We examine in detail three classic reasoning fallacies, that is, supposedly ``incorrect'' forms of argument. These are the so-called argumentam ad ignorantiam, the circular argument or petitio principii, and the slippery slope argument. In each case, the argument type is shown to match structurally arguments which are widely accepted. This suggests that it is not the form of the arguments as such that is problematic but rather something about the content of those examples with which they are typically justified. This (...) leads to a Bayesian reanalysis of these classic argument forms and a reformulation of the conditions under which they do or do not constitute legitimate forms of argumentation. (shrink)

Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such probability from the same notion in empirical science. Yet it is hard to see how there could be probabilistic relations between the necessary truths of pure mathematics. The existence of such logical relations, short of certainty, is defended using the theory of logical probability (or objective Bayesianism (...) or non-deductive logic), and some detailed examples of its use in mathematics surveyed. Examples of inductive reasoning in experimental mathematics are given and it is argued that the problem of induction is best appreciated in the mathematical case. (shrink)

Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. -/- The book begins by first challenging the (...) assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics. ​. (shrink)

This paper offers a probabilistic treatment of the conditions for argument cogency as endorsed in informal logic: acceptability, relevance, and sufficiency. Treating a natural language argument as a reason-claim-complex, our analysis identifies content features of defeasible argument on which the RSA conditions depend, namely: change in the commitment to the reason, the reason’s sensitivity and selectivity to the claim, one’s prior commitment to the claim, and the contextually determined thresholds of acceptability for reasons and for claims. Results contrast with, and (...) may indeed serve to correct, the informal understanding and applications of the RSA criteria concerning their conceptual dependence, their function as update-thresholds, and their status as obligatory rather than permissive norms, but also show how these formal and informal normative approachs can in fact align. (shrink)

Hamblin’s Fallacies remains one of the crucial documents in the development of informal logic and argumentation theory. His critique of traditional approaches to the fallacies (what he dubbed ‘The Standard Treatment’) helped to revitalize the study of fallacies. Recently I had occasion to reread Fallacies and came to the conclusion that some of my earlier criticisms (1989, 1990) had missed the real force of what was going on there, that I and others have perhaps not fully appreciated what Hamblin is (...) up to. In this paper, I plan to revisit Fallacies and make manifest its coherence. (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 paper argues that the traditional characterization of the notion of paradox — an apparently valid argument with apparently true premises and an apparently false conclusion — is too narrow; there are paradoxes that do not satisfy it. After discussing, and discarding, some alternatives, an outline of a new characterization of the notion of paradox is presented. A paradox is found to be an apparently valid argument such that, apparently, it does not present the kind of commitment to the conclusion (...) that should be implied by an acceptance of the truth of the premises and the validity of the argument. (shrink)

I argue in a non-reductive sense for a plausible epistemic principle, which can (1) theoretically and instrumentally unify or systematize all fallacies, and (2) provide a justification for using such a principle for characterizing an erroneous argument as a fallacy. This plausible epistemic principle involves the idea of an error in the method of justification, which results in a failure to provide relevant evidence to satisfy certain standards of adequate proof. Thus, all fallacies are systematically disguised failures to provide substantive (...) proof: a failure in the attempt to persuade rationally, as opposed to emotionally or rhetorically. I argue that the epistemic idea of begging the question is essential to this idea of a fallacy as an inadequate proof. (shrink)

Lawrence Powers advocates a one-fallacy theory in which the only real fallacies are fallacies of ambiguity. He defines a fallacy, in general, as a bad argument that appears good. He claims that the only legitimate way that an argument can appear valid, while being invalid, is when the invalid inference is covered by an ambiguity. Several different kinds of counterexamples have been offered from begging the question, to various forms of ad hominem fallacies. In this paper, I outline three potential (...) counterexamples to Powers' theory, including one that has been addressed already by Powers, and two which are well known problems, but until now have never been applied as counterexamples to Powers' theory. I argue that there is a simpler explanation of these 'hard' cases than positing ambiguities that are not obviously there. (shrink)

In this paper I claim that the reason we are reluctant to call many informal fallacies fallacies of relevance is because we can interpret them as providing contextual information about how the argument is to be interpreted. This interpretative dilemma is that the logical form is determined in part by whether the analyst wishes to be charitable to the proponent or the opponent. The evaluation of the argument is nonetheless purely logical.

To understand what a fallacy is one needs to understand what a bad argument is and what it is for an argument to appear good. I will argue that from an intuitive standpoint a good argument should be understood in roughly the way Richard Feldman has proposed, that is, as an argument that gives people reason to believe its conclusion. However, I will also argue that an externalist condition that requires that the premises really do support the conclusion must be (...) added to the internalist account which only requires that a person be justified in believing the premises support the conclusion. (shrink)