Logical Studies

Abstract One of the methods of immediate inference in logic is the conversion. Logicians have identified three types of conversion: conversion, obverted contraposition, and contraposition. The present study, by means of a dichotomous division demonstrates that a further valid and new type of conversion can be posited which has been overlooked by logicians. In this newly identified form, after the conversion of subject and predicate, only the subject is complemented, in such a way that, assuming the truth of the original proposition, the converted proposition is likewise true. This study names this newly identified type “complemented subject conversion” and establishes its logical variations due to the various forms of categorical propositions, whether predicative or conditional. Accordingly, the complemented subject conversion of affirmative propositions (both universal and particular) yields a particular negative proposition, while in the case of a universal negative proposition, it’s a universal affirmative proposition. Particular negative propositions have no valid complemented subject conversion. By employing this innovative type of conversion, a greater number of true propositions can be inferred and derived from a given true proposition, which endows it with a logical value comparable to that of the other recognized types of conversion.

Abstract Standard deontic logic is unable to distinguish between arguments that contain ought-to-be and those that contain ought-to-do, using the same formalization for both. Yet these two types of “ought” are semantically and logically different, and a logician who works with Standard deontic logic cannot separate them. Ignoring this important distinction creates serious problems, most notably the neglect of the role of the agent in moral action. In this paper, we demonstrate that drawing inferences from one type of “ought” to the other is not valid, and that the only relation that may be drawn between them is an empirical one rather than a logical one. Finally, we examine NDL deontic logic, which is introduced by James Forrester as a solution to this problem, and show that although it resolves some of the shortcomings of Standard deontic logic, it has not succeeded in preserving its neutrality with respect to ethical theories.

Abstract The treatise al-Shakl al-Rābiʿ min Aškāl al-Qiyās al-Ḥamlī by Abu’l-Futūḥ Najm al-Dīn Aḥmad b. Muḥammad b. al-Sarī b. al-Ṣalāḥ (d. 548/1153) is the oldest systematic defense of the fourth figure of the categorical syllogism in Islamic logic. This text remained unknown until the 1960s, when its first publication was made by Nicholas Rescher (1966) based on the incomplete manuscript Ayasofya 4830. Asadullah Fallāḥī (2014) claimed to provide a corrected edition, making the text more pedagogical but introducing numerous additions and personal interpretations. Muhammad Çelik (2021), by discovering the more complete manuscript Ayasofya 4845, offered the first true critical edition and criticized Fallāḥī’s work for its additions and alterations.
This article, through a comparison of the three editions, demonstrates that textual and manuscript variations profoundly alter our understanding of Abu’l-Futūḥ: in Rescher he appears incomplete and raw, in Fallāḥī decisive and Galen-aware, and in Çelik cautious and independent from the Hellenistic tradition. These differences affect key innovations (the definition of qasīm, refutation of objections, superiority of multiple conclusions) and render the history of Islamic logic less Galen-centered and more indigenous.