Charles Stevenson introduced the term 'persuasive definition’ to describe a suspect form of moral argument 'which gives a new conceptual meaning to a familiar word without substantially changing its emotive meaning’. However, as Stevenson acknowledges, such a move can be employed legitimately. If persuasive definition is to be a useful notion, we shall need a criterion for identifying specifically illegitimate usage. I criticize a recent proposed criterion from Keith Burgess-Jackson and offer an alternative.

Stephen Toulmin once observed that ”it has never been customary for philosophers to pay much attention to the rhetoric of mathematical debate’ [Toulmin et al., 1979, An Introduction to Reasoning, Macmillan, London, p. 89]. Might the application of Toulmin’s layout of arguments to mathematics remedy this oversight? Toulmin’s critics fault the layout as requiring so much abstraction as to permit incompatible reconstructions. Mathematical proofs may indeed be represented by fundamentally distinct layouts. However, cases of genuine conflict characteristically reflect an underlying (...) disagreement about the nature of the proof in question. (shrink)

It is explained that, in the sense of the sociologist Erving Goffman, mathematics has a front and a back. Four pervasive myths about mathematics are stated. Acceptance of these myths is related to whether one is located in the front or the back.

We present a logic-based formalism for modeling ofdialogues between intelligent and autonomous software agents,building on a theory of abstract dialogue games which we present.The formalism enables representation of complex dialogues assequences of moves in a combination of dialogue games, and allowsdialogues to be embedded inside one another. The formalism iscomputational and its modular nature enables different types ofdialogues to be represented.

Complete inferential rigour is achieved by breaking down arguments into steps that are as small as possible: inferential ‘atoms’. For example, a mathematical or philosophical argument may be made completely inferentially rigorous by decomposing its inferential steps into the type of step found in a natural deduction system. It is commonly thought that atomization, paradigmatically in mathematics but also more generally, is pro tanto epistemically valuable. The paper considers some plausible candidates for the epistemic value arising from atomization and finds (...) that none of them fits the bill. In particular, atomized arguments do not ground the correctness of their unatomized counterparts; they are typically not credence-preserving; and they need not reveal the source of inferential disagreement. The moral this suggests is that complete rigour is not even a defeasible epistemic ideal. (shrink)

Much work in MKM depends on the application of formal logic to mathematics. However, much mathematical knowledge is informal. Luckily, formal logic only represents one tradition in logic, specifically the modeling of inference in terms of logical form. Many inferences cannot be captured in this manner. The study of such inferences is still within the domain of logic, and is sometimes called informal logic. This paper explores some of the benefits informal logic may have for the management of informal mathematical (...) knowledge. (shrink)

An abstract framework for structured arguments is presented, which instantiates Dung's ('On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming, and n- Person Games', Artificial Intelligence , 77, 321-357) abstract argumentation frameworks. Arguments are defined as inference trees formed by applying two kinds of inference rules: strict and defeasible rules. This naturally leads to three ways of attacking an argument: attacking a premise, attacking a conclusion and attacking an inference. To resolve such attacks, preferences may (...) be used, which leads to three corresponding kinds of defeat: undermining, rebutting and undercutting defeats. The nature of the inference rules, the structure of the logical language on which they operate and the origin of the preferences are, apart from some basic assumptions, left unspecified. The resulting framework integrates work of Pollock, Vreeswijk and others on the structure of arguments and the nature of defeat and extends it in several respects. Various rationality postulates are proved to be satisfied by the framework, and several existing approaches are proved to be a special case of the framework, including assumption-based argumentation and DefLog. (shrink)

Some authors have begun to appeal directly to studies of argumentation in their analyses of mathematical practice. These include researchers from an impressively diverse range of disciplines: not only philosophy of mathematics and argumentation theory, but also psychology, education, and computer science. This introduction provides some background to their work.

For people to contribute to discourse, they must do more than utter the right sentence at the right time. The basic requirement is that they add to their common ground in an orderly way. To do this, we argue, they try to establish for each utterance the mutual belief that the addressees have understood what the speaker meant well enough for current purposes. This is accomplished by the collective actions of the current contributor and his or her partners, and these (...) result in units of conversation called contributions. We present a model of contributions and show how it accounts for a variety of features of everyday conversations. (shrink)

Ralph Johnson argues that mathematical proofs lack a dialectical tier, and thereby do not qualify as arguments. This paper argues that, despite this disavowal, Johnson’s account provides a compelling model of mathematical proof. The illative core of mathematical arguments is held to strict standards of rigour. However, compliance with these standards is itself a matter of argument, and susceptible to challenge. Hence much actual mathematical practice takes place in the dialectical tier.

In this paper, planning models developed in artificial intelligence are applied to the kind of planning that must be carried out by participants in a conversation. A planning mechanism is defined, and a short fragment of a free‐flowing videotaped conversation is described. The bulk of the paper is then devoted to an attempt to understand the conversation in terms of the planning mechanism. This microanalysis suggests ways in which the planning mechanism must be augmented, and reveals several important conversational phenomena (...) that deserve further investigation. (shrink)

The paper describes four dialogue systems, developed in the tradition of Charles Hamblin. The first system provides an answer for Achilles in Lewis Carroll's parable, the second an analysis of the fallacy of begging the question, the third a non-psychologistic account of conversational implicature, and the fourth an analysis of equivocation and of objections to it. Each avoids combinatorial explosions, and is intended for real-time operation.