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Baruch Spinoza (1632–1677) was born and educated in the Portuguese Jewish community of Amsterdam. The influence of medieval Jewish philosophy on him was formative. He studied the major Jewish philosophers, like Rabbis Abraham ibn Ezra and Moses Maimonides, long before he read contemporary European philosophers, like René Descartes and Thomas Hobbes. He was put under the ban (ḥerem) in 1656. However, even in his last years he continued to study Hebrew books. Spinoza's philosophic position is often 'Maimonidean' but sometimes 'anti-Maimonidean.' In this Element, the author discusses Spinoza's debt to Saadia Gaon, Rashi and Pseudo-Rashi, Judah Halevi, Abraham ibn Ezra, Moses Maimonides, Abraham Abulafia, Joseph Kaspi, Isaac Polgar, Levi Gersonides, Ḥasdai Crescas, Profayt Duran alias Efodi, and Joseph Albo.
This chapter focuses on the aesthetic appeal of inanimate nature, plants, and animals. Hegel’s ontological privileging of living beings, and especially of animal bodies, comes hand in hand with their aesthetic privileging, and so particular focus is given to the beauty of animateness, and especially to that of animal bodies. It is argued that, while most appearances of animal life serve to disclose their finitude, and so their ontological dependency, there are striking moments in which their remarkable animateness stands out as such. And given that Hegel gives us good reason to think of life, in its ontology, as an essentially infinite and autonomous movement, this conspicuousness of animation provides us with an ephemeral glimpse of a more profound beauty. As the various dimensions of animation and its ways of appearing are explored in some detail, the chapter comes to argue, somewhat counter to Hegel though for Hegelian reasons, that it is particularly in animal movement – as opposed to the more static shape of the animal body, which is largely Hegel’s focus – that the full splendor of animateness is revealed.
Does it make sense to call God both infinite and absolutely simple. Goodman explores God’s biblical boundlessness, in dialogue with Plato, Philo, Plotinus, Maimonides, Spinoza, William Blake, Georg Cantor, and the Kabbalah?
This chapter applies the Pascalian picture developed in the rest of the book to the famous “wager.” With that background in place, we can see how the wager has been misunderstood, and that the correct interpretation is far more defensible than the standard one. The so-called wager is an argument designed to convince a very particular kind of person – one with only self-interest in their heart – to seek a change of heart. It is a predictable part of Pascal’s general aim in his philosophy, and it doesn’t make the silly mistakes that are often attributed to him. Pascal’s innovations, such as the notion of infinity, the ambiguity of the world, the dependence of reasons on the heart, and corrupting influence of bad desires, are brought to bear on the wager to present a plausible, and less radical picture of the role of belief in Pascal. Topics such as self-deception, alternative conceptions of God, and the benefits of seeking the love of God are addressed throughout.
This chapter traces the development of ideas concerning the divine nature over the course of the early scholastic period. In particular, it traces a shift which occurred over the course of the period, at the start of which scholastic theologians generally described God's nature as fundamentally simple, but over the course of which members of the Franciscan order in particular began to speak of God's nature as primarily infinite.
Some philosophers and theologians argue that if God will save everyone, then earthly life is pointless. No matter how good earthly life is, heaven would be far better. So we would have been better off if God had started us off in heaven. I present and defend two objections to this argument. First, time on earth does not result in a deduction from time in heaven. Pick whatever amount of time you might wish to spend in heaven. You will spend that much time in heaven whether you are on earth first or not. Second, given origin essentialism, we could not start off in heaven rather than earth. Our very existence depends on our earthly origins.
The aim of this paper is to give a full exposition of Leibniz’s mereological system. My starting point will be his papers on Real Addition, and the distinction between the containment and the part-whole relation. In the first part (§2), I expound the Real Addition calculus; in the second part (§3), I introduce the mereological calculus by restricting the containment relation via the notion of homogeneity which results in the parthood relation (this corresponds to an extension of the Real Addition calculus via what I call the Homogeneity axiom). I analyze in detail such a notion, and argue that it implies a gunk conception of (proper) part. Finally, in the third part (§4), I scrutinize some of the applications of the containment-parthood distinction showing that a number of famous Leibnizian doctrines depend on it.
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.
Many philosophers are aware of the paradoxes of set theory (e.g. Russell's paradox). For many people, these were solved by the iterative conception of set which holds that sets are formed in stages by collecting sets available at previous stages. This Element will examine possibilities for articulating this solution. In particular, the author argues that there are different kinds of iterative conception, and it's open which of them (if any) is the best. Along the way, the author hopes to make some of the underlying mathematical and philosophical ideas behind tricky bits of the philosophy of set theory clear for philosophers more widely and make their relationships to some other questions in philosophy perspicuous.
Most interpreters hold that Kant rejects actually infinite tota synthetica as conceptually impossible. This view is attributed to Kant to relieve him of the charge that the first antinomy’s thesis argument presupposes transcendental idealism. I argue that important textual evidence speaks against this view, and Kant in fact affirms the conceptual possibility of actually infinite tota synthetica. While this means the first antinomy may not be decisive as an indirect argument for idealism, it gives us a better account of how our ideas of the unconditioned generate the antinomies, and it allows us to see important and often overlooked elements in Kant’s account of the infinite.
The final two Metaphysical Expositions argue that our original representation of space must be intuitive. I draw some surprising connections between Kant’s discussion and Leibniz’s account of the continuum. These connections indicate that the point of Kant’s analysis of <space> is to show that our original representation of space is infinitely complex in content. Since no discursive representation can be infinitely complex, our concept <space> cannot derive its content from discursive spontaneity. Its content must rather be given to the mind in order to be thought at all and thus originates in receptive intuition. Kant’s argument does not hinge on the singularity or holistic structure of space, as many hold, but on its infinite complexity and consequent givenness. I develop a novel account of the discursivity of conceptual representation that preserves the validity of Kant’s argument, defend Kant’s account of the infinity of space against prominent objections, and finally indicate how Kant’s argument entails the singularity of intuition (rather than presupposing it).
In this book Daniel Smyth offers a comprehensive overview of Immanuel Kant's conception of intuition in all its species – divine, receptive, sensible, and human. Kant considers sense perception a paradigm of intuition, yet claims that we can represent infinities in intuition, despite the finitude of sense perception. Smyth examines this heterodox combination of commitments and argues that the various features Kant ascribes to intuition are meant to remedy specific cognitive shortcomings that arise from the discursivity of our intellect Intuition acting as the intellect's cognitive partner to make knowledge possible. He reconstructs Kant's conception of intuition and its role in his philosophy of mind, epistemology, and philosophy of mathematics, and shows that Kant's conception of sensibility is as innovative and revolutionary as his much-debated theory of the understanding.
This essay introduces and explores David Tracy’s notion of ‘analogical imagination’ as something that prevents reason, theology, and social life from collapsing ‘into equivocation or else hopeless stupid conflict’. A capacious reflective reason, after Tracy, depends on imaginative habits and sensibilities that stay faithful to the discordant plurality and ambiguity of things while also acknowledging their analogies or ‘similarities-in-difference’. The essay argues that the continuing integrity and scope of Tracyean analogical imagination depends upon understanding that the negations that belong to apparently contrasting ‘dialectical imaginations’ reach ‘all the way down’ within analogical imagination itself. Aided by classic expressions of culture, furthermore, analogical imaginative possibility shades into contingent vision when organised by ‘focal meanings’ to fashion some global sense of the world. This is then brought into dialogue with Richard Kearney’s comparatively recent notion of ‘anatheism’, to help consideration of how Tracyean analogical imagination might maintain its imagination and ana- at the perilous point that it becomes also a matter of religious believing.
This introductory essay to the volume sets out the volume’s form and purpose, and then provides advance introduction of each of its component essays in turn. Since the volume comes together as a tightly organised and cumulative introduction to David Tracy, this essay forms its own concerted introduction to Tracy parallel to the performance of the book as a whole.
This essay begins with a close reading of Tracy’s recent programmatic formulations concerning: (1) the ‘strong fragments’ of culture that ‘shatter, fragment, negate any closed totality system’; and (2) those ‘most powerful fragments’ that ‘show themselves not as substances but as events and positively open to liminal Infinity’. If some cultural fragments are mere ‘period pieces’ without enduring truth or transformative power, and others are dangerously nostalgic, these fragments, Chase suggests, can act strongly when collaged into some ‘new form of witness against any false whole or claim to completeness’. T. S Eliot’s The Waste Land is an ambiguous example here. The pinnacle of the fragment for Tracy, however, is the ‘frag-event’ that opens towards the creative liminality of an invisible Infinity. ‘Marxist-Kabbalist’ Walter Benjamin is ‘the projective force’ behind Tracy’s forays into the fragment. The essay proposes the role of assemblage or collage for both fragmenting fragments and the Tracyean frag-event, stressing the role of edges and unexpected connections, and concluding by wondering how far Christian theology is really ready to think in such a manner of collage.
This article contributes to discussions about the problem of evil and Schelling studies by analysing Schelling's conception of the problem in his 1809 Freiheitsschrift essay. I explicate Schelling's critical response to four classic solutions to the problem (embodiment, degree, dualism, and divine forms) and outline his positive solution. My thesis is that Schelling offers a unique theodicy by arguing for a dialectical conception of the infinite omnipotence of God. In contrast to traditional notions of the infinite as the opposite of the finite, Schelling claims that God is only truly infinite if also embodied in the finite, an embodiment enacted through the human freedom to do evil. To explore Schelling's project, I draw parallels between his account of God's omnipotence and Hegel's ‘good infinite’ and situate Schelling's thesis within Mackie's discussion of the problem of evil in ‘Evil and Omnipotence’.
In this article, I take on a classic objection to Kant’s arguments in the Antinomy of Pure Reason: that the arguments are question-begging, as they draw illicit inferences from claims about representation to claims about reality. While extant attempts to vindicate Kant try to show that he does not make such inferences, I attempt to vindicate Kant’s arguments in a different way: I show that, given Kant’s philosophical backdrop, the inferences in question are not illicit. This is because the transcendental realists that Kant was arguing against have certain philosophical commitments about the nature of ground which, if true, warrant the inferences that Kant draws. This historical corrective not only allows us to better understand Kant’s own thinking in the Antinomies but it also has important upshots for our understanding of Kant’s transcendental idealism.
David Tracy is arguably the most influential Roman Catholic theologian writing in English of the past fifty years, both internationally and beyond confessional borders. His generous and ever-expanding conversations (says contributor Willemien Otten) 'make the future of theology now'. Tracy himself says that they lead him, like Dante, to 'the love that moves the sun and the other stars'. Tracy's most famous book, The Analogical Imagination, is now over four decades old. Yet, in two volumes of his essays published in 2020, Tracy emphasises the ground-breaking new work that he did in the 2010s. His mature theological and cultural vision is in need of fresh assessment, which this book provides. An international cohort of experts introduces the core themes of Tracy's thought, critically exploring their relevance for theology today. Tracy offers a short response of his own, as well as the edited text of a previously unpublished and recent lecture.
Thematically, formally and structurally, Wallace’s writing concerned itself with the infinite, from the antinomies of set theory and the obese Bombardini in The Broom of the System to the featureless horizon of Peoria in The Pale King, by way of the title of Infinite Jest and the brief and not wholly successful exploration of Cantorian mathematics in Everything and More, the idea of the infinite was never far from any of Wallace’s writing. Moreover, the structures of the writing continually reinscribe this obsession with infinity, with none of the novels conforming to a traditional boundaried structure and the collections of short fiction troubling the very concept of order in their use of pagination and enumeration. This chapter illuminates the importance of infinity to Wallace’s writing by exploring its formal and thematic development through his career, demonstrating that infinity worked as a conceptual counterpoint to solipsism, both an existential threat and a source of profound hope for the disassociated subject of contemporary culture.
Compares Cassirer and Heidegger's take on the human being's capacity to orient itself in the world in a meaningful way. Cassirer's theory of the functions of consciousness, the only meat to his functional conception of human subjectivity, is used to describe the diverse, cultural compasses by means of which the 'symbolic animal' navigates the human world (7.1). Heidegger's accounts of 'the they' and of owned ('authentic') existence in turn provide a theory of Dasein's capacity to orient itself within and towards its world (7.2). In view of their shared interest in orientation, I discern an important distinction for both Cassirer and Heidegger between an orienting and an oriented self. With regard to both, they ultimately disagree about the infinite (cultural) or finite (temporal) nature of the human being (7.3).