Mohammad Saleh Zarepour’s research while affiliated with University of Manchester and other places

Discussing various versions of two medieval arguments for the impossibility of infinity, this Element sheds light on early stages of the evolution of the notion of INFINITIES OF DIFFERENT SIZES. The first argument is called 'the Equality Argument' and relies on the premise that all infinities are equal. The second argument is called 'the Mapping Argument' and relies on the assumption that if one thing is mapped/ superposed upon another thing and neither exceeds the other, the two things are equal to each other. Although these arguments were initially proposed in the context of discussions against the possibility of infinities, they have played pivotal roles in the historical evolution of the notion of INFINITIES OF DIFFERENT SIZES.

Appealing to some analytic tools developed by contemporary analytic philosophers, I discuss Avicenna’s views regarding the problem(s) of linguistic and mental reference to non-existents, also known as the problem(s) of ‘empty intentionality’. I argue that, according to Avicenna, being in an intentional state directed towards an existing thing involves three elements: (1) an indirect relation to that thing, (2) a direct relation to a mental representation of that thing, and (3) a direct relation to the essence of that thing. Empty intentionality does not involve the first element. Moreover, depending on the nature of the non-existent we are thinking about, the third element may not be involved either. Thus, the necessary element of being in an intentional state towards something is to be related to a mental representation of that thing. The nature of this representation may vary depending on the nature of the non-existent towards which our thought is directed.

The Successive Addition Argument (SAA) is one of the arguments proposed by the defenders of the Kalām Cosmological Argument to support the claim that the universe has a beginning. The main premise of SAA states that a collection formed by successive addition cannot be an actual infinite. This premise is challenged by an argument originally proposed by Fred Dretske. According to Dretske’s Argument (DA), the scenario of a counter who starts counting numbers and never stops can provide a counterexample to the main premise of SAA. I argue that neither DA nor its past-oriented counterpart—which discusses the scenario of a counter who has always been counting negative integers from the infinite past—can play a decisive role in our evaluation of the strength of the arguments that are intended to establish the finitude of the past based on the impossibility of an actually infinite number of successive additions.

Avicenna believes that God must be understood in the first place as the Necessary Existent (wâǧib al-wuǧûd). In his various works, he provides different versions of an ingenious argument for the existence of the Necessary Existent—the so-called Proof of the Sincere (burhân al-ṣiddîqîn)—and argues that all the properties that are usually attributed to God can be extracted merely from God's having necessary existence. Considering the centrality of tawḥîd to Islam, the first thing Avicenna tries to extract from God's necessary existence is God's oneness. The aim of the present Element is to provide a detailed discussion of Avicenna's arguments for the existence and unity of God. Through this project, the author hopes to clarify how, for Avicenna, the Islamic concept of monotheism is intertwined with the concept of essential existence.

At face value, intentionality is a relational notion. There are, however, arguments intended to show that it is not. I categorize the strongest arguments against the relationality of intentionality into three major groups: Brentanian arguments, Fregean arguments, and Quinean arguments. I argue that, despite their prima facie plausibility, none of these arguments eventually succeeds. I then conclude that, in the absence of defeating evidence against what at face value looks correct, we are justified to consider intentionality as a relational notion.

According to Avicenna, some of the objects of mathematics exist and some do not. Every existing mathematical object is a non-sensible connotational attribute of a physical object and can be perceived by the faculty of estimation. Non-existing mathematical objects can be represented and perceived by the faculty of imagination through separating and combining parts of the images of existing mathematical objects that are previously perceived by estimation. In any case, even non-existing mathematical objects should be considered as properties of material entities. They can never be grasped as fully immaterial entities. Avicenna believes that we cannot grasp any mathematical concepts unless we first have some specific perceptual experiences. It is only through the ineliminable and irreplaceable operation of the faculties of estimation and imagination upon some sensible data that we can grasp mathematical concepts. This shows that Avicenna endorses some sort of concept empiricism about mathematics.

Employing Constructive Type Theory (CTT), we provide a logical analysis of Ibn Sīnā’s descriptional propositions. Compared to its rivals, our analysis is more faithful to the grammatical subject-predicate structure of propositions and can better reflect the morphological features of the verbs (and descriptions) that extend time to intervals (or spans of times). We also study briefly the logical structure of some fallacious inferences that are discussed by Ibn Sīnā. The CTT-framework makes the fallacious nature of these inferences apparent.

This volume is a collection of essays in honour of Professor Mohammad Ardeshir. It examines topics which, in one way or another, are connected to the various aspects of his multidisciplinary research interests. Based on this criterion, the book is divided into three general categories. The first category includes papers on non-classical logics, including intuitionistic logic, constructive logic, basic logic, and substructural logic. The second category is made up of papers discussing issues in the contemporary philosophy of mathematics and logic. The third category contains papers on Avicenna’s logic and philosophy. Mohammad Ardeshir is a full professor of mathematical logic at the Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran, where he has taught generations of students for around a quarter century. Mohammad Ardeshir is known in the first place for his prominent works in basic logic and constructive mathematics. His areas of interest are however much broader and include topics in intuitionistic philosophy of mathematics and Arabic philosophy of logic and mathematics. In addition to numerous research articles in leading international journals, Ardeshir is the author of a highly praised Persian textbook in mathematical logic. Partly through his writings and translations, the school of mathematical intuitionism was introduced to the Iranian academic community.