6:1:
Preface. Conditional:
Conceptual and Historical Analysis
The logic of conditional is developed hereby in a series of papers, contributing to a historical and critical analysis of what the logical constant is expected to mean.
The Semantics and Pragmatics of the Conditional
in al-Fārābī’s and Avicenna’s Theories
In this paper, I examine al-Fārābī's and Avicenna's conceptions of the conditional. I show that there are significant differences between the two frames, despite their closeness. Al-Fārābī distinguishes between an accidental conditional and two “essential” conditionals. The accidental conditional can occur only once and pragmatically involves succession. In the first “essential” conditional, the consequent follows regularly the antecedent; pragmatically it involves likeliness. The second “essential” conditional can be either complete or incomplete. Semantically the former means “if and only if”; pragmatically it means “necessarily if and only if”. The latter is expressed by ‘if, then’ and means entailment; pragmatically, it involves necessity and the inclusion of the antecedent into the consequent. As to Avicenna, he rejects explicitly al-Fārābī’s complete conditional and distinguishes between the luzūm (real implication) and what he calls ittifāq. He quantifies over situations (or times) to express the various conditionals. The two universals AC and EC are expressed by “In all situations, if…, then…”, while the two particulars IC and OC are expressed by “In some situations, if…, then..”. This gives them a modal connotation, and makes the universals close to strict implications. Pragmatically, AC presupposes the truth of the antecedent, but there is no such presupposition in EC, while what is presupposed in both IC and OC is a (possible) conjunction.
Despite these differences, in both systems, the conditional is not truth functional, unlike the Stoic conditional.
Implications and Limits of Sequences
This paper analyzes the problem of implication and attempts to
characterize conditionals by a criterion of adequacy. A definition of implication
based on the notion of limit of an infinite sequence is proposed.
Assertions and Conditionals:
A Historical and Pragmatic Stance
The assertion candidate expresses a potential logical-linguistic object that can be asserted. It differs from both the act and the product of assertion; it needs not to be actually asserted and differs from the assertion made. We investigate the medieval origins of this notion, which are almost neglected in contemporary logic. Our historical analysis suggests an interpretation of the assertion candidate within the system of logic for pragmatics.
Conditionals in Interaction
There are several issues with the standard approach to the
relationship between conditionals and assertions, particularly when the
antecedent of a conditional is (or may be) false. One prominent alternative is to
say that conditionals do not express propositions, but rather make conditional
assertions that may generate categorical assertions of the consequent in certain
circumstances. However, this view has consequences that jar with standard
interpretations of the relationship between proofs and assertion. Here, I analyse
this relationship, and say that, on at least one understanding of proof,
conditional assertions may reflect the dynamics of proving, which (sometimes)
generate categorical assertions. In particular, when we think about the
relationship between assertion and proof as rooted in a dialogical approach to
both, the distinction between conditional and categorical assertions is quite
natural.
The Football of Logic
An analogy is made between two rather different domains, namely: logic, and football (or soccer). Starting from a comparative table between the two activities, an alternative explanation of logic is given in terms of players, ball, goal, and the like. Our main thesis is that, just as the task of logic is preserving truth from premises to the conclusion, footballers strive to keep the ball as far as possible until the opposite goal. Assuming this analogy may help think about logic in the same way as in dialogical logic, but it should also present truth-values in an alternative sense of speech-acts occurring in a dialogue. The relativity of truth-values is focused by this way, thereby leading to an additional way of logical pluralism.
