Douglas Walton’s multitudinous contributions to the study of argumentation seldom, if ever, directly engage with argumentation in mathematics. Nonetheless, several of the innovations with which he is most closely associated lend themselves to improving our understanding of mathematical arguments. I concentrate on two such innovations: dialogue types (§1) and argumentation schemes (§2). I argue that both devices are much more applicable to mathematical reasoning than may be commonly supposed.

In the pragma-dialectical approach, fallacies are considered incorrect moves in a discussion for which the goal is successful resolution of a dispute. Ten rules are given for effective conduct at the various stages of such a critical discussion. Fallacies are discussed as violations of these rules, taking into account all speech acts which are traditionally recognized as fallacies. Special attention is paid to the role played by implicitness in fallacies in everyday language use. It is stressed that identifying and acknowledging (...) fallacies in ordinary discussions always has a conditional character. Differences between the pragma-dialectical perspective, the Standard Treatment, and the formal logic approach to fallacy analysis are discussed. (shrink)

Various logic texts offer explanations of a fallacy identified as an appeal to tradition. The identification of this fallacy should be scrutinized for any faulty reasoning. Whether this fallacy is committed depends on the kind of relation asserted be tween the present and the past. An understanding of its relations clarifies when an appeal to tradition could be fallacious. This is illustrated by the views of Socrates, Bentham, Scruton, and others. I argue tradition transfers something from the past to the (...) present. Whether the transfer is fallacious depends on what and how something is transferred. (shrink)

I begin by formulating the problem of the nature of fallacy in terms of the logic of the negative evaluation of argument, that is, in terms of a theory of logical criticism; here I discuss several features of my approach and several advantages vis-à-vis other approaches; a main feature of my approach is the concern to avoid both formalist and empiricist excesses. I then define six types of fallaciousness, labeled formal, explanatory, presuppositional, positive, semantical, and persuasive; they all involve arguments (...) whose conclusion may be said not to follow from the premises, that is, they involve the logical evaluation of relationships among propositions. I also provide a set of data consisting of four historical cases or nine specific instances of fallacious arguments; these all pertain to the Copernican controversy about the earth's motion in the seventeenth century. I end with a discussion of further problems and inquiries that deserve attention. (shrink)

Authority arguments generate support for claims by appealing to an agent’s authority status, rather than to reasons independent of it. With few exceptions, the current literature on argument schemes acknowledges two basic authority types. The _epistemic_ type grounds in knowledge, the_ deontic_ type grounds in power. We review how historically earlier scholarship acknowledged an_ attractiveness-based_ and a _majority-based_ authority type as equally basic type. Crossing these with basic speech act types thus yields authority argument sub-schemes. Focusing on the_ epistemic-assertive_ sub-scheme (...) (‘an epistemic authority _A_ _E_ asserts a proposition _P_’), we apply a meta-level approach to specifying critical questions. Results improve the evaluation of this sub-scheme and show how similar improvements are obtainable for other schemes. (shrink)