In this paper, I investigate whether the intuitions that make connexive logics seem plausible might lie in pragmatic phenomena, rather than the semantics of conditional statements. I conclude that pragmatics indeed underwrites these intuitions, at least for indicative statements. Whether this has any effect on logic choice (and what that effect might be), however, heavily depends on one’s semantic theory of conditionals and on how one chooses to logically treat pragmatic failures.

The post-classical (or post-Avicennan, post-Rāzian) genre of the “protocols for dialectical inquiry and disputation” (ādāb al-baḥth wa-l-munāẓara) has its more proximate origins in the famed Risāla of Shams al-Dīn al-Samarqandī (d. 722/1322). The greater part of his conceptions and methodology, however, consists in a streamlining and universalizing of the more strictly juristic dialectic (jadal / khilāf) of his teacher Burhān al-Dīn al-Nasafī (d. 687/1288); and this in turn draws on the highly logicized dialectic of Rukn al-Dīn al-ʿAmīdī (d. 615/1218) and (...) his teacher Raḍī al-Dīn al-Nīsābūrī (d. 617/1220). At the heart of methods in this lineage, and carried forward by al-Samarqandī into the universal ādāb al-baḥth, are three truth-preserving logical relationships critical to the truth-seeking enterprise of dialectic: entailment (talāzum / mulāzama), mutual negation or exclusion (tanāfin / munāfā), and causal concomitance (dawarān). The practical elaboration of these relations reveals a logic in action—a premodern dialogical logic for living disputation praxis. In fact, so critical were these to the dialectical enterprise that al-Samarqandī devoted a specialized treatise entirely to summarizing their defining features and rules, aptly naming it the ʿAyn al-Naẓar, or “Wellspring of Rational Investigation.” In this article, and drawing upon a recently published digital critical edition, I will present an analytical outline of these core logical relations as presented in the ʿAyn al-Naẓar. Then I will address a number of points of interest in this text, grouped under six themes: the potential for cross-disciplinary advancement; notions in discursive development; significant or uniquely contributive formulations; peculiarities of content; signs of an evolving, universalist agenda; and evidence that the ʿAyn al-Naẓar was designed as an aide-mémoire for the active disputant. (shrink)

In this paper I examine Avicenna’s conception of the consequence relation. I will consider in particular his categorical and hypothetical logics. I will first analyse his definition of the implication and will show that this relation is not a consequence relation in his frame. Unlike the medieval logicians, he does not distinguish explicitly between material and formal consequences. The arguments discussed in al-Qiyās, where the conclusion is true only in some matters, and would seem close to a material consequence for (...) that reason, are rejected explicitly as not syllogistic. He also rejects the ‘enthymemes’ unless they are complemented by their missing premise and the superfluous premises which, according to him, should promptly be ruled out. It seems then that the consequence relation in his theory is formal. It can be characterized as being ‘productivity in all matters’ or ‘necessary truth preserving’. It is illustrated by some single premise arguments, and above all by all kinds of syllogisms which, in his theory, are more numerous and various than in Aristotle’s one. The syllogism may contain two or more premises, including disjunctive ones. When it is hypothetical, it may lead to several conclusions. The premises may be in conflict, but then, the conclusion is false. He thus rejects the principle according to which ‘anything follows from a contradiction’. But, unlike what some scholars say, he does not admit any connexive principle. In the compound syllogisms, the conclusion follows by steps, each step taking two premises at once. (shrink)

In this paper, I investigate whether the intuitions that make connexive logics seem plausible might lie in pragmatic phenomena, rather than the semantics of conditional statements. I conclude that pragmatics indeed underwrites these intuitions, at least for indicative statements. Whether this has any effect on logic choice, however, heavily depends on one’s semantic theory of conditionals and on how one chooses to logically treat pragmatic failures.

A number of medieval Arabic logicians discussed inferences that combine the principles of propositional and term logic, for example: Whenever H is Z then Every J is DNo D is AWhenever H is Z then S...