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.

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.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)

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)

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)

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)

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...

ABSTRACT W.L. Craig has argued that the universe has a beginning because the infinitude of the past entails the existence of actual infinite multitudes of past intervals of time, and the existence of actual infinite multitudes is impossible. Puryear has rejected 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)

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.

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)

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)