Burt C. Hopkins presents the first in-depth study of the work of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Accounts of the ...philosophical origins of formalized concepts-especially mathematical concepts and the process of mathematical abstraction that generates them-have been paramount to the development of phenomenology. Both Husserl and Klein independently concluded that it is impossible to separate the historical origin of the thought that generates the basic concepts of mathematics from their philosophical meanings. Hopkins explores how Husserl and Klein arrived at their conclusion and its philosophical implications for the modern project of formalizing all knowledge.
Dallas Willard’s contribution to phenomenology is presented in terms of his articles on, and translations into English of, Edmund Husserl’s early philosophical writings (i.e., those in the decade ...prior to Husserl’s
1900
publication
Logical Investigations
), which single-handedly prevented them from falling into oblivion, both literally and philosophically. Willard’s account of Husserl’s “negative critique” of formalized logic in those writings, and argument for its contemporary relevance, is presented and largely endorsed.
The philosophy of Husserl Hopkins, Burt C
The philosophy of Husserl,
2010, 2011, 20150128, 20110101, 2008, 2015-01-28, 2010-10-31, Volume:
11
eBook
As the founder of phenomenology, Edmund Husserl has been hugely influential in the development of contemporary continental philosophy. In The Philosophy of Husserl, Burt Hopkins shows that the unity ...of Husserl's philosophical enterprise is found in the investigation of the origins of cognition, being, meaning, and ultimately philosophy itself. Hopkins challenges the prevailing view that Husserl's late turn to history is inconsistent with his earlier attempts to establish phenomenology as a pure science and also the view of Heidegger and Derrida, that the limits of transcendental phenomenology are historically driven by ancient Greek philosophy.
Part 1 presents Plato's written and unwritten theories of eidê and Aristotle's criticism of both. Part 2 traces Husserl's early investigations into the formation of mathematical and logical concepts and charts the critical necessity that leads from descriptive psychology to transcendentally pure phenomenology. Part 3 investigates the movement of Husserl's phenomenology of transcendental consciousness to that of monadological intersubjectivity. Part 4 presents the final stage of the development of Husserl's thought, which situates monadological intersubjectivity within the context of the historical a priori constitutive of all meaning. Part 5 exposes the unwarranted historical presuppositions that guide Heidegger's fundamental ontological and Derrida's deconstructive criticisms of Husserl's transcendental phenomenology.
The Philosophy of Husserl will be required reading for all students of phenomenology.
I investigate the phenomenological significance of Husserl's appeal to the "numerical identity" of irreality as it appears in recollected manifolds of lived-experience in his mature account of the ...transcendental constitution of transcendence and find it wanting. I show that what is at stake for Husserl in this appeal is the descriptive mark that exhibits the distinction between a unit of meaning as it is constituted in psychologically determined lived-experience and as it is constituted in lived-experience that is determined transcendentally. In other words, I show that numerical identity functions for Husserl as the criterion that signals transcendental psychologism has been overcome. I then present the argument that it has not been overcome in Husserl's investigations, because the collective unity characteristic of numerical unity is presupposed by those investigations rather than made evidentially manifest and articulated.
I compare Plato’s and Husserl’s accounts of (i) the non-original appearance (termed phantasma in Plato and phantasm in Husserl) and (ii) the original with a focus on their methodologies for ...distinguishing between them and the phenomenological—i.e., the answer to the question of the what and how of their appearance—criteria that drive their respective methodologies. I argue that Plato’s dialectical method is phenomenologically superior to Husserl’s reflective method in the case of phantasmata that function as apparitions (the false phantasma/phantasm that is not recognized as such). Plato’s method has the capacity to discern the apparition on the basis of criteria that appeal solely to its appearance, whereas Husserl’s method presupposes a non-apparent primitive distinction between the original qua primal impression and the phantasm as its reproductive modification. On the basis of Plato’s methodological superiority in this regard, I sketch a reformulation of the Husserlian approach to appearances guided by the original interrogative context of Plato’s dialectical account of the distinction between true and false appearances, eikones and phantasmata.
Jacob Klein's own account of the change from the ancient to the modern mode of thinking presented in his seminal Greek Mathematical Thought and the Origin of Algebra included the observation that it ...did not consider the larger perspective of this change. The discussion to follow proposes to view the larger perspective of this transition through the lens provided by the Kantian concept of a "critique" of pure reason. By asking and attempting to answer the question of whether Klein's account of what he calls the "symbolic abstraction" responsible for the genesis of the modern concept of number can be seen as what Kant characterizes as an "assessment" of pure reason, it is my intent to venture a prolegomenon to a critique of what, following Klein, I want to argue is most properly called "symbolic reason."
The paper argues for three things. First, that the abstract concepts of ancient Greek and modern mathematics are fundamentally different. The general treatment of mathematical things in ancient Greek ...mathematics manifestly does not presuppose a general mathematical object, while in modern mathematics the generality of the method presupposes precisely such a general mathematical object. Two, that this difference in abstract concepts of mathematics makes a difference in our understanding of a discipline other than mathematics, specifically, in the discipline of history. And, three, that what is at issue in this difference is whether it is necessary for human beings to understand themselves from the perspective of history in order to understand themselves properly as human.Keywords: mathematical objects, concept of number, history, self-consciousness.Vienumas antikos ir naujųjų laikų filosofijoje ir visuotinės istorijos hipotezėBurt C. HopkinsSantraukaŠiame straipsnyje ginamos trys tezės. Pirma, kad abstrakčios antikos ir naujųjų laikų matematikos sąvokos yra fundamentaliai skirtingos. Bendras matematinių dalykų traktavimas antikos matematikoje akivaizdžiai nesuponuoja tokios matematinio objekto sąvokos, kokią numato naujųjų laikų matematikos metodas. Antra, šis abstrakčių matematikos sąvokų skirtingumas turi įtakos kitos, nematematinės disciplinos, o būtent – istorijos, supratimui. Trečia, šio skirtumo esminis aspektas yra klausimas, ar savęs kaip žmogaus suvokimui būtina suprasti save iš istorijos perspektyvos.Pagrindiniai žodžiai: matematiniai objektai, skaičiaus sąvoka, istorija, savimonė.
Husserl and Jacob Klein Hopkins, Burt C.
The European legacy, toward new paradigms,
08/2016, Volume:
21, Issue:
5-6
Journal Article
Peer reviewed
The article explores the relationship between the philosopher and historian of mathematics Jacob Klein's account of the transformation of the concept of number coincident with the invention of ...algebra , together with Husserl's early investigations of the origin of the concept of number and his late account of the Galilean impulse to mathematize nature. Klein's research is shown to present the historical context for Husserl's twin failures in the Philosophy of Arithmetic: to provide a psychological foundation for the proper concept of number (Anzahl), and to show how this concept of number functions as the mathematical foundation of universal (symbolic) arithmetic. This context establishes that Husserl's failures are ultimately rooted in the historical transformation of number documented in Klein's research, from its premodern meaning as the unity of a multitude of determinate objects to its modern meaning as a symbolic representation with no immediate relation to a concrete multiplicity. The argument is advanced that one significant result of bringing together Klein's and Husserl's thought on these issues is the need to fine-tune Husserl's project in The Crisis of European Sciences and Transcendental Phenomenology of de-sedimenting the mathematization of nature. Specifically, Klein's research shows that "a 'sedimented' understanding of numbers" "is superposed upon the first stratum of 'sedimented' geometrical 'evidences'" uncovered by Husserl's fragmentary analyses of geometry in the Crisis. In addition then to the task of "the intentional-historical reactivation of the origin of geometry," recognized by Husserl as intrinsic to the reactivation of the origin of mathematical physics, Klein discloses a second task, that of "the reactivation" of the "complicated network of sedimented significances" that "underlies the 'arithmetical' understanding of geometry."
The New Yearbook for Phenomenology and Phenomenological Philosophyprovides an annual international forum for phenomenological research in the spirit of Husserl's groundbreaking work and the extension ...of this work by such figures as Scheler, Heidegger, Sartre, Levinas, Merleau-Ponty and Gadamer.
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