Most areas of philosopher Edmund Husserl’s thought have been explored, but his views on logic, mathematics, and semantics have been largely ignored. These essays offer an alternative to discussions of the philosophy of contemporary mathematics. The book covers areas of disagreement between Husserl and Gottlob Frege, the father of analytical philosophy, and explores new perspectives seen in their work.

Frege's semantics of sense and reference and two husserlian alternatives are discussed. it is shown that husserl neither took his semantics of sense and reference from frege nor abandoned psychologism under his influence. frege's arguments on behalf of his choice of truth values as the reference of statements and of concepts as the reference of conceptual words are submitted to criticism. some algebraic considerations are sketched in the last part of the article.

Examining the scholarly interest of the last two decades in the origins of logical empiricism, and especially the roots of Rudolf Carnap's Der logische Aufbau der Welt, Rosado Haddock challenges the received view, according to which that book should be inserted in the empiricist tradition.

Quine’s criticism of the notion of analyticity applies, at best, to Carnap’s notion, not to those of Frege or Husserl. The failure of logicism is also the failure of Frege’s definition of analyticity, but it does not even touch Husserl’s views, which are based on logical form. However, some relatively concrete number-theoretic statements do not admit such a formalization salva veritate. A new definition of analyticity based not on syntactical but on semantical logical form is proposed and argued for.

Guillermo E. Rosado Haddock, ed. Husserl and Analytic Philosophy. Berlin/Boston: Walter de Gruyter GmbH, 2016. ISBN 978-3-11-049655-0 ; 978-3-11-049737-3 ; 978-3-11-049418-1. Pp. viii + 338.

Analytic philosophy has been the most influential philosophical movement in 20th century philosophy. It has surely contributed like no other movement to the elucidation and demarcation of philosophical problems. Nonetheless, the empiricist and sometimes even nominalist convictions of orthodox analytic philosophers have served them to inadequately render even philosophers they consider their own and to propound very questionable conceptions.

Gottlob Frege is one of the greatest logicians ever and also a philosopher of great significance. In this book Rosado Haddock offers a critical presentation of the main topics of Frege's philosophy, including, among others, his philosophy of arithmetic, his sense-referent distinction, his distinction between function and object, and his criticisms of formalism and psychologism. More than just an introduction to Frege's philosophy this book is also a highly critical and mature assessment of it as a whole in (...) which the limitations, confusions and other weaknesses of Frege's thought are closely examined. The author is also a Husserlian scholar and this book contains valuable discussions of Husserl's neglected views and comparisons between the two great philosophers. (shrink)

This paper discusses Husserl’s views on physical theories in the first volume of his Logical Investigations, and compares them with those of his contemporaries Pierre Duhem and Henri Poincaré. Poincaré’s views serve as a bridge to a discussion of Husserl’s almost unknown views on physical geometry from about 1890 on, which in comparison even with Poincaré’s—not to say Frege’s—or almost any other philosopher of his time, represented a rupture with the philosophical tradition and were much more in tune with the (...) physical geometry underlying the Einstein-Hilbert general theory of relativity developed more than two decades later. (shrink)

Husserl's contributions to the nature of mathematical knowledge are opposed to the naturalist, empiricist and pragmatist tendences that are nowadays dominant. It is claimed that mainstream tendences fail to distinguish the historical problem of the origin and evolution of mathematical knowledge from the epistemological problem of how is it that we have access to mathematical knowledge.

In this paper six of the most important issues in the philosophy of logic are examined from a standpoint that rejects the First Commandment of empiricist analytic philosophy, namely, Ockham’s razor. Such a standpoint opens the door to the clarification of such fundamental issues and to possible new solutions to each of them.

This paper is concerned with the use of logic to solve philosophical problems. Such use of logic goes counter to the prevailing empiricist tradition in analytic circles. Specifically, model-theoretic tools are applied to three fundamental issues in the philosophy of logic and mathematics, namely, to the issue of the existence of mathematical entities, to the dispute between first- and second-order logic and to the definition of analyticity.

This paper offers an exposition of Husserl's mature philosophy of mathematics, expounded for the first time in Logische Untersuchungen and maintained without any essential change throughout the rest of his life. It is shown that Husserl's views on mathematics were strongly influenced by Riemann, and had clear affinities with the much later Bourbaki school.

The present collection of seventeen papers, most of them already published in international philosophical journals, deals both with issues in the philosophy of logic, the philosophy of mathematics, the philosophy of language and epistemology. The first part contains critical assessments and somewhat deviant renderings of the work of two seminal philosophers, Frege and Husserl, as well as of the young Carnap and Kripke. The second part contains analyses of central issues in the philosophy of logic, the philosophy of mathematics and (...) semantics, including arguments on behalf of Platonism in the philosophy of mathematics, a defense of second-order logic, a new definition of analyticity, a sketch of a semantics for mathematical statements and a critique of Kripke s possible world semantics for modal logic.". (shrink)

Matthias Schirn (ed.), Frege:Importance and Legacy, Berlin, Walter De Gruyter, 1996, viii + 466pp.

In this critical study of the valuable collection of essays edited by Cirera, Ibarra and Mormann, the present author not only critically assesses the different renderings of Carnap’s writings propounded by the different authors therein represented, but also sketches his own interpretation and subjects to criticism some of the presumed consequences of the demise of logical empiricism.

Quine’s criticism of the notion of analyticity applies, at best, to Carnap’s notion, not to those of Frege or Husserl. The failure of logicism is also the failure of Frege’s definition of analyticity, but it does not even touch Husserl’s views, which are based on logical form. However, some relatively concrete number-theoretic statements do not admit such a formalization salva veritate. A new definition of analyticity based not on syntactical but on semantical logical form is proposed and argued for.

There is a lot of misunderstanding and ignorance about Husserl’s philosophy among analytic philosophers. The present paper attempts to help correct that situation. It begins with some quotations of Husserl written around 1890, which clearly establish that he arrived at the distinction between sense and reference with independence from Frege. Then follows a brief survey of the most important themes of Husserl’s Logical Investigations, emphazising those that are of special interest to analytic philosophers. The paper concludes by mentioning other interesting (...) issues treated in later Husserlian writings, including his valuable conferences on ancient and modern logic from 1908-1909.Existen muchos malentendidos y mucha ignorancia acerca de la filosofía de Husserl entre los filósofos analíticos. El presente artículo intenta contribuir a corregir esa situacion. Él comienza con algunas citas de Husserl de aproximadamente 1890, que claramente establecen que Husserl obtuvo la distinción entre sentido y referente con independenica de Frege. Luego sigue un breve recuento de los más importantes temas de las Investigaciones Lógicas de Husserl, destacando aquéllos que son de particular interés para los filósofos analíticos. El artículo concluye haciendo référencia a otros temas tratados en escritos posteriores de Husserl, incluyendo sus valiosas conferencias acerca de lógica antigua y moderna de 1908-1909. (shrink)

Frege had not one but two different notions of sense, namely, that of ?Über Sinn und Bedeutung? and one implicit in a letter to Husserl of 1906 and elsewhere. This last one originates in Frege's notion of conceptual content. The distinction is used to clarify some obscurities in Frege's thought. In the last section a sort of ?explicans? of Frege's notion of conceptual content is introduced and applied to the semantic analysis of mathematics.

Matthias Schirn (ed.), Frege:Importance and Legacy, Berlin, Walter De Gruyter, 1996, viii + 466pp.

This paper discusses Husserl’s views on physical theories in the first volume of his Logical Investigations , and compares them with those of his contemporaries Pierre Duhem and Henri Poincaré. Poincaré’s views serve as a bridge to a discussion of Husserl’s almost unknown views on physical geometry from about 1890 on, which in comparison even with Poincaré’s—not to say Frege’s—or almost any other philosopher of his time, represented a rupture with the philosophical tradition and were much more in tune with (...) the physical geometry underlying the Einstein-Hilbert general theory of relativity developed more than two decades later. (shrink)

Guillermo E. Rosado Haddock. A Critical Introduction to the Philosophy of Gottlob Frege. Aldershot, Hampshire, and Burlington, Vermont: Ashgate Publishing, 2006. ISBN 978-0-7546-5471-1. Pp. x+157.

Guillermo E. Rosado Haddock's critical introduction to the philosophy of Gottlob Frege is based on twenty-five years of teaching Frege's philosophy at the University of Puerto Rico. It developed from an earlier publication by Rosado Haddock on Frege's philosophy which was, however, available only in Spanish. This introduction to Frege is meant to steer a path between the two main approaches to Frege studies: on the one hand, we have interpretations of Frege which portray him (...) as a neo-Kantian and thus as some kind of idealist; on the other, we have writings like those of Dummett in which Frege is portrayed as a type of ‘philosophical Adam’, i.e., as completely separated from his philosophical tradition. Rosado Haddock succeeds in placing Frege's thinking into a broader philosophical context — mainly by reference to his contemporary Edmund Husserl — while also avoiding a Kantian reading of Frege's work.The structure of the book follows Frege's writing chronologically. In this way, Rosado Haddock leads the reader through the whole of Frege's philosophy while highlighting important changes and developments in Frege's thought from the Begriffsschrift to his Grundgesetze and other later writings. Chapter 1 introduces us to the core philosophical themes of Frege's Begriffsschrift with a special emphasis on Frege's notions of ‘conceptual content’ and ‘judgeable content’. Here, Rosado Haddock anticipates further discussion and points towards changes and developments of Frege's core notions of ‘identity’, ‘function’, and ‘content’. Chapters 2 and 3 focus on Frege's Grundlagen der Arithmetik. Chapter 2 discusses Frege's methodological principles as outlined in Frege's introduction and his criticisms of psychological, naturalistic, and Kantian approaches to the philosophy of mathematics. Chapter 3 focuses exclusively on Frege's own logicist account of arithmetic while emphasizing differences between Frege's views and Kantian …. (shrink)