## Associated Products

*Logic and General Theory of Science (Book)***Title**: Logic and General Theory of Science

**Author**: Edmund Husserl

**Abstract**: This is my translation of Logik und Allgemeine Wissenschaftsheorie, a course that Husserl at gave at the Universities of Göttingen and Freiburg dealing precisely with issues of interest to what became mainstream philosophy in the United States. It will be an official publication of the Husserl Archives in Leuven, Belgium and published by Springer Verlag.

**Year**: 2016

**Access Model**: It will be a book and will probably be published electronically as well.

**Publisher**: Springer

**Type**: Translation

**Type**: Scholarly Edition

**ISBN**: Forthcoming

**Translator**: Claire Ortiz Hill

**Copy sent to NEH?**: No

*The Road Not Taken, Husserl's Philosophy of Logic and Mathematics (Book)***Title**: The Road Not Taken, Husserl's Philosophy of Logic and Mathematics

**Author**: Jairo José da Silva

**Author**: Claire Ortiz Hill

**Abstract**: For different reasons, Husserl’s original, thought-provoking ideas on the philosophy of logic and mathematics have been ignored, misunderstood, even despised, by analytic philosophers and phenomenologists alike, who have been content to barricade themselves behind walls of ideological prejudices.
Yet, for several decades, Husserl was almost continuously in close professional and personal contact with those who created, reshaped and revolutionized 20th century philosophy of mathematics, logic, science and language in both the analytic and phenomenological schools, people whom those other makers of 20th century philosophy, Russell, Frege, Wittgenstein and their followers, rarely, if ever, met. Independently of them, Husserl offered alternatives to the well-trodden paths of logicism, nominalism, formalism and intuitionism. He presented a well-articulated, thoroughly argued case for logic as an objective science, but was not philosophically naïve to the point of not seeing the role of subjectivity in shaping the sense of the reality facing objective science.
Given the preeminent role that philosophy of logic and philosophy of mathematics have played in transforming the way philosophy has been done since Husserl’s time, and given the depth of his insights and his obvious expertise in those fields, his ideas need to be integrated into present-day, mainstream philosophy. Here, philosopher Claire Ortiz Hill and mathematician-philosopher Jairo da Silva offer a wealth of interesting insights intended to subvert the many mistaken idées reçues about the development of Husserl’s thought and reestablish broken ties between it and philosophy now.

**Year**: 2013

**Primary URL**:

http://www.collegepublications.co.uk/philosophy/?00021**Primary URL Description**: Website of College Publications

**Access Model**: Book

**Publisher**: College Publications

**Type**: Multi-author monograph

**ISBN**: 9781848900998

**Copy sent to NEH?**: Yes

*"Husserlian Sets or Fregean Sets?", (Article)***Title**: "Husserlian Sets or Fregean Sets?",

**Author**: Claire Ortiz Hill

**Abstract**: Few realize that Edmund Husserl theorized about sets and the causes of the set-theoretical paradoxes. Interpreted here are his statements that: 1) the paradoxes show that his contemporaries did not yet have the real and genuine concept of set needed; 2) that if one is clear and distinct with respect to meaning, one readily sees the contradiction involved in the set-theoretical paradoxes; 3) that the solution to them would lie in demonstrating the shift in meaning that makes it that one is not immediately aware of the contradiction and once it is perceived it one cannot indicate wherein it lies. I study these convictions in connection with Frege’s and Russell’s ideas about sets and the conclusions that they came to regarding the causes of the paradoxes derivable within Frege’s system.

**Year**: 2013

**Primary URL**:

http://gcfcf.com.br/pt/files/2013/07/Hill-Claire-Ortiz-NPSF-vol.2-n.1.pdf**Primary URL Description**: Notae Philosophicae Scientiae Formalis, vol. 2, n. 1, p. 22 - 32, maio 2013, online

**Access Model**: Open access

**Format**: Journal

**Periodical Title**: Notae Philosophicae Scientiae Formalis

**Publisher**: Notae Philosophicae Scientiae Formalis

*"The Strange Worlds of Actual Consciousness and the Purely Logical" (Article)***Title**: "The Strange Worlds of Actual Consciousness and the Purely Logical"

**Author**: Claire Ortiz Hill

**Abstract**: Husserl strove until the end of his life to find solutions to puzzles about the interrelation and intrinsic unity of the “strange” worlds of the purely logical and actual consciousness. Here, I situate the analyses of the subjective foundations of the part of formal logic to which Experience and Judgment is devoted on the map of those worlds that can be pieced together from his writings. I say that one must have a firm grasp on his theories about what belonged in those worlds, and in the different parts of them, in order to keep from ascribing ideas to him against which he strenuously militated. I further contend that his theories about the structure of the world of pure logic may be of great significance for philosophy of logic and mathematics now.

**Year**: 2013

**Primary URL**:

https://www.routledge.com/The-New-Yearbook-for-Phenomenology-and-Phenomenological-Philosophy-Volume/Hopkins-Drummond/p/book/9781138819900**Primary URL Description**: Routledge website

**Access Model**: It is a journal published in the form of a book

**Format**: Journal

**Periodical Title**: New Yearbook for Phenomenology and Phenomenological Philosophy

**Publisher**: Routledge

*"Husserl's Way Out of Frege's Jungle" (Book Section)***Title**: "Husserl's Way Out of Frege's Jungle"

**Author**: Claire Ortiz Hill

**Editor**: Denis Seron

**Editor**: Bruno Leclercq

**Editor**: Sébastien Richard

**Abstract**: Influential twentieth-century philosophers and mathematicians turned philosophers leapt upon new theories of representation, meaning, judgment, arithmetic and sets elaborated during the late 19th century to remodel, if not all together eliminate, many traditional ideas about what Bertrand Russell once colorfully called the ultimate furniture of the universe. One of the principal strategies adopted by Russell, Rudolf Carnap, Willard Van Orman Quine and like-minded philosophers was to use logic to throw out the old furniture and replace it with new furniture of their liking. The full implications of those new theories about the ultimate structure of reality have yet to be drawn because, for many reasons, many avenues of research have yet to be pursued. Here, I wish to add new dimensions to standard discussions by looking at the ontological implications for analytic philosophy of Edmund Husserl’s theory that numbers and sets function in an entirely different way in the sphere of propositions and states of affairs than in arithmetic and in set theory

**Year**: 2015

**Primary URL**:

http://www.degruyter.com/view/product/448621**Primary URL Description**: Publisher's website

**Access Model**: Book

**Publisher**: de Gruyter

**Book Title**: Objects and Pseudo-Objects Ontological Deserts and Jungles from Brentano to Carnap

**ISBN**: 978-1-5015-013

*"Husserl and Frege on Functions," (Book Section)***Title**: "Husserl and Frege on Functions,"

**Author**: Claire Ortiz Hill

**Editor**: Guillermo E. Rosado Haddock

**Abstract**: Groundwork is lain for answering questions as to how to situate Husserl’s theory of functions in relation to Frege’s. I examine Husserl’s ideas about analyticity and mathematics, logic and mathematics, formalization, calculating with concepts and propositions, the foundations of arithmetic, extensions to show that, although he knew, studied and lauded Frege’s ideas about functions and concepts, each man approached the issues from different angles. Seduced by the siren of transcendental phenomenology Husserl did not pursue the issues, implications, and consequences of his ideas about functions. I ask whether so doing could provide new insight into, or even solutions to, the problems involving functions that beset Frege, Russell and have beset their successors.

**Year**: 2016

**Primary URL**:

http://www.degruyter.com/view/product/476718?rskey=uhUD4u&result=1**Primary URL Description**: Publisher's website

**Access Model**: Hardback and e-book, not open access

**Publisher**: de Gruyter

**Book Title**: Husserl and Analytic Philosophy

**ISBN**: 978-3-11-04973

*"Limning the True and Ultimate Structure of Reality" (Book Section)***Title**: "Limning the True and Ultimate Structure of Reality"

**Author**: Claire Ortiz Hill

**Editor**: Paul Hackett

**Abstract**: for a number of reasons, Husserl’s strategy for keeping knowledge of reality from collapsing into a formless blob of facts became buried in all the excitement, both positive and negative, generated by his transcendental phenomenology, and so its implications for logic and philosophy nowadays have barely been explored. Fortunately though, since the 1980s, the Husserl Archives has been publishing the material we need to recuperate Husserl’s blueprint for discovering the underlying objective structure of reality as he saw and conveyed it. I endeavor to outline Husserl’s prescription for finding clarity with respect to the central traits of reality. In particular, I seek to disinter the parts and members of the categorial skeleton designed by Husserl to uphold knowledge in a way that stands in sharp contrast to the logical point of view that has underpropped phenomenology’s rival school of thought, analytic philosophy, of which Quine was one of the foremost exponents.

**Year**: 2017

**Primary URL Description**: Forthcoming

**Access Model**: Book

**Publisher**: Lexington Books

**Book Title**: Mereologies, Ontologies, and Facets: The Categorical Structure of Reality

**ISBN**: Forthcoming

*Husserl and Cantor (Book Section)***Title**: Husserl and Cantor

**Author**: Claire Ortiz Hill

**Editor**: Stefana Centrone

**Abstract**: Husserl and Cantor were colleagues and close friends during the last fourteen years of the 19th century, when Cantor was at the height of his creative powers and Husserl in the throes of an intellectual struggle during which he drew apart from people and writings to whom he owed most of his intellectual training and drew closer to the ideas of thinkers whose writings he had not been able to evaluate properly and had consulted too little. I study ways in which Husserl and Cantor might be said to have been alike, while pointing to dissimilarities between them. In particular, I discuss how their ideas overlapped and crisscrossed with regard to mathematics and philosophy, Platonic idealism, abstraction, empiricism, psychologism, actual consciousness and pure logic, Frege’s reviews of their works, metaphysics and mysticism, sets, arithmetization, strange and imaginary numbers and manifolds. I conclude that Cantor was among those of his mentors from whose ideas Husserl drew away and Lotze and Bolzano were among those to whose ideas he drew closer.

**Year**: 2017

**Access Model**: Book

**Publisher**: Springer

**Book Title**: Essays on Husserl's Logic and Philosophy of Mathematics

**ISBN**: Forthcoming

*"Husserlian Sets or Fregean Sets?", (Conference Paper/Presentation)***Title**: "Husserlian Sets or Fregean Sets?",

**Author**: Claire Ortiz Hill

**Abstract**: Few realize that Edmund Husserl theorized about sets and the causes of the set-theoretical paradoxes. Here I interpret his statements that: 1) the paradoxes show that his contemporaries did not yet have the real and genuine concept of set needed; 2) that if one is clear and distinct with respect to meaning, one readily sees the contradiction involved in the set-theoretical paradoxes; 3) that the solution to them would lie in demonstrating the shift of meaning that makes it that one is not immediately aware of the contradiction and that once one perceives it one cannot indicate wherein it lies. I study these convictions in connection with Frege’s and Russell’s ideas about sets and the conclusions that they came to regarding the causes of the paradoxes derivable within Frege’s system.

**Date**: 11/09/2012

**Primary URL**:

http://w3.ufsm.br/filosofia/?p=2498**Primary URL Description**: Conference website

**Conference Name**: XVI Coloquio Conesul de Filosofia das Ciencias Formais, Teoria dos Conjuntos/Mereologia

*"Husserl on Sets and the Causes of the Set-theoretical Paradoxes," (Article)***Title**: "Husserl on Sets and the Causes of the Set-theoretical Paradoxes,"

**Author**: Claire Ortiz Hill

**Abstract**: Abstract. Few realize that Edmund Husserl theorized about sets and the causes of the set-theoretical paradoxes. Interpreted here are his statements that: 1) the paradoxes show that his contemporaries did not yet have the real and genuine concept of set needed; 2) that if one is clear and distinct with respect to meaning, one readily sees the contradiction involved in the set-theoretical paradoxes; 3) that the solution to them would lie in demonstrating the shift in meaning that makes it that one is not immediately aware of the contradiction and once it is perceived it one cannot indicate wherein it lies. I study these convictions in connection with Frege’s and Russell’s ideas about sets and the conclusions that they came to regarding the causes of the paradoxes derivable within Frege’s system.

**Year**: 2019

**Format**: Journal

**Periodical Title**: Meta: Research in Hermeneutics, Phenomenology, and Practical Philosophy Vol. XI, no. 2, December 2019

*"Husserl's Purely Logical Chastity Belt," (Book Section)***Title**: "Husserl's Purely Logical Chastity Belt,"

**Author**: Claire Ortiz Hill

**Editor**: Christina Weiss

**Abstract**: What follows is about Husserl, whose phenomenology, I believe, can be understood as a form of constructivism. However, I generally write about Husserl’s philosophy of logic and mathematics, which he repeatedly said had nothing to do with transcendental phenomenology. So, my aim here is to discuss some things that I believe people interested in constructivism and Husserl’s transcendental phenomenology need to keep in mind. I say that, despite appearances, phenomenology was not everything for Husserl. As much as he loved it, he placed definite limits on what one should do with it and believed that it required an objective complement in the form of pure logic, that it had to be subject to a priori laws to keep phenomenologists from falling into psychologism, naturalism, empiricism, relativism and associated evils. According to this interpretation, Husserl the possible constructivist, Husserl the phenomenologist, Husserl the Platonist, Husserl the realist, Husserl the idealist were one and the same person from the late 1890s until his death, something which is particularly well expressed in the volumes of his lecture courses published since the 1980s, which shed considerable light on his thought.

**Year**: 2019

**Publisher**: Springer Nature Switzerland, 2019,

**Book Title**: Constructive Semantics, Meaning in Between Phenomenology and Constructivism

*"Hilbert's Fight for Philosophy" (Book Section)***Title**: "Hilbert's Fight for Philosophy"

**Author**: Claire Ortiz Hill

**Editor**: Iulian Apostolescu

**Abstract**: Abstract: For Hilbert, mathematics was connected to philosophy by the deepest fibres of its being. He acted on several fronts to keep philosophical concerns alive in mathematical circles and to tear down walls separating the concerns of philosophically-minded mathematicians and mathematically-minded philosophers. This is a contribution to integrating Hilbert’s ideas as found in unpublished and published writings into the philosophical discussions where they belong in order to bring important issues back into focus and open new avenues in philosophy, because philosophers are still trying to solve problems that have their roots in problems that have remain unsolved since his time. I study his fight for the philosophers Edmund Husserl and Leonard Nelson. Then I set out what Hilbert called the basic philosophical position and look at his views on theory of knowledge, experience, pure thought, finitism, the axiomatic method, the a priori, the ideal, pre-established harmony, a priori intuition, truth, logical consistency and existence, and his avowed Kantianism.

**Year**: 2021

**Publisher**: Springer

**Book Title**: Husserl and Awakened Reason: Critical Essays on Mathematics, Science and Phenomenology

**ISBN**: Forthcoming

*"Husserl and Frege on Imaginaries and the Deep Nature of Things" (Article)***Title**: "Husserl and Frege on Imaginaries and the Deep Nature of Things"

**Author**: Claire Ortiz Hill

**Abstract**: The efforts of mathematicians turned philosophers to find secure foundations for arithmetic during the last years of the 19th century and the first years of the last century ended up determining the uncompromisingly different courses that Analytic philosophy and continental philosophy subsequently pursued. In particular, it is not too much to say that, the very different ways in which Edmund Husserl and Gottlob Frege responded to perplexing questions about the ways in which mathematicians use “imaginaries” ‒ a broad heading stretched to include negative, irrational, complex numbers and transfinite numbers, fractions, negative square roots, imaginary classes and domains, the null class, infinite sets, the actual infinite… ‒ played a key role in determining the future of their own work and so that of their successors. Here I wish to defend that claim.

**Year**: 2022

**Format**: Journal

**Periodical Title**: Rivista di Filosofia, Forthcoming

*"Spencer-Brown's Laws of Form and Husserl's Strange World of the Purely Logical" (Conference Paper/Presentation)***Title**: "Spencer-Brown's Laws of Form and Husserl's Strange World of the Purely Logical"

**Author**: Claire Ortiz Hill

**Abstract**: I suggest some connections between Laws of Form and what Husserl called the "strange world of the purely logical." Specifically, I talk about: Husserl's background, especially as a mathematician, and his use of symbolic notation. Then, I compare his and Spencer-Brown's views on: the relationship between mathematics and logic, mentioning Boole; the fundamental particles from which numbers can be made; the structure of knowledge of the universe, especially Husserl's theory of manifolds; imaginary entities; Russell's theory of types. For lack of time, I only mention Spencer-Brown's and Russell's exchange on propositional functions and Husserl's theories about them.

**Date**: 08/04/2022

**Conference Name**: Laws of Form Conference 2022 held at Liverpool University