This essay examines the ambiguous role of imagination in Kierkegaard's work, arguing that the concept of imagination is fundamental to his existential transformation of the question of reality.

Problem: There is currently a great deal of mysticism, uncritical hype, and blind adulation of imaginary mathematical and physical entities in popular culture. We seek to explore what a radical constructivist perspective on mathematical entities might entail, and to draw out the implications of this perspective for how we think about the nature of mathematical entities. Method: Conceptual analysis. Results: If we want to avoid the introduction of entities that are ill-defined and inaccessible to verification, then formal systems need to (...) avoid introduction of potential and actual infinities. If decidability and consistency are desired, keep formal systems finite. Infinity is a useful heuristic concept, but has no place in proof theory. Implications: We attempt to debunk many of the mysticisms and uncritical adulations of Gödelian arguments and to ground mathematical foundations in intersubjectively verifiable operations of limited observers. We hope that these insights will be useful to anyone trying to make sense of claims about the nature of formal systems. If we return to the notion of formal systems as concrete, finite systems, then we can be clear about the nature of computations that can be physically realized. In practical terms, the answer is not to proscribe notions of the infinite, but to recognize that these concepts have a different status with respect to their verifiability. We need to demarcate clearly the realm of free creation and imagination, where platonic entities are useful heuristic devices, and the realm of verification, testing, and proof, where infinities introduce ill-defined entities that create ambiguities and undecidable, ill-posed sets of propositions. Constructivist content: The paper attempts to extend the scope of radical constructivist perspective to mathematical systems, and to discuss the relationships between radical constructivism and other allied, yet distinct perspectives in the debate over the foundations of mathematics, such as psychological constructivism and mathematical constructivism. (shrink)

I conceive of Spinoza’s substance monism as a response to Aristotle’s prohibition against actual infinity for one key reason: nature, being all things, is necessarily infi nite. Spinoza encapsulates his substance monism with the phrase, “Deus sive Natura,” implying that there is only one infinite substance, which also possesses an infi nity of attributes, of which we are but modes. These logical delineations of substance never actually break up God’s reality. Aristotle’s well-known argument against the reality of an actual infinity (...) in his Physics prohibits the existence of an actually infinite bodily substance because it would necessarily “destroy” (Physics 204b26-27) all other elements or bodies. On Aristotle’s view, there is a fundamental and concrete distinction between things: each substance is primarily a this (Categories 3b10). I maintain that Spinoza’s rationalism and radicalization of the principle of sufficient reason lends him greater explanatory potential than Aristotle to justify the (non) existence of actual infinity. (shrink)

In this paper two paradoxes of infinity are considered through the lens of counterfactual logic, drawing heavily on a result of Fine (2012b). I will argue that a satisfactory resolution of these paradoxes will have wide ranging implications for the logic of counterfactuals. I then situate these puzzles in the context of the wider role of counterfactuals, connecting them to indicative conditionals, probabilities, rationality and the direction of causation, and compare my own resolution of the paradoxes to alternatives inspired by (...) the theories of Lewis and Fine. Here is a quick overview of the paper. Sections 17.1 and 17.2 introduce two paradoxes of infinity that rest on certain principals concerning the logic of counterfactuals. Section 17.3 considers three possible ways to weaken the counterfactual logic that would resolve these paradoxes, and examines three concrete theories of conditionals which make those weakenings — Lewis (1973), Fine (2012a) and Bacon (2015). With the first two theories found wanting, Sect. 17.4 develops my preferred solution in (Bacon, 2015) a little further, and provides some simple models to show that the paradoxes can indeed be resolved in that framework. (shrink)

Essays by 14 Levinas scholars provide a fresh acount of the argument and purpose of Emmanuel Levinas's major work, Totality and Infinity, drawing parallels between Levinas and other thinkers; considering Levinas's relationship to other disciplines such as nursing, psychotherapy, and law; and bringing this seminal text to bear on specific, concrete issues of present-day concern"--Provided by publisher.

An analysis of the counter-intuitive properties of infinity as understood differently in mathematics, classical physics and quantum physics allows the consideration of various paradoxes under a new light (e.g. Zeno’s dichotomy, Torricelli’s trumpet, and the weirdness of quantum physics). It provides strong support for the reality of abstractness and mathematical Platonism, and a plausible reason why there is something rather than nothing in the concrete universe. The conclusions are far reaching for science and philosophy.

We informally discuss some recent results on the incompleteness of formal systems. These theorems, which are of great importance to contemporary mathematical epistemology, are proved using a variety of conceptual tools provably stronger than those of finitary axiomatisations. Those tools require no mathematical ontology, but rather constitute particularly concrete human constructions and acts of comprehending infinity and space rooted in different forms of knowledge. We shall also discuss, albeit very briefly, the mathematical intelligence both of God and of computers. (...) We hope in this manner to help the reader overcome formalist reductionism, while avoiding naive Platonist ontologies, typical symptoms of Godelitis which affected many in the last seventy years. (shrink)

Many results in logic and mathematics rely on techniques that allow for concrete, often visual, representations of abstract concepts. A primary example of this phenomenon in logic is the distinction between syntax and semantics, itself an example of the more general duality in mathematics between algebra and geometry. Such representations, however, often rely on the existence of certain maximal objects having particular properties such as points, possible worlds or Tarskian first-order structures. -/- This dissertation explores an alternative to such (...) representations known as possibility semantics. Its core idea is to replace maximal objects with ordered systems of partial approximations. Although it originates in the semantics of modal logic and the representation of abstract ordered structures, I argue that it has far-reaching mathematical, foundational and philosophical significance, especially in the context of semiconstructive mathematics, a foundational framework that does not assume any fragment of the Axiom of Choice beyond the Axiom of Dependent Choices. -/- The dissertation is divided in two main parts. The first part explores various applications of the mathematical framework underlying possibility semantics to lattice theory and non-classical propositional logics. A major theme is the development of constructive dualities for various categories of lattices, which are related to standard non-constructive dualities via Vietoris constructions. -/- The second part of the dissertation explores the alternative foundational setting of semi-constructive mathematics, focusing on three applications of possibility semantics for classical first-order logic to the philosophy of the mathematical infinite. In particular, we introduce generic powers, a semi-constructive analogue of ultrapowers in classical model theory, and we explore the merits of these structures from a foundational, conceptual and historical viewpoint. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Flipping the DeckOn Totality and Infinity’s Transcendental/Empirical PuzzleJack Marsh (bio)How does one perceive a transcendental condition?— Martin Kavka... if it is legitimate to hold Levinas to the standards that he himself imposes on certain other philosophers.— Robert BernasconiI do not believe that there is a transparency possible in method. Nor that philosophy might be possible as transparency.— Emmanuel LevinasThe question of the precise methodological status of the face has (...) yet to be satisfactorily resolved. The best evidence for this claim perhaps lies in texts intended to introduce Levinas to a general philosophical audience. If even first-rate philosophers wrestle still with the puzzle Totality and Infinity bequeaths us, we seem to still await a full and precise diagnosis. For example, Michael Morgan holds the “face-to-face and the responsible self — they are one thing characterized from [End Page 79] two perspectives — are” “the transcendental condition for meaningful human life,” yet elsewhere concedes, “it is unavoidable that in some sense or other the face-to-face does occur as an actually lived experience.” If Morgan’s own nuanced treatment of this question still lands him in equivocation, the problem is certainly not Morgan’s own.1 As Atterton notes, Morgan must finally hold that Levinas’s method is a “transcendental enterprise of a certain sort.”2 But of what sort? Indeed, this question has been asked or analyzed in one way or another from the beginning of Totality and Infinity’s English-language reception.3 Of course, Derrida was the first to broach the question of Totality and Infinity’s general intelligibility, alleging that Levinas ultimately succumbs to a form of empiricism. Of course, de Boer was the first to mount a rigorous Cartesian reading of the text as an (apparently) “ethical transcendental philosophy.” Of course, Bernasconi’s response to de Boer, and his creative repetition of Derrida’s critical point, was the first to give the problem a precise formulation.4 Derrida, de Boer, and Bernasconi hand us the now canonical problem of what I will call the text’s “transcendental/empirico-metaphysical puzzle.”5 The issue boils down to Levinas’s dual insistence that the face “cannot... be stated in terms of experience,” yet is nevertheless “reflected within experience” (TI 25, 23, 67, 260). How should we understand Levinas’s references to various “formal structure[s]” — “of language,” “of interpellation,” “of the idea of infinity” — next to talk of “pure” or “concrete moral experience” (195, 79, 64, 53)? Does the Other occur in “pure experience,” or is she “deduced” as a condition of possibility for experience in general? In this essay, I will propose an internal explanation for Totality and Infinity’s longstanding methodological puzzle. By proposing to “explain” this puzzle, I am making at least three distinct claims: to show (1) that the text suffers from genuine incoherence, thus confirming the general criticism of Derrida, Bernasconi, and others, (2) precisely how this incoherence follows from the details of Levinas’s own explicit method, and (3) precisely why, philosophically, he may have constructed and performed his method as he did.6 By proposing to explain the book’s incoherence, I can [End Page 80] also make specific hermeneutic predictions. If Totality and Infinity’s transcendental/empirico-metaphysical puzzle is genuinely aporetic, it follows that no resolution to it is possible on the text’s own terms.7 As such, any attempt to resolve the puzzle must either (1) augment the text’s own descriptions, (2) utilize other philosophical resources to render its claims coherent, or (3) precisely attempt resolution in either a transcendental or empirico-metaphysical direction. As it turns out, extant scholarship reflects just these hermeneutic strategies.Over the years many philosophers have contributed to this longstanding debate, variously arguing for or against the general intelligibility of Levinas’s account of the face. On the one hand, scholarship that questions the text’s intelligibility does so from a variety of methodological perspectives.8 On the other hand, scholarship that mounts a defense of the text seems to proceed in one of three ways: by (1) apparently repeating Totality and Infinity’s methodological problems, (2) anticipating Levinas’s later work, read... (shrink)

Lévinas is the philosopher of the absolutely Other, the thinker of the primacy of the ethical relation, the poet of the face. Against the formalism of Kantian subjectivity, the totality of the Hegelian system, the monism of Husserlian phenomenology and the instrumentalism of Heideggerian ontology, Lévinas develops a phenomenological account of the ethical relation grounded in the idea of infinity, an idea which is concretely produced in the experience with the absolutely other, particularly, in their face. The face of the (...) other, irreducible to any ontological structure of being or any epistemological intentionality of representation, reaches out from on high across the abyss of the isolated ego, commanding respect all the while granting the possibility of murder. This experience overflows the subjective capacity of the separated ego, forcing it “beyond being.” This anarchic relation with the Other is the groundless condition of possibility for ethical life, that is, truly human life. The structure of the ethical relation can then be determined in hindsight as the ground of meaning for what it is to be an I at all. -/- This is a pretty uncontroversial reading of Lévinas' work, especially Totality and Infinity. And yet, there is one small problem. If this is what Lévinas is doing, then why does the largest section of Totality and Infinity – section II, “Interiority and Economy” – have nothing to do with ethics, the other, or the face at all? Why is it devoted to an arduous analysis of what he calls separation, egoism, economy, enjoyment, labour, and possession? In other words, why does Lévinas spend so much energy on writing about the egoist at the heart of his magnum opus, which is supposedly a text devoted to the Other? And furthermore, why is this section one of the least discussed in the secondary literature on Lévinas? -/- These questions motivate the present inquiry, which modestly seeks to understand what Lévinas is up to in this section. Once laying out the basic story, I will focus on the concepts of labour and possession, for I think these are the unrecognized pivots upon which the transition from ego to Other turns. I will also make some slight attempts to interpret Lévinas' direct or indirect comments on Plato, Kant, Hegel, Husserl and Heidegger. For although he distances himself from these giants, he stands on their shoulders as well. (shrink)

This book develops a novel argument which combines the Kalam with the Thomistic Cosmological Argument. It approaches an ongoing dispute concerning whether there is a First Cause of time from a radically new point of view, namely by demonstrating that there is such a First Cause without requiring the controversial arguments against concrete infinities and against traversing an actual infinite (although the book presents original defenses of these arguments as well). This book also develops a novel philosophical argument (...) for the Causal Principle, namely that ‘everything that begins to exist has a cause’, and offers a detailed discussion on whether a First Cause of time can be avoided by a causal loop. It also addresses epistemological issues related to the Cosmological Argument which have been relatively neglected by recent publications, and demonstrates (contra Hawking et al) the continual relevance and significance of philosophy for answering ultimate questions. -/- . (shrink)

This paper offers a new formulation of the “Hilbert's Hotel Argument” (HHA) which is superior to existing formulations because it (1) demonstrates that HH is logically impossible in the concrete world, (2) takes into account the need to consider the assumptions of HHA, and (3) offers a reply to an important objection concerning the validity of HHA. In addition, this paper contributes to the discussion by using the new HHA to defend a relevant difference between the past and the (...) future by demonstrating that the HHA applies to the former but not to the latter. Finally, this paper demonstrates the significance of metaphysical arguments such as the HHA for physical cosmology. (shrink)

This paper offers a new formulation of the “Hilbert's Hotel Argument” (HHA) which is superior to existing formulations because it (1) demonstrates that HH is logically impossible in the concrete world, (2) takes into account the need to consider the assumptions of HHA, and (3) offers a reply to an important objection concerning the validity of HHA. In addition, this paper contributes to the discussion by using the new HHA to defend a relevant difference between the past and the (...) future by demonstrating that the HHA applies to the former but not to the latter. Finally, this paper demonstrates the significance of metaphysical arguments such as the HHA for physical cosmology. (shrink)

Did the universe begin to exist? If so, did it have a cause? Or could it have come into existence uncaused, from nothing? These questions are taken up by the medieval-though recently-revived-kalam cosmological argument, which has arguably been the most discussed philosophical argument for God's existence in recent decades. The kalam's line of reasoning maintains that the series of past events cannot be infinite but rather is finite. Since the universe could not have come into being uncaused, there must be (...) a transcendent cause of the universe's beginning, a conclusion supportive of theism. This anthology on the philosophical arguments for the finitude of the past asks: Is an infinite series of past events metaphysically possible? Should actual infinites be restricted to theoretical mathematics, or can an actual infinite exist in the concrete world? These essays by kalam proponents and detractors engage in lively debate about the nature of infinity and its conundrums; about frequently-used kalam argument paradoxes of Tristram Shandy, the Grim Reaper, and Hilbert's Hotel; and about the infinity of the future. (shrink)

I shall argue that Hegel’s concept [Begriff] has emancipatory power [Macht]. In the Science of Logic, Hegel rejects both essentialist conceptions of identity and historical necessity, and he shows that conceiving [begreifen] (or ‘grasping’) is an anticipatory self-movement of thought. The relation between ‘essence’ and ‘concept’ in Book II of the Science of Logic is unlike the relation between ‘essence’ and ‘form’ in Plato to Kant. I will defend this claim not by comparing Hegel’s ‘essence [Wesen]’ with similar categories in (...) the texts of Plato or Kant but, rather, by focusing more narrowly on two transitions in the Logic that illustrate Hegel’s break from prior philosophy with respect to his account of essence. The transition in Book I from ‘the ought [das Sollen]’ to infinity, in combination with the transitions in Book II from Existenz (‘concrete existence’) and appearance to actuality [Wirklichkeit] compose the core of Hegel’s rejection of a Platonic/Kantian normative model of essence. The category of actuality is the turning point of the Logic and shows that Hegel rejects all essentialist conceptions of form. For Herbert Marcuse, actuality is the core of thought’s self-movement, its motility (or, referring to Aristotle as Marcuse does, Hegelian thought’s being qua being). I shall extend Marcuse’s interpretation of the Logic to treat the category of actuality in the context of recent feminism and political theory. (shrink)

Dieser Essay stellt die Idee einer Gastlichkeit menschlicher Subjektivität vor, wie sie Levinas bereits in seinem ersten Hauptwerk, Totalität und Unendlichkeit,entwickelt hat. Er erörtert darüber hinaus die konkreten ethisch-politischen Implikationen dieses Begriffs speziell im Hinblick auf die Gastlichkeit kulturellen Lebens, insofern es Anderen eine »Bleibe« verspricht, die ihrer bedürfen. Kritisch nimmt der Essay zur Frage Stellung, inwiefern die Gastlichkeit einer religiösen Überlieferung als ihr genuines Erbe vorbehalten bleibt.This paper examines the idea of hospitality in Levinas' first major work, Totality and (...) Infinity. It discusses furthermore the concrete ethical and political implications of this notion; especially with respect to the hospitality of cultural forms of life which should promise to shelter others in need of what Levinas calls demeure. Critical considerations are directed against a certain religious »occupation« of the notion of hospitality. (shrink)

This article focuses on three questions. First it tries to understand why the difficulty man experiences when he is praying, is an inherent part of prayer. Everyone who prays, will experience that God is intangible. Rahner’s analysis of the human transcendental experience is a help in understanding this experience. Rahner shows that humans, by interacting in the concrete world, are capable of going beyond it. In deeds of for example love, freedom, wisdom one transcends concrete existence, and experiences (...) to be finitum capax infiniti. Yet, this possibility implies a very particular tension: man is naturally inclined to a transcendental reality but will never be able to fully capture it. Limiting oneself to concrete existence will be unsatisfying. Avoiding concrete existence will not work neither, for the transcendental experience only exists if linked to the tangible life we live here and now. Transcendental theology explains that living with this difficult but at the same time necessary tension between transcendental and categorical is the conditio sine qua non for meeting God.This means that, if prayer is such a meeting with God, it will always have an element of difficulty in it. He who prays, knows this. By subject and content this article is at the junction of philosophy, theology and spiritually. The author argues that this is necessary as Rahner’s transcendental theology is based on spirituality, a view shared by others, but which, in the opinion of the writer, is lacking in most of the secondary literature. Finally the author is of the opinion that aforementioned approach should not be limited to Rahner’s work. Should, out of contextual, theological as well as strategic reasons, contemporary theology not pay more attention to spirituality? (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Literature 27.2 (2003) 456-470 [Access article in PDF] Ethics without Exit:Levinas and Murdoch Bob Plant Hearts open very easily to the working class, wallets with more difficulty. What opens with the most difficulty of all are the doors of our own homes. —Emmanuel Levinas, Nine Talmudic Readings... there is no debt to acquit. From the outset, I am not exonerated. I am originally in default. —Emmanuel Levinas, (...) God, Death, and TimeIN HIS RECENT ARTICLE "Emmanuel Levinas and Iris Murdoch: Ethics as Exit?," C. Fred Alford highlights a number of insightful comparisons—and many important contrasts—between the respective conceptions of ethics proffered by Levinas and Murdoch. Alford's avowed objective is to "criticize Levinas sympathetically," or to "disrupt" what has come to be known as "the Levinas Effect" and the tendency of many commentators to make Levinas "become everything to everyone." 1 Given what one commentator calls "the facile 'postmodern' temptation to lump together all differences under the general rubric of the 'Other,'" 2 Alford's objective is, I believe, wholly commendable. (As Arthur Schopenhauer pithily remarks: "the man who is everyone's friend is no one's friend." 3) Nevertheless, in the following discussion I want to "disrupt" Alford's own reading of Levinas; not, I hope, to make the latter simply a conduit for saying "whatever.... [I] wanted to say in the first place" (p. 24), but to present a fuller picture of Levinas's singularly difficult, evocative and often puzzling philosophy. I shall do this by critically responding to and developing a number of points [End Page 456] Alford explicitly raises. To what extent my reading of Levinas aligns him with Murdoch, I leave for others far better qualified to assess.Let us be clear from the start, Levinas is—as Hilary Putnam rightly notes—a "moral perfectionist." 4 But this is not to say that Levinas's work is "otherworldly." Although Alford does not use this latter term, it is clearly implied in his analysis. Thus, contrasting Levinas and Murdoch, he remarks that, "like Levinas, Murdoch's goal is to go beyond the limits of the self. Unlike Levinas, Murdoch is content to remain within a world of beings" (p. 37), and likewise, that Murdoch wants us to "climb the ladder of love only high enough to be free of their vanity and egoism, but never so high as to leave the world behind" (p. 38). According to Alford, "the other is an abstraction for Levinas.... Only at a distance is the other abstract enough to remind us of infinity" (p. 25)—indeed, a "barely contained passion for otherness, exit, and transcendence runs through Levinas" (p. 40). In a similar vein we are told that, for Levinas, "the self is remarkably real, a tangible fleshy thing.... and a barrier to infinity," and it is "for this reason,... a shattering experience is necessary, like that of Saul on the road to Damascus, an experience that does not bring me closer to my deliverer.... Only this can open me up—not to reality, but to infinity" (p. 38). More pointedly still, Alford asserts: "Levinas was never interested in the concrete reality of the other person, whose fleshy reality can only get in the way of transcendence" (p. 37). Thus, although he acknowledges that Levinas "often writes about ethical relationships as though they were real relationships with real people" ("what is not true is that Levinas is talking about some Other more august and transcendent than real other people.... we know the infinite only through other people"), Alford nevertheless defends his own "turning to Murdoch" on the grounds that she is "a theorist who remains strictly within the realm of everyday life, finding there subtleties of knowing, caring, and being that Levinas believes come only by way of the infinite" (p. 34).While Levinas's attitude toward the "everyday" or "ordinary" is hardly transparent (after all, the imperative of the other's face is said to come "from most high outside the world" 5 ), Alford overstates the "otherworldly" aspect of the former's ethics. Against the allegation that Levinas... (shrink)

Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes. Yanofsky describes (...) simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known. Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there. (shrink)

Contemporary philosophers of mathematics are deadlocked between two alternative ontologies for numbers: Platonism and nominalism. According to contemporary mathematical Platonism, numbers are real abstract objects, i.e. particulars which are nonetheless “wholly nonphysical, nonmental, nonspatial, nontemporal, and noncausal.” While this view does justice to intuitions about numbers and mathematical semantics, it leaves unclear how we could ever learn anything by mathematical inquiry. Mathematical nominalism, by contrast, holds that numbers do not exist extra-mentally, which raises difficulties about how mathematical statements could be (...) true or false. Both theories, moreover, leave inexplicable how mathematics could have such a close relationship with natural science, since neither abstract nor mental objects can influence concrete physical objects. The Thomist understanding of quantity as an accident inhering in concrete substances breaks this deadlock by granting numbers a foundation in extra-mental reality which explains why numeric expressions are relevant in natural science and how we come to know the truth or falsity of mathematical statements. Further, this kind of moderate realism captures the semantic advantages of the Platonists and the ontological parsimony of the nominalists (since for Thomists quantity is not a separate, free-standing ontological addition). Despite these advantages, the Thomistic understanding of number has been out of favor since the work of Cantor, who argued that actual infinities (regarded by Aristotelians as impossible) are required for modern developments in mathematics. This paper frees philosophers of mathematics to embrace the advantages of Thomistic realism by showing that Cantor’s understanding of actual and potential infinity is not the same as Aquinas’s, and that potential infinities (in Aquinas and Aristotle’s sense) can do all the work Cantor claims for actual infinities in modern mathematics. (shrink)

Mathematics often seems incomprehensible, a melee of strange symbols thrown down on a page. But while formulae, theorems, and proofs can involve highly complex concepts, the math becomes transparent when viewed as part of a bigger picture. What Is a Number? provides that picture. Robert Tubbs examines how mathematical concepts like number, geometric truth, infinity, and proof have been employed by artists, theologians, philosophers, writers, and cosmologists from ancient times to the modern era. Looking at a broad range of topics (...) -- from Pythagoras's exploration of the connection between harmonious sounds and mathematical ratios to the understanding of time in both Western and pre-Columbian thought -- Tubbs ties together seemingly disparate ideas to demonstrate the relationship between the sometimes elusive thought of artists and philosophers and the concrete logic of mathematicians. He complements his textual arguments with diagrams and illustrations. This historic and thematic study refutes the received wisdom that mathematical concepts are esoteric and divorced from other intellectual pursuits -- revealing them instead as dynamic and intrinsic to almost every human endeavor. (shrink)

In sharp contrast with Heidegger's insistence that the metaphysics of presence, in particular the objectivation of beings in terms of their being “ready at hand” culminating in the techno‐scientific world‐view, be destructed and overcome in light of a more fundamental thinking of “presencing” or “coming into presence” (Anwesen), the philosophy of the infinitely Other introduced (or should we say: rearticulated) by Emmanuel Levinas marks a radical rupture with all ontology. Indeed, it breaks away from every thought of Being, from the (...) notion of the event or eventhood (Ereignis) of Being, but also from the notion of the gift implied in Heidegger's formula that Being “is” what “there is,” that Being “is” what essentially “gives,” or, finally, that Being “is” (what is) fundamentally given (Es gibt das Sein). From the publication of his earliest phenomenological studies in the 1930s and late 1940s onwards, but especially since the appearance, in 1961, of his first major book Totalité et Infini: Essai sur l'extériorité (Totality and Infinity: An Essay on Exteriority), Levinas has left no doubt that the central concern of his philosophical thinking was to leave the parameters – indeed, the very “climate” – of Heideggerian thought behind. This flight, as it were, not merely from ontology but also from Heidegger's later thinking‐of (Andenken) of Being consists, in its first phase, in the reorientation rather than destruction or deconstruction of traditional Western philosophy – a tradition which, according to Levinas, has been by and large a philosophy of the Same (le Même) – in the direction of the Other (l'Autre) or, more precisely, other human beings (autrui). At first glance, therefore, Levinas's first major work is characterized by the attempt to establish ethics as the genuine first philosophy. The ethical relation here is at once the primum intelligibele that puts an end to the essential arbitrariness and the anarchy of the world of opinions and truths, of appearances and idealized constructs. For all its apparent abstraction, it signals itself in the concrete event of obligation, more specifically in the introduction of a responsibility that precedes and exceeds contracts and rules, reciprocity and recognition, norms and conventions. In Totality and Infinity this relation of the self to the other is described in terms of the asymmetrical structure of discourse, of dialogue, and, most importantly, of the face‐to‐face with the other's visage. For, so the argument goes, it is solely in the face‐to‐face that the Desire (désire) for the other arouses, provokes, or evokes. It is in this singular relation without relation alone that the self is accused and made responsible. (shrink)

Hegel believes that the immanent ascent of finite spirit and its immersion in its uncreated foundation-in absolute spirit-is a true transition and he cannot use the so-called proofs of the existence of God. Besides, he sees an advantage here in that this transition results in the ascent of the human spirit to the most concrete and true, to God in His absolute truth-to Absolute Spirit. In connection with this, Hegel emphasizes in the manuscript of his lectures on the philosophy (...) of religion that the speculative meaning of the religious idea of the immortality of the soul lies in attaining the absoluteness and infinity of self-consciousness, the fact that "the self-consciousness of the spiritual is itself an eternal, absolute factor.". (shrink)

Augustyn Jakubisiak (1884-1945), Polish priest, philosopher and theologian, undertook polemics with Jan Łukasiewicz, whom he knew personally. A dispute concerning the so-called logistics (mathematical logic) and its relationship with philosophy developed between the two. The most important arguments were laid out, primarily in the following works: in the case of Jakubisiak, in the book From Scope to Content and in the case of Łukasiewicz, in the texts Logistics and Philosophy and In the Defense of Logistics. Jakubisiak criticized logistics for its (...) anti-metaphysical, anti-theological and anti-religious attitude, which was based on neo-positivist philosophy, and led, in consequence to atheism. He also claimed that one should focus on what is concrete, avoiding idealization and abstraction (meaning the content of concepts, not their scope). Łukasiewicz defended logistics claiming that it possesses its own methods based on intellect, and is also an area of independent knowledge (but not completely detached) from philosophy, due to the fact it can consider the most important philosophical problems such as finiteness and infinity. This dispute, as the researchers identified, basically concerned the reduction of philosophy to the study of language (analytic philosophy) and initiated one of the most important discussions concerning the relationship between philosophy and logic. This debate was crucial because it also concerned questions related to fundamental metaphysical issues (naturalism – supranaturalism, rationalism – irrationalism) and epistemological issues (realism – idealism, boundaries and structure of cognition). (shrink)

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 97 supposed by actual idealism is above all moral and involves what Gentile describes as an aspect of divinity or infinity,as well as a concrete, historical aspect. The following chapter treats of the philosophy of "actual" idealism and compares the views of Kant and Gentile on relations between moral conscience and freedom. According to Yalentini, Gentile's idealism is essentially an ethical view. This chapter concludes with (...) noting that Gentile 's solution to the problem of historical knowledge differs profoundly from that of Hegel and Croce. For "reason" is not, for Gentile, a particular interpretation of historical process, but is rather the "reason" of consciousness in activity. In Chapter In, Valentini discusses Gentile's views on art and religion. The section on art concludes with a comparison between Gentile on feeling and Kant on the transcendental unity of apperception. Whereas art is supposed to be one abstract moment of spirit, religion is the other abstract moment. Valentini suggests that Gentile and Feuerbach hold similar religious views on the attributes of divinity, which are nothing other than the loftiest qualities which man feels to possess in his essence. The history of religion is then the history of the progressive humanization of God. Gentile's religion represents a sort of modem Catholicism in that it understands revelation as a fact of conscience, church as a historical institution, dogma as having a negative character and God as a member of the dialogue between God and man. Moreover, Gentile's Catholicism has a national character; it is the religion of the Italian people. Chapter Iv treats of the relations between individual and state. For, according to Gentile, an individual is inconceivableapart from the social relations which lie within him. Here Valentini distinguishes in detail the differences and similarities between the views of Hegel and Gentile on the relations between state and individual. The differences between the views of these two philosophers are due to the differences between their methods. The method of Hegel is empirical and historical, and examines the state (which remains historical) from an external point of view. According to an idealistic method, however, thought is not to be the spectator of a process, but in every instance, an actor, and philosophizing does not result from an analysis of historical reality, but from the negation of this reality in the name of an ideal, which philosophy is to draw from it (reality). The Appendix includes a critical evaluation of the theory of the dialectic. Here Valentini hopes to distinguish between the imaginary and the real or historical applications of the dialectic. He begins his evaluation by asking: Does the doctrine of the dialectic, like the philosophy of idealism, possess negative connotations, which cannot be separated from it? Valentini suggests that in order to answer this question, we must determine the extent to which the dialectical scheme is constitutive of every concept or truth in general. For this is the way in which Hegel intended that the dialectic be understood and evaluated. Some views in Hegel's philosophy of nature are then criticized according to empirical criteria. In conclusion, Valentini attempts to answer both "internal" and "external" criticisms of Marx's view of the dialectic, and shows that there are problems involved in its application, which still have to be resolved. Mv~ M. MILBURN 9 ~an Jos~ ~ate College Husserl und Kant: eine Untersuchung ~ber Husserls Verh~iltni~ zu Kant und zum Neubantianismus. By Iso Kern. (The Hague : Martinus Nijhoff, 1964.Pp. xxiii q- 448.) This is a very important book. In fact, it is indispensable for a study of Husserl and is, at the same time, almost as valuable for a study of Kant, for it deals with the kind of searching questions that must be asked when one deals with transcendental idealism in any one of its forms. But two reasons in particular, make this book significant. One is the fact that Iso Kern was able to make extensive use of hitherto unpublished materials (manuscripts, lecture notes, letters, etc.), available only in the Husserl Archives and here quoted for the first time--and 98 HISTORY OF PHILOSOPHY quoted in great numbers. The other is Kern's philosophical competence... (shrink)

Descartes e a ideia de homem. Imperfeição e perfeição do homem Resumo: O autor nota, por um lado, que Descartes se refere a uma compreensão muito larga, mas também comum e corrente, do homem e, por outro, que o homem não pode ser identificado nem ao corpo, nem à alma, nem mesmo à união do corpo e da alma. Quando falamos da natureza humana, ela evoca o caráter de uma perfeição limitada, cuja particularidade é sua capacidade de ter o livre-arbítrio. (...) A noção do homem enquanto sujeito de (não) perfeição é baseada sobre uma ideia que se define por uma relação à ideia do infinito sob a forma da aspiração a ser mais perfeito. O exercício do livre-arbítrio se articula concretamente a um esforço de atenção e de vigilância que permite evitar um juízo errôneo. A tese exposta se desenvolve, em seguida, em três tópicos. Primeiramente, a razão se apresenta como um instrumento universal do homem, que, por sua vez, aparece como ser polivalente que o utiliza, sendo capaz de se adaptar às situações as mais diversas. Em segundo lugar, a perfeição especificamente humana significará a capacidade de exercer a dúvida e de recorrer às suposições e probabilidades no plano cognitivo. Isso significa, entre outros, que, para a aquisição da perfeição, é preciso reconhecer a sua própria imperfeição. Enfim, em terceiro lugar, a capacidade de usar propriamente o livre-arbítrio conduz à definição de homem como generoso, em que o homem é compreendido no sentido moral mais que no metafísico. Palavras-chave: Homem; Perfeição; Finitude; Atenção; Livre arbítrio; Generosidade. Descartes et l’idée de l’homme. Imperfection et perfection de l’homme. Résumé: L'auteur note que, d'une part, Descartes se réfère à une compréhension très large, mais aussi commune et courante de l'homme, et de l'autre que l'homme ne peut pas être identifié ni au corps, ni à l'âme, ni même à l'union du corps et de l'âme. Lorsqu’on parle de la nature humaine, elle porte le caractère d'une perfection limitée, dont la particularité est sa capacité d'avoir le libre arbitre. La notion de l'homme en tant que sujet de (non) perfection est basée sur une idée qui se définit par rapport à l'idée de l'infini sous la forme de l'aspiration à être plus parfait. L’exercice du libre arbitre se joint concrètement à un effort d'attention et de vigilance qui permet d’éviter un jugement erroné. La thèse ci-dessus se développe ensuite en trois points. Premièrement, la raison se présente comme un instrument universel de l'homme qui à son tour apparait comme être polyvalent l'utilisant et étant capable de s'adapter aux situations les plus diverses. Deuxièmement, la perfection spécifiquement humaine signifiera la capacité d’exercer le doute et de recourir aux suppositions et probabilités sur le plan cognitif. Cela signifie entre autres que pour l'acquisition de la perfection, il faut reconnaître sa propre imperfection. Enfin, troisièmement, la capacité d'user proprement le libre arbitre conduit à la définition de l'homme comme généreux, où l'homme est compris au sens moral plus que métaphysique. Mots clé: Homme; La Perfection; Finitude; Attention; Libre arbitre; La Générosité. Descartes and the idea of man. Imperfection and perfection of man Abstract: The author notes that, on the one hand, Descartes refers to a very broad, but also common and current understanding of man, and on the other that man cannot be identified nor with the body, neither to the soul, nor even to the union of body and soul. When we speak of human nature, it carries the character of a limited perfection, the particularity of which is the ability to have free will. The notion of man as the subject of (non) perfection is based on an idea which is defined in relation to the idea of ​​infinity in the form of the aspiration to be more perfect. The exercise of free will is joined concretely to an effort of attention and vigilance which makes it possible to avoid erroneous judgment. The thesis above then develops in three points. First, reason presents itself as a universal instrument of man who in turn appears to be versatile, using it and being able to adapt to the most diverse situations. Second, specifically human perfection will mean the ability to exercise doubt and use cognitive assumptions and probabilities. Among other things, this means that in order to acquire perfection, you have to recognize your own imperfection. Finally, thirdly, the ability to use free will properly leads to the definition of man as generous, where man is understood more in the moral sense than in the metaphysical sense. Keywords: Man; Perfection; Finitude; Attention; Free will; Generosity. (shrink)

The philosophy of Hitler is simplistic [primaire]. But the primitive powers that burn within it burst open its wretched phraseology under the pressure of an elementary force. They awaken the secret nostalgia within the German soul. Hitlerism is more than a contagion or a madness; it is an awakening of elementary feelings.But from this point on, this frighteningly dangerous phenomenon becomes philosophically interesting. For these elementary feelings harbor a philosophy. They express a soul's principal attitude towards the whole of reality (...) and its own destiny. They predetermine or prefigure the meaning of the adventure that the soul will face in the world.The philosophy of Hitlerism therefore goes beyond the philosophy of Hitlerians. It questions the very principles of a civilization. The conflict is played out not only between liberalism and Hitlerism. Christianity itself is threatened in spite of the careful attentions or Concordats that the Christian churches took advantage of when Hitler's regime came to power.But it is not enough to follow certain journalists in distinguishing between Christian universalism and racist particularism: a logical contradiction cannot judge a concrete event. The meaning of a logical contradiction that opposes two forms of ideas only shows up fully if we go back to their source, to intuition, to the original decision that makes them possible. It is in this spirit that we are going to set forth the following reflections. Emmanuel Levinas has been professor of philosophy at the Ecole Normale Superieure Israelite de Paris and at the University of Paris I . Among his books that have been translated into English are Totality and Infinity, Ethics and Infinity, Otherwise Than Being or Beyond Essence, and The Levinas Reader. His essay "As If Consenting to Horror" appeared in the Winter 1989 issue of Critical Inquiry. Sean Hand is lecturer in French at the University College of Wales, Aberystwyth. He is the editor of The Levinas Reader and the translator of Levinas's Difficult Freedom . He is currently completing a book on Michel Leiris. (shrink)

In the present article, we are faced with two phenomenological philosophers who, in two different intellectual traditions, namely philosophical hermeneutics and moral phenomenology, have referred to the concept of the Other as the fundamental possibility of the individual. The other, as an ontological and common concept in the thought of Gadamer and Levinas, is the turning point of the condition for the possibility of understanding and ethics. Focusing on the concept of the other, while addressing the points of difference and (...) commonality between Gadamer and Levinas, this article will show that Levinas’s preoccupation with the other as a philosopher refers to the foundations of ethics, and the condition for the possibility of foundations of ethics is encountering the other. In Gadamer, the turning point is the determination of the possibilities of understanding in dialectical and dialogue-oriented relationships. Without the other, in Levinas’s thought, ethics, and moral matter, and in Gadamer’s thought, the process of understanding will not occur in the form of a fusion of horizons. Therefore, this article shows that the other is a common concept between these two philosophers, which both of them cannot avoid in their philosophical analyses of ethics or the process of understanding. Introduction The analysis of ethics is one of the important and innovative achievements of Levinas’s philosophical intellectual structure. Levinas’s concern is to refer to the foundations of morality itself, regardless of institutionalizing the moral in the form of law, and the foundation of morality is in face-to-face relationships with others. Regardless of Levinas’s plan about the concept of the other, Gadamer imagines the determination of understanding in a new way in the face of the other. The other is the comprehensible strain in philosophical hermeneutics, in such a way that the process of understanding is formed by the presence of the other and the face-to-face encounter with it. According to Gadamer, the other is the factor of openness in the process of understanding. The fusion of horizons is the product of openness and mutual encounters in dialogue, which is not possible without the other. The other is the condition of determining the possibility of understanding in each of the parties who are allowed to reveal a part of their being and allow the other to open up and talk. In fact, understanding is a kind of event that is revealed in a two-way conversation in an event-like way. This type of understanding depends on the presence of another. The main focus of the research is the analysis of the concept of the other, which has been done with emphasis on two important works: Truth and method, Totality and infinity. Body & discussion In general, the process of understanding is a dialogical process, whether the other side of the conversation is a text or a person, the foundation of understanding is formed in a relationship with the other. Determining the other as an independent personality and a different perspective is an ontological determination. The other thinks and becomes meaningful beyond the subject or object and even beyond my intellectual position, it belongs to its own independent world and its own experience. In conversation, it plays a significant role in the production of truth. Openness provides the possibility of dialogue and mutual agreement. In dialogue, the final product is not reproduced. The other condition for the production of the final product is dialogue According to Gadamer, facing the other is facing his world. At the moment of facing me, the other makes his abstract aspects concrete and opens his lived experience to me. He believes that the question-and-answer process is a kind of encounter with the world of experience and openness toward it. According to Gadamer, the process of understanding is the result of dialectical-hermeneutic relations between me (the interpreter) and you (the other). The dialogical relationships that allow each other to enter the other’s history are relationships that are formed based on questions and answers. From Gadamer’s point of view, questions and answers are the opening of a new horizon based on tradition and contemporary history. Levinas phenomenologically refers to the philosophical tradition of the West to reread the process of the formation of the concept of the other. Many commentators and interpreters of Levinas’s works believe that it is possible to determine the foundations of ethics from Levinas’s point of view from face-to-face relationships. The condition for the possibility of morality is to pay attention to others. To describe another concept, Levinas analyzes the negative and positive aspects of this concept. In a negative way, Levinas first answers what the other is not, and for this reason, he criticizes the history of Western metaphysics and the criticism of Husserl and Heidegger’s phenomenology. Positively, the other is relative to me and different from me. The other is beyond subject and object. The other is not subjugated by any concept and recognizes its independent identity. The other and the encounter with him are the conditions for determining fundamental ethics from Levinas’s point of view. Another condition of concreteness refers to another person. According to Levinas, it is the condition for the formation of moral form. He believes that ethics is a kind of double encounter in the context of bilateral relations. Many moral concepts are formed in relation to a concrete other. In Levinas’s genealogy of ethics, we are faced with the presence of the other in a concrete way and with the subjectivity of the subject in an abstract and a priori way. Levinas specifies two approaches with the description of the other in the form of an infinite idea. First of all, there is an infinite gap between the other and the same. This issue shows its foreignness and otherness, its independence, and being true to its essence towards me. Second, it is the determination of another in a concrete or abstract form, which in both cases evokes an identity independent of me. Conclusion According to the explanations of the concept of the other in the thought of Gadamer and Levinas, we are faced with two phenomenological philosophers who have paid attention to the ontological aspects of the concept of the other in the fields of philosophical hermeneutics and ethics. In Gadamer’s thought, the other is an ontologically dialectical relationship between I-Thou and the starting point of the conversation process. The fusion of horizons is the turning point of the formation of the relation to the other, which is manifested in another area. The other has its own history, world, tradition, and authority, regardless of the formation of dialogical relationships, and has an independent identity. The other is allowed to share his lived experience in the conversation. The other creates new worlds. The other has opened himself and in return can be self-interpreting and self-revealing. Regardless, the other is the consistency of the complex relationship between language and the world. This form of bilateral relations, which is manifested in the presence of another, is a linguistic form that is the cause of a deep connection between language and the world. The other, whether concrete or abstract, is the turning point of our connection with the world in an ontological way. Regardless of Gadamer’s point of view, Levinas returns to another concept in his new thought project entitled “How to determine the possibilities of ethics.” According to Levinas, finding the foundations of ethics and determining the condition of moral possibilities is in facing the other and in face-to-face relationships. The other is concretely a kind of bilateral encounter which is the basis of many moral events and is manifested abstractly in the form of the subject’s subjectivity. This kind of infinite aspect of the other is revealed in subjectivity is implied in sense. Encountering another in an abstract form within itself is the encounter of the subject’s subjectivity with the sense, and the sense is in the encounter with the other. Sense is the basis of the subjectivity of the subject. Sense is a kind of concrete and visual face-to-face encounter that adds to the importance of determining another. Therefore, both Gadamer and Levinas raise many possibilities about the concept of the other, which shows the importance of this concept in the Western philosophical tradition. (shrink)

David Hilbert sought to secure the epistemic foundations of mathematics by providing consistency proofs of axiomatized mathematical theories from within the finite standpoint. This standpoint requires concrete constructions without reference to completed infinities. In 1938, Gerhardt Gentzen proved the consistency of first-order Peano Arithmetic relying on the well-ordering of certain ordinal notations. This was thought by Gentzen and Paul Bernays to be finitistically acceptable. However, a finitistically acceptable proof of the relevant well-ordering was not available until Gaisi Takeuti’s (...) proof in 1978. Beginning with the proposition that Takeuti’s proof conforms to the finite standpoint, this chapter explores the limits of a finitism based on the methods of Gentzen and Takeuti. It is argued that the upper limit is the Feferman-Schütte ordinal, and thus that finitism may be extended to strong subsystems of second-order arithmetic-systems strong enough to provide a theory of the ordinals for which Gentzen employed notations. (shrink)

Il saggio propone una lettura del materialismo speculativo di Ernst Bloch interpretandolo come “scienza della speranza”. La filosofia politica di Bloch viene presentata come un pensiero dell’emancipazione determinato da un’antropologia e un’ontologia sviluppate attorno alle categorie di “anticipazione” e di “materia”, entrambe indicizzate dalla logica della “possibilità oggettivo-reale”. Infine, il saggio propone di considerare il contributo filosofico-politico di Bloch come un pensiero marxista aperto a processi di soggettivazione plurale che rappresentano concrete possibilità di emancipazione nel quadro della dimensione globale (...) della formazione sociale capitalistica. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Literature 26.1 (2002) 24-42 [Access article in PDF] Emmanuel Levinas and Iris Murdoch: Ethics as Exit? C. Fred Alford THE LEVINAS EFFECT it has been called, the ability of Emmanuel Levinas's texts to say anything the reader wants to hear, so that Levinas becomes a deconstructionist, theologian, proto-feminist, or even the reconciler of postmodern ethics and rabbinic Judaism. Talmudic scholar and postmodern philosopher, Levinas has become everything (...) to everyone. Abstract and evocative, writing in what can only be described as the language of prophecy, we pretend we understand what he is talking about, writing in much the same style, so as to say whatever we wanted to say in the first place. Even those who disagree with Levinas generally criticize him from within the framework of his project, sharing his assumptions while trying to make Levinas more Levinassian. 1How might one disrupt the Levinas Effect? By disrupt, I mean criticize Levinas sympathetically, from a perspective outside his "system," but not outside his world. Levinas's world is one in which the self is the enemy not only of the other, but of authentic existence. Iris Murdoch shares this view with Levinas. Like Levinas, Murdoch sees the self as the enemy. "Unselfing," as she calls it, is the means; the end is to overcome totality, which means the subjection of the other to my categories and my experience. Levinas means much the same thing by totality. It is his philosophical idée maîtresse, the troubling tendency of Western thought from Plato to Hegel and beyond."What breaks the drive of consciousness to totality is not an appeal to an abstract social or linguistic whole, but an encounter with the concrete other person." Levinas did not say this, nor did Iris Murdoch. Maria Antonaccio says it in a book about Murdoch, in which she compares Murdoch's views to those of Levinas. What they share, says [End Page 24] Antonaccio, is this critique of totality, even if "Murdoch would reject the language of command, lordship and accusation that pervade Levinas's account." 2Certainly Levinas's language of persecution is one of the most striking aspects of his account, and I will not ignore it. But it is not the most important thing that distinguishes him from Murdoch. One might argue that it is the "concrete other person" that distinguishes Levinas from Murdoch, for in many respects the other is an abstraction for Levinas. "The best way of encountering the Other is not even to notice the color of his eyes!" says Levinas. 3 Only at a distance is the other abstract enough to remind us of infinity.This distinction comes closer to capturing the difference between them. Even more important, Levinas shares Sartre's nausea at the thingyness of the world. Levinas calls it the il y a, the "there is." It is this that makes his account closer to Sartre's than one might imagine, and more distant from Murdoch. This does not, of course, make Levinas wrong. The comparison with Murdoch is a way of getting out from under the Levinas Effect.My goal is to better understand Levinas by comparing him with Murdoch. This requires that Murdoch's philosophy be seriously considered, but perhaps not as seriously as that of Levinas. Murdoch is the other, Levinas the subject. Possibly we will end up understanding the other better than the subject. I The outlines of Levinas's philosophy will be familiar to many readers. I will elaborate upon a story told by Levinas to recount it. 4 Imagine that someone rings your doorbell and disturbs your work. As you walk to the door you are distracted, still thinking about your latest project. It takes you a moment to recognize your neighbor at the door, the one who lives upstairs; as soon as you recognize his face you invite him in. You talk for a while. He tells you his problem, you tell him what you might do to help him. You share some pleasant conversation, and soon enough your neighbor leaves. What you originally experienced... (shrink)

The paper outlines a project in the philosophy of mathematics based on a proposed view of the nature of mathematical reasoning. It also contains a brief evaluative overview of the discipline and some historical observations; here it points out and illustrates the division between the philosophical dimension, where questions of realism and the status of mathematics are treated, and the more descriptive and looser dimension of epistemic efficiency, which has to do with ways of organizing the mathematical material. The paper’s (...) concern is with the first. The grand tradition in the philosophy of mathematics goes back to the foundational debates at the end of the 19th and the first decades of the 20th century. Logicism went together with a realistic view of actual infinities; rejection of, or skepticism about actual infinities derived from conceptions that were Kantian in spirit. Yet questions about the nature of mathematical reasoning should be distinguished from questions about realism (the extent of objective knowledge– independent mathematical truth). Logicism is now dead. Recent attempts to revive it are based on a redefinition of “logic”, which exploits the flexibility of the concept; they yield no interesting insight into the nature of mathematics. A conception of mathematical reasoning, broadly speaking along Kantian lines, need not imply anti–realism and can be pursued and investigated, leaving questions of realism open. Using some concrete examples of non–formal mathematical proofs, the paper proposes that mathematics is the study of forms of organization—-a concept that should be taken as primitive, rather than interpreted in terms of set–theoretic structures. For set theory itself is a study of a particular form of organization, albeit one that provides a modeling for the other known mathematical systems. In a nutshell: “We come to know mathematical truths through becoming aware of the properties of some of the organizational forms that underlie our world. This is possible, due to a capacity we have: to reflect on some of our own practices and the ways of organizing our world, and to realize what they imply.. (shrink)

In this paper I present Levinas' account of excendence in On Escape and Existence and Existents and show its continuity with his subsequent discussions of transcendence in Time and the Other, Totality and Infinity, and Otherwise than Being. I argue that Levinas' critique of the traditional idea of identity plays a decisive role in establishing the continuity between these various accounts as it provides the key to unlocking his account of transcendence as a formal structure. However, the meaning of trascendence (...) lies not in the structure but in its concretization. Although Levinas initially presents fecundity as the concretization of transcendence, he ultimately identifies it as ethics. This development explains why Levinas himself preferred to think of himself as a thinker of transcendence or the holy rather than to be identified with ethics. (shrink)

Il lavoro di dottorato condotto apre la ricerca filosofica ed etica, riguardo il pensiero e l’agire dell’aver cura, alla possibilità teoretico-pratica e valutativa di un’analitica della relazione fondamentale, originaria e vivente sussistente tra essere e speranza nella dimensione ontologica, esistenziale e trascendente della cura. Attraverso un’ermeneutica del rapporto contemporaneo tra cura, limite e speranza nel tempo della tecnica, sviluppata a partire dalle riflessioni avanzate su tali questioni da Heidegger, Jaspers e Marcel, si sono venute ad individuare, affrontare e verificare, nella (...) prima parte analitica del lavoro, le condizioni ermeneutiche di uno sguardo rinnovato verso l’essere della cura, orientato dalla possibilità della speranza. A partire dalla possibilità di un necessario confronto con la concettualizzazione della dimensione e del tempo dell’aver cura nell’analitica heideggeriana dell’esserci, dalla ricomprensione della chiarificazione jaspersiana di situazione limite quale orizzonte ermeneutico della cura, così come dalla possibilità dell’apertura marceliana alla speranza nelle situazionalità concrete dell’aver cura, la ricerca ha potuto dunque indirizzarsi, nella seconda parte sintetica, verso la possibilità di un’ontologia esistenziale della speranza; così come verso la messa in luce della trascendenza valoriale propria della dimensione della cura. La possibilità di ricerca di un’ermeneutica ontologico-esistenziale e trascendente della speranza, a partire dalle pratiche ontiche dell’aver cura della vita e della salute, ha permesso così di avanzare, grazie al confronto interdisciplinare intrapreso con le rispettive e integrative riflessioni di Heidegger, Jaspers e Marcel sulle questioni della cura, del limite e della speranza e l’ermeneutica teoretico-pratica operata a partire da queste, una valutazione circa la possibilità di un’analitica della dimensione della cura alla luce della speranza. In tale orizzonte ermeneutico si sono manifestati, infine, i possibili apporti ontologico-esistenziali del lavoro ad una filosofia ed etica dell’aver cura che si ricerchi quanto più autentica e omnicomprensiva, alla luce di una speranza aperturale di bene comunionale che si invera quotidianamente e straordinariamente nella dimensione ontologica, esistenziale e trascendente della cura. (shrink)

A boat is a floating piece of space, a place without place, which lives by itself, which is closed in on itself and that is at the same time exposed to the infinity of the sea. Nowadays one cannot conceive a utopia that does not address itself to nomads, peoples and individuals, to the homeless, to the excluded. After World War I a concrete barge made its way up and down the Seine between Rouen and Paris.1 It was called (...) the Liège, and its mission was to supply the French capital with English coal. When it was decommissioned in 1929, the Armée du salut (the French Salvation Army) bought it with the aid of a donation from Madeleine Zillhardt, the recently bereaved long-term companion of the painter .. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Levinas versus Levinas:Hebrew, Greek, and Linguistic JusticeOona EisenstadtI argue in this paper that Levinas's philosophical writings and his Jewish writings are not easily read as compatible. But I do not make the argument on what might seem to be the obvious grounds, namely, that the philosophical writings represent what Levinas calls the "Greek" while the Jewish writings represent what he calls the "Hebrew." On the contrary, my claim is (...) almost precisely the opposite. As Levinas uses the terms "Greek" and "Hebrew," each refers to a "sub-textual... way of thinking and speaking" (Richard Kearney, quoted in Cohen 1986, 18–19). The "Greek" is the ontological mode that seeks to describe the whole—this is essentially the mode I believe Levinas works the reader toward in the Jewish writings. The "Hebrew" is the dialogical mode that is never complete and preserves dissent—this is the mode he works the reader toward in the philosophical works. The first half of this paper contains a general discussion of the meaning of the two terms, the way in which Jacques Derrida brings out what is at stake in their use with the introduction of the more critically clarified terms "Jewgreek" and "Greekjew," and, finally, the beginning of my argument that Levinas is at odds with himself. The second half illustrates the argument with brief examinations of text: we look first at the "Hebrew" or "Jewgreekish" Levinas of the final chapter of Otherwise than Being, a Levinas in many ways comparable to Plato's dialogical Socrates; and second, at the "Greek" or "Greekjewish" Levinas of the Talmudic reading "The Pact," a Levinas who praises universality, universal translatability, mutuality, and reciprocality.As is well known, the juxtaposition Greek/Hebrew, as Levinas uses it, does the same work as several other juxtapositions he employs, including same/other, politics/ethics, said/saying, and totality/infinity. In each of these formulations, the first term refers to a way of thinking that pulls things [End Page 145] together into a larger order, and the second term to a rupture that operates as thought's origin and at the same time thought's challenge. On a first reading of Levinas, the reader has the impression that the juxtaposed elements stand in opposition to one another, but as one reads more one sees that this is only part of how he intends the juxtapositions to be understood; in particular, one sees that justice of any kind requires both elements. The reasons for this can be variously described. There are, for instance, the concrete organizational requirements of justice: a just society must, on the one hand, treat people as parts of ordered wholes (as citizens, as members of family groups or income groups, and so forth) and, on the other hand, allow those designations to be called into question by the rupturing ipseity of individuals. And there are, to introduce an example more pertinent to this paper, the concrete linguistic requirements of justice. A just discourse, or a good book, places its elements into a coherent order; this can be described by saying that it assumes or imposes a certain sameness by addressing its readers as a group, or that it stands as a said, but is most simply described by saying that the book speaks in Greek. However, it must also remain open to rupture by readers and writers who came before its having been written and readers and writers yet to come; this can be described as an other-in-the-same or a saying-in-the-said, but is most simply described, in Levinas's shorthand, as the incorporation or preservation of the Hebrew in the Greek.At the end of his first essay addressed to Levinas, "Violence and Metaphysics," Derrida plays, in a serious way, with the Greek/Hebrew distinction, and especially with the fact that the two sides depend on one another. This mutual dependence rests not only on the requirements of justice, but also, and first, on what seems to be a contradiction in Levinas's thinking. Levinas says (repeatedly, in almost all of his works) that it is the experience of rupture that calls us, in the first place, to totalize, which... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 97 supposed by actual idealism is above all moral and involves what Gentile describes as an aspect of divinity or infinity,as well as a concrete, historical aspect. The following chapter treats of the philosophy of "actual" idealism and compares the views of Kant and Gentile on relations between moral conscience and freedom. According to Yalentini, Gentile's idealism is essentially an ethical view. This chapter concludes with (...) noting that Gentile 's solution to the problem of historical knowledge differs profoundly from that of Hegel and Croce. For "reason" is not, for Gentile, a particular interpretation of historical process, but is rather the "reason" of consciousness in activity. In Chapter In, Valentini discusses Gentile's views on art and religion. The section on art concludes with a comparison between Gentile on feeling and Kant on the transcendental unity of apperception. Whereas art is supposed to be one abstract moment of spirit, religion is the other abstract moment. Valentini suggests that Gentile and Feuerbach hold similar religious views on the attributes of divinity, which are nothing other than the loftiest qualities which man feels to possess in his essence. The history of religion is then the history of the progressive humanization of God. Gentile's religion represents a sort of modem Catholicism in that it understands revelation as a fact of conscience, church as a historical institution, dogma as having a negative character and God as a member of the dialogue between God and man. Moreover, Gentile's Catholicism has a national character; it is the religion of the Italian people. Chapter Iv treats of the relations between individual and state. For, according to Gentile, an individual is inconceivableapart from the social relations which lie within him. Here Valentini distinguishes in detail the differences and similarities between the views of Hegel and Gentile on the relations between state and individual. The differences between the views of these two philosophers are due to the differences between their methods. The method of Hegel is empirical and historical, and examines the state (which remains historical) from an external point of view. According to an idealistic method, however, thought is not to be the spectator of a process, but in every instance, an actor, and philosophizing does not result from an analysis of historical reality, but from the negation of this reality in the name of an ideal, which philosophy is to draw from it (reality). The Appendix includes a critical evaluation of the theory of the dialectic. Here Valentini hopes to distinguish between the imaginary and the real or historical applications of the dialectic. He begins his evaluation by asking: Does the doctrine of the dialectic, like the philosophy of idealism, possess negative connotations, which cannot be separated from it? Valentini suggests that in order to answer this question, we must determine the extent to which the dialectical scheme is constitutive of every concept or truth in general. For this is the way in which Hegel intended that the dialectic be understood and evaluated. Some views in Hegel's philosophy of nature are then criticized according to empirical criteria. In conclusion, Valentini attempts to answer both "internal" and "external" criticisms of Marx's view of the dialectic, and shows that there are problems involved in its application, which still have to be resolved. Mv~ M. MILBURN 9 ~an Jos~ ~ate College Husserl und Kant: eine Untersuchung ~ber Husserls Verh~iltni~ zu Kant und zum Neubantianismus. By Iso Kern. (The Hague : Martinus Nijhoff, 1964.Pp. xxiii q- 448.) This is a very important book. In fact, it is indispensable for a study of Husserl and is, at the same time, almost as valuable for a study of Kant, for it deals with the kind of searching questions that must be asked when one deals with transcendental idealism in any one of its forms. But two reasons in particular, make this book significant. One is the fact that Iso Kern was able to make extensive use of hitherto unpublished materials (manuscripts, lecture notes, letters, etc.), available only in the Husserl Archives and here quoted for the first time--and 98 HISTORY OF PHILOSOPHY quoted in great numbers. The other is Kern's philosophical competence... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 44.2 (2006) 321-322 [Access article in PDF] Thomas Holden, The Architecture of Matter: Galileo to Kant. Oxford: Clarendon Press, 2004. Pp. x + 305. Cloth $74.00. Most scholars believe that the problem of infinite divisibility that plagued early modern natural philosophy was an entirely mathematical issue and, therefore, resulted from the short-comings of early modern mathematics. Accordingly, advances in geometry, topology and the (...) logic of infinity are often thought to lay this debate to rest, thereby reducing it to some quaint footnote in the history of natural philosophy. Thomas Holden, however, through thorough textual and philosophical analysis, convincingly argues that this debate was more metaphysical in nature than previously supposed. He shows how the various paradoxes concerning the structure of matter stem from two widely-accepted theses central to the new science. The first resulted from the early modern method of applying the principles of geometry to physics. This geometrical method dictated that bodies are metaphysically divisible (m-divisible) in infinitum, because they occupy regions of space that can, at least by the power of God, be subdivided into those parts occupying corresponding sub-regions of space, and those sub-parts into those sub-sub-parts occupying their respective corresponding sub-sub-regions of space in infinitum. The other thesis is that "the parts of material bodies are each concrete existents in their own right" (3). Such actual parts exist prior to any act of division, whereas parts that are only potential would not exist prior to division but only after a divisive act has occurred. Holden argues that the actual parts doctrine was a metaphysical thesis just as fundamental to Enlightenment natural philosophers as the geometrization of matter. Indeed, it is these two theses that came into conflict and gave rise to a plethora of antimonies at the heart of the new science.Holden should be applauded for the skill he employs in challenging the received scholarship. In chapter 1, after some historical and terminological preliminaries, Holden reconstructs several of the more popular paradoxes of material structure found throughout the period's vast literature and successfully shows how these paradoxes would not arise if the problems of material structure were merely mathematical. He shows how the metaphysical doctrine of actual parts gave rise to these difficulties because of its conflict with the assumed geometrical doctrine that extension is infinitely m-divisible. For example, some thought it followed from the actual parts doctrine that there must be an actual infinity of parts, because actual parts exist prior to any process of division and, therefore, in order for both actual parts and infinite m-divisibility to be true, there must be an actual infinity of parts. This raised issues about the intelligibility and piety of an actual infinite as well as issues about equal and unequal infinities, e.g., half an infinite number of parts would still be infinite but half as much as the whole collection of parts. Hence, this and other paradoxes would not arise in the absence of the actual parts doctrine, and so the debate is more metaphysical in nature than previously supposed. [End Page 321]Chapter 2 examines in more detail the actual parts metaphysic and how it leads to tension with infinite m-divisibility. Chapter 3 examines various "short-circuit" arguments designed to undermine the actual parts doctrine. And chapter 4 examines the actual parts doctrine via the argument from composition found in Kant's pre-critical work, Physical Monadology. In chapter 5, Holden briefly examines the potential parts doctrine and how some actual-parts partisans tried to undermine it. It is eventually concluded that actual-parts and potential-parts advocates are at an impasse due to the question-begging nature of their respective arguments. Finally, chapter 6 is "something of an addendum" (74), since it examines a fascinating synthesis of the two conflicting positions, viz. the Kant-Boscovich force-shell atom theory.Given that the book is about material structure, it is a propos that my critical comment is about the structure of the book. It seems... (shrink)

In this article, as implied by the title, I intend to argue for the unattainability of Cantor’s Absolute at least in terms of the proof-theoretical means of set-theory and of the theory of large cardinals. For this reason a significant part of the article is a critical review of the progress of set-theory and of mathematical foundations toward resolving problems which to the one or the other degree are associated with the concept of infinity especially the one beyond that of (...) the natural intuition of natural numbers. Naturally the review includes the foundation and development of the theory of large cardinals, especially after Cohen’s revolutionary introduction of the forcing method, insofar as it paved the way toward a transcendence of the delimitative character of Gödel’s constructible universe L and further toward ever stronger infinity assumptions. Given that Cantor in his theory of transfinite numbers defined the mathematical absolute in ontological rather than concrete mathematical terms, I proceed in the last section to a philosophical discussion with certain prompts from phenomenology regarding the transposability of the formal conception of the infinite to the level of subjective constitution and argue in these terms on the infeasibility of acceding to an ‘absolute’ infinite cardinality. Of course the argumentation is strongly based on a view of the set-theoretical universe V of von Neumann’s cumulative hierarchy as a formal representative of the essential traits one would seek from a model of Cantor’s Absolute. It is also based on the conclusions reached from the whole discussion within the context of formal-theoretical structures as such. (shrink)

French translation by G. B. Côté and Roger Lapalme of "A Geneticist's Roadmap to Sanity" (G. B. Côté, 2019) with added bibliography. -/- À voir le monde d’aujourd’hui, on pourrait croire que nous avons perdu la raison. Je veux explorer ici les fondements mêmes de notre existence. Je discuterai brièvement du libre arbitre, de l’éthique, de la religion, de la souffrance, du dualisme cartésien et de l’état de conscience, avec un arrière-plan promulguant l’importance de la physique quantique d’aujourd’hui et de (...) l’intemporel. Pour ce faire, je devrai d’abord établir que le platonisme mathématique est une prémisse essentielle pour qu’un univers (ou même un multivers) prenne forme, et j’introduirai les trois modes d’existence abstrait, virtuel et concret (en philosophie) correspondant respectivement aux concepts d’information, d’énergie et de masse (en physique). Cet article constitue un bref exposé de ma théorie du tout. (shrink)

Ordinal polytheism is motivated by the cosmological and design arguments. It is also motivated by Leibnizian–Lewisian modal realism. Just as there are many universes, so there are many gods. Gods are necessary concrete grounds of universes. The god-universe relation is one-to-one. Ordinal polytheism argues for a hierarchy of ranks of ever more perfect gods, one rank for every ordinal number. Since there are no maximally perfect gods, ordinal polytheism avoids many of the familiar problems of monotheism. It links theology (...) with counterpart theory, mathematics and computer science. And it entails that the system of universes has an attractive axiological structure. (shrink)

Le paradigme des diasporas peut-il répondre à la nécessité de prendre en compte les changements opérés dans le champ des migrations humaines? Elles s'inscrivent au coeur d'une dialectique entre la dispersion des migrants au sein de sociétés pluralistes et le maintien de liens concrets et spirituels avec les sociétés d'origine. Les sciences sociales ont privilégié longtemps le paradigme de la diversité. De même, l'opposition de l'option multiculturaliste à la « sociologie de l'intégration » a enfermé les débats dans une fausse (...) alternative. L'expérience des diasporas, à commencer par l'exemple juif, entre dispersion à l'infini et maintien d'une référence commune, montre que les figures migrantes évoluent aux marges d'identités prédéfinies.The paradigm of diaspora can answer the need to take into account the changes in the field of human migration? They are at the heart of a dialectic between the dispersion of migrants in pluralistic societies and maintaining links with practical and spiritual societies of origin. The social sciences have long favored the paradigm of diversity. Similarly, opposition to multiculturalism option "sociology of integration" has locked the discussion in a false alternative. The experience of diaspora, starting with the example Jewish dispersion between infinity and maintaining a common reference, the figures show that migrants move to the margins of predefined identities. (shrink)

In his metaphysical summa of 1986, The Plurality of Worlds, David Lewis famously defends a doctrine he calls ‘modal realism’, the idea that to account for the fact that some things are possible and some things are necessary we must postulate an infinity possible worlds, concrete entities like our own universe, but cut off from us in space and time. Possible worlds are required to account for the facts of modality without assuming that modality is primitive – that there (...) are irreducibly modal facts. We argue that on one reading, Lewis’s theory licenses us to assume maverick possible worlds which spread through logical space gobbling up all the rest. Because they exclude alternatives, these worlds result in contradictions, since different spread worlds are incompatible with one another. Plainly Lewis’s theory must be amended to exclude these excluders. But, we maintain, this cannot be done without bringing in modal primitives. And once we admit modal primitives, bang goes the rationale for Lewis’s modal realism. (shrink)

‘Mathematics is the science of the infinite, its goal the symbolic comprehension of the infinite with human, that is finite, means.’ Along this line, in The Open World, Hermann Weyl contrasted the desire to make the infinite accessible through finite processes, which underlies any theoretical investigation of reality, with the intuitive feeling for the infinite ‘peculiar to the Orient,’ which remains ‘indifferent to the concrete manifold of reality.’ But a critical analysis may acknowledge a valuable dialectical opposition. Struggling to (...) spell out the infinity of real numbers mathematicians come to see the active role of emptiness. Pondering over the essence of self-awareness, the Japanese philosopher Nishida Kitarō comes to see the ‘place’ where it abides as absolute nothingness. Thus, the two ways of seeing coalesce into a perspective in which infinity and nothingness mirror each other. (shrink)

This paper investigates the possibility of understanding the rudimentary elements of clinical sensitivity by investigating the works of Edmund Husserl and Emmanuel Levinas on sensibility. Husserl's theory of intentionality offers significant reflections on the role of pre-reflective and affective intuition as a condition for intentionality and reflective consciousness. These early works of Husserl, in particular his works on the constitution of phenomenological time and subjective time-consciousness, prove to be an important basis for Levinas’ works on an ethics of alterity and (...) infinite responsibility for the other person. In fact, it is difficult to understand the core of Levinasian ethics, of vulnerability as proximity, of ethical sensitivity as passivity and a suffering for the suffering of another, without understanding the influence from Husserl's work. Crucially, the paper will, on the basis of Levinasian ethics, establish an understanding of sensibility as vulnerability and receptivity that is fundamental also for understanding significant intuitions in clinical nursing. Clinical sensitivity and carefulness in nursing are shaped by the concrete and also bodily expressions of vulnerabilities in a receptivity that is pre-reflective and pre-ontological. (shrink)

For over a decade, the hypercomputation movement has produced computational models that in theory solve the algorithmically unsolvable, but they are not physically realizable according to currently accepted physical theories. While opponents to the hypercomputation movement provide arguments against the physical realizability of specific models in order to demonstrate this, these arguments lack the generality to be a satisfactory justification against the construction of any information-processing machine that computes beyond the universal Turing machine. To this end, I present a more (...) mathematically concrete challenge to hypercomputability, and will show that one is immediately led into physical impossibilities, thereby demonstrating the infeasibility of hypercomputers more generally. This gives impetus to propose and justify a more plausible starting point for an extension to the classical paradigm that is physically possible, at least in principle. Instead of attempting to rely on infinities such as idealized limits of infinite time or numerical precision, or some other physically unattainable source, one should focus on extending the classical paradigm to better encapsulate modern computational problems that are not well-expressed/modeled by the closed-system paradigm of the Turing machine. I present the first steps toward this goal by considering contemporary computational problems dealing with intractability and issues surrounding cyber-physical systems, and argue that a reasonable extension to the classical paradigm should focus on these issues in order to be practically viable. (shrink)