In recent years, substructural approaches to paradoxes have become quite popular. But whatever restrictions on structural rules we may want to enforce, it is highly desirable that such restrictions be accompanied by independent philosophical motivation, not directly related to paradoxes. Indeed, while these recent developments have shed new light on a number of issues pertaining to paradoxes, it seems that we now have even more open questions than before, in particular two very pressing ones: what (independent) motivations do we have (...) (if any) for restrictions on structural rules, and what to make of the plurality of new logics emerging from these restrictions, i.e. how to ‘choose’ among the different options. In this paper, we address these two questions from the perspective of a dialogical conception of logic that we've been advocating in recent years. We will argue that dialogical interpretations of structural rules, that is, as rules determining specific properties of the dialogues in question, provide a conveniently neutral framework to adjudicate between the different substructural proposals that have been made in the literature on paradoxes. (shrink)

In this paper we provide an interpretation of Aristotle's rule for the universal quantifier in Topics Θ 157a34–37 and 160b1–6 in terms of Paul Lorenzen's dialogical logic. This is meant as a contribution to the rehabilitation of the role of dialectic within the Organon. After a review of earlier views of Aristotle on quantification, we argue that this rule is related to the dictum de omni in Prior Analytics A 24b28–29. This would be an indication of the dictum’s origin in (...) the context of dialectical games. One consequence of our approach is a novel explanation of the doctrine of the existential import of the quantifiers in dialectical terms. After a brief survey of Lorenzen's dialogical logic, we offer a set of rules for dialectical games based on previous work by Castelnérac and Marion, to which we add here the rule for the universal quantifier, as interpreted in terms of its counterpart in dialogical logic. We then give textual evidence of the use of that rule in Plato's dialogues, thus showing that Aris... (shrink)

(1) If a deductive argument is valid, then the conclusion is not novel. (2) If the conclusion of an argument is not novel, the argument is not useful. So, (3) if a deductive argument is valid, it is not useful. This conclusion, (3), is unacceptable. Since the argument is valid, we must reject at least one premise. So, should we reject (1) or (2)? This puzzle is usually known as the ‘scandal of deduction’. Analytic philosophers have tried to reject (1) (...) but have assumed premise (2). I argue here that Aristotle would deny (2). Aristotle thinks that at least some deductive arguments are useful, even though they present no new conclusions. Thus, Aristotle’s view contrasts with analytic philosophers of logic, who assume that all useful deductive arguments present novel conclusions. I don’t claim that Aristotle ‘solves’ the problem: it was never posed in Aristotle’s time. Rather, I suggest that Aristotle does not face the problem because he assumes deductions can be useful, without presenting novel conclusions. Aristotle’s view of deduction tames the scandal. (shrink)

Sweet Analytics, ‘tis thou hast ravish'd me,Bene disserere est finis logices.Is to dispute well logic's chiefest end?Affords this art no greater miracle?(Christopher Marlow, Doctor Faustus, Act 1,...

"However that may be, Aristotelian syllogistic concerned itself exclusively with monadic predicates. Hence it could not begin to investigate multiple quantification. And that is why it never got very far. None the less, the underlying grammar of Aristotle's logic did not in itself..

My dissertation is devoted to an examination of the resolution of fallacy in Plato's Euthydemus. It is a familiar claim that the Euthydemus champions Socratic argumentation over sophistical or eristic reasoning. No consensus however exists regarding either the nature or philosophical significance of Socrates’ treatment of the fallacies he confronts. I argue that a careful reading of the dialogue reveals that the Socratic response to fallacious reasoning is conducted at two different levels of philosophical sophistication. Socrates relies upon the resources (...) of Socratic dialectic in responding to sophisms due to ignorance of refutation. Insofar as Socratic dialectic is grounded in a grasp of the nature of genuine refutation, the objections it raises to false refutation are fully explanatory. On the other hand, Socrates employs various self-refutation arguments against theses which depend on false assumptions regarding the nature of predication---for example, the thesis that false speaking is impossible. It is however characteristic of Socratic dialectic that this method of examination cannot explain why the sophists’ theses are false. The Socratic response to fallacy in these cases is non-explanatory in this sense. On the other hand, these limitations on Socratic expertise are overcome in other passages in the dialogue which are replete with clues to the reader that point to a genuine explanation and resolution of the sophists’ arguments for their various theses. In particular, the reader is invited at every turn to modify, clarify, or reject various assumptions made by the brothers regarding the nature of predication. Here Plato implicitly relies on the results of what I call higher dialectic. This theory, which receives explicit formulation in the Sophist, is conceptually rich enough to expose and dispose of the various false assumptions upon which the sophists’ theses rest. I conclude that the Euthydemus is concerned to identify Socratic dialectic as only a part of philosophy, and to locate and strictly delimit its epistemological status as lying above eristic and the rhetorical arts, but below that of dialectic as that is conceived in the Republic and even later dialogues---thus anticipating the Sophist’s conception of Socrates as the practitioner of a ‘noble sophistry’, and the elenchus as a propaedeutic to philosophy, which purges the soul of false beliefs. (shrink)