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Appendix A:
Demystifying the Fregean and Psychological Husserl

A.1 - Biographical Misconceptions
A.2 - Frege's Semantic Theory Compared to Husserl's
A.3 - Frege's and Husserl's Philosophies of Mathematics

A.1 - Biographical Misconceptions

    At the very beginning of writing the book, I did not wish to include this appendix, but I was very surprised to see how very well rooted are the myths against Edmund Husserl, and how deep the rejection of his doctrine in the analytic tradition has been.¹⁵⁷

    My use of Husserl's philosophy of logic and mathematics as a starting point to clarify the relation between formal sciences and natural sciences would surprise many philosophers. Most analytic philosophers completely ignore Husserl's philosophy of mathematics, even if it is, perhaps, the one that best describes mathematics in the twenty-first century. Even in the case of mathematicians, they regard Gottlob Frege as being far superior to Edmund Husserl and much more worthy of recognition.

    I want to explain briefly why this is so in the analytic world. First, there is an unfounded myth that began with Dagfinn Føllesdal's master's thesis: Husserl and Frege: A Contribution to Elucidating the Origins of Phenomenological Philosophy and his article “Husserl's Notion of Noema”, where he says that at first Husserl began favoring psychologism, and from that perspective he wrote his Philosophy of Arithmetic (1891). Later, he changed his mind due to Frege's review against this work (Frege, 1894/1972). The myth further states that Husserl became a kind of fregean semanticist and that his phenomenological notions (like the notions of noema and object (Gegenstand)) are nothing more than an extension of the fregean distinction between sense (Sinn) and referent (Bedeutung). And as if that were not enough, many other authors accuse Husserl of falling into the claws of psychologism once again.

    None of this is true. As it turns out, apparently Frege's review of Husserl's Philosophy of Arithmetic had nothing to do with him changing his mind. As some studies have shown, some of Frege's criticisms were valid, but others were not. He exaggerated Husserl's position to the point of caricaturing it. Many authors consider Frege's criticism against Husserl's notion of abstraction as accurate, when in reality Husserl did not favor the silly assertions Frege accused him of saying.¹⁵⁸  It is possible that Frege's attack was not directed exclusively to Husserl, but to Georg Cantor, who was Husserl's close friend, colleague, and mentor, who, like Husserl, was also a disciple of the renowned mathematician Karl Weierstrass, whom Frege opposed.¹⁵⁹  Frege would charge Cantor exactly with the same errors he charged Husserl with.¹⁶⁰

    The myth that Husserl adopted fregean semantics after the famous fregean review (1894) is also false. Husserl already had his own theory of sense (meaning) and referent (objectuality) by 1890. We can accept that Philosophy of Arithmetic was published in 1891, but that only means it was published that year. He finished writing it in 1890. So, Philosophy of Arithmetic represents his thinking on mathematics up to 1890. J. N. Mohanty also offers this information:


    It was Frege, in a letter addressed to Husserl (May 24, 1891), who recognized that he made a distinction between sense and referent, and he (Frege) compares correctly both theories of sense and referent of concept words. Husserl himself recognized that by the time Philosophy of Arithmetic was published, he already disagreed with its content. He says that he began having doubts about psychologism from the very beginning. He attributes his change from psychologism to his reading of Gottfried Wilhelm von Leibniz, Bernard Bolzano, Rudolf Hermann Lotze, and David Hume. He makes no mention of Frege as being decisive for the change.¹⁶²  In fact, in his Logical Investigations Husserl mentions Frege only twice: the first one in a footnote to point out that he retracted three pages of his criticism of Frege's The Foundations of Arithmetic,¹⁶³ and the other one to question his use of the word “Bedeutung” to denote referent rather than meaning (sense).¹⁶⁴

    Finally, contrary to what many people think, Husserl did not fall again into psychologism. He maintained basically the core of the criticism against psychologism made in the “Prolegomena” throughout his life, and we can find some of them in works as late as Formal and Transcendental Logic (1929). That accusation usually is the product of a misunderstanding between husserlian semantics and his phenomenological doctrine.  But even the ideal realm plays a very important role in phenomenology, noemata are the irreal (ideal) necessary correlates of real noetic acts of consciousness.

    Another reason why some philosophers do not know about Husserl's doctrine of formal sciences has to do with the fact that many phenomenologists have not paid attention at all to it, either because they do not know it, or because they are not acquainted enough with logic and mathematics to notice it. They mostly focus on Husserl's phenomenological doctrine in general as well as his doctrine of the crisis of the European sciences.

    There are also those husserlian scholars who make some distorted expositions of Husserl's philosophy of mathematics. For example, some authorities in this area give the impression that Husserl said that using eidetic intuition and eidetic variation we are able to abstract numbers, sets, etc. This is false. For Husserl, as we have seen in Chapter 2, numbers and sets are constituted by consciousness through categorial intuition. I do agree with Rosado (1997) that not to mention categorial intuition in Husserl's philosophy of mathematics would be like trying to explain newtonian mechanics without mentioning the three laws of motion.¹⁶⁵ Others confuse categorial intuition and eidetic intuition, leading to confusing notions of state-of-affairs and situation-of-affairs, therefore, unable to understand mathematical intuition as being categorial intuition and categorial abstraction.¹⁶⁶

    Up to now, we have presented most of the reasons why people have dismissed Husserl's philosophy of logic and mathematics. So, to finish exorcising some philosophers' image of Husserl, I will present his background in mathematics and philosophy of mathematics.

1.  While Husserl was a student at the University of Berlin, he studied with great mathematicians such as Leopold Kronecker and Karl Weierstrass (1878-1881). Later, Husserl became Weierstrass' assistant (1883-1884).¹⁶⁷

2.  After being Franz Brentano's disciple (1884-1886), he went to the University of Halle, where he was under the supervision of Carl Stumpf, who was also Brentano's disciple and to whom Husserl later dedicated his Logical Investigations. Claire Ortiz Hill points out that it was through Carl Stumpf that he increasingly became interested in platonic ideas and led him away from Brentano's philosophy.¹⁶⁸ Stumpf was the one who convinced Gottlob Frege to elaborate a philosophy to clear up the purpose of his recently created conceptual notation (Begriffsschrift), which led Frege to write his philosophical masterpiece The Foundations of Arithmetic.¹⁶⁹

3.  It was during his years in Halle where he befriended Georg Cantor, the father of set theory, who would become his mentor (1886-1901).¹⁷⁰

4.  Husserl's first philosophical works were precisely about mathematics. In Halle, he presented his professorship doctoral dissertation On the Concept of Number about the psychological origins of sets and numbers, and later in 1891 he published his Philosophy of Arithmetic: Psychological and Logical Investigations. We also have to take into account the first volume of Logical Investigations titled “Prolegomena of Pure Logic” where Husserl exposes his definitive doctrine on logic and mathematics. In all of these works he was concerned about logic and mathematics, and he wanted to develop a proper epistemology.

5.  He revealed Franz Brentano in 1892 that he had already concluded that non-euclidean geometry was as legitimate as euclidean geometry. For him, space does not need to be euclidean space to be consistent, and that there could be many other a priori possible spaces. This happened years before the general theory of relativity legitimized the use of non-euclidean geometry in natural science.¹⁷¹

6.  Later, when Husserl went to the University of Götingen, he was a colleague of David Hilbert, the great mathematician who was looking for a definitive proof of the completeness of mathematics. He also believed in such completeness, and formed part of Hilbert's Circle (1901-1916).¹⁷²

7.  Husserl was deeply interested in the paradoxes of set theory. Ernst Zermelo, a mathematician known for his works on set theory, was Husserl's friend. Zermelo found a paradox and in 1902 communicated it to Husserl and Hilbert. The reason for this is that Husserl had discussed a similar paradox in a review he wrote in 1891. Bertrand Russell also found this very same paradox and told Frege that his logical foundation of arithmetic as presented in Basic Laws of Arithmetic made this paradox possible. This is the reason why the world knows it as the “Russell Paradox”, even though Zermelo found it first. Here we will call it the “Zermelo-Russell Paradox”. Many of Husserl's works on set paradoxes (which are hundreds of pages) still remain unpublished.¹⁷³

8.  Even in later works such as Formal and Transcendental Logic (1929) and Experience and Judgment (1938), Husserl elaborated his semantic theory and his philosophy of mathematics in its final form.

9.  Apparently Husserl contributed to the field of logic more than analytic philosophers realize. For example, some suspect that the difference between the “formation rules” and the “transformation rules” proposed by Rudolf Carnap, was originally proposed by Husserl, but with different names (“laws to prevent non-sense” and “laws to prevent counter-sense”).¹⁷⁴  We must remember that Carnap, in his Der Raum includes much of Husserl's thinking in his philosophy of space, and that between 1924 and 1925 he assisted advanced seminars given by Husserl for three semesters.¹⁷⁵  We also have to remember that Husserl influenced some Polish thinkers such as Alfred Tarski and Stanislaw Leśniewski, the founder of mereology. Leśniewski's studies of Husserl's Logical Investigations (specifically the Third Investigation, often disregarded by Husserl's scholars and analytic philosophers) made him interested in developing a theory of parts and wholes.

A.2 - Frege's Semantic Theory Compared to Husserl's

    We talked in Chapter 1 and 2 about Husserl's conceptions of propositions, states-of-affairs, and situation-of-affairs. This subject has been explored thoroughly by J. N. Mohanty, Claire Ortiz Hill, and especially Rosado Haddock, who has written extensive articles about this specific subject. Here I will not present anything new, just a scheme to compare both semantic doctrines. To illustrate their differences, I am going to use Table 10, 11 and 12.

Semantic Notion	Gottlob Frege	Edmund Husserl
Sign	Proper Name	Proper Name
Sense	Sense of Proper Name	Sense of Proper Name
Referent	Object	Object

    Another frequent point of dispute is that many believe that Frege's view of logic and mathematics is far superior to Husserl's. If we remember Frege's original project, he was solely interested in showing that arithmetic could be reduced to logic. We all know the outcome of his work, the Zermelo-Russell Paradox practically destroyed all the logical building which could derive arithmetic from logic. Even other projects like that of A. N. Whitehead and Bertrand Russell, who tried to show in Principia Mathematica that all of mathematics could be reduced to logic, failed miserably, especially after Kurt Gödel's proof of mathematics' incompleteness.

    Husserl, on the other hand, did not hold this point of view. As we have seen in Chapter 1, he did see mathematics as logic's ontological correlate, but the former is not reducible to the latter. He even held that some formal-ontological categories cannot be reduced to other formal-ontological categories. For example, he did not accept the reducibility of arithmetic to set theory. Every effort to try to provide a foundation of mathematics on logic has failed. It seems that Husserl was right after all.

    An interesting point of comparison of both of their doctrines has to do with non-euclidean geometry and other mathematical notions. Frege, did not accept non-euclidean geometry as a legitimate mathematical enterprise. Husserl was more careful than that. His idea of a mathesis universalis as theory of manifolds did allow the mathematical truths of non-euclidean geometries as well as the scientificity of what he called then “imaginary numbers” (negative roots, fractions, irrational numbers, decimals, among many others).¹⁸¹

    Another point of advantage of Husserl's views with respect to Frege's is that his philosophy of mathematics and mathematical epistemology are able to overcome the paradoxes of naïve set theory. Frege's logicism collapsed because of the Zermelo-Russell Paradox. However, in Experience and Judgment, Husserl uses sets as examples of objectual categorial acts, and, as we have seen in Chapter 2, in principle a new set can always be constituted on top of other ones. Rosado (in Hill & Rosado, 2000) has pointed out the way this hierarchy of objectualities practically blocks the paradoxes of naïve set theory. For example, the fact that in principle every set can be constituted on another set and that there is a hierarchy blocks the possibility of a set of all sets. This prevents the Cantor Paradox from happening. The hierarchical aspect of objectual acts also blocks the Zermelo-Russell Paradox, since we cannot form sets which are elements of themselves.¹⁸²

    And last, but not least, Husserl's view of mathematics has provided perhaps the only platonist epistemology that can be explained naturally. Unfortunately, Frege could not provide such an epistemology, he was content only with grasping thoughts and senses, but nothing more than that.

    Frege made many contributions to the fields of logic and mathematics, but the truth is that Husserl not only contributed to them, but also his view of them is extremely close to the way they are developed in the twenty-first centuries.



Footnotes:

¹⁵⁷For a more thorough study on this subject, and a full demystification of wrong conceptions about Husserl see: Hill, 1991; Hill & Rosado, 2000; Bernet, Kern & Marbach, 1999, pp. 13-57; Mohanty, 1974, 1982b; Hintikka, 1995, pp. 78-105; and Rosado, 2008b.  [Return to Text]

¹⁵⁸Coffa, 1998, pp. 68-69; Frege, 1894/1972, pp. 323-330; Hill, 1991, pp. 14-16, 58-62, 66-70, 71-86. [Return to Text]

¹⁵⁹Hill & Rosado, 2000, pp. 96-97.  [Return to Text]

¹⁶⁰Hill & Rosado, 2000, p. 98.  [Return to Text]

¹⁶¹Mohanty, 1974, pp. 22-23.  [Return to Text]

¹⁶²Hill, 1991, pp. 16-17.  [Return to Text]

¹⁶³Notice that it is only three pages, not eight as the typographical mistake of the old English edition seems to imply. This typographical mistake, unfortunately has fueled the myth about Husserl being dramatically changed by Frege. In reality, Husserl leaves most of his criticism to Frege intact after his turn from psychologism (see LI. Vol I. §46; see also Hill & Rosado, 2000, pp. 4-5).  [Return to Text]

¹⁶⁴LI. Vol. II. Inv. I. §15.  [Return to Text]

¹⁶⁵Tieszen (1995) seems to fall in this kind of error. See also Rosado, 1997, pp. 387-395.  [Return to Text]

¹⁶⁶Moran (2000) makes an excellent summary of Husserl's phenomenological doctrine, but his exposition has many flaws, among them the confusion between categorial intuition and eidetic intuition (see pp. 119-120), and he also confuses the concepts of state-of-affairs and situation-of-affairs (p. 112). In Logical Investigations eidetic intuition appears as just one among other kinds of categorial intuitions.(LI. Vol. II. Inv. VI. §52) However, in his later works, there is a qualitative difference between both intuitions (I. §§3-4).  [Return to Text]

¹⁶⁷Hill & Rosado, 2000, p. xi; Verlade, 2000, p. 3.  [Return to Text]

¹⁶⁸Hill, 1991, p. 17.  [Return to Text]

¹⁶⁹Hill & Rosado, 2000, p. 3.  [Return to Text]

¹⁷⁰Hill & Rosado, 2000, p. xi.  [Return to Text]

¹⁷¹Rosado, 2008b, p. 31.  [Return to Text]

¹⁷²Hill & Rosado, 2000, p. xi.  [Return to Text]

¹⁷³Hill, 1991, pp. 2-3.  [Return to Text]

¹⁷⁴Hill & Rosado, 2000, p. 203.  [Return to Text]

¹⁷⁵Friedman, 1999, pp. 46-48; Hill & Rosado, 2000, pp. 202-203.  [Return to Text]

¹⁷⁶SR. p. 32.  [Return to Text]

¹⁷⁷LI. Vol. II. Inv. I. §12. It is very interesting that in a letter to P. Linke, Frege borrowed Husserl's example and changes it a bit so he can explain his notion of the sense of proper names: “the loser of Waterloo” and “the victor of Austerlitz” (Hill, 1991, pp. 93-94). [Return to Text]

¹⁷⁸LI. Vol. II. Inv. I. §12.  [Return to Text]

¹⁷⁹See Rosado's article “On Frege's Two Notions of Sense” in Hill & Rosado, 2000, pp. 53-66.  [Return to Text]

¹⁸⁰T. p. 74.  [Return to Text]

¹⁸¹Hill & Rosado, 2000, pp. 161-178.  [Return to Text]

¹⁸²pp. 235-236.  [Return to Text]