Thought And Logic: The Debates Between German-Speaking Philosophers And Symbolic Logicians at the Turn of the 20th Century by Jarmo Pulkkinen (Europaische Studien Zur Ideen- Und Wissenschaftsgeschichte, Bd. 12.: Peter Lang Publishing) In this book, Pulkkinen discussed the reception and critique of symbolic logic and the logicist programme among German-speaking philosophers at the beginning of the 20th century. His starting-point was the well-known historical fact that although several of those philosophers who are nowadays considered the founders of the analytic tradition (e.g. Frege and Wittgenstein) lived and worked in the German-speaking world, their ideas gained almost no support among contemporary German and Austrian philosophers. In his opinion, the main weakness of earlier historical studies dealing with this period of philosophy is that historians have treated the subject from the viewpoint of their own philosophical tradition, i.e. historians have written their studies from the viewpoint of either the analytic or the Continental tradition. Pulkkinen suggested that if we want to have a clearer understanding of our recent philosophical past, we need a new point of view, i.e. a point of view that is independent of these philosophical traditions. Moreover, Pulkkinen argued that this new point of view can be found with the help of the sociology of scientific knowledge. In particular, he emphasizes the importance of studying the philosophical debates that took place between the founders of the analytic tradition and other contemporary German and Austrian philosophers.
The first part of the book discusses the period from the late
1870s up to the end of the 19th century. The main issue was the
arrival of the Boolean algebra of logic in
After this Pulkkinen discussed how the German-speaking
philosophical community resisted these attempts of translation and
enrolment (Chapter four). The wider philosophical reception of
symbolic logic in the German-speaking world started with the
appearance of the texts by Riehl (1877),
Next, Pulkkinen studied the debates that took place between symbolic logicians and the philosophers of the German-speaking world. That is to say, who took part in these debates, what were the debated issues and the arguments employed. First, Pulkkinen discussed the early reception of the Boolean algebra of logic at the turn of the 1880s. At first the Boolean algebra of logic was able to acquire the support of three notable German-speaking philosophers: F.A. Lange, Alois Riehl and Wilhelm Wundt. However, the algebra of logic also gained influential critics: Hermann Ulrici, Hermann Lotze, and Carl Prantl. The publication of the first volume of Schröder's Vorlesungen uber die Algebra der Logik (1890) made the algebra of logic once more a hot topic in the German-speaking world. Edmund Husserl's review of Schröder's Vorlesungen caused a debate between Husserl and Andreas Voigt, a followerof Schroder. Although the review' was not published in a major philosophical journal, it helped to sway general philosophical opinion against Schröder's algebra of logic. And lastly, Pulkkinen discussed the reception of Frege's logicist programme. Although Frege's work gained the attention of two young German-speaking philosophers, Benno Kerry and Edmund Husserl, Frege's views were for the most part either criticised extensively or ignored completely by German-speaking philosophers.
In the fifth chapter Pulkkinen situated the aforementioned debates in the wider social and political context. First, Pulkkinen suggested that the "resurrection" of German philosophy helped to create favourable circumstances for the arrival of the Boolean algebra of logic in the German-speaking world. The general improvement of the external situation of philosophy, e.g. the founding of new philosophical journals, made it easier to introduce new philosophical ideas. Second, he discussed the reasons why German-speaking philosophers did not find the arguments in favour of symbolic logic at all convincing. Although Leibniz's ideas on the imprecision or ambiguity of ordinary language were familiar to the philosophers of the German-speaking world, the imprecision of ordinary language was not considered to be a serious and urgent problem for logic or philosophy, nor to be a problem that could be solved by adopting a symbolical notation in logic. Instead the attention of German philosophers and linguists with philosophical interests was directed towards the notion of the so-called innere Sprachform. The prospect of a solution to logical problems did not succeed in arousing the interest of the German-speaking philosophical community. Logic was understood in a much wider sense than nowadays and the solution of logical problems was generally considered a task which had almost no value in logic. Moreover, German-speaking philosophers never grew tired of emphasising the mathematical and non-philosophical nature of the new logic. And lastly, Pulkkinen showed that the references to the laws or processes of thought made by German-speaking philosophers were connected to the larger issue of psychologism.
After this, Pulkkinen pointed out that the initial interest towards symbolic logic soon disappeared in the German-speaking world. In the last two decades of the 19th century symbolic logic was not able to acquire any new supporters, and it even lost its old ones. Both Riehl and Wundt soon abandoned their earlier sympathetic views regarding the algebra of logic. He also showed that while the arguments in favour of symbolic logic did not convince the philosophers of the German-speaking world, the counter-arguments against symbolic logic did convince Riehl and Wundt.
While discussing the reception of Schröder's Vorlesungen and the
debate between Husserl and Voigt, Pulkkinen pointed out that in
Moreover, Pulkkinen argued that although the debate had no winner from a philosophical point of view, in other respects Husserl was the clear winner. Husserl's review of Schröder's Vorlesungen got the attention of several prominent philosophers. Husserl's correspondence reveals that he sent the paper at least to Frege, Meinong, Brentano, Höffer, Munsterberg, Riehl and Venn. Almost all of them agreed with Husserl. It seems safe to say that Husserl's review had a considerable influence on the German-speaking philosophical community. Furthermore, after the debate Voigt published nothing on philosophy or logic. He devoted himself exclusively to the study of political economy. Although there is no direct evidence that the debate contributed to his decision to move into the field of political economy, Husserl's harsh criticism certainly did not encourage him to continue his logical investigations. It the end, it could be said that Husserl's review not only proved to be detrimental to the reputation of Schröder's Vorlesungen in the German-speaking philosophical community, but it also cost Schröder his most talented (and only) disciple at the time.
Finally, Pulkkinen discussed the reasons Frege was unsuccessful in his attempts to draw the attention of philosophers to his logicist programme. Pulkkinen emphasized the importance of two things. First, Frege's conceptual notation was too difficult for philosophers and mathematicians alike. A study of the statements of Frege's contemporaries clearly showed that Frege's notation presented difficulties even to the leading logicians of this period, including Peano and Russell. Furthermore, on some occasions Frege could not even get his writings published because of the cumbersomeness of the symbols he used. Second, I referred to Frege's ability to make enemies with his critiques. Although Frege's critical abilities have later been much admired, the targets of Frege's critiques were not equally full of admiration. In particular, Pulkkinen mentioned Frege's very critical review of Husserl's Philosophie der Arithmetik which changed Husserl from a possible ally into a certain adversary. Frege's style became even more sarcastic and satirical as time went by. The result was that sometimes he was not even taken seriously. A good example of this was Frege's debate with Thomae.
Finally, Pulkkinen discussed the reasons why Schröder's and
Frege's teaching and scientific activities did not result in the
formation of schools of thought. In my opinion, the main reason for
this was their low academic status, i.e. they were not full
university professors. In
The last four chapters dealt with the first two decades of the 20th century. The main topic of inquiry was the reception of Bertrand Russell's and Louis Couturat's ideas in the German-speaking world. Pulkkinen first summarised Russell's and Couturat's critiques of Kant and their arguments in favour of symbolic logic and the logicist programme as presented in Russell's The Principles of Mathematics (1903) and Couturat's Les principes des mathematiques (1905) (Chapter six). Russell and Couturat argued that Kant's main mistake was his strict separation of logic and mathematics, i.e. Kant believed that while logic was based on the principle of contradiction and its propositions were analytic, mathematics was based on intuition and its propositions were synthetic. Russell and Couturat claimed that the logicist programme had shown that intuition had no place in mathematics, and that the Kantian philosophy of mathematics was now capable of a "final" refutation. Moreover, Russell and Couturat argued that symbolic logic had become not only absolutely essential for every philosophical logician but also necessary for the comprehension of mathematics generally, that is to say, for the comprehension that all pure mathematics deal exclusively with concepts definable in terms of a small number of fundamental logical concepts, and that all its propositions are deducible from a small number of fundamental logical principles. The only difficulty that stood in the way of the realisation of the logicist programme was Russell's paradox. Finally, the "irreproachable" definition of number in purely logical terms was to define it as a class of classes.
After this Pulkkinen briefly discussed the contributions of German mathematicians in the field of symbolic logic and the foundations of mathematics in the first two decades of the 20th century (Chapter seven). This is followed by a summary of the arguments employed against Russell and Couturat by the members of the German-speaking philosophical community. Pulkkinen pointed out that the publication of a German translation of Couturat's Les principes des mathematiques in 1908 was a very important event in the reception of Russell and Couturat. Within a period of a few years Couturat's work incited several philosophers to state their opinion about symbolic logic and the logicist programme: Cassirer 1907, Cohn 1908, Geyser 1909, Jakowenko 1909, Schnippenkötter 1910, Natorp 1910, Rickert 1911-12, Heidegger 1912, Coralnik 1913, Bon 1913 and Kleinpeter 1913.
Ernst Cassirer was also the neo-Kantian philosopher who undertook the defence of Kant's philosophy of mathematics. According to Cassirer, the reason Couturat's critique of Kant failed was that it was based on an erroneous interpretation of Kant's notions of analytic and synthetic. Moreover, German-speaking philosophers did not have a very high opinion of Russell's and Couturat's symbolic logic. The only exception was Russell's calculus of relations which was praised by several philosophers. In particular, philosophers criticised the employment of "indefinable" concepts and "unprovable" propositions as the foundation of logic. As they saw it, since Russell and Couturat did not define all the concepts they introduced, their expositions did not meet the most elementary requirement of scientific investigation. The main argument against the logicist programme was that if it is carried out, then no line of demarcation will exist between logic andmathematics. Neo-Kantians, in particular, argued that although mathematics should be based on a logical foundation, these two sciences must be strictly separated from one another. Neo-Kantians were also busy writing critiques of the "logicist" definition of number, arguing that the attempt to deduce the number concept from the class concept is a petitio principii.
In chapter nine Pulkkinen discussed the reasons why the members of the most important German-language philosophical schools rejected Russell's and Couturat's ideas. In particular, Pulkkinen concentrated on the relationship between Russell and neo-Kantians. Pulkkinen pointed out that the main difference between the earlier reception of symbolic logic and the reception of Russell and Couturat was that while the Boolean algebra of logic did initially get the support of some German philosophers (i.e. Riehl, Lange and Wundt), Russell's views gained almost no support at all from the German-speaking philosophical community.
Moreover, Pulkkinen argued that although it is sometimes hard to avoid the feeling that neo-Kantians, for whatever reason, misread or misunderstood Russell's views, the neo-Kantian critique cannot be explained away as an elementary logical mistake. First, Pulkkinen discussed the differences between Russell's A critical exposition of the philosophy of Leibniz (1900) and Cassirer's Leibniz' System in seinen wissenschaftlichen Grundlagen (1902). Although both Russell and Cassirer believed that Leibniz's logical views had a decisive importance in the formation of his metaphysics, in other respects their interpretations were fundamentally different. Although both Russell and Cassirer believed that Leibniz's philosophy was still interesting from the viewpoint of "modern" philosophy, their respective definitions of "modem" philosophy were very different. According to Cassirer, the main reason Leibniz's philosophy was still interesting from the "modem" point of view was that it formed a part of the historical course of events that culminated in Kant's philosophy. In other words, Cassirer understood Leibniz's philosophy in terms of the neo-Kantian movement to which he belonged. Russell, in turn, approached Leibniz's philosophy from the viewpoint of symbolic logic and modern mathematics. Moreover, I pointed out that their respective interpretations of Leibniz's philosophy were based on very different interpretative resources. In conclusion, Pulkkinen argued that the difference between Russell's and Cassirer's definitions of modern philosophy and the difference between their interpretative resources were the main reasons that their interpretations of Leibniz's philosophy were incompatible.
Next, Pulkkinen discussed the reasons why Couturat's paper on
Kant did not cause any wider debate in
After this Pulkkinen compared Natorp's and Russell's conceptions of philosophy in order to show that Natorp's and Russell's views regarding the fundamental method of philosophy were irreconcilable. While Russell emphasised the importance of analysis in philosophy and believed that symbolic logic provided a new powerful method of analysis, Natorp believed that in philosophy and logic synthesis was more fundamental than analysis. In Natorp's view, synthesis was the fundamental function of thought and primary for the logical understanding of knowledge. Although Natorp admitted the advantages of symbolic logic as a tool of analysis, he still believed that there were more fundamental logical problems which could not be reached by means of analysis and symbolic logic, for example, the meaning of Russell's "indefinable" concepts. Natorp believed that although analysis cannot provide us with knowledge of the meaning of these concepts, there was a philosophical method which could, i.e. synthesis. In the German-speaking world Natorp was not the only philosopher whoemployed this kind of argument against symbolic logic. German-speaking philosophers did not accept Russell's conception of philosophy and the role that Russell assigned to symbolic logic in philosophy. However, their respective answers to the question of how real logical problems could be studied were very different. For Natorp one suitable method was his own version of Kant's transcendental philosophy and, for example, for Husserl it was the phenomenological method.
Next, Pulkkinen pointed out that the debate over the relationship between logic and mathematics had similarities with the psychologism debate. Some philosophers had a similar attitude towards symbolic logic as they had towards experimental psychology. As they saw it, just as experimental psychology threatened to absorb one of the main parts of traditional philosophy, so mathematics threatened to do the same for another part of philosophy: logic. Consequently, they saw Frege's and Russell's logicist programme as a threat to philosophy. For example, Rickert argued that once the threat of psychologism had been successfully refuted, the greatest threat for logic remained "logical mathematism" in which the logical was in danger of losing its specific character because it was confused with the mathematical. The debate between Husserl and Palagyi showed that Husserl, too, considered the separation of logic and mathematics to be almost as important as the separation of logic and psychology.
Pulkkinen also mentioned that while the older neo-Kantians Natorp and Rickert did not believe that Russell's ideas had anything to offer to their own philosophical systems, the younger neo-Kantians Cassirer and Cohn were more optimistic in this regard. Both Cassirer and Cohn emphasised the importance of Russell's calculus of relations. In particular, in his attempt to develop further Kant's transcendental philosophy Cohn borrowed some ideas from Russell's logic of relations. However, although Cohn adopted some ideas from the calculus of relations, in other respects his philosophical and logical views were very different from those of Russell. Cohn did not accept Russell's views on the method of philosophy or the importance of symbolic logic as the tool of analysis and took from Russell's theories only that small part which suited his own purposes.
The main argument used by neo-Kantians against the logicist definition of number was that deducing the number concept from the class concept is a petitio principii. However, Pulkkinen also mentioned that Russell anticipated the argument employed by neo-Kantians and attempted to overcome it in The Principles of Mathematics. Russell argued that the sense in which every object is "one" must be distinguished from the sense in which "one" is a number. From the viewpoint of Russell, Couturat and Frege, neo-Kantians were making here an elementary logical mistake.
However, Pulkkinen argued that the neo-Kantian critique cannot be explained away as a mere logical error. Pulkkinen pointed out that to accept Russell's distinction would be to accept at least part of Russell's logicist programme. As neo-Kantians saw it, although the notion "a class with one object" does not presuppose the number "one" if one accepts the logicist definition of number, it does presuppose it if one advocates a neo-Kantian theory of number. Pulkkinen proved this by discussing the different number theories of neoKantians. While Cassirer and Natorp saw number as a product of pure thought, Cohn, in turn, saw it as the most abstract object possible. In both cases the number concept is seen to be something logically more fundamental than the class concept. In other words, Pulkkinen argued that neoKantians did not misunderstand or fail to understand the logicist theory of number. Neo-Kantians interpreted Russell's theory of number with the help of the interpretative resources at their disposal, i.e. with the help of their own theories of number. That is to say, neo-Kantians understood Russell's logicist programme and the logicist definition of number in terms of the neoKantian movement to which they belonged. In conclusion, Pulkkinen claimed that this result can be seen as a demonstration of the influence of social variables on knowledge outcomes. The social variable in question is the neo-Kantian tradition of philosophy and the outcome is the specific critique of Russell's theory of number.
After discussing the relationship between Russell, Couturat and neoKantians, Pulkkinen also pointed out that Russell's and Couturat's views were not received any more favourably by other German philosophical schools. In particular, I discussed the views of Husserl, neo-Friesians and neo-Thomists. In Husserl's case Pulkkinen showed that although Husserl did not publish any detailed critique of Russell and the logicist programme, it was clear that his philosophical and logical views were incompatible with those of Russell. Thus, although Husserl praised the achievements of symbolic logicians, he still believed that symbolic logic could not reach true logical problems. Moreover, I discussed the reasons why Russell's paradox was ignored by the majority of the German-speaking philosophical community. For example, since several neo-Kantian philosophers discussed Russell's views in detail, it was surprising to notice that none of them paid any attention to Russell's paradox.
Moreover, I pointed out that Russell's paradox and other similar
paradoxes were well-known in the German-speaking world and that
these paradoxes were discussed in the context of set theory. This
was also the reason why members of the neo-Friesian school were
interested in Russell's paradox. The neo-Friesian school, like
Hilbert and his school, was situated in
While discussing the relationship between Meinong and Russell, Pulkkinen pointed out that although Meinong's writings contained many references to Russell's views, these references mostly concerned their debate with regard to non-existent objects. Meinong did not show any particular interest in the other parts of Russell's philosophy, e.g. in symbolic logic and the logicist programme. Moreover, when Ernst Mally, Meinong's disciple, attempted to show that symbolic logic forms a part of Meinong's theory of objects, he based his attempt on Schröder's algebra of logic and did not even mention Russell's writings.
Finally, Pulkkinen dealt with the reasons why Russell's views
gained no more support from the German-speaking mathematical
community than they did from the philosophical community. Pulkkinen
pointed out that in
In this book, Pulkkinen has attempted to throw some light on the reception of symbolic logic and the logicist programme among the German-speaking philosophers at the beginning of the 20th century. Of course hedoes not claim that the above reasons were the only ones contributing to the neglect of Schröder's, Frege's and Russell's ideas. There were also other reasons, some of which were perhaps more philosophical. For instance, Schröder was, to use Jourdain's expression, "the least subtle of mortals" Jourdain 1911: 486). The first volume of Schröder's Vorlesungen has more than 700 pages. Even the introduction is 125 pages long. Moreover, the introduction is not very original. Schröder borrows heavily from other authors and the text is sometimes extremely confusing. Thus, Vorlesungen provided an easy target for a philosopher of such high caliber as Husserl. On the other hand Frege's Begriffsschrift contained many new and difficult ideas, expressed in a very concise way. Later Russell said that he had not understood Frege's Begriffsschrift until he had "independently discovered most of what it contained" (Russell 1967: 68). Thus, an average German philosopher of the period can hardly be blamed for not understanding Frege's new ideas.
Moreover, Pulkkinen has argued that the reception of Schröder's, Frege's and Russell's ideas by their German-speaking contemporaries cannot be adequately explained by studying solely the views of Schröder, Frege, Russell and their contemporary critics but that the wider social and political context in which these views were presented must also be taken into consideration. However, it is a common misconception that a sociological approach to the history of philosophy would necessarily reduce philosophical views or theories to social causes, e.g. to class interests. It should be clear by now that Pulkkinen is not guilty of this kind of reduction. With the help of the sociology of scientific knowledge Pulkkinen has carefully placed philosophical views and theories in their social and political context.
Hans-Georg Gadamer has said that when he began his university studies in 1918, it was obvious to his generation that merely accepting and continuing what the older generation had accomplished was no longer feasible: "In the First World War's grisly trench warfare and heavy-artillery battles for position, the neo-Kantianism which had up to then been accorded a truly worldwide acceptance [...] was just as thoroughly defeated as was the proud cultural consciousness of that liberal age, with its faith in scientifically based progress" (Gadamer 1997: 4). Gadamer was attracted to a new philosophical orientation which was labelled with the "dark, magical word, 'phenomenology'." In particular, Gadamer says that the intensity with which Heidegger evoked Greek philosophy worked on him like "a magical spell" (Gadamer 1997: 7-8).The transformation German-speaking philosophy underwent naturally raises the question: How did this transformation influence the reception of the founding fathers of the analytic tradition in the German-speaking world? In short, the situation changed from bad to worse. The distance between the ideas of Russell, Wittgenstein and the
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