Die grundlagen der arithmetik: by G. Frege. English translation by J. L. Austin. 119 pages, 14 × 22 cm. Breslau, Verlag von Wilhelm Koebner, 1884, and New York, Philosophical Library, 1950. Price, $4.75

A representational analysis of numeration systems

Review: G. H. von Wright, A Note on Deontic Logic and Derived Obligation

x ChapterI: Introduction 1-15 1.1. Background of the Problem 1 1.2. Issues of the Study Undertaken 6 1.3. Review of Literature 7 1.4. Statement of the Problem 11 1.5. Objectives of the Study 11

(An) Exploration of Subjectivity in the Phenomenology of Edmund Husserl : From Epistemic Subject to Ethical Person

One of the most stringent criticisms aimed at Husserl’s version of phenomenology comes from Stumpf himself in his posthumous book Erkenntnislehre (1939 Section 13), in which he tackles the transcendental phenomenology developed by Husserl in the first volume of Ideas Pertaining to a Pure Phenomenology and to a Phenomenological Philosophy (Ideas I). This criticism is all the more credible when one considers that the two philosophers maintained a close relationship for over fifty years and that Stumpf followed with interest the evolution of the thought of a friend who was once his student in Halle. This criticism addresses, in fact, the very principles of Husserl’s “pure” phenomenology, and we will see that it is motivated largely by the principles of what he also called phenomenology understood in its narrower sense as the field of sensory phenomena. It is clear from his discussion of Ideas I that his own motives in this criticism are as philosophical as those that led Husserl to a form of transcendental philosophy. However, since the latter broke with the philosophical program that Husserl still defended in his Logical Investigations and to which Stumpf always remained faithful (see Fisette 2009), the question raised in Erkenntnislehre concerns precisely the reasons for his emancipation from the initial program and to what extent it innovates compared to the phenomenology of the Logical Investigations understood as descriptive psychology. Stumpf basically wanted to show that this new version of phenomenology not only presupposes the essential elements of the original program (including intentionality), but where it claims to innovate in relating itself to the Kantian tradition, it espouses a philosophical cause which is one of the main targets of Brentano’s criticism.

/pdf/stumpf-and-husserl-on-phenomenology-and-descriptive-1ghp1blyqx.pdf

Stumpf and Husserl on Phenomenology and descriptive Psychology

Burt C. Hopkins, The Origin of the Logic of Symbolic Mathematics. Edmund Husserl and Jacob Klein. Bloomington and Indianapolis: Indiana University Press. 2011. 592 pp. $49.95. ISBN 978-0-253-35671-...

The Origin of the Logic of Symbolic Mathematics. Edmund Husserl and Jacob Klein

/pdf/reflections-on-the-foundations-of-mathematics-univalent-xmtn4jvbao.pdf

Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts

In his booklet ‘Contributions to a better founded presentation of mathematics’ of 1810 Bernard Bolzano made his first serious attempt to explain the notion of a rigorous proof. Although the system of logic he employed at that stage is in various respects far below the level of the achievements in his later Wissenschaftslehre, there is a striking continuity between his earlier and later work as regards the methodological constraints on rigorous proofs. This paper tries to give a perspicuous and critical account of the fragmentary logic of Beytrage, and it shows that there is a tension between that logic and Bolzano's methodological ban on ‘kind crossing’.

Strenge Beweise und das Verbot der metábasis eis állo génos

Begründungen bei Bolzano und beim frühen Husserl

The Philosophy of Arithmetic,1 Husserl’s youthful work dedicated to a philosophical, or better, epistemological foundation of mathematics, shows the shift in his interests from more properly mathematical issues to those regarding the philosophy of mathematics. Husserl strives to understand and clarify what numbers and numerical relations are, a problem that he recasts in terms of the subjective origin2 of the fundamental concepts of set theory and finite cardinal arithmetic. We will try to show that on the whole this work of Husserl’s does not deserve the criticism and ensuing neglect that it suffered from, ever since Frege published his well-known Review.3 Besides its hotly contested psychologism, we find ideas and conceptualizations that not only were original then, but are still interesting today, such as those concerning the autonomy of the formal-algorithmic aspect of abstract algebra and mathematics. Moreover, it is here that the Husserlian idea of a universal arithmetic receives its first formulation, the full elaboration of which will take at least ten more years, until his research on these topics reaches its stable form in 1901.4

Philosophy of Arithmetic

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