This monograph proposes a new way of implementing interaction in logic. It also provides an elementary introduction to Constructive Type Theory. The authors equally emphasize basic ideas and finer technical details. In addition, many worked out exercises and examples will help readers to better understand the concepts under discussion. One of the chief ideas animating this study is that the dialogical understanding of definitional equality and its execution provide both a simple and a direct way of implementing the CTT approach (...) within a game-theoretical conception of meaning. In addition, the importance of the play level over the strategy level is stressed, binding together the matter of execution with that of equality and the finitary perspective on games constituting meaning. According to this perspective the emergence of concepts are not only games of giving and asking for reasons, they are also games that include moves establishing how it is that the reasons brought forward accomplish their explicative task. Thus, immanent reasoning games are dialogical games of Why and How. (shrink)

According to Aristotelian logic, in categorical logic, there are three kinds of judgements (qaḍīyya): affirmative, negative, and metathetic (ma‘dūla). Khūnajī, a famous Muslim logician in the 13th century, introduces a different judgement (or statement) entitled “affirmative judgement with the negative predicate” (mūjiba al-sāliba al-maḥmūl; henceforth, ANP judgement). Although in the Arabic language, formally, ANP judgement is similar to definite negative (sāliba muḥaṣṣala) and also metathetic judgements, the way of its construction is different from both of them and its truth conditions (...) are different from metathetic ones. From a modern logic viewpoint, ANP may indicate equality judgement; however, attributing it to Muslim logicians is questionable, although some of their wordings may implicitly show it. According to Ḥāʾirī, an Iranian contemporary philosopher and logician, the new judgement is supposed to solve some problems, especially logical explanation of the division of modalities into necessity, impossibility, and contingency (imkān khāṣṣ). However, Ṭabāṭabāʾī, another Iranian contemporary philosopher, disagrees with Ḥāʾirī and regards ANP judgement the same as an affirmative metathetic one. In this paper, while examining Ṭabāṭabāʾī’s and Ḥāʾirī’s reasons, by using some insights into modern logic, I will try to strengthen Ṭabāṭabāʾī’s views, although it may be confronted with some questions or deficiencies. (shrink)