Few, if any, logicians deserve the title 'precursor of modern argumentation theory' more than the largely neglected English logician, Alfred Sidgwick. Sidgwick developed a coherent and original theory of argumentation with a distinctly 'mo dern' flavour. This paper outlines his idea of a 'negative' view of logic, an important aspect of which is the thesis that the distinctions and inference schemata of formal logic should not be applied as criteria of the validity or invalidity of natural language arguments, but rather (...) 'rogatively'--as suggesting the kinds of objections or demands for clarification that are relevant at specific stages of a discussion. (shrink)

EVOLUTIONARY EPISTEMOLOGY, THEORY OF RATIONALITY, AND THE SOCIOLOGY OF KNOWLEDGE by Gerard Radnitzky and W. W. Bartley, III La Salle, Ill.: Open Court, 1987. 475 pp., $39.95, $14.95 (paper).

A prized property of theories of all kinds is that of generality, of applicability or least relevance to a wide range of circumstances and situations. The purpose of this article is to present a pair of distinctions that suggest that three kinds of generality are to be found in mathematics and logics, not only at some particular period but especially in developments that take place over time: ‘omnipresent’ and ‘multipresent’ theories, and ‘ubiquitous’ notions that form dependent parts, or moments, of (...) theories. The category of ‘facets’ is also introduced, primarily to assess the roles of diagrams and notations in these two disciplines. Various consequences are explored, starting with means of developing applied mathematics, and then reconsidering several established ways of elaborating or appraising theories, such as analogising, revolutions, abstraction, unification, reduction and axiomatisation. The influence of theories already in place upon theory-building is emphasised. The roles in both mathematics and logics of set theory, abstract algebras, metamathematics, and model theory are assessed, along with the different relationships between the two disciplines adopted in algebraic logic and in mathematical logic. Finally, the issue of monism versus pluralism in these two disciplines is rehearsed, and some suggestions are made about the special character of mathematical and logical knowledge, and also the differences between them. Since the article is basically an exercise in historiography, historical examples and case studies are described or noted throughout. (shrink)

We seek means of distinguishing logical knowledge from other kinds of knowledge, especially mathematics. The attempt is restricted to classical two-valued logic and assumes that the basic notion in logic is the proposition. First, we explain the distinction between the parts and the moments of a whole, and theories of ?sortal terms?, two theories that will feature prominently. Second, we propose that logic comprises four ?momental sectors?: the propositional and the functional calculi, the calculus of asserted propositions, and rules for (...) (in)valid deduction, inference or substitution. Third, we elaborate on two neglected features of logic: the various modes of negating some part(s) of a proposition R, not only its ?external? negation not-R; and the assertion of R in the pair of propositions ?it is (un)true that R? belonging to the neglected logic of asserted propositions, which is usually left unstated. We also address the overlooked task of testing the asserted truth-value of R. Fourth, we locate logic among other foundational studies: set theory and other theories of collections, metamathematics, axiomatisation, definitions, model theory, and abstract and operator algebras. Fifth, we test this characterisation in two important contexts: the formulation of some logical paradoxes, especially the propositional ones; and indirect proof-methods, especially that by contradiction. The outcomes differ for asserted propositions from those for unasserted ones. Finally, we reflect upon self-referring self-reference, and on the relationships between logical and mathematical knowledge. A subject index is appended. (shrink)

The din and deadlock of public life in America--where insults are traded, slogans proclaimed, and self-serving deals made and unmade--reveal the deep disagreement that pervades our democracy. The disagreement is not only political but also moral, as citizens and their representatives increasingly take extreme and intransigent positions. A better kind of public discussion is needed, and Amy Gutmann and Dennis Thompson provide an eloquent argument for "deliberative democracy" today. They develop a principled framework for opponents to come together on moral (...) and political issues.Gutmann and Thompson show how a deliberative democracy can address some of our most difficult controversies--from abortion and affirmative action to health care and welfare--and can allow diverse groups separated by class, race, religion, and gender to reason together. Their work goes beyond that of most political theorists and social scientists by exploring both the principles for reasonable argument and their application to actual cases. Not only do the authors suggest how deliberative democracy can work, they also show why improving our collective capacity for moral argument is better than referring all disagreements to procedural politics or judicial institutions. Democracy and Disagreement presents a compelling approach to how we might resolve some of our most trying moral disagreements and live with those that will inevitably persist, on terms that all of us can respect. (shrink)