Noam Cohen

This paper argues that Heidegger’s thought from Being and Time up to his 1934 lectures reveals an increasingly fundamental instability in the ontological distinction between individuality and collectivity. Engaging with two major lines of interpretation - one claiming that Heidegger subordinates the individual to a collectivist vision of destiny, the other emphasizing a holism of self, world, and others – I argue that Heidegger moves beyond both. Rather than securing a stable account of the social self, Heidegger progressively dismantles the conceptual foundations of social ontology, showing that both individual and collective selfhood are rooted in a deeper historical movement of appropriation and decision. Grounded in Dasein’s historicity, this movement precedes and disrupts any fixed schema of either individual or communal subjectivity. By tracing this trajectory, the paper brings to light an often-overlooked dimension of Heidegger’s early and middle-period thought: his radical recasting of the self as a fluid dynamic that underlies and exceeds both individuality and collectivity.

This paper argues that the shared intersubjective accessibility of mathematical objects has its roots in a stratum of experience prior to language or any other form of concrete social interaction. On the basis of Husserl’s phenomenology, I demonstrate that intersubjectivity is an essential stratum of the objects of mathematical experience, i.e., an integral part of the peculiar sense of a mathematical object is its common accessibility to any consciousness whatsoever. For Husserl, any experience of an objective nature has as its correlate a “we,” which he terms the “community of monads”. Thus, even before mathematical objects gain expression, formalization, and axiomatization through natural and scientific language, from a phenomenological viewpoint their objectivity has its roots in raw pre-linguistic though intersubjective experience. Accordingly, I demonstrate the different senses in which the experience of mathematical objects is permeated by intersubjectivity, suggesting a picture of mathematical intersubjectivity as pre-linguistic common experience based on Husserl’s idea of a “community of monads”.

The main problem in making sense of Mitsein as an aspect of Dasein in Being and Time concerns the sense in which individual Dasein is an ‘I’, given that it can be either an ‘anyone-self’ or an ‘authentic self’. Though it is clear that the anyone-self relates directly to das Man, the relation of the authentic self to others is debatable. In this paper, I reexamine the relations between self and others by making sense of the referent of each mode of selfhood, with special attention to the problem of explaining the relations between the two. The problem, I claim, can be solved by bringing into relief a certain conception of mereology (theory of parthood relations) that underlies Heidegger’s arguments. As I will demonstrate, Heidegger uses a mereological terminology that appropriates Husserl’s logic of parts and wholes from the Logical Investigations. In view of this, I suggest understanding individual Dasein, both qua anyone-self and qua authentic self, as a moment, i.e. a dependent part of an open-ended whole. The apparent gap between anyone-self and authentic self can be better understood as a shift of focus between two different aspects of being the same type of dependent part of a whole.

Most scholars have not assigned much interpretive importance to the specific use of the term ‘persuasion’ in the cosmology of Plato’s Timaeus. This paper suggests understanding cosmological ‘persuasion’ in conjunction with ‘force,’ another trait of divine agency in the Timaeus. It analyses the nature of intelligent causation in the cosmology of the Timaeus, particularly in the construction of the cosmic body and soul. Then, it gives a detailed characterization of the causation of necessity, appearing in the Timaeus in three different versions, and relates it to the complex notion of intelligent agency. Ultimately, it claims that the cosmic music in the Timaeus, the primary agent of ordered causation in the cosmos, functions on two levels of conflict with the disorder of the sensible aspect of the world.

It is well-known that in the fifth of his Cartesian Meditations, Husserl puts forth a theory of intersubjectivity. Most commentators of Husserl have read his Cartesian Meditations as presenting a theory of intersubjectivity whose basis is empathy, in the form of a process of constituting the sense of “other” in one’s own experience, as the primary origin of the intersubjective layer of experience. In this paper, I claim that the structure of intersubjectivity as Husserl presents it in the Cartesian Meditations is articulated as being governed by a logic of parts and wholes rather than that of a phenomenology of empathy, and that the articulation of this logic demonstrates that the transcendental ego is intrinsically intersubjective. My main philosophical claim in this regard is that the way Husserl’s account of transcendental empathy unfolds in the Cartesian Meditations implies a prior fundamental mereological structure of which the individual transcendental ego is only a part. That is, the transcendental ego has an eidetic a-priori intersubjective structure, in the sense of being a moment of an intersubjectively structured transcendental whole. In this sense, rather than being a singulare tantum, it is more fitting to say that transcendental subjectivity is actually a plurale tantum.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Logos and Alogon: Thinkable and Unthinkable in Mathematics, from the Pythagoreans to the Moderns by Arkady PlotnitskyNoam CohenPLOTNITSKY, Arkady. Logos and Alogon: Thinkable and Unthinkable in Mathematics, from the Pythagoreans to the Moderns. Cham: Springer, 2023. xvi + 294 pp. Cloth, $109.99The limits of thought in its relations to reality have defined Western philosophical inquiry from its very beginnings. The shocking discovery of the incommensurables in Greek mathematics not only reintroduced these limits with greater force but also instigated two different forms of coping with the unthinkable in Western philosophy, mathematics, and science. As Arkady Plotnitsky sets forth, in response to the incommensurability crisis in the ancient Greek intellectual world, there appeared two different attitudes toward the alogon, that is, the unthinkable or irrational. Plato and his followers sought to overcome the unthinkable, of which the incommensurables in mathematics are only an example, through philosophy. In contrast, the Pythagoreans continued to hold on to mathematics as the primary means of knowing the world, but put a larger emphasis on geometry. Plotnitsky [End Page 359] claims that by not putting aside the primacy of mathematics, the Pythagorean shift from arithmetic to geometry established in Western thought a certain tolerance toward the unthinkable within the realm of the thinkable, “a possibility of the alogon in the logos.” Until modern times this remained no more than a possibility. However, in modern mathematics and mathematical physics Plotnitsky identifies a certain fulfillment of this potential, a “radical Pythagorean mathematics.” In his comprehensive and thought-provoking study, Plotnitsky recounts the development of such radical modern Pythagoreanism, not only to tell its history but also to suggest that the unthinkable is a condition of possibility for thought, and that a proper recognition of this role it plays is crucial for the advancement of mathematical thinking and thinking in general.Plotnitsky begins by portraying in broad strokes the two defining characteristics of radical Pythagorean mathematics: the presence of the unthinkable within mathematical thought itself, and the interplay of algebra and geometry. Relying on an extensive knowledge of the history of modern mathematics and physics, in the first two chapters of the book Plotnitsky gradually demonstrates the key role that the alogon plays in some theories of modern mathematical thought, such as Gödel’s incompleteness theorems and quantum mechanics. He also presents and clarifies his own conception of the history of Western thought as a creative process of concept-forming. By creating rather than discovering concepts, great mathematicians break new ground for thinking. The book as a whole argues in length for these two main theses.In chapter 3, the author addresses the thought of Bernhard Riemann to make the case that Riemann’s mathematical thought puts an emphasis on creative conceptual thinking and is not defined merely by calculations or logic. Such thinking is problem-posing rather than axiomatic. Riemann’s central innovation in this respect is the concept of manifold (Mannigfaltigkeit), which enabled him to think anew space and geometry in a radical non-Euclidean fashion, implying an infinite number of possible geometries. Plotnitsky argues—borrowing Deleuze and Guattari’s terminology—that this opened up a “plane of immanence,” which is to say that Riemann created a concept-generating movement of thought. However, we cannot grasp the generation of concepts in modern mathematics without giving proper attention to the interplay of algebra and geometry that defines it. Chapter 4 demonstrates this interweaving of the two fields by recounting the history of the idea of the curve in modernity, from the analytic geometry and calculus of Fermat and Descartes to its modification in the concept of a Riemann surface, up to its more recent developments in the algebraic geometry of Weil and Grothendieck. It gives a historical account of the algebraization of the curve that at the same time brings into relief the irreducible geometrical aspect, continuity, of all modern mathematical conceptualizations of the curve.The next two chapters provide further case studies. Chapter 5 expands and solidifies the argument of chapter 2. It discusses three examples of mathematical practice, each displayed by a pair of important [End Page 360] mathematicians: Abel and Galois, Lobachevsky and Riemann, Weil and Grothendieck. Each case...

This paper argues that the shared intersubjective accessibility of mathematical objects has its roots in a stratum of experience prior to language or any other form of concrete social interaction. On the basis of Husserl’s phenomenology, I demonstrate that intersubjectivity is an essential stratum of the objects of mathematical experience, i.e., an integral part of the peculiar sense of a mathematical object is its common accessibility to any consciousness whatsoever. For Husserl, any experience of an objective nature has as its correlate a “we,” which he terms the “community of monads”. Thus, even before mathematical objects gain expression, formalization, and axiomatization through natural and scientific language, from a phenomenological viewpoint their objectivity has its roots in raw pre-linguistic though intersubjective experience. Accordingly, I demonstrate the different senses in which the experience of mathematical objects is permeated by intersubjectivity, suggesting a picture of mathematical intersubjectivity as pre-linguistic common experience based on Husserl’s idea of a “community of monads”.

This study seeks to explore the relation between geometric shapes and ethical values in Plato's Timaeus. As is well known, geometric terms play a prominent part in the account of nature in that dialogue. The two prominent terms, in this regard, are the circular and the rectilinear, which characterize two distinct components of the cosmos in general and human life in particular, both as extended figures and as motions. A main debate in the scholarship over this issue has revolved around the question of the priority of a literal understanding of these shapes as part of natural mechanical processes, over a metaphorical interpretation, particularly focusing on the question of the circular motion of the rational mind. In this paper, after suggesting reasons to support the literal view, I will nonetheless also claim that the mechanistic accounts of biological and psychological processes in terms of circular and rectilinear shapes and motions also have a certain metaphorical dimension. That is to say, they convey a way of thinking about the cosmos and human life which extends beyond their literal function in the cosmic mechanics described in the dialogue. It is my contention that though one indeed cannot ignore the prominent place of extended figures in Timaeus' general mechanics of human nature, a full understanding of his account nonetheless must simultaneously maintain that the two categories of geometric shapes together imply an overall ethical view. Such a reading of the dialogue will prove to shed important light on what Plato may have considered to be the geometric manifestation of virtue, and, accordingly, will require that we reconsider our general understanding of that which constitutes Platonic virtue. I limit this study to the Timaeus, so as to gain a whole understanding of the ethical meanings of its geometric accounts before pursuing, in future studies, their likely possible connections with other Platonic dialogues.

Among the categories of the Science of Logic, contradiction is one of the basic concepts of all Hegelian philosophy. Hegel depicts contradiction not as a fallacy, but rather elevates it to the level of a basic logical metaphysical principle, which "is the root of all movement and life". As such, contradiction necessarily plays a central role in the course of human life, by logically structuring its movement and development. Thus it also conditions the content and meaning of morality, which is ultimately a disposition to will what is good over evil. In his Philosophy of Right, Hegel remarks that "the human being is good – but only in so far as he can also be evil." In what follows, I set out to cast light upon the meaning of this claim, by examining the relation between the category of contradiction and Hegel’s account of good and evil, as these themes are discussed in the Science of Logic and the Elements of the Philosophy of Right.