Mohammad Saleh Zarepour

Analysing the theory of future contingency that Ibn Sīnā (Avicenna) has developed in chapter I.10 of his The Interpretation (Al-ʿIbāra from the logic part of Al-Shifāʾ) and criticising the rival interpretations of this chapter, I argue that, according to him, the future is open not only epistemically but also ontically and alethically. This means that there are future propositions expressing future states of affairs whose occurrence or nonoccurrence is not yet settled. Such a proposition does not have a settled truth-value. It is neither true nor false. Accordingly, neither such a proposition nor its negation can be known.

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.

In his discussions of the various readings of modal propositions, Ibn Sīnā’s focus is mostly on a distinction which was later labelled the distinction between descriptional (waṣfī) and substantial (ḏātī) readings of a modal proposition. Given that for Ibn Sīnā all categorical propositions are either implicitly or explicitly modal, the substantial–descriptional distinction is in some sense applicable to the readings of all categorical propositions. This distinction is based on how (i.e., under which conditions) the predicate of a categorical proposition is true of its subject. According to the substantial reading, the predicate is true of the subject (perhaps with a certain alethic or temporal modality) as long as the substance of the subject exists. On the other hand, according to the descriptional reading, the predicate is true of the subject (again, perhaps with a certain modality) as long as the substance of the subject is truly described by the subject. To be clearer, consider the following proposition:(1) Every S is P. The difference between the substantial and descriptional readings of (1) can be articulated as follows:Substantial Reading of (1): Every S, as long as it exists, is P.Descriptional Reading of (1): Every S, as long as it is S, is P.It is in principle possible that a proposition is true on one of these readings and false on the other. It is only the context which determines how a proposition must be read to be true. To give an example, consider the following proposition:(2) Every bachelor is unmarried. The substantial and descriptional readings of (2) are respectively as follows: (3) Every bachelor, as long as he exists, is unmarried.(4) Every bachelor, as long as he is bachelor, is unmarried.These two propositions have different truth values. Contrary to (3)—which is false—(4) is true. This is because a bachelor is unmarried only insofar as he is described as a bachelor. So (4) is true. By contrast, it is in principle possible for a person who is a bachelor in some period(s) of time to be married in some other period(s) of time; this is so at least if we assume that ‘as long as’ has a temporal meaning. In other words, it is not necessary for such a person to be always unmarried. The mere existence of the substance of this person does not guarantee his being unmarried. Thus (3) is false. There are, however, other propositions that are true on the substantial reading. For example, consider the following proposition:(5) Every human is animal.The predicate Animal is true of every human as long as s/he exists. Put otherwise, what makes it true to say that every human is animal is the mere existence of human substances. This means that not only the descriptional but also the substantial reading of (5) is true. Indeed, since every human exists if and only if s/he is human, the substantial and descriptional readings of (5) express one and the same fact. As Ibn Sīnā himself insists, he is the first logician to have focused on the above distinction and pondered on its fruitfulness for removing some difficulties with Aristotle’s syllogistic. Since the distinction plays a crucial role in Ibn Sīnā’s syllogistic, it is discussed in several places in his logical oeuvre. Moreover, the distinction was subject to continually heated discussions in Arabic logic after Ibn Sīnā. For instance, the distinction was accepted by Rāzī and Khūnaǧī, on the one hand, and was seen as redundant by Ibn Rushd. The substantial sense of propositions corresponds to what is called the ‘divided’ sense of propositions in the Latin tradition. However, although the descriptional sense of propositions is plays an important role in Arabic syllogistic, it has no widely discussed counterpart in the Latin tradition. These observations strongly suggest that a comprehensive picture of Arabic syllogistic from Ibn Sīnā onwards cannot be achieved unless we have a clear logical analysis of the aforementioned distinction. An effective and popular strategy for providing such an analysis is to look at the different readings of a proposition through the lens of modern formal logic. Therefore, it is important to find out which formal language has the best capacity to capture various aspects of this distinction and the insights behind it. In the literature, several attempts have been made to formalize the different readings of propositions in the languages of classical predicate or temporal logics. In this chapter, we put forward an alternative based on Martin-Löf’s constructive type theory (CTT). 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). It is worth noting that our focus will mostly be on the analysis of the descriptional reading of propositions (which can also be called ‘the descriptional propositions’ for the sake of brevity).

It has been contended that the Principle of Sufficient Reason (PSR) implies necessitarianism—that is, the view that everything occurs out of necessity. Discussing a well‐known argument for this claim developed by contemporary metaphysicians, I show that Ibn Sīnā has anticipated a counterpart of this argument, and that is precisely why he is usually described as a necessitarian. This raises a puzzle because he also appears to endorse the existence of contingencies in the world. In particular, he seems to believe that the future is open, not only epistemically and alethically but also ontically. This means that there are future states of affairs that are genuinely contingent and the truth values of the propositions expressing these states are not determined now. Focusing on Ibn Sīnā's commitment to the Coexistence Principle—according to which the cause coexists with the effect—I will provide a solution to the aforementioned puzzle.

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.

AbstractṢadr 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 Naṣīr al-Dīn al-Ṭūsī (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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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).

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...

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...

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.

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.