We discuss the relationships between the notions of $\kappa $ -cub game on $\lambda $ , $\kappa $ -cub subset of $\lambda $ , the ideal of good subsets of $\lambda $ and the problem of adding a $\kappa $ -cub into a given $\kappa $ -stationary subset of $\lambda $ . We also give a short introduction to the ideal of good subsets of $\lambda $.

The present article, which is a revised version of part of [Hu1], deals with various relations between models which might serve as exact formulations for the vague concept "similar" or "almost isomorphic". One natural class of such formulations is equivalence in a given logic. Another way to express similarity is by potential isomorphism, i.e., isomorphism in some extension of the set-theoretic universe. The class of extensions may be restricted to give different notions of potential isomorphism. A third method is to (...) study the winning strategies for an Ehrenfeucht-Fraisse-game played between the two models, and the properties of the resulting equivalence and nonequivalence trees. The basic question studied here is whether one such notion of similarity implies another. Some implications and counterexamples listed in this part are previously known or trivial, but all are mentioned for completeness' sake. Only models of cardinality ℵ 1 are considered. Some results are therefore connected with the Continuum Hypothesis. (shrink)

We show in the paper that for any non-classifiable countable theory T there are non-isomorphic models and that can be forced to be isomorphic without adding subsets of small cardinality. By making suitable cardinal arithmetic assumptions we can often preserve stationary sets as well. We also study non-structure theorems relative to the Ehrenfeucht-Fraïssé game.

Hyttinen and Väänänen study extensively the so-called Scott and Karp trees. Their paper leaves some open interesting questions:1. Are Scott trees closed under infimums?2. Are Karp trees closed under infimums?3. Does every Karp tree contain a subtree of small cardinality which is itself also a Karp tree?The present article addresses these questions. It turns out that there are counterexamples dictating a negative answer to and . The answer to question , however, is independent of the standard ZFC axioms of set (...) theory provided that the existence of a strongly compact cardinal is consistent. (shrink)

This paper introduces Basic Intuitionistic Set Theory BIST, and investigates it as a first-order set theory extending the internal logic of elementary toposes. Given an elementary topos, together with the extra structure of a directed structural system of inclusions on the topos, a forcing-style interpretation of the language of first-order set theory in the topos is given, which conservatively extends the internal logic of the topos. This forcing interpretation applies to an arbitrary elementary topos, since any such is equivalent to (...) one carrying a dssi. We prove that the set theory BIST+Coll is sound and complete relative to forcing interpretations in toposes with natural numbers object . Furthermore, in the case that the structural system of inclusions is superdirected, the full Separation schema is modelled. We show that all cocomplete and realizability toposes can be endowed with such superdirected systems of inclusions.A large part of the paper is devoted to an alternative notion of category-theoretic model for BIST, which, following the general approach of Joyal and Moerdijkʼs Algebraic Set Theory, axiomatizes the structure possessed by categories of classes compatible with BIST. We prove soundness and completeness results for BIST relative to the class-category semantics. Furthermore, BIST+Coll is complete relative to the restricted collection of categories of classes given by categories of ideals over elementary toposes with nno and dssi. It is via this result that the completeness of the original forcing interpretation is obtained, since the internal logic of categories of ideals coincides with the forcing interpretation. (shrink)

This paper introduces Basic Intuitionistic Set Theory BIST, and investigates it as a first-order set theory extending the internal logic of elementary toposes. Given an elementary topos, together with the extra structure of a directed structural system of inclusions on the topos, a forcing-style interpretation of the language of first-order set theory in the topos is given, which conservatively extends the internal logic of the topos. This forcing interpretation applies to an arbitrary elementary topos, since any such is equivalent to (...) one carrying a dssi. We prove that the set theory BIST+Coll is sound and complete relative to forcing interpretations in toposes with natural numbers object. Furthermore, in the case that the structural system of inclusions is superdirected, the full Separation schema is modelled. We show that all cocomplete and realizability toposes can be endowed with such superdirected systems of inclusions.A large part of the paper is devoted to an alternative notion of category-theoretic model for BIST, which, following the general approach of Joyal and Moerdijkʼs Algebraic Set Theory, axiomatizes the structure possessed by categories of classes compatible with BIST. We prove soundness and completeness results for BIST relative to the class-category semantics. Furthermore, BIST+Coll is complete relative to the restricted collection of categories of classes given by categories of ideals over elementary toposes with nno and dssi. It is via this result that the completeness of the original forcing interpretation is obtained, since the internal logic of categories of ideals coincides with the forcing interpretation. (shrink)

We study the non-Fregean propositional logic with propositional quantifiers, denoted by $\mathsf{SCI}_{\mathsf{Q}}$. We prove that $\mathsf{SCI}_{\mathsf{Q}}$ does not have the finite model property and that it is undecidable. We also present examples of how to interpret in $\mathsf{SCI}_{\mathsf{Q}}$ various mathematical theories, such as the theory of groups, rings, and fields, and we characterize the spectra of $\mathsf{SCI}_{\mathsf{Q}}$-sentences. Finally, we present a translation of $\mathsf{SCI}_{\mathsf{Q}}$ into a classical two-sorted first-order logic, and we use the translation to prove some model-theoretic properties of (...) $\mathsf{SCI}_{\mathsf{Q}}$. (shrink)

We show that there are continuum many different extensions of SCI (the basic theory of non-Fregean propositional logic) that lie below WF (the Fregean extension) and are closed under substitution. Moreover, continuum many of them are independent from WB (the Boolean extension), continuum many lie above WB and are independent from WH (the Boolean extension with only two values for the equality relation), and only countably many lie between WH and WF.

We study a new formal logic LD introduced by Prof. Grzegorczyk. The logic is based on so-called descriptive equivalence, corresponding to the idea of shared meaning rather than shared truth value. We construct a semantics for LD based on a new type of algebras and prove its soundness and completeness. We further show several examples of classical laws that hold for LD as well as laws that fail. Finally, we list a number of open problems. -/- .

In 2011, Andrzej Grzegorczyk formulated Logic of Descriptions, a new logical system in which the classical equivalence has been replaced with the descriptive equivalence. Two sentences are descriptively equivalent whenever they describe the same state of affairs. Grzegorczyk’s logic LD is built from the ground up by revising the axioms of classical propositional logic and rejecting those that do not correspond to the intended interpretation of the descriptive equivalence as the connective expressing equimeaning relations between sentences. Grzegorczyk’s last paper, which (...) introduced in detail philosophical motivations of LD and its axiomatization, has become an inspiration for investigating the properties of LD and its various modifications. In this paper we present the basics of Grzegorczyk’s logic LD and then we survey the recent results on LD that have shed light on mysterious properties of the Grzegorczyk’s descriptive equivalence connective. (shrink)

This chapter contains section titled: “If This Is the Work of a Higher Power, Then They Have One Hell of a Sense of Humor” “I Am God” Giving Oneself Over to God “Could There Be A Connection…?” Notes.

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 38.4 (2000) 479-502 [Access article in PDF] Possible Worlds in the Tahâfut al-Falâsifa Al-Ghazâlî on Creation and Contingency Taneli Kukkonen University of Helsinki 1. This article is the second half in an inquiry into the debate between al-Ghazâlî (1058-1111) and Averroes (1126-1198) on the metaphysical basis of modalities. The first article focused on Averroes' exposition of the Arabic Aristotelian position on the (...) eternity of the world and the modalities, as found in the Tahâfut al-tahâfut, the "Incoherence of the Incoherence [of the Philosophers]" from ca. 1180.1 In this paper I propose to sketch the outlines to a very different conception suggested by al-Ghazâlî in the Tahâfut al-falâsifa (1095) and quoted verbatim and commented upon by Averroes in the Tahâfut al-tahâfut.2 In contrast to the naturalistic model of modalities propounded by [End Page 479] Averroes, al-Ghazâlî develops an interpretation of possibility in which conceivability and co-assertability are central. In several key respects al-Ghazâlî's approach mirrors that of John Duns Scotus in the fourteenth century: it makes possible, for instance, a distinction between conceptual and natural possibilities in a manner reminiscent of later Latin medieval theory, and, reflecting this, a distinction between the (non-temporal) moments of conception and causation in the divine mind. The parallels between al-Ghazâlî's and Augustine's basic conceptions, meanwhile, highlight the theological motives lying at the heart of the new thinking.As in the previous article, the dialectical form of Averroes' later Tahâfut al-tahâfut is used for critical insight. Averroes' criticism of al-Ghazâlî's modal theoretical innovations gives rise to an important question about the lengths to which al-Ghazâlî's proposals could be taken. The issue is to an extent unresolveable; one would do well to note why. Whereas Averroes' formulations in the Tahâfut al-tahâfut are made readily understandable against the backdrop of his Aristotelian commentaries and wider systematic teaching, it is less easy to determine how far al-Ghazâlî is willing to develop his own ideas. The materials given in the Tahâfut al-falâsifa leave the impression of being inconclusive and open-ended—perhaps deliberately so—and the ambiguities are mirrored in al-Ghazâlî's other texts.3Taken as they stand, al-Ghazâlî's formulations retain a substantial Avicennian residue, for better or for worse. This makes for a curious mixture of old and new in his overall scheme, a feature which Averroes can exploit by criticizing al-Ghazâlî from a strict Aristotelian viewpoint (just as he criticized Avicenna), while all the time maintaining that his adversary's proposals do not add up to a coherent and full-bodied alternative to that venerable tradition. But Averroes' criticisms do not touch on the way al-Ghazâlî's suggestions, vague as they may be, do represent a genuine breakthrough. Al-Ghazâlî's interpretation of the modal terms bypasses the connection traditionally made between true possibility and temporal instantiation. This allows for a freer handling of counterfactual possibilities, an important feature in any refiguring of the limits of possibility. 2. Al-Ghazâlî's innovations have their root in the idea of God freely choosing (arbitrating) between alternatives equal to him. This simple kernel of an idea, seated in the kalâm conception of possibility, allows for a recognition of the genuineness of synchronic alternatives: a seemingly small shift, but all-important [End Page 480] to the ensuing debate. Al-Ghazâlî has defended the notion of God's genuine choice earlier,4 but in refuting "the third proof of the philosophers for the world's eternity," he begins to make systematic use of the notion of possibility. A brief recapitulation of the philosophers' argument will serve to recall the reasoning from which al-Ghazâlî takes his cue. The philosophers, in al-Ghazâlî's words, had... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Possible Worlds in the Tahâfut al-tahâfut:Averroes on Plenitude and PossibilityTaneli Kukkonen1.It has become customary to credit John Duns Scotus with having first systematically laid out the basis for treating the modal terms as referring to synchronic alternative states of affairs. This has been viewed as constituting a genuine shift in modal paradigms, as no former model had included the idea of genuine synchronic alternative possibilities. Historians of modal logic (...) and contemporary logicians alike have found it interesting that certain key features of Duns Scotus's theory and subsequent late medieval work markedly resemble the so-called possible worlds semantics approach of modern modal theory.1Duns Scotus' innovations were not completely without precedent. Several key elements in Scotus' theory were foreshadowed by twelfth-century developments. Perhaps somewhat amusingly, one of the most important forerunners to the Latin discussion was one in whose context the expression "possible worlds" would have made sense in a very special way.2 This is the medieval Arabic debate on the eternity of the world and its modal status. In this paper I propose to take stock of the positions the Arabs reached, and to do so by way of [End Page 329] consulting one of the documents central to the debate, the Tahâfut al-tahâfut or the "Incoherence of the Incoherence," by Abû al-Walîd Ibn Rushd (the Latin "Averroes," 1126-1198). In the first part I examine Averroes' exposition of the received Aristotelian tradition; in the second I assess the revisions to modal theory suggested by al-Ghazâlî (1058-1111), in the latter's comprehensive critique of philosophical doctrine. Though the two inquiries are obviously complementary, they can be accomplished independently of each other.It will be seen that Averroes' and his formidable adversary's views on the interpretation of the modal concepts differ quite fundamentally. What makes the ensuing debate, often fraught with misunderstandings and misrepresentation, so engaging is that both parties, in spite of their differences, refer to a common Aristotelian backdrop in questions of terminology and mode of argumentation. Both Averroes and al-Ghazâlî are well-placed to present a considered and balanced account of what they take to be crucial in the issues involved. It is on account of this that the complex interplay between the old and the new comes to the fore with exceptional force and clarity in the Tahâfut debates.2.The Tahâfut al-tahâfut, first published in 1180, is a philosophical rejoinder to an attack on philosophy, Abû Hâmid al-Ghazâlî's Tahâfut al-falâsifa or "The Incoherence of the Philosophers" (1095). In that celebrated work al-Ghazâlî had claimed to expose certain philosophical doctrines as not only contrary to orthodox Muslim belief, but also internally incoherent.3 Averroes' reply in turn was written in order "to show the different degrees of assent and conviction attained by the assertions in The Incoherence of the Philosophers, and to prove that the greater part has not reached the degree of evidence and of truth."4 The work is thus of a doubly dialectical nature. Whereas al-Ghazâlî tries to show the philosophers' reasoning to be defective, Averroes has to show both that al-Ghazâlî is likewise lacking in intellectual rigor and that philosophy, properly understood, is innocent of the charges leveled at it. If the Islamic philosophers (al-Fârâbî and, above all, Avicenna) have in fact erred, this is only to the extent that they have misrepresented correct Aristotelian doctrine. [End Page 330]Averroes' presentation is appropriately delicate considering the complexity of the task at hand. Averroes quotes al-Ghazâlî exclusively in full, lengthy passages, with the result of incorporating almost all of the Tahâfut al-falâsifa in his own work. In so doing he gives us an adequate and comparably fair representation of al-Ghazâlî's views. Averroes then goes on to discuss what al-Ghazâlî says both in the philosophers' name and in his own, and points out their respective deviations from Aristotelian doctrine. The text thus comes laid out in three successive layers, with Averroes' own... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Ideas 61.4 (2000) 539-560 [Access article in PDF] Plenitude, Possibility, and the Limits of Reason: A Medieval Arabic Debate on the Metaphysics of Nature Taneli Kukkonen In a recent article Simo Knuuttila has examined the argumentative patterns of modern cosmology, especially the search in fundamental physics for an "ultimate explanation," a unified "Theory of Everything" that would subsume all more local theories under (...) its aegis. Knuuttila goes on to compare contemporary modes of explanation with previous ways of conceiving of the metaphysics of understanding. As it turns out, on the cosmological borderline where physics shades into metaphysics desires similar at heart have fueled the efforts of thinkers throughout the history of western thought. When what is at stake is the final intelligibility of the world, shared ideals of necessity, transparency, and simplicity come to the fore. More often than not, theological concerns and preconceptions accompany these notions. 1One can react to this finding in one of two ways, either by retorting that the moderns have not gotten very far or by pointing out that earlier discussions on the topic were often quite philosophically sophisticated. In this article I propose to investigate how some of the issues raised by Knuuttila figure in a specific historical context. This is the debate on the pre-eternity of the world initiated by the celebrated Muslim theologian Abû Hâmid al-Ghazâlî (1058-1111) in his polemic arguing for The Incoherence of the Philosophers (Tahâfut al-falâsifa, 1095) and later picked up by the Andalusian philosopher Averroës (1126-98) in [End Page 539] his reply, The Incoherence of the Incoherence (Tahâfut al-tahâfut, 1180). 2 The exceptionally rich cosmological materials could be taken in any number of directions, but I will focus on three main issues: the discussants' construction of the domain of possibilities (i.e. the relation of the possible to the actual), their understanding of the reasonability of creation, and the question of its finitude and infinity. The study is undertaken partly to illustrate the sophistication with which the topics were handled in medieval Islamic philosophy, but in each case I will also draw parallels with certain modern conceptions, and I submit that in each case al-Ghazâlî's and Averroës's debate throws light on the contemporary discussion. In the final section I will develop this contention further by pointing to a connection between finitude and possibilities which I believe has both heuristic and existential value. Plenitude and Possibility Among historians of philosophy it is now acknowledged that in late medieval discussions certain modal theoretical innovations were instrumental in bringing about profound change in the western worldview. A conceptual shift occurred where, roughly speaking, a single intelligible universe was exchanged for several possible worlds. In Knuuttila's estimation this change in worldviews was in some ways more fundamental than anything modern science has produced since. 3 This claim deserves consideration but I would like first to outline what the change was about, for in al-Ghazâlî's and Averroës's debate this shift in modal paradigms is clearly discernible.Representative of the philosophers' point of view, Averroës holds onto the received Arabic Aristotelian interpretation of setting possibilities in a statistical temporal-frequency framework. According to this account, what is truly possible must at some time be realized--this is a technical interpretation of what has after Lovejoy commonly become known as the principle of plenitude. 4 As a [End Page 540] corollary, what always is is necessarily. The cosmological consequences of these assumptions can be outlined as follows. First, lest God's creative possibilities be limited, it must be admitted that the world could have been created however long ago in the past. By extension God must have been able to create the world an infinite time ago. But if it is a genuine possibility that the world is eternally old, then according to the principle of plenitude, this possibility is an actual fact. Once it is... (shrink)

Taneli Kukkonen - Jean Fernel's On the Hidden Causes of Things. Forms, Souls and Occult Diseases in Renaissance Medicine - Journal of the History of Philosophy 45:1 Journal of the History of Philosophy 45.1 158-159 Muse Search Journals This Journal Contents Reviewed by Taneli Kukkonen University of Victoria Jean Fernel's On the Hidden Causes of Things. Forms, Souls and Occult Diseases in Renaissance Medicine. Edited and translated by John M. Forrester. Annotated and introduced by John M. Forrester and (...) John Henry. Leiden: Brill, 2005. Pp. x + 779. Cloth, $237.00. Our understanding of how early modern conceptions of human nature emerged out of the intellectual tumult of the Renaissance and the Reformation has been greatly enhanced by a growing recognition of the way in which these developments built not only on contemporary scientific advances and a recovery of ancient learning, but also on the philosophical.. (shrink)

Taneli Kukkonen - Medieval Islamic Philosophical Writings - Journal of the History of Philosophy 44:3 Journal of the History of Philosophy 44.3 471-472 Medieval Islamic Philosophical Writings. Edited and translated by Muhammad Ali Khalidi. Cambridge: Cambridge University Press, 2005. Pp. xlviii + 186. Cloth, $65.00. With late ancient philosophy and Latin scholasticism entering the mainstream of teaching the history of Western philosophy, it is natural that attention should turn next to the Arabic falsafah of the classical period, bridging as (...) it does the two traditions. Designated courses on Arabic or Islamic philosophy have begun to appear in the curricula of forward-thinking philosophy departments. This most welcome development has so far been hampered by the lack of affordable anthologies: the publication of Muhammad Ali Khalidi's collection therefore marks a watershed moment, and the translator and the publisher.. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Avicenna’s Metaphysics in ContextTaneli KukkonenRobert Wisnovsky. Avicenna’s Metaphysics in Context. Ithaca, NY: Cornell University Press, 2003. Pp. ix + 305. Cloth, $65.00.The challenges facing the contemporary writer on Arabic philosophy are many, but none more daunting than that of striking a satisfying balance between faithfully reproducing what is there in the text (alongside a lineage of likely sources, perhaps), and actively engaging the materials philosophically. From among the (...) current crop of scholars, the more cautious will argue that as long as we lack critical editions of even basic works, and as long as ambiguities remain concerning who was reading what, where, and when, any ambitious statements regarding the substance of Arabic thought, its development, and (especially) what its distinctive contributions might be, must remain hopelessly premature. The counterargument goes that by refusing the philosophically impatient the licence to speculate, at least, about the relevance of the materials at hand—however rough and ready—one will end up stifling just those endeavours the philologist hopes to promote. For without the promise of philosophical rewards, what incentive remains for the thankless and endless task of textual refinement and identification of sources? Strides made in late ancient and Latin medieval scholarship seem to indicate that philosophical curiosity serves to feed historical acuity, rather than hinder it. Yet with the study of Arabic philosophy the perceived opposition between philosophy and philology has led to a precious few works escaping charges of being found lacking either in textual or philosophical sophistication, or indeed both.To this select company one may now add Robert Wisnovsky's aptly titled Avicenna's Metaphysics in Context. The author pursues a particularly deft course of action: honing in on themes for whose evaluation sufficient materials are available, then infusing his exposition at every turn with philosophical insight and a scholar's eye for detail, Wisnovsky demonstrates by example what a resourceful scholar can accomplish in this day and age. Wisnovsky takes it as his task to situate the very doctrines Abû 'Alî Ibn Sînâ (980-1037) is most famous for—the essence-existence distinction, the distinction between contingent and necessary existence, and the created and embodied yet ultimately separable perfection of the human soul—in a continuous line of discussion stretching from Alexander of Aphrodisias to the kalâm theologians of Avicenna's own age.The resulting narrative threads together a dizzying array of thinkers and discussions, showing just how fertile the scholarship ranging from late antiquity to Arabic thought was, both considered in its original setting and in terms of the contemporary scholarly imagination. Among other things, Wisnovsky's book constitutes the fullest study to date of the [End Page 112] evolution of the concepts of final and efficient causality in the increasingly Neoplatonising interpretations of Aristotle. The cosmological and metaphysical motifs behind these developments are rightly pointed out by Wisnovsky, and their impact on Avicenna's metaphysics of the soul and his views on process and return receive thorough attention.In the midst of all this, sight may be lost of Avicenna's original achievement, and it has to be said that Wisnovsky does not play this aspect up by much. But this, the reader suspects, is part of the point. In order to appreciate a thinker's intellectual prowess it is not necessary to insist that he or she be conjuring up concepts out of thin air. A great mind may instead be a synthetic one, one that is able to negotiate between various conceptual schemes and commitments, and this is the picture Wisnovsky paints of Avicenna. Avicenna's deep engagement with the Peripatetic tradition is evident to any scholar, yet it is often difficult to determine exactly whose opinions he references, as contending viewpoints are typically introduced by enigmatic preambles such as "if it is said... " or, "some contend." Wisnovsky's attention to how terminological shifts reflect philosophical ones succeeds in demonstrating Avicenna's reliance in general not only on ancient sources, but on al-Fârâbi and the kalâm as well. His subtle analysis of the development of key Avicennian doctrines simultaneously serves to lend credence to the picture that is currently emerging concerning the... (shrink)

the history and philosophy of thought experiments has attracted considerable attention in recent years. Of particular interest to philosophers as well as historians of science has been the emergence of thought experiments as a common procedure in early modern science, along with the methodological presuppositions that underwrite this practice.1 From a philosophical perspective, the notion of thought experiments is intimately tied in with the much-debated connection between conceivability and possibility, as exemplified by the radical affirmation of the Conceivability Criterion of (...) Possibility by David Hume.2 Consequent upon this, historians of ancient and medieval philosophy have also expressed interest in .. (shrink)

The proofs for God's existence advanced in the most prominent theological work of Averroes (d. 1198), the Kita^b al-kashf, have been neglected, largely because the book has commonly – and correctly – been viewed as being meant for popular consumption. This article argues that although Averroes' arguments are non-technical, the Commentator nevertheless takes pains not to speak against his philosophical beliefs. Averroes distinguishes between inductive and deductive arguments, with conventional arguments from design falling into the former camp. Averroes also assigns (...) a place for teleological argumentation when assigning a special role for the prime mover within the hierarchy of unmoved movers. (shrink)

Al-Ghazālī's most detailed explanation of how signification works occurs in his treatise on The Beautiful Names of God. Al-Ghazālī builds squarely on the commentary tradition on Aristotle's Peri hermeneias : words signify things by means of concepts and correspondingly, existence is laid out on three levels, linguistic, conceptual, and particular (i.e. extramental). This framework allows al-Ghazālī to put forward what is essentially an Aristotelian reading of what happens when a name successfully picks out a being: when a quiddity is named (...) by some kind term, its referent in the mind is formally identical to the quiddity of an individual existent which belongs to that natural kind. Al-Ghazālī then proceeds to tease out the implications of this scheme for the special problem of signifying God. It turns out that the Peripatetic theory, which al-Ghazālī appropriates from Ibn Sīnā, is ill equipped for the task as al-Ghazālī envisions it. (shrink)

The volume under review presents the state of the art when it comes to tracking the reception of Ibn Rushd, the famed Aristotelian commentator from Andalusia, within medieval Latin philosophy. These are all very high-quality essays, each brimming with subtle insights into the way that themes and philosophical puzzles in Aristotle were framed in Averroes's works through the lens of late antique commentary, and how the Latin scholastics then furthered the agenda through their own creative work as well as further (...) comparisons with other eminent philosophers of the likes of Augustine and Avicenna. A standing theme that emerges is the contested relationship between tradition and... (shrink)

Al-Ghazālī's most detailed explanation of how signification works occurs in his treatise on The Beautiful Names of God . Al-Ghazālī builds squarely on the commentary tradition on Aristotle's Peri hermeneias : words signify things by means of concepts and correspondingly, existence is laid out on three levels, linguistic, conceptual, and particular . This framework allows al-Ghazālī to put forward what is essentially an Aristotelian reading of what happens when a name successfully picks out a being: when a quiddity is named (...) by some kind term, its referent in the mind is formally identical to the quiddity of an individual existent which belongs to that natural kind. Al-Ghazālī then proceeds to tease out the implications of this scheme for the special problem of signifying God. It turns out that the Peripatetic theory, which al-Ghazālī appropriates from Ibn Sīnā, is ill equipped for the task as al-Ghazālī envisions it. (shrink)

Die arabische Rezeption des Aristoteles lässt sich grob in drei Stadien einteilen. Während ihrer Anfangs- und Endphase – in den ersten Anfängen der islamischen Zivilisation und in der nachklassischen Periode – war das Bild, das man in der islamischen Welt von Aristoteles hatte, ziemlich vage, um nicht zu sagen: nebulös. Aristoteles wurde als eine Art Allzweckweiser behandelt, zunächst, weil man ihn nicht hinreichend gut verstand, dann aber auch, weil er zu sehr das war, was man eine alte Bekanntschaft nennt: Eine (...) zwar achtunggebietende Figur, vielleicht sogar ein Stellvertreter für die griechische Philosophie insgesamt, der aber doch mehr Karikatur als wirklicher Mensch war. (shrink)

Ibn Ṭufayl’s story of the solitary philosopher Ḥayy who, aided only by the power of his natural reason, comes to his own on an uninhabited equatorial island, attractively portrays the neo-Platonic worldview of the Muslim falāsifah . At the same time it forces to the foreground the most trenchant problem in any intellectualist ethics. If the highest virtue consists in the unmixed contemplative life, what good can a thinker do any longer, in any more mundane context? In this article, a (...) reading is proposed that integrates Ḥayy’s cosmological explorations with his relations towards nature and his fellow human beings. (shrink)

This excellent new monograph does everything it promises: it sets the excerpts we have of Proclus's teaching on the Cratylus in their proper historical setting, carefully laying out what Proclus thought Plato's dialogue accomplishes in light of the questions the intervening philosophical tradition had posed. This alone would justify the use in the title of the otherwise tired "in Context" trope; but van den Berg does much more. In recounting the steps that bring us from Plato's Cratylus to Proclus's Cratylus, (...) van den Berg provides a comprehensive history of ancient accounts of names and naming. The work thereby richly earns its subtitle as well.The first of van den Berg's book's many virtues is the attention it gives to Plato's Cratylus itself. In chapter one, van den Berg persuasively argues that Plato is engaged in a different sort of project than his many successors: Plato's concern is with how names can be incorrectly assigned, and his answer hinges on the contention that such assignments reflect the divisions in being that they presuppose. Everyday language, crafted on the model of the sensible world, is thus an altogether unreliable guide to ultimate reality. This stands in stark. (shrink)