who became a Franciscan theologian in 1238, after teaching Aristotelian natural philosophy as a secular master in Paris. Lecturing on Aristotle’s De generatione et corruptione, around the year 1235, he offered his students a solution to the problem of mixture that we believe satisfies Aristotle’s seven criteria.     

How to tell causes from effects: Kant’s causal theory of time and modern approaches

I attempt a reconstruction of Kant’s version of the causal theory of time that makes it appear coherent. Two problems are at issue. The first concerns Kant’s reference to reciprocal causal influence for characterizing simultaneity. This approach is criticized by pointing out that Kant’s procedure involves simultaneous counterdirected processes—which seems to run into circularity. The problem can be defused by drawing on instantaneous processes such as the propagation of gravitation in Newtonian mechanics. Another charge of circularity against Kant’s causal theory was leveled by Schopenhauer. His objection was that Kant’s approach is invalidated by the failure to deliver non-temporal criteria for distinguishing between causes and effects. I try to show that the modern causal account has made important progress toward a successful resolution of this difficulty. The fork asymmetry, as based on Reichenbach’s principle of the common cause, provides a means for the distinction between cause and effect that is not based on temporal order (if some preconditions are realized).