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. (shrink)

Avicenna believes that God must be understood in the first place as the Necessary Existent. 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 —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. (shrink)

ABSTRACT W.L. Craig has argued that the universe has a beginning because (1) the infinitude of the past entails the existence of actual infinite multitudes of past intervals of time, and (2) the existence of actual infinite multitudes is impossible. Puryear has rejected (1) and argued that what the infinitude of the past entails is only the existence of an actual infinite magnitude of past time. But this does not preclude the infinitude of the past, Puryear claims, because there can (...) be no justification for the claim that actual infinite magnitudes are impossible. I argue, against Puryear, that there can be such a justification. I claim, nevertheless, that, for reasons entirely different from Puryear’s, the finitude of the past cannot be established based either on the impossibility of actual infinite multitudes or on the impossibility of actual infinite magnitudes. My arguments in this paper draw on insights from al-Kindī and Avicenna. (shrink)

The intuition that we can think about non-existent objects seems to be in tension with philosophical concerns about the relationality of intentionality. Tim Crane’s psychologism removes this tension by proposing a psychologistic account of intentionality according to which intentionality is a purely non-relational notion. I argue that his account has counterintuitive consequences regarding our thoughts about existing objects, and as such is insufficiently plausible to convince us to reject the relationality of intentionality.

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. (shrink)

The medieval Islamic solutions to the liar paradox can be categorized into three different families. According to the solutions of the first family, the liar sentences are not well-formed truth-apt...

W.L. Craig has argued that the universe has a beginning because (1) the infinitude of the past entails the existence of actual infinite multitudes of past intervals of time, and (2) the existence of actual infinite multitudes is impossible. Puryear has rejected (1) and argued that what the infinitude of the past entails is only the existence of an actual infinite magnitude of past time. But this does not preclude the infinitude of the past, Puryear claims, because there can be (...) no justification for the claim that actual infinite magnitudes are impossible. I argue, against Puryear, that there can be such a justification. I claim, nevertheless, that, for reasons entirely different from Puryear’s, the finitude of the past cannot be established based either on the impossibility of actual infinite multitudes or on the impossibility of actual infinite magnitudes. My arguments in this paper draw on insights from al-Kindī and Avicenna. (shrink)

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.

RésuméSelon Avicenne, certains objets des mathématiques existent et d'autres non. Chaque objet mathématique existant est un attribut connotationnel non sensible d'un objet physique et peut être perçu par la faculté d'estimation. Les objets mathématiques non existants peuvent être représentés et perçus par la faculté d'imagination en séparant et en combinant des parties d'images d'objets mathématiques existants qui sont précédemment perçues par estimation. Dans tous les cas, même les objets mathématiques non existants doivent être considérés comme des propriétés d'entités matérielles. Ils (...) ne peuvent jamais être saisis comme des entités totalement immatérielles. Avicenne pense que nous ne pouvons saisir aucun concept mathématique à moins d'avoir au préalable des expériences perceptives spécifiques. Ce n'est que par l'opération non éliminable et irremplaçable des facultés d'estimation et d'imagination sur certaines données sensibles que nous pouvons saisir les concepts mathématiques. Cela montre qu'Avicenne approuve une sorte d'empirisme conceptuel sur les mathématiques. (shrink)

The medieval Islamic solutions to the liar paradox can be categorized into three different families. According to the solutions of the first family, the liar sentences are not well-formed truth-apt sentences. The solutions of the second family are based on a violation of the classical principles of logic (e.g. the principle of non-contradiction). Finally, the solutions of the third family render the liar sentences as simply false without any contradiction. In the Islamic tradition, almost all the well-known solutions of the (...) third family are inspired by the solution proposed by At_īr al-Dīn al-Abharī (d. 1265). Providing a logical analysis of his discussion of the liar paradox, I show that his solution is based on a conception of truth according to which every sentence signifies, usually among other things, its own truth. This makes Abharī’s solution of the same spirit as certain solutions that were later developed in the Latin tradition, in particular by John Buridan (d. 1358) and Albert of Saxony (d. 1390). (shrink)

Avicenna believed in mathematical finitism. He argued that magnitudes and sets of ordered numbers and numbered things cannot be actually infinite. In this paper, I discuss his arguments against the actuality of mathematical infinity. A careful analysis of the subtleties of his main argument, i. e., The Mapping Argument, shows that, by employing the notion of correspondence as a tool for comparing the sizes of mathematical infinities, he arrived at a very deep and insightful understanding of the notion of mathematical (...) infinity, one that is much more modern than we might expect. I argue, moreover, that Avicenna’s mathematical finitism is interwoven with his literalist ontology of mathematics, according to which mathematical objects are properties of existing physical objects. (shrink)

Some authors have proposed that Avicenna considers mathematical objects, i.e., geometric shapes and numbers, to be mental existents completely separated from matter. In this paper, I will show that this description, though not completely wrong, is misleading. Avicenna endorses, I will argue, some sort of literalism, potentialism, and finitism.

Leading scholars representing the world's five great religious traditions--Buddhism, Hinduism, Judaism, Christianity, and Islam--discuss fundamental philosophical questions on revelation and religious experience; analysis of faith; science and religion; the foundation of morality; and life and the afterlife.

Employing Constructive Type Theory Constructive Type Theory, we provide a logical analysis of[aut]Ibn SīnāIbn Sīnā’sIbn Sīnā 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 that extend time to intervals. 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.

The Polish researcher in the field of logic and philosophy, Jan Woleński, in one of his recent articles, "Metalogical Observations About the Underdetermination of Theories by Empirical Data," logically formalized two weak and strong versions of the underdetermination of theories by empirical data (or UT by abbreviation) and with these formalization has metalogically analyzed these two versions. Finally he has deducted that the weak version is defensible while the strong version is not. In this paper we will critically study Woleński’s (...) analysis of the strong version of UT. (shrink)

adr al-Dīn al-Dashtakī (d. 1498) has proposed a solution to the liar paradox according to which the liar sentence is a self-referential sentence in which the predicate ‘false’ is iterated. Discussing the conditions for the truth-aptness of the sentences with nested and iterated instances of the predicates ‘true’ and/or ‘false’, Dashtakī argued that the liar sentence is not truth-apt at all. In the tradition of Arabic logic, the central elements of Dashtakī's solution—the self-referentiality of the liar sentence and the implicit (...) iteration of the predicate ‘false’—were initially highlighted in two earlier solutions proposed by Naīr al-Dīn al-ūsī (d. 1274) and Shams al-Dīn al-Samarqandī (d. 1322), respectively. Here I investigate all three solutions and show that Dashtakī's solution can be taken as a synthesis of the other two. None of these solutions seems to be convincing at the end of the day. Nevertheless, all of them include significant logical and philosophical insights. In particular, although Dashtakī's solution is not itself compelling, it is only a few steps away from a promising solution. The appendix to this paper includes translations of the relevant passages. (shrink)

In an illuminating article, Dimitri Gutas has tried to show that Avicenna's theory of knowledge should be understood within a full-blown empiricist framework very similar to that of John Locke.1 Gutas' argument is based on an analysis of Avicennian 'principles of syllogism'2. The principles of syllogism are those judgments and propositions that form the irreducible and axiomatic foundations of syllogisms and definitions.3 Avicenna categorizes these principles based on how we accept and acknowledge the truth of them. This categorization appears, with (...) some slight modifications, in many places in Avicenna's oeuvre, for example in the Kitāb al-Burhān of al-Šifā',4 and the logic parts of... (shrink)

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. (shrink)

Defenders of the Kalām Cosmological Argument appeal to the so-called Hilbert’s Hotel Argument to establish the finitude of the past based on the impossibility of actual infinites. Some of their opponents argue that this proves too much because if the universe cannot be beginningless due to the impossibility of actual infinites, then, for the same reason, it cannot be endless either. Discussing four different senses of the existence of an actual infinite, I criticize both sides of the debate by showing, (...) on the one hand, that the Hilbert’s Hotel Argument is not powerful enough to rule out the possibility of the infinitude of the past and, on the other hand, that the soundness of the argument for the finitude of the past from the impossibility of actual infinites does not establish the soundness of the parallel argument for the finitude of the future. (shrink)

Criticizing Richard Swinburne’s conception of God, John Hick argues that God cannot be personal because infinity and personhood are mutually incompatible. An essential characteristic of a person, Hick claims, is having a boundary which distinguishes that person from other persons. But having a boundary is incompatible with being infinite. Infinite beings are unbounded. Hence God cannot be thought of as an infinite person. In this paper, I argue that the Hickian argument is flawed because boundedness is an equivocal notion: in (...) one sense it is not essential to personhood, and in another sense—which is essential to personhood—it is compatible with being infinite. (shrink)

This volume focuses on Islamic philosophy of religion with a range of contributions from analytic perspectives. It opens with methodological discussions on the relationship between the history of Islamic philosophy and contemporary analytic philosophy. The book then offers a philosophical examination of some specific Islamic beliefs as well as some approaches to general beliefs that Islam shares with other religions. The chapters address a variety of topics from the existence and attributes of God through to debates on science and religion. (...) The authors are predominantly scholars from Muslim backgrounds who tackle philosophical issues concerning Islam as their own living religion, representing internal perspectives that have never been vocal in analytic philosophy of religion so far. This is valuable reading for scholars and students of philosophy, theology, and religious studies. (shrink)

In his "The Empiricism of Avicenna," Dimitri Gutas interprets Avicenna as an empiricist.1 He analyzes Avicennian 'principles of syllogism' and claims that none of them are a priori. Moreover, regarding awwalīyāt and fiṭrīyāt—which are two groups of such principles—Gutas suggests that "[i]t appears that both kinds of propositions would be analytic, in Kantian terms. As for Locke, they would be what he called 'trifling.'"2 In my first comment in this issue, I disagreed with this view and argued that these two (...) groups of propositions are a priori in the Kantian sense. Assenting to their truth is internal to the intellect and independent of empirical information. I also argued that at least some fiṭrīyāt are synthetic... (shrink)

I will briefly argue that theological fatalism is not a genuine ‘theological’ problem, for it can be reduced to another alleged incompatibility that arises independently of the existence or non-existence of God. I will conclude that the way of arguing against the existence of God or His omniscience by appealing to theological fatalism is blocked for libertarian atheists.

Concept originalism, recently introduced and defended by Sainsbury and Tye, Tye, and Sainsbury, holds that “atomic concepts are to be individuated by their historical origins, as opposed to their semantic or epistemic properties”. The view is immune to Gareth Evans’s “Madagascar” objection to the Causal Theory of Reference since it allows a concept to change its reference over time without losing its identity. The possibility of reference-shift, however, raises the problem of misleading belief reports. S&T try to tackle the problem (...) by strengthening the sufficient condition for a truthful belief report. We will argue that, first, their solution fails, second, and more importantly, their diagnosis of the root of the problem is misguided, third, two initially appealing ways out of the problem fail, and fourth, the prospect of finding a solution to the problem within CO is dim. The view opens the Pandora’s box of reference-shift, in a wide range of cases, without providing the necessary semantic means to take care of them. (shrink)