Online research in philosophy

ABSTRACT: 'Aristotelian logic', as it was taught from late antiquity until the 20th century, commonly included a short presentation of the argument forms modus (ponendo) ponens, modus (tollendo) tollens, modus ponendo tollens, and modus tollendo ponens. In late antiquity, arguments of these forms were generally classified as 'hypothetical syllogisms'. However, Aristotle did not discuss such arguments, nor did he call any arguments 'hypothetical syllogisms'. The Stoic indemonstrables resemble the modus ponens/tollens arguments. But the Stoics never called them 'hypothetical syllogisms'; nor did they describe them as ponendo ponens, etc. The tradition of the four argument forms and the classification of the arguments as hypothetical syllogisms hence need some explaining. In this paper, I offer some explanations by tracing the development of certain elements of Aristotle's logic via the early Peripatetics to the logic of later antiquity. I consider the questions: How did the four argument forms arise? Why were there four of them? Why were arguments of these forms called 'hypothetical syllogisms'? On what grounds were they considered valid? I argue that such arguments were neither part of Aristotle's dialectic, nor simply the result of an adoption of elements of Stoic logic, but the outcome of a long, gradual development that begins with Aristotle's logic as preserved in his Topics and Prior Analytics; and that, as a result, we have a Peripatetic logic of hypothetical inferences which is a far cry both from Stoic logic and from classical propositional logic, but which sports a number of interesting characteristics, some of which bear a cunning resemblance to some 20th century theories.

This paper investigates the kind of empiricism combined with an operationalist perspective that, in the first decades of our Century, gave rise to a turning point in theoretical physics and in probability theory. While quantum mechanics was taking shape, the classical (Laplacian) interpretation of probability gave way to two divergent perspectives: frequentism and subjectivism. Frequentism gained wide acceptance among theoretical physicists. Subjectivism, on the other hand, was never held to be a serious candidate for application to physical theories, despite the fact that its philosophical back-ground strongly resembles that underlying quantum mechanics, at least according to the Copenhagen interpretation. The reasons for this are explored.

Von Mises thought that an adequate account of objective probability required a condition of randomness. For frequentists, some such condition is needed to rule out those sequences where the relative frequencies converge towards definite limiting values, and where it is nevertheless not appropriate to speak of probability … [because such a sequence] obeys an easily recognizable law (von Mises, Probability, Statistics, and Truth). But is a condition of randomness required for an adequate account of probability, given the existence of decisive arguments against frequentism? To put it another way: is it characteristic of the probability role that probability should have a connection to randomness? I will answer this question in the negative.

ABSTRACT: In this paper I argue (i) that the hypothetical arguments about which the Stoic Chrysippus wrote numerous books (DL 7.196) are not to be confused with the so-called "hypothetical syllogisms", but are the same hypothetical arguments as those mentioned five times in Epictetus (e.g. Diss. 1.25.11-12); and (ii) that these hypothetical arguments are formed by replacing in a non-hypothetical argument one (or more) of the premisses by a Stoic "hypothesis" or supposition. Such "hypotheses" or suppositions differ from propositions in that they have a specific logical form and no truth-value. The reason for the introduction of a distinct class of hypothetical arguments can be found in the context of dialectical argumentation. The paper concludes with the discussion of some evidence for the use of Stoic hypothetical arguments in ancient texts.

According to finite frequentism, the probability of an attribute A in a finite reference class B is the relative frequency of actual occurrences of A within B. I present fifteen arguments against this position.

According to finite frequentism, the probability of an attribute A in a finite reference class B is the relative frequency of actual occurrences of A within B. I present fifteen arguments against this position.

This is the sequel to my “Fifteen Arguments Against Finite Frequentism” ( Erkenntnis 1997), the second half of a long paper that attacks the two main forms of frequentism about probability. Hypothetical frequentism asserts: The probability of an attribute A in a reference class B is p iff the limit of the relative frequency of A ’s among the B ’s would be p if there were an infinite sequence of B ’s. I offer fifteen arguments against this analysis. I consider various frequentist responses, which I argue ultimately fail. I end with a positive proposal of my own, ‘hyper-hypothetical frequentism’, which I argue avoids several of the problems with hypothetical frequentism. It identifies probability with relative frequency in a hyperfinite sequence of trials. However, I argue that this account also fails, and that the prospects for frequentism are dim.