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Taking Frege Seriously

Phenomenology and Existentialism
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2022-06-22
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Joan Weiner, Taking Frege at His Word, Oxford University Press 2020, xxvii + 317 pp.

In 1936 Edmund Husserl wrote in a private letter to Heinrich Scholz, the collector of Frege’s writings, that he had never met Frege in person and that Frege was considered at the time “a sharply intelligent outsider who bore fruit neither as a mathematician nor as a philosopher.”[1] That was, of course, a misjudgment. We can see now more clearly that Frege contributed, in fact, at least three things to mathematics and philosophy after him. The first was his new logic (the propositional and predicate calculus) that replaced the old Aristotelian logic. Given the important role that the Aristotelian syllogistic had played in philosophy for more than two thousand years that was, indeed, a significant achievement. The second was Frege’s attempt to show that arithmetic can be reduced to logic. Frege’s logicist thesis has not remained uncontested and his way of trying to prove it has turned out to be defective, but the considerations that led him to it are still being taken seriously by philosophers of mathematics. The third are his thoughts about signs – the symbols and formulas of his logical calculus and the words and sentences of ordinary language – and the way they serve to convey meaning. These “semantic” considerations have contributed much to the subsequent development of the philosophy of language.[2]

Joan Weiner’s new book pays a great deal of attention to the logical calculus that Frege developed, his Begriffsschrift, whose originality and significance she fully recognizes. Her account of that logic is detailed, precise, and illuminating. She also acknowledges clearly that Frege constructed his logic precisely to establish the truth of the logicist thesis. According to her: “Frege was engaged, for virtually all his career, in a single project: that of showing that the truths of arithmetic are truths of logic.” (p. vii) For all that, she does not delve far into the philosophy of mathematic and Frege’s place in it. She does not concern herself, in particular, with the difficulties the logicist thesis faces and whether it can be salvaged. Her discussion focuses, rather, on the question whether or to what extent we should think of Frege as a philosopher of language.

The object of her critical attention is specifically what she calls “The Standard Interpretation” of Frege’s work which she summarizes in four points: (1) Frege aimed at constructing a theory of meaning, (2) he sought to develop a compositional semantics, (3) he was concerned with giving metatheoretical proofs in his logic, and (4) he was an ontological Platonist. Weiner’s ambition is to set out an interpretation of Frege that is “deeply at odds with the Standard Interpretation.” (p. ix) That interpretation, she believes, is now so deeply entrenched in the literature that it takes a most careful re-reading of Frege’s words to dislodge it. In undertaking that task, Weiner seeks to expose “the difference between the words that actually appear on Frege’s pages, and the words that many contemporary philosophers believe are on Frege’s pages.” (p. 10)

Weiner’s book puts forward a compelling case for rejecting all the four assumptions of the Standard Interpretation that she identifies. Others, myself included, have repeatedly made similar claims. This leaves me with two questions. The first is whether she does full justice to the adherents of the Standard Interpretation and the second whether her alternative interpretation gives us a fully rounded view of the real Frege. As to the first question, we need to consider that when philosophers read the writings of others they are sometimes motivated by the question “what did the author mean by his words?” and sometimes with the question “what can we do with the author’s words?” And these two questions are not always clearly distinguished in their minds. They are trying to get at the meaning but always with an eye to the usefulness of what they find to their own way thinking. And they also often assume that what they themselves think may be a clue to what the other author must have meant. This is the way Aristotle read the Presocratics and Plato’s dialogues and this is how contemporary philosophers read Frege among others. From a scholarly and hermeneutic perspective that can be annoying. It is from this point of view that Weiner’s irritation with the adherents of the Standard interpretation stems.

Weiner traces the belief that we should read Frege as being primarily a philosopher of language and theorist of meaning back to Michael Dummett’s seminal book Frege: The Philosophy of Language from 1973. I find myself agreeing with her that Dummett is mistaken in maintaining that Frege’s explicit goal was to construct a theory of meaning for natural languages. But this does not undermine the fact that Frege did, indeed, make observations that have since led to the construction of such theories. Weiner does not explore the question how Dummett came to read Frege in the way he did. She seems to ascribe it simply to a lack of reading skill. That surely does injustice to Dummett’s competence as a philosopher.  We can grant that Dummett overstated his case, but that may still leave it worth asking why he came to read Frege the way he did. This is not something Weiner is interested in. Dummett was, of course, well aware of Frege’s preoccupation with the logicist thesis.  But by the time he wrote Frege: The Philosophy of Language he had given up on the idea that this thesis could be salvaged and he had opted instead for an intuitionist constructivism. That view, as developed by Brouwer, Heyting and others, seemed to him, however, to lack a proper philosophical grounding. Expanding the constructivist view to non-mathematical statements, Dummett ended up questioning Frege’s apparently “realistic” conception of meaning and its associated notion of truth in the hope of developing in this way an alternative constructivist sort of semantics. His engagement with Frege had turned thus into dialogue concerning language and meaning.

That linguistic turn in the interpretation of Frege was not entirely Dummett’s doing. He had, in fact, been anticipated in this by Wittgenstein. It is Wittgenstein more than Russell who has brought Frege to the attention of English-speaking philosophers and he was concerned from early on more with Frege’s thoughts on language and meaning than with his logicism. That logicism he had already rejected in the Tractatus and over time he was to become increasingly sympathetic to the mathematical formalism that Frege had so vigorously attacked.  He remained, however, very much interested in Frege’s thoughts on language and meaning. Not that he found all of it plausible. Like Dummett after him, he completed rejected Frege’s idea that propositions are names of a sort and that they refer to truth-values. But he remained attracted to Frege’s principle that words have meaning only in the context of a sentence which he repeated both in the Tractatus and in Philosophical Investigations. He also retained an interest in Frege’s distinction between the sense and the reference, the Sinn and the Bedeutung, of words and sentences to which he returned again in those two books while giving the distinction his own very different slant. When Max Black consulted with him over which of Frege’s writings he might most usefully translate into English, Wittgenstein advised him to take on the essay “Über Sinn und Bedeutung.” The translation appeared in Philosophical Review in 1948 and was the first piece of Frege’s writings available in English. For many English-speaking philosophers it became the gateway into Frege’s thinking and it is still today the one piece of Frege’s work with which students are most familiar. It is this text more than any other one in Frege’s oeuvre that may give the impression that he was a philosopher of language, that he sought, in fact, to advance a theory of meaning for ordinary language, and that this theory had the intended form of a compositional semantics.

Weiner is right in arguing that this imisinterprets Frege’s intentions. She writes that in order to understand Frege’s purpose in “Über Sinn und Bedeutung” we must read the essay as one of three which together set out a major revision of the Begriffsschrift logic of 1879. The first and most important of those pieces is the monograph “On Function and Concept,” (1891), the second the essay on “Concept and Object,” (1892) and the third “Über Sinn und Bedeutung,”(1892). This last essay was, in effect, a mere corollary to  the initial monograph and quite possibly only a belated addition. That it did not refer to Frege’s logical calculus but discussed the issues only in terms of examples taken from ordinary language was the result of limitations set by the editor of the journal in which Frege published the essay.[3] Frege had argued in “On Concept and Object,” among other things, for a revision of his earlier account of identity and “Über Sinn und Bedeutung” was meant to show that this revision called for a distinction between the sense and the reference of signs that he had not made in the first exposition of his logic in 1879. While I find myself in substantive agreement with Weiner’s account of “Über Sinn und Bedeutung,” I don’t think that she takes her case far enough. She does not ask herself, in particular, why Frege considered his revision of the earlier account of identity was so important. The answer, I believe, is to be found in the fact that the axiom V he was to add to his logic in Basic Laws in order to achieve the desired derivation of arithmetic is for Frege an identity statement and one that, according to the 1879 characterization of identity would not have counted as a logical truth. Frege’s new account of identity allowed him, however, to argue that the two parts of axiom V conjoined by the identity sign do not only have the same reference (that axiom V is true) but also that they have the same sense and that this allows us to see that the axiom is a logical truth. I have myself argued repeatedly for that view since 1980.[4] I am surprised to find that Weiner does not pursue that point.

I agree once more with Weiner that the single most important new idea in Frege’s logic of 1879 was his introduction of the concept of function and that the single most important revision of his logic in 1891 concerned that notion. In terms of the history of mathematics, Frege should be seen as a descendant of the Gaussian school for which the notion of a mathematical function had become increasingly important. Frege himself had studied at Göttingen, the headquarter of the Gaussians, and so had his teacher and mentor Ernst Abbe. Both Abbe and Frege had, moreover, worked on the theory of function. Frege’s Habilitationsschrift of 1874 had dealt with the topic even before his interest in logic and the logicist thesis had developed. This function-theoretical view stood in contrast to the set theoretical conception, elaborated by Cantor, for which functions were simply certain kinds of ordered sets. Weiner bypasses this historical context and thus misses out on two important insights into Frege’s work. The first is the conflict between the function-theoretical and the set-theoretical view of logic in which the former was represented by Frege, Russell, and the early Wittgenstein but in which the latter has largely prevailed. The second is the paradox that Frege’s attempt to show that the truths or arithmetic are truths of logic required as a first step a mathematization of logic.

Her silence on this historical context is characteristic of Weiner’s entire approach to Frege. Her book is an exemplar of classical analytic philosophy: clear, organized, thoroughly argued, but moving in a narrow circle of formal concepts and in this respect almost old-fashioned in style. It has certainly all the limitations of classical analytic philosophy in particular in being so thoroughly unhistorical.  Concepts exist for this kind of thinking in a vacuum and their meaning and interrelations can be analyzed without reference to any historical realities. In this respect, Wiener is certainly just like Michael Dummett, whom she otherwise dismisses. Dummett once wrote that Frege’s thought sprang from his head almost entirely unfertilized by outside ideas. In her own account of Frege, Wiener tells us correctly that Frege was for much of his philosophical life preoccupied with sowing that arithmetical propositions are logical truths. But she does not and cannot explain to us why this project should have mattered to him. Ordinary mathematicians and everyday used of mathematics may, in fact, not be much concerned with this matter. But it is one of major importance for Kant and subsequently for John Stuart Mill, both figures of the greatest significance, as Frege was writing. Frege himself made clear in his Foundations of Arithmetic that he sided with Kant’s apriorism and against Mill’s radical empiricism.  This conformed to the position of the Neo-Kantians of Frege’s own time. For both Kant and Mill the question of the epistemic status of mathematics was a key to their thinking very broadly about human knowledge and the way it maps on to the world.

Weiner describes Frege’s new logic as “a major advance”; but over whom and over what? She mentions Boole in this respect, but one would think that Frege’s logic was first of all an advance over the Aristotelian syllogism and then over the logics developed by some of his contemporaries (Lotze, Sigwart, Wundt, to name a few). One thing that distinguished Frege from all of these is that he approached logic from the perspective of a mathematician. We can discern this most clearly in his introduction of the notion of function into his logic. Mathematically inspired was also his use of inductive proofs in his logic. The paradox is that Frege sought to reduce arithmetic to logic by making logic more mathematical. The first to understand this circularity in Frege’s argument was Wittgenstein who, for this reason, rightly rejected Russell’s and Frege’s logicist program.

Weiner’s preoccupation with showing the failings of the standard interpretation limits her reading of Frege also in some further respects. She has no interest in the fact Frege was almost as much interest in geometry and its foundations as he was in arithmetic. It is not easy to say what this came to. His discussion of this topic in The Foundations of Arithmetic is rudimentary and other relevant (but unpublished) writings were destroyed in the Second World War. But there can be no doubt that Frege was committed to the idea of synthetic apriori truths.

However far she seeks to distance herself from the way analytic philosophers read Frege today, she stays close to them in one significant respect. Her reading of Frege is just as ahistorical as theirs. Frege’s own words remain for her placed in a historical vacuum and so are the words of those who subscribe to the Standard Interpretation. We are told in neither case from where those words come. That limits what we can learn from Weiner’s take on Frege. Why did he concern himself so much with the logicist thesis? In his Foundations of Arithmetic he writes that both mathematical and philosophical reasons motivated him. The fist concerned the nature of the numbers and the second the epistemic status of the arithmetic propositions. And with respect to the second we find him arguing vigorously against the view that they are empirical generalizations and for the view that they are apriori truths. John Stuart Mill and Immanuel Kant are for him the respective representatives of those two views. Their names refer us, in turn, to an ongoing struggle in Frege’s time between an influential empiricist naturalism on the one hand and a reviving Kantianism on the other. The urgency of logicism for Frege derived precisely from this historical constellation. That is, however, something with which Weiner doesn’t concern herself. Similarly, she does not try to explain to us the conditions for the rise of the Standard Interpretation. She does seek to explain in the last two chapters of her book what her own interpretation of Frege can do for us.

 

 

NOTES

 

[1] Gottlob Frege, Wissenschaftlicher Briefwechsel, p. 92. It is unclear from the formulation whether Husserl agreed with that judgment or was only reporting a widely held opinion.

[2] In light of the fact that Frege may have been instrumental in Husserl’s turning away from his early, psychologistic view of arithmetic, we may want to add that Frege contributed also to the decline of psychologism and the rise of the phenomenological movement in philosophy.

[3] Hans Sluga, „Wie Frege zu Sinn und Bedeutung kam,“ in Frege: Freund(e) und Feind(e), Proceedings of the  Gottlob Frege Conference 2013, Logos Verlag, Berlin 2015, pp. 14-23.

[4] Hans Sluga, Gottlob Frege, Routledge, London 1980, pp. 149-157.  See also Sluga, „Frege on Meaning,” Ratio, vol. 9, 1996, pp. 218-223, and most recently and most succinctly in „Wie Frege zu Sinn und Bedeutung kam,“ loc. cit.