Philosophy of logic and mathematics has been the bailiwick of the analytic school of philosophy, many of whose basic tenets are antithetical to those of the phenomenological school founded by Edmund Husserl. This fact, along with unfortunately many other factors, has conspired to keep Husserl's ideas on meaning, objectivity, logic, and mathematics from penetrating very deeply, or very well, into mainstream discussions of the subject in the United States, Britain and other English-speaking countries, where analytic philosophy especially developed and flourished during the twentieth century.
Yet Husserl was the student and assistant (1878-1881, 1883) of the great mathematician Karl Weierstrass and for fifteen years (1886-1901) he was the colleague and close friend of Georg Cantor, the creator of set theory. Husserl then spent as many years (1901-1916) in David Hilbert's circle in Göttingen. Thus, Husserl was in close professional contact over extended periods of time (almost continuously between the ages of 19 and 57!) with the greatest and most influential German mathematicians of his time, men whom Bertrand Russell, Gottlob Frege and their followers rarely, if ever, came into contact with. Husserl tangled long and hard with the very ideas that went into the making of analytic philosophy, and the problems he struggled to solve are still under discussion now.
The principal goal of this collection of papers is to work to integrate Husserl's thought into philosophical discussions in which it rightfully belongs by establishing the legitimate ties between his ideas and those of philosophers and mathematicians who have been more readily accepted into the pantheon reserved for those deemed to have made significant contributions to the field.
Before tackling this, however, it is important to name some of the many frustrating obstacles that have stood in the way of any accurate assessment of Husserl's contribution to the field. It is also important to review the history of the attempts that have been made to integrate Husserl's ideas into mainstream philosophy of logic and mathematics.
Two devastating wars on the European continent that ultimately left Europe (Germany and the former Austro-Hungarian Empire in particular) divided into two opposing ideological camps obviously played no small role in clouding the picture. Intellectual ties were severed and obscured. Many voices were stifled or altogether silenced. Valuable documents were lost or destroyed.
The very same political events also uprooted many German-speaking intellectuals and transplanted them in English-speaking countries. This grafting of continental ideas onto American and British philosophy fostered the dissemination and rich cross-fertilization of ideas, but it also cut those ideas off from their original roots and context.
In conjunction with this, key terms of the German language common to so many of the thinkers were translated in disparate and often misleading ways. In particular, language that Husserl used in common with those of his German-speaking contemporaries who actually had a hand in shaping mainstream twentieth century philosophy of logic and mathematics made its way into English in a sometimes unrecognizable, and frequently indigestible form. This often distorted the issues and made it exceedingly difficult to make sense of what Husserl wanted to say, thus doing its share to break down the transmission of his ideas to the English-speaking world. So, when interested, analytic philosophers, who have generally been loath to learn foreign languages, have only too often found themselves facing a daunting number of linguistic barriers.
In addition, phenomenologists themselves have been loath to study Husserl's ideas about mathematics and logic, which they have considered to be the product of an early, immature, pre-phenomenological period of his philosophical career. To do so they would have had to acquire the expertise necessary to manipulate ideas that they have not usually found interesting them in order to communicate with philosophers whose general orientation they do not share. One consequence of this lack of priority Husserlians have been willing to accord to Husserl's work in this field has been that texts indispensable to piecing together his views (his unpublished writings and lectures for example) were for a long time only available in archives in the Austrian shorthand that Husserl used. Needless to say, they are for the most part still not available in English. So analytic philosophers looking into Husserl's writings still mainly find a mass of writings on precisely the kind of views they oppose and expressed in language that they could only find repulsive.
Besides, Husserl unfortunately was not himself always as explicit as one would like when it came to spelling out the precise nature of the links binding his ideas to those of his contemporaries. He rarely named names and when he did he seemed to believe that connections were obvious that are all but invisible to us nowadays. For example, in a note to Ideas § 72, he wrote that the close relation between his own concept of definiteness and the axiom of completeness introduced by Hilbert in his foundations of arithmetic would be apparent to every mathematician without further remark, a remark that I have tried to elucidate in Chapter 10.
So many such factors conspired to obscure Husserl's contribution to twentieth century philosophy of logic and mathematics that the necessary facts may have never come to the fore but for interest in the subject aroused by Dagfinn Føllesdal, a disciple of the pre-eminent analytic philosopher Willard van Orman Quine. As a student at the University of Oslo in the mid-fifties, Føllesdal wrote a master's thesis on Frege and the origins of the phenomenological movement, in which he hypothesized that Frege's1894 review of Husserl's Philosophy of Arithmetic might have had a crucial impact on Husserl's thought at a critical point in his career. In addition, work that Føllesdal began publishing in the late sixties about similarities existing between Husserl's and Frege's theories of meaning attracted a great deal of interest. A 1983 bibliography prepared by Ethel Kersey inventoried no less than 104 English language items on the subject. Indeed, Føllesdal's work appeared at time when philosophers were actively debating such theories of meaning and growing increasingly enthusiastic about Frege's contributions to their field. Føllesdal's hypotheses also surely played a significant role in stimulating research into the Austro-German origins of analytic philosophy.
In 1973, Guillermo E. Rosado Haddock, the co-author of the present work, argued in his Edmund Husserls Philosophie der Logik und Mathematik im Lichte der gegnwärtigen Logik und Grundlagenforschung that Frege had not had any major impact on Husserl's thought and that Føllesdal's theses were untenable. The following year, J.N. Mohanty published "Husserl and Frege: A New Look at their Relationship". In it, he argued at length that the basic change in Husserl's mode of thinking that could in itself have led to his explicit rejection of psychologism and to his advocacy of a theory of logic as a science of objective meanings had taken place before Frege published his review.
In my 1979 Sorbonne Master's thesis on Husserl, Frege and Jaakko Hintikka's Possible World Semantics, I advanced additional arguments to show that Frege had not influenced Husserl in the ways and to the extent that it was then fashionable to believe that he had. In spite of a wealth of objective evidence in favor of this thesis, much of it only available in German, analytic philosophers still found it congenial to believe the contrary. So such arguments still fell on deaf ears.
A new era in the study of Husserl's philosophy of logic and mathematics began opening up in 1982. In that year Mohanty published his book Husserl and Frege. In it he endeavored to show the extent to which phenomenology and analytic philosophy had grown out of common problems and concerns and often from a common set of distinctions and theses. He argued that despite the fact that there had been virtually no fruitful communication between Husserl's and Frege's followers, distinct conceptual routes linking phenomenology and analytic philosophy did indeed exist.
The same year, Professor Rosado Haddock's "Remarks on Sense and Reference in Frege and Husserl" (Chapter 2 of this book) appeared in Kant-Studien, more than three years after it had been submitted. In it he concluded that the theory that Frege's influence on Husserl had both turned him away from psychologism and taught him to distinguish between sense and reference was completely unfounded.
Now analytic philosophers began to listen to arguments that Frege's influence on Husserl had been exaggerated. This might have put an end to any further inquiry. Some found it reassuring to believe that Frege had not influenced Husserl and considered that the matter should then be dropped. Indeed, if Husserl had not been influenced by Frege in any significant way, then why should his ideas be of interest to specialists in the field Frege had opened up? It was unfortunate that Husserl had not listened to Frege. He had had his chance and missed it. That line of reasoning was congenial in its way too, and many may have hoped that that was the proper attitude to adopt.
Those knowledgeable about Husserl's unique contribution, however, now saw the door finally opened to investigations into what Husserl's views truly were and how they truly connected up with mainstream philosophy of logic and mathematics. The field could now get off to a fair start.
The two authors of the present book fall into that last category of philosophers who saw the ground finally prepared for a fair assessment of Husserl's contribution to their field. The papers published here contain a very interesting progression and intertwining of ideas. They explore what for a long time has been terra incognita, territory that largely went unexplored, and even undetected, because of the misconceptions and obstacles (to which many more could be added) cited above.
However, the papers anthologized here are not merely expositions and assessments of neglected parts of Husserl's writings. A few of them are not primarily concerned with Husserl, but are actually the development of ideas barely sketched by him or not even present in his writings at all. But even those papers that may seem less dependent on Husserl's writings are "in the spirit" of the unknown Husserl that rest of the papers are endeavoring to expose and critically assess. They serve both to buttress positions he took and the major arguments of this book. Claire Ortiz Hill