In 1902 there arrived in Jena a letter from Russell laying out a proof that shattered Frege’s confidence in logicism, which is widely taken to be the doctrine according to which every truth of arithmetic is re-expressible without relevant loss as a provable truth about a purely logical object. Frege was persuaded that Russell had exposed a pathology in logicism, which faced him with the task of examining its symptoms, diagnosing its cause, assessing its seriousness, arriving at a treatment option, (...) and making an estimate of future prospects. The symptom was the contradiction that had crept into naïve set theory in the form of the set that provably is and is not its own member. The diagnosis was that it is caused by Basic Law V of the Grundgesetze (Frege, In: Grundgesetze der Arithmetik: Begrifsschriftlich abgeleitet, Jena: Herman Pohle, 1893/1903. Translated into English as Basic Laws of Arithmetic, also edited by Philip A. Ebert and Marcus Rossberg, with Crispin Wright, Oxford: Oxford University Press, 2013). Triage answers the question, “How bad is it?” The answer was that the contradiction irreparably destroys the logicist project. The treatment option was nil. The disease was untreatable. In due course, the prognosis turned out to be that a scaled-down Fregean logic could have an honourable life as a theory inference for various domains of mathematical discourse, but not for domains containing the logical objects required for logicism. Since there aren’t such objects, there aren’t such domains. On the face of it, Frege’s logicist collapse is astonishing. Why wouldn’t he have repaired the fault in Law V and gone back to the business of bringing logicism to an assured realization? In the course of our reflections, we will have nice occasion to consider the good it might have done Frege to have booked some time with Aristotle had he been able to. By the time we’re finished, we’ll have cause to think that in the end the Russell might well have begged the question against Frege. (shrink)

It has been said that there is no scholarly consensus as to why Aristotle’s logics of proof and refutation would have borne the title _Analytics._ But if we consulted Tarski’s (Introduction to logic and the methodology of deductive sciences, Oxford University Press, New York, 1941) graduate-level primer, we would have the perfect title for them: _Introduction to logic and to the methodology of deductive sciences._ There are two strings to Aristotle’s bow. The methodological string is the founding work on the (...) epistemology of science, and the logical string sets down conditions on the proofs that bring this knowledge about. The logic of proof presents a difficulty whose solution exceeds its theoretical reach. The logic of refutation takes the problem on board, and advances a solution whose execution is framed by fallacy-avoidance at the beginning and fallacy-adoption at the end. But with a difference: the avoidance-fallacies are of Aristotle’s own conception, whereas the adoption-fallacies, so judged in the modern tradition, aren’t fallacies at all for Aristotle. The avoidance-fallacies are begging the question and _ignoratio elenchi_, and the adoption-fallacies, fallacies in name only, are the _ad hominem_ and _ad ignorantiam_, an inductive turning in the first instance, and an abductive finish in the second. (shrink)

When in classical formal logic the notions of deduction, valid inference and logical consequence are defined, causal language plays no role. The founder of western logic, Aristotle, identified ‘non-cause’, or ‘positing as cause what is not a cause’, as a logical fallacy. I argue that a systematic re-examination of Aristotle's analysis of NCF, and the related language of logical causality, in the Sophistical Refutations, Topics, Analytics and Rhetoric, helps us to understand his conception of. It reveals that Aristotle's syllogismhood is (...) non-monotonic, and thus narrower than classical validity as consisting in, or coextensive with, necessary truth-preservation. It also supports the conclusion that a syllogism is a form of relevant consequence: the premisses must be causes of the conclusion in the sense that they are not only sufficient but also necessary for the conclusion to follow. Close analysis of NCF also suggests that syllogistic relevance is not a semantic matter, but a syntactic.. (shrink)

This essay addresses the collapse/incoherence problem for normative frameworks that contain both fundamental values and rules for promoting those values. The problem is that in some cases, we would bring about more of the fundamental value by violating the framework’s rules than by following them. In such cases, if the framework requires us to follow the rules anyway, then it appears to be incoherent; but if it allows us to make exceptions to the rules, then the framework “collapses” into one (...) that doesn’t make use of rules in the first place. The chapter begins with an examination of happiness and truth as fundamental values in Mill’s work, which lead into parallel versions of the collapse/incoherence problem in ethics and epistemology. It then sets out the collapse problem for rule-consequentialist approaches in ethics, truth-directed accounts of justification in epistemology, and epistemological approaches to argument cogency. The chapter closes with discussion of two potential solutions to the problem. (shrink)

This presentation seeks to understand informal logic as a set of methods for the logical evaluation of natural language arguments. Some of the methods identified are the fallacies method, deductivism, warrantism and argument schemes. A framework for comparing the adequacy of the methods is outlined consisting of the following categories: learner- and user-efficiency, subjective and objective reliability, and scope. Within this framework, it is also possible to compare informal and formal logic.

The translation into French of the English word “fallacy” opens a discussion on the difference between fallacy and sophism in English. The two words are sometimes synonyms, but a difference is sometimes made on the ground that a sophism is deliberate and a fallacy is non-deliberate. In a second part of the paper this distinctive criterion is taken seriously to discuss the relative frequency of sophisms and of fallacies for a typical kind of fallacious argument. I claim that this aspect (...) should be taken into account by a theory of fallacious argument. (shrink)