When Frege set out in 1919 to summarize his intellectual achievements for the historian of science Ludwig Darmstaedter, he called it distinctive of his conception of logic that it gives pre-eminence to “the content of the word ‘true.’”(Frege 1979, p. 362) This insight had come to him, in fact, only slowly and over the course of some forty years. It had certainly not yet been evident in his earliest and most original work on logic, the Begriffsschrift of 1879. I have described the development of Frege’s thinking on truth elsewhere and I won’t repeat what I have said on those occasions. (Sluga 2001 and 2003) My goal here is, rather, to explore a paradox that appears to arise from Frege’s idea that logic gives pre-eminence to the content of the word “true” when it is conjoined to his slightly earlier statement – in the note “My Basic Logical Insights” from 1915 – that the word “seems devoid of content.” (Frege 1979, p. 323) My question is: how can the content of a word that seems devoid of content be distinctive of a conception of logic?
There is, of course, no direct contradiction in Frege’s words since he writes in the 1915 text only that the word “true” seems devoid of content, not that it actually is so. But other things he says in that same note only reinforce our sense of paradox. While he rejects the idea that the word “true” might have no sense – since any sentence in which it occurred would then also lack sense – he maintains that it has only a sense that “contributes nothing to the sense of the whole sentence in which it occurs as a predicate,” and thus “does not make any essential contribution to the thought.” (Frege 1979, p. 323) But how could the content of a word that contributes nothing essential to a thought be at the same time distinctive of a particular conception of logic? This is, however, exactly what Frege maintains not only in his note to Darmstaedter but also in “My Basic Logical Insights” itself where he writes that precisely because the word “true” contributes nothing essential to a thought, “precisely for this reason” the word “seems fitted to indicate the essence of logic.” (Frege 1979, p. 323)
That the concept of truth indicates the essence of logic was no incidental idea on Frege’s part. He highlighted it also in the introductory paragraph of “The Thought” in 1918-19 – an essay which was meant to serve as an introduction to a final, informal, and philosophically inspired review of his entire work. It was at this exposed and decisive point that he spoke of the laws of logic as being nothing but laws of truth. (Frege 1979, p. 325) In order to appreciate the full implications of this assertion one must recall that Frege also understood arithmetic to be part of logic or, at least, as relying in its deductive structure on logic and that he considered arithmetic, in turn, to be the basis for probability theory and hence for a theory of induction and thus as the methodological base for the entire edifice of empirical science. It follows then that truth was, on Frege’s view fundamental to human knowledge and certainly also fundamental to the edifice of Frege’s own thought. But how could Frege imagine that truth plays such a fundamental role if he also thought that the word “true” was or seemed devoid of content, if it contributed nothing essential to a thought? We are, so it seems, left with a puzzle – one that forces us to go back to the question how Frege actually understood the concept of truth and how his bewildering remarks about truth can be accommodated.
There was a time when it was said with confidence that Frege had held simply and straightforwardly to a correspondence conception of truth. Some interpreters treated him even as a precursor of Tarski and his theory of truth in formalized languages. The view was not wholly unreasonable since it could draw on two connected considerations. The first was that Frege’s logic seemed to account for the truth and falsity of molecular and general propositions in terms of the truth and falsity of atomic ones and the second that his sense-reference semantics seemed to speak of atomic sentences of the subject-predicate form as true if the thing named by the subject-term falls under the concept designated by the predicate and analogously of relational sentences. The view of Frege as a correspondence theorist was, however, shaken by the belated realization that in “The Thought” he had argued strongly against that theory. For a while, some readers continued to ignore or downplay that essay as being perhaps a late aberration. Such dismissals were swept aside, however, with the appearance of Frege’s Posthumous Writings which revealed that he had repeatedly argued against the correspondence theory of truth in papers going back to at least 1897.At this point the significance of a remark from the essay “On Sense and Reference” began to dawn on some of Frege’s interpreters according to which “closer examination shows” that the sentence “the thought that 5 is a prime number is true” says nothing more than the simple sentence “5 is a prime number.” (Frege 1997, p. 158) In consequence, Frege was reclassified now as a redundancy theorist of truth who holds that the predicate “is true” can simply be dropped from the language without any substantive loss. That characterization appeared at first sight confirmed also by “My Basic Logical Insights.” The note restates, in fact, the earlier claim of “On Sense and Reference” varying in essence only the example. The sentence “It is true that sea water is salty” Frege writes in that note says the same (no more and no less) than the sentence “Seawater is salty.” (Frege 1979, p. 322) But a more careful reading of the 1915 note should have alerted readers that their characterization of Frege as a redundancy theorist was nevertheless unsatisfactory and just as much so as his earlier identification with the correspondence theory of truth. The redundancy theory would imply that the word “true” can be dropped from our language wherever it occurs as a predicate attached to a sentence. But Frege maintains, in fact, in “My Basic Logical Insights” that this is not generally possible. He asks himself therefore: “How is it then that this word ‘truth’ though it seems devoid of content, cannot be dispensed with?” And he answers this question claiming boldly: “That we cannot do so is due to the imperfection of language.” (Frege 1997, p. 323)
Here we encounter one more of those puzzling remarks that are so frequent in Frege’s discussions on truth. The assertion that we cannot dispense with the word “true” because of the imperfection of languages calls certainly for explication and my discussion here is concerned with precisely that. That discussion will take us beyond the ascription of a redundancy view to Frege. It will lead us to conclude, instead, that he held a view more closely related to the old correspondence theory than might be suspected. While Frege rejected the idea that the truth of a sentence consists in its correspondence to a part of reality he held, instead, that in trying to express truth we must find a language that is adequate to the matters of which it speaks. I conclude therefore that in place of the idea of a theory of truth Frege adopted, in the end, what we may call an adequacy view of language.
Off-hand, one might consider the issues thus raised to belong to the narrow and specialized field of Frege studies or somewhat more broadly as belonging to the philosophical and technical examination of the concept of truth. I want to look at those issues here in a more encompassing fashion. I begin with a review of what Frege actually said about truth specifically in his later writings and I then proceed to put his remarks and the issues they raise in a broader historical context. In looking at logical matters in this fashion I model my exposition on Jean van Heijenoort’s seminal essay “Logic as Language and Logic as Calculus.” I am aware that just like van Heijenoort’s piece mine will have a somewhat speculative character.
The indefinability of truth
I turn here to what Frege writes about truth in “The Thought.” He argues there that the attempt to define truth as correspondence breaks down since the concept is already implicitly presupposed in the definition. When we try to determine whether an idea (or, for that matter, a sentence) is true, the correspondence view invites us to consider whether the idea (or the sentence) corresponds to reality but this, Frege holds, comes to considering whether it is true that the idea or the sentence corresponds to reality. This counterargument can clearly be generalized to any other definition of truth. Any definition would have to say that the sentence is true if and only if it has a certain property T. But then in order to establish that that a sentence is actually true, we would have to determine that it has the property T and this means for Frege we would have to establish that it is true that the sentence has property T. Frege draws therefore the radical conclusion that not only the correspondence theory but also “any other attempt to define truth also breaks down.” In any such definition a characteristic would have to be specified that makes an idea or sentence true. But whenever we try to apply such a definition “the question would arise whether it were true that the characteristic were present.” It becomes apparent then “that the content of the word ‘true’ is sui generis and indefinable.” (Frege 1997, p. 327)
One is tempted to compare this argumentation to G. E. Moore’s proof in Principia Ethica that “good” is simple and indefinable. Any such definition, Moore holds, would have to be of the form “x is good if and only if x is P” where P is some none-evaluative or natural property; but any such definition would implicitly presuppose an independent grasp of the concept of good we are trying to define. For whenever we try to find out of some x whether it is good, we will have to determine not only that x actually has property P but also that having that property is really good. Moore understands, moreover, that the same kind of argument will apply to any other evaluative term. A definition of the term “beautiful” in natural terms is, for instance, equally ruled out for the same reasons. (Moore 1903, ch. ) Behind these considerations lay Moore’s commitment to a conceptual atomism according to which there are certain absolutely simple and, hence, indefinable concepts. In the essay “On the Nature of Judgment” of 1899 that served as a springboard for his and Russell’s defection from monistic idealism, Moore writes explicitly of truth as one such simple and indefinable concept and on that ground attacks Bradley’s relational theory of truth. Instead, he holds that “truth and falsehood are not dependent on the relation of our ideas to reality.” (Moore 1899, p. 177) A proposition is, rather, constituted by a number of concepts together with a relation between them and “according to the nature of this relation the proposition may be either true or false.” However, this “cannot be defined, but must be immediately recognized.” (Moore 1899, p. 180) While the formal parallels between Frege’s and Moore’s argument are striking we must not overlook that their conclusions are markedly different. For Moore good is a quality that things may possess but it is a non-natural quality since it cannot be defined in natural terms. Frege, on the other hand, takes the indefinability of truth to show that it is no quality at all. It is for this reason that the addition of the predicate is true does not make an essential contribution to a thought. We can compare his conclusion to the one that R. M. Hare drew from Moore’s “naturalistic fallacy” argument. According to R. M. Hare that argument establishes not that good is a non-natural quality but that the word “good” has a performative rather than a descriptive meaning. When we say “x is good” we are saying as much as “I like x, do so as well” ad our utterance is thus, in other words, expressive and imperative in character.
To get further insight into the conclusions that Frege drew from the indefinability of the concept of truth, we may want to his incomplete and hence unpublished essay from 1897 – a piece he entitled simply “Logic.” The text constitutes one of several attempts to formulate his ideas in an informal manner and it is to be considered an immediate predecessor of the series of essays that Frege initiated with “The Thought.” Just like this latter piece the 1897 manuscript begins with a comparison between the terms good, beautiful, and true. We are told that the first term characterizes the “goal” of ethics and the second that of aesthetics, while the word “true” characterizes the goal of science. All science is concerned with truth, but logic is concerned with it in a unique manner for it is “the science of the most general laws of being true.” Like ethics, logic can be even called a normative science. Frege continues:
Now it would be futile to try to make clearer by a definition what is to be
understood by “true.” If one were to say: “An idea is true if it corresponds to
reality”, nothing would be gained, for in order to apply it we would have to ask
in each case whether an idea corresponds to reality, in other words, whether it is
true that the idea corresponds to reality. One would have to presuppose what is to
be defined. The same would hold of any explanation of this form: “A is true if it
has such and such a property or if it stands in this or that relation to this or that.”…
Truth is obviously something so primordial and simple that a reduction to
something even simpler is impossible. We are therefore forced to illuminate what
is unique in our predicate through a comparison with others. (Frege 1997, p. 228)
These considerations should, in turn, be read in conjunction with what Frege told his students in lecture in the Winter of 1910. According to Rudolf Carnap’s notes on these lectures devoted almost all his attention to a description of the formal machinery of the Begriffsschrift. But he would allow himself occasional asides of a more general, philosophical nature. On one of those occasions he said, according to Carnap: “Truth cannot be defined as ‘correspondence of an idea with reality;’ for something objective cannot be compared to something subjective. Truth cannot be defined, analyzed, or reduced [to anything else]. It is something simple, primordial.” (Frege 1996, p. 15) It appears that Frege was speaking here in a somewhat dogmatic fashion without trying to fully justify his general conclusion that truth is simple and primordial. But he offered in passing a partial reason. In doing so, he appears to ake it for granted that a correspondence would, in the first instance, have to be thought of as holding between our ideas correpresentations and reality. But we know from other contexts that Frege considered ideas to be subjective and incommunicable. He reasons therefore that ideas cannot be compared to something objective. To assume that they could, would lend them, it seems, some degree of objectivity. They would also become indirectly communicable. If it is possible for me to determine that an idea I is true in that it corresponds to a bit of reality R and you discover that your idea J corresponds to the same R, then, presumable we can say that in an important respect our ideas coincide. I can then, in other words, communicate my idea to you by informing you that it is the idea that for me corresponds to R and you will be able to understand that this is what you have as idea J. But if ideas are strictly subjective and incommunicable, as Frege assumes, it follows by contraposition that they cannot be said to correspond to reality. But why does that show that truth cannot consist in a correspondence of something to something? Could we not think of truth as a correspondence between a sentence and a piece of reality. Sentences are certainly objective things in the world. But the same sentence, the same inscription, can have different meanings and can hence be considered both truth and false. Frege considers it evident that we must speak here not of sentences but of their meanings or, more precisely, their senses and such senses are for him fully objective. Why then should we not think of truth as a correspondence between the sense of a sentence and a bit of reality and the objective sense of a sentence? If we follow Frege in calling the senses of sentences thoughts, why should we not think of the truth of a thought as consisting in its correspondence to a piece of reality?
This question forces to consider more precisely how Frege conceived of thoughts. He did not, in fact, assume that besides the objectively real thoughts there exist also an ontologically independent realm of facts to which these thoughts may or may not correspond. In “The Thought” Frege declares, instead: forthrightly that “a fact is a true thought.” (Frege 1997, p. 342) The remark repeats what he had already said in other words twenty years in 1897: “Examples of thoughts are laws of nature, mathematical laws, historical facts.” (F 1997, pp. 230-231) Facts are, on this view, evidently, not what thoughts are about but are themselves thoughts. While we tend to speak of those thoughts as correlates of possible facts such correlates would, in Frege’s terms, be at best ideas or representations (Vorstellungen). But these are, as we have seen unsuitable as truth-bearers for Frege, not only because they are subjective but also because they are strictly speaking incommunicable. Fregean thoughts, on the other hand, are not only truth-bearers they also constitute the world instead of being its representation. This idea is not without its attractions. For it is surely plausible to assume that the identity criteria of facts must be intensional. The fact that Venus is the morning star is certainly different from the fact that Venus is the evening star. Facts can therefore, on Frege’s scheme, not be located at the level of reference where identity criteria are unfailingly extensional and the truth and falsity of thought cannot be explained through a correlation or lack of such between thoughts and facts. Frege’s recognition that there are objectively true thoughts which no one has grasped comes thus to the assertion that there are facts unknown to us and this is surely something we want to grant. It follows that Frege does not engage in a duplication of facts and correlated propositions in themselves.
In his notes for Ludwig Darmstaedter, Frege summarized his conclusions with regard to the notion of truth in these words:
What is distinctive about my conception of logic is that I give primacy to the
content of the word ‘true’, and then immediately go on to introduce a thought
as that to which the question ‘Is it true?’ is in principle applicable. So I do not
begin with concepts and put them together to form a judgment; I come to the
parts of a thought by analyzing the thought. (Frege 1997, p. 362).
The formulation suggests that truth must be considered a semantically primitive term. Other semantic notions may be explained by means of it, but since they all presuppose the notion of truth, they cannot, in turn, be used to explain it. The notes for Darmstaedter seek to show, for that reason, how by starting with the notion of truth as basic one can come to the notions of sense and reference, to the distinction of functions and objects, and to the other fundamental notions of Fregean logic. But Frege’s formulations are not as sharp here as one would like them to be. For they allow the possibility that we might think of truth as a simple, “non-natural” quality in Moore’s sense. This is, however, by no means Frege’s intention as he makes clear in “My Basic Logical Insights.” There it becomes clear that his actual understanding of the concept of truth is closer to Hare’s interpretation of the naturalistic fallacy. Frege’s conclusion is not really that the concept of truth is semantically simple; he holds rather that nothing can be said about the concept in semantic terms, if that means reducing it to other, more primitive semantic notions. But there are still lots of other ways to speak about truth. We can speak about truth, above all, in epistemic terms. We can ask under what conditions we are justified in asserting something as true. This may lead us to say, for instance, that we take certain propositions as self-evidently true or that we regard them as true because we have made this or that empirical observation or because they are derivable in this or that manner from other established truths. We can, thus, speak of the ways in which the truth and falsity of one proposition depends on the truth or falsity of certain other propositions. In other words, we can explore inference relations between propositions. Frege suggests that the laws of logic, that is, the laws of our object-language propositional and quantificational logic, should be considered “laws of truth.” He does not mean by this that these laws contain the word “true” and say something about it. He means rather that those laws explicate our understanding of what “truth” means by showing us truth-relations between propositions.
Frege vs. Bolzano on truth
It helps at this point to introduce the name of Bolzano and to contrast his treatment of truth to Frege’s.[1] For Bolzano holds precisely the view about which we are now inquiring. He holds that truth is correspondence between reality and something objective. We need then to examine why Bolzano underwrote this idea and why Frege did not. Such a comparison of Bolzano and Frege can serve a variety of purposes. The first is that it highlights some apparent affinities between the two thinkers. Both Frege and Bolzano hold, in particular, that our sentences have objective meanings. Following Lotze’s terminology, Frege calls these objective meanings “thoughts” while Bolzano speaks of them as “propositions in themselves.” This affinity has led some interpreters to conclude that Frege must have derived his view from Bolzano, even though no direct connection between the two thinkers has ever been found. A closer look at the two conceptions reveals, however, that they are less similar to each other than they look at first sight. This becomes clear when we reflect on the question of what Bolzano and Frege respectively mean when they speak of the truth or falsity of a proposition in itself or a thought. The answer suggests to me that Bolzano’s thinking belongs after all to the first half of the nineteenth century, that he is not part of the renewal of philosophy that began in the last quarter of that century, that is not a direct antecedent for Frege and that he is therefore also not directly related to the analytic tradition in philosophy.
My primary reason for these conclusions is that Bolzano accepts the traditional Aristotelian conception of truth so uncritically and that he also accepts its broad implications. Bolzano certainly knows that some ancient and some modern philosophers have sought to revise the Aristotelian account of truth, but he himself holds firmly on to it.[2] “The first and most distinctive” use of the term “true,” he writes, is the one according to which we understand it as a certain characteristic of propositions “by means of which they state something as it is.” (Sect. 24, p. 108) This is, indeed, Bolzano adds, also the opinion of Aristotle. Bolzano takes the Aristotelian conception to mean moreover specifically that a proposition is true “whenever the object with which it deals really has the properties that it ascribes to it.” (Sect. 25, p. 112) More precisely, he says, that “in every proposition there must be an object with which it deals (the subject) and also a certain something that is said of this object (the predicate). In a true proposition, moreover, that which is said of the object must really belong to it.” (Sect. 28, p. 122) He thus subscribes not only to Aristotle’s general formula but to that particular interpretation of it which assumes that judgments are essentially composed of subjects and predicates.
He goes beyond Aristotle, however, in one important respect. While he agrees explicitly with Malebranche’s formula that “veritas nil aliud est, quam relatio realis sive aequalitatis sive inaequalitatis,” (Sect. 27, p. 119) he balks at calling this a correspondence theory of truth and writes: “I cannot omit the demand that one should indicate precisely what is meant to be understood by the correspondence (Übereinstimmung) which is supposed to obtain between ideas or propositions and their correlated objects. One can certainly not imagine here an absolute identity or sameness. For propositions or ideas are not absolutely the same as the objects to which they refer; nor are the properties of the former also properties of the latter. (Sect. 29, p. 128)
The relation must, in fact, not be conceived as one of similarity between our ideas and reality. Bolzano worries that this kind of characterization would introduce a subjective element into the concept of truth. The threat of subjectivism constitutes, indeed, one of the major concerns of Bolzano’s entire Wissenschaftslehre. In order to escape it, he considers it necessary to “separate the logical from all admixture of the psychological.” Agreeing with Herbart in this respect he also writes of the necessity to reveal “the judgment as no appearance in the mind, but as something objective.” (Sect. 21, p. 85) The term “proposition” (Satz) – which Bolzano conceives to be the bearer of truth and falsity – must thus not be taken in its ordinary sense. We must not imagine that a proposition is something we “propose” (setzen). Bolzano writes: “Through its derivation from the verb “to propose” the term “proposition” used here suggests admittedly an action, a something proposed by someone (in other words, something that is produced or altered in some way). But in the case of truths in themselves one must ignore this.” (Sect. 25, p. 114f.) Similarly, when we declare that a proposition “says” or “states” something we must take this to be strictly figurative (uneigentlich). When we speak of an assertion (Aussage) as true or false, that too must be considered a figurative expression. For in reality truth or falsity are not asserted.
Since a proposition in itself is not produced by human action it cannot strictly be identified with a sentence or a thought. Hobbes may have believed that only verbal assertions can be considered true and false, and that truth belongs to words and not to things and that therefore only beings capable of language can possess truths. But this view is either “merely love for the absurd” or rests on confusing representations (Vorstellungen) with the words we use to indicate them. (Sect. 29, p. 144) A proposition is, in Bolzano’s competing view, rather “the sense which a certain combination of words can express.” (Sect. 28, p. 121) Propositions, understood in this way, “have no real existence, i.e., they are not something that is in any particular place, at any particular time, or is in any other way something real.” (Sect. 25, p. 112) To illustrate this point, Bolzano writes that “the number of blossoms that were on a certain tree last spring is a statable, if unknown figure. Thus, the proposition which states this figure I call an objective truth, even if nobody knows it.” (Ibid.)
All this suggests affinities to Frege’s thoughts in the manner in which he characterizes them for instance, in the essay “The Thought.” But the last quotation also indicates a significant difference between them. For Bolzano there are statable facts as well as propositions in themselves that state them. This suggests the possibility of the existence of what there is (a fact) even when there is no corresponding proposition. Thus, we may hold that the blossoming tree last spring had, indeed, a specific number of flowers, but this does not by itself imply the existence pf an a proposition in itself corresponding to this fact. Bolzano seems caught here in a puzzling duplication of entities. This is precisely where Frege differs.
We may still find Bolzano’s position closer to common sense but that means only that he is closer to what tradition has taught us. Bolzano’s conception of truth remains committed to that tradition; he holds on for that reason also to the idea that judgments are essentially composed of subjects and predicates and for this reason he is, in the end, incapable of getting beyond the limitations of classical logic. In all this he stands on the other bank of the great divide that splits nineteenth century thought. He cannot seriously be considered part of the analytic sort of philosophizing that emerges in the last decades of that century and of which Frege is surely a representative.
Frege’s rejection of the correspondence view of truth puts him on our modern side of philosophy. But it is, as such, so far only a negative view. His claim that truth is simple and indefinable still demands explication. If it is not correspondence, not complex, and not definable, we still need to ask how we should positively think about it.
The correspondence theory
Frege’s work must be seen, I have said, as part of the new lease on life that philosophy was gaining in the last quarter of the nineteenth century. This was, of course, also the time when Neo-Kantianism emerged with its new bargain between science and philosophy, when Nietzsche began to deconstruct the entire edifice of philosophical reason, when Wilhelm Dilthey mapped out the methods of a historical hermeneutics, when Ernst Mach formulated the principles of a scientific positivism, and when Edmund Husserl constructed his transcendental phenomenology. This broad-ranging philosophical revival was helped along, moreover, by a generation of scientists who saw their own disciplines – fields as diverse as mathematics, physics, psychology, sociology, and political science – in crisis and believed that philosophy was essential for helping to overcome this condition. The names of Georg Cantor and Richard Dedekind, Albert Einstein and Max Planck, Wilhelm Wundt, Georg Simmel, and Max Weber come readily to mind in this connection. But Frege, true, can be seen as occupying such mediating position in his attempt to make bear logic on the foundations of mathematics. The development I am describing was not, of course, confined to Germany. Elsewhere powerful new philosophical impulses were also felt in the last quarter of the nineteenth century. The American pragmatists generated the first indigenous American form of philosophy, defeating the German inspired idealist tradition that had until then dominated the scene. In Britain the radical empiricism of the mid-century came under fire first from British idealists and then from Moore and Russell and their logical atomism. In France, Bergson gave philosophy a new face. The confluence of these movements produced, in turn, far-reaching effects in the twentieth century which revealed themselves in the logical positivism of the Vienna Circle, the existential philosophy of Jaspers and Heidegger, the Marxist humanism of Sartre, the ordinary language philosophizing of Wittgenstein and the Oxford philosophers, in American analytic philosophy, and the structuralist and post-structuralist philosophies of Foucault and Derrida.
The philosophical thought that began to emerge in the last quarter of the nineteenth century is thus notable for its diversity and it is for that reason not at all easy to describe the overall character of the renewal of philosophy that began at that time. So far, at least, we possess only partial histories of this period: of the phenomenological school, of existentialism, of logical positivism, of analytic philosophy, and of French structuralism. The question remains, therefore, what, if anything, holds these different movements together. Is there a common thread to the philosophizing of this period? Some such commonalities reveal themselves, of course, even to the glancing eye. We easily notice the pervasive effort to accommodate philosophy in one way or other to the empirical sciences. We also notice a prevailing preoccupation with the mind, the subject, or consciousness and its states. Philosophers from various schools are, furthermore, attracted to questions of language and meaning. Finally (and most significantly for our discussion) there emerged also a widely shared concern with the question and the concept of truth. To realize that this is so we need to think here only of Nietzsche’s reflections on the value of truth and of Frege’s characterization of the logical laws as laws of truth, of Bradley’s monistic theory of truth and Moore and Russell’s characterization of truth as a simple property of judgments or propositions, of Wittgenstein’s picture conception of truth and of Tarski’s definition of truth for formalized languages, of the positivist critique of truth in the name of verifiability and falsifiability and of Donald Davidson’s programmatic linkage of meaning and truth in ordinary language; of Heidegger’s redefinition of truth as aletheia and of Foucault’s concatenation of truth and power.
This intense preoccupation with the concept of truth contrasts sharply with the disregard of the question of truth in early modern philosophy. Thus, Kant writes of it in a bemused tone as “the question famed of old, by which logicians were supposed to be driven into a corner.” For common purposes he is willing to take “the nominal definition of truth” as “agreement of knowledge with its object” for granted but also holds that with respect to the actual content of knowledge no general criterion of truth can be given. And he concludes shortly that “further than this logic cannot go.”[3] This is not to suggest that Kant’s attitude is universally shared in modern philosophy. But there is no doubt that in this period the Aristotelian conception of truth remains largely untested. When Aristotle had declared that “to say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, or of what is not that it is not, is true” he appeared to many of those thinkers to have said as much as possible on the matter. That Aristotle formulation implied, moreover, that every judgment has a subject and a predicate and that a judgment is true specifically when the object named by the subject term has the property (is in the state, is engaged in the activity, occupies the location, etc.) identified by the predicate struck these philosophers, moreover, as entirely plausible. It was only in the late nineteenth century that this attitude began to give way to substantial unrest over the question how truth should be understood. This is evident from the sharp and differentiated criticisms that thinkers as different as Nietzsche, Bradley, Russell, the logical positivists, Davidson, Heidegger, and Foucault direct against the traditional conception. The new kind of philosophizing that emerges in the late nineteenth century can, indeed, be characterized comprehensively by its rejection of the correspondence conception of truth and the search for alternatives.
This characterization may, however, be met with resistance in the light of Wittgenstein’s picture conception of truth and of Tarski’s definition of truth in formalized languages. Both Wittgenstein and Tarski seem, at first sight, to be recasting rather than replacing the traditional view of truth as correspondence. How then can the recent philosophical concern with truth be explained as the result of a pervasive unhappiness with the correspondence view? Part of the answer is surely that even if we take the early Wittgenstein and Tarski to be exponents of such a view of truth, we must recognize that they substitute something entirely new for the old theory, something that goes far beyond the summary formulas traditional correspondence theory had offered, and also something that was no longer committed to the subject-predicate view of propositions. But I am inclined to argue that to speak in this way this still fails to acknowledge the gulf that separates Wittgenstein and Tarski from traditional correspondence theory. Wittgenstein’s picture conception of truth is, indeed, radically different from the traditional view in that it nowhere allows for the possibility of a comparison of our propositions with the facts. All we have available according to Wittgenstein are the propositions of our language and the a priori certainty that they must mirror something, if they are to have a definite meaning. Tarski has, admittedly, characterized his theory at times as a version of the classical correspondence view of truth. But if we are to speak of correspondence at all in Tarski’s account, it is only one between the sentences of the object- and those of the meta-language not one between language and world. Donald Davidson is surely right when he says that Tarski has given us a formal definition of truth (or, rather, a definition of true in some language L) but no comprehensive theory of truth since the latter would also have to speak of the relations between truth, on the one hand, and our beliefs and desires, on the other and Tarski’s treatment provides us with nothing of the kind.
I continue thus to believe that the critique of the correspondence view of truth has been at the heart of the philosophical concern with truth over the last 130 years and that Frege’s critical confrontation with that view marks him as a characteristic thinker of that period. We are familiar with his remarks to that effect in his essay “The Thought.”
Frege as a nineteenth century thinker
My historical canvas is large and concerns the last 130 years in philosophy. When we look back at that period today, we can see that our discipline has passed in them through a phase of exceptional productivity from which we may be emerging now into an era of less assured fortunes. That productive phase had itself been preceded by a period of retreat, stagnation, and even decline and a resulting ebb in the public estimation of philosophical ideas. We are still operating today in the light of that astonishing renewal of philosophical thought which began in the last quarter of the nineteenth century, and which lasted through the entire twentieth. But we are also increasingly conscious that the sun of philosophical creativity may once again be setting. Instead of generating radically new concepts, our philosophizing occupies itself mostly now with the elaboration and refinement of ideas that were produced in the preceding age and public interest in philosophy is understandably once again waning.
My overall goal is to situate Gottlob Frege in this broadly described landscape and to illuminate in this way particularly what he says about the concept of truth and the imperfection of language. Frege is to many interpreters still a figure detached from his historical background. Thus, Michael Dummett once wrote that Frege’s new logic appears to have been born from his brain “unfertilized by external influences.” (Dummett 1973, p xvii) We can let this stand as a tribute to Frege’s originality, but the statement can hardly satisfy us as an objective assessment. As Michel Foucault once put it, truth is, after all, not “the reward of free spirits, the child of protracted solitude, nor the privilege of those who have succeeded in liberating themselves. Truth is a thing of this world.” (Foucault 1980, p. 130) Scholarly research in the last twenty-five years has, in any case, firmly established that Frege’s work must be seen in relation to the philosophical, mathematical, and scientific life of his own time and place. Frege, we have come to realize, was after all a nineteenth century thinker and he was in fruitful ways tied to the currents of German thought in his period. This is, of course, not in any way to relativize or diminish his achievements. We are certainly not diminishing Plato by discovering that he was a man of fourth century Athens. Far from bringing Frege’s stature down by looking at him historically, such a perspective can teach us that he was part of a heroic age in philosophy to which we have difficulty now of measuring up and to discriminate what is genuinely original in his work from where he draws on the thought of others.
In order to appreciate Frege’s remarks on the inadequacies of language I must expand a little on the peculiar state of philosophy when he began to work. The three developmental phases of philosophy in the nineteenth century of which I have spoken were perhaps most sharply defined in Germany.[4] The premature death of Hegel in 1831 had foreshadowed an impending loss of philosophical momentum. The currents that Kant’s philosophy had set into motion half a century earlier were definitely running out by the 1830’s; German idealism was losing its former allure and the Germans were turning their attention, instead, to the more pressing needs of politics and economics, to the rapidly expanding natural sciences and to the practical problems of an evolving industrial technology. The leading philosophical figure in the mid-nineteenth century was Herman Lotze, a respected, knowledgeable, and even weighty professional, but also, indubitably, a transitional figure whose name has largely vanished from our consciousness and whose writings make today for difficult reading. Lotze served, nevertheless, an important bridge function. He sought to reconcile Kant with Hegel, idealism with naturalism, and science with revelation and to maintain and restore in this way the old philosophical tradition. He served thereby also as a stimulus for the new that was to appear in the last quarter of the century. He became a forerunner for the Neo-Kantians; he inspired the British idealists; his work on psychology proved an important source for Brentano and Husserl; and he also helped to set Frege’s logico-philosophical project in motion.
When Frege came into contact with Lotze as a student at Göttingen he had only a rudimentary philosophical training but still one that was eventually to form the basis for his entire philosophical agenda. In Cuno Fischer’s Kant course in Jena he had heard that the question of the status of mathematical truth was fundamental to the entire Kantian system. For Kant the decisive issue was, according to Fischer, whether mathematical truths were synthetic a priori or empirical in character since they could obviously not be analytic. Transcendental idealism stood and fell with this issue. Lotze’s Logic taught Frege the very different and Leibnizian message that the propositions of mathematics might be considered logical truths. Lotze thought it, in fact, evident that “the principles of mathematics have their systematic place in logic” and that mathematics must be considered “an independently progressive branch of universal logic.” But he was also convinced that the complexity of modern mathematics “forbids any attempt to re-insert it in universal logic.” (Lotze, p. 35) This proved a challenge to Frege’s ingenuity. He soon attempted to carry out the reduction of arithmetic to logic that Lotze had declared to be practically unfeasible. In trying to carry this project through, Frege wrote, he “had to see how far one could get in arithmetic by inferences alone, supported only by the laws of thought that transcend all particulars.” (Frege 1997, p. 48) But he found it difficult to make sure that chains of inference were free of gaps and that no intuitive assumptions were being smuggled into the lengthy deductions. The difficulty, he concluded, was due to “the inadequacy”, “cumbersomeness, and “lack of precision” of language.(Frege 1997, p. 48)
That conclusion was brought home to him through Adolf Trendelenburg’s Historische Beiträge zur Philosophie, a three-volume collection of essays that included a discussion of Leibniz’s characteristic language.[5] Leibniz, so Trendelenburg explained, had endeavored to construct such an artificial language in order to make up for the shortcomings of ordinary language. Leibniz’s language, so Trendelenburg, was in contrast to the natural ones means to represent concepts directly and in a written notation and could therefore be called a Begriffsschrift. Whatever the reasons had been for Frege’s initial interest in Trendelenburg’s collection it was the essay on Leibniz that seems to have caught his imagination. Not only did he borrow the name for his new logic from Trendelenburg’s essay but, that essay is, in fact, the only text referred to in Frege’s Begriffsschrift and when Frege sought to account for his new symbolism in philosophical terms three years later in the essay “On the Scientific Justification of a Begriffsschrift” he once again drew on Trendelenburg for his argumentation. In his piece on Leibniz, Trendelenburg had strongly argued that signs are necessary for human thinking, “both for the solitary process of thought by itself and the busy exchange of thought in human life” but he had added at once that in ordinary language the linguistic signs “have only to a small part an inner relation to the designated idea.” The connection between the sign and what it designates was, rather, ordinarily, as Trendelenburg had put it, “one-sided,” “indeterminate and arbitrary,” “obscured,” and the result of “blind habit,” rather than a discriminating consciousness; it was, in other words, “psychological, rather than logical” in character. (Trendelenburg, p. 3) The realization of these shortcomings, Trendelenburg went on, had led Leibniz to conceive of the possibility of a characteristic language, but that project, though undoubtedly worthwhile, had remained incomplete in Leibniz’s hands. Having begun work on it around 1676, and thus shortly after his invention of the calculus, Leibniz had largely abandoned it ten years later when he went on his journey to Italy to carry out historical research. Frege’s essay “On the Scientific Justification of a Begriffsschrift” was to pick up Trendelenburg’s remarks on the promise of a Begriffsschrift and used them in defense of Frege’s own new logic and its symbolic representation. “Language [and this means, of course, ordinary language],” we read in Frege’s essay, “proves to be deficient… when it comes to protecting thought from error.”[6] Frege notes also that “language is not governed by logical laws” and that its shortcomings “are rooted in a certain softness and instability.”[7] Its words are often ambiguous and this proves to be “most dangerous” in the possibility that “the same word may designate a concept and a single object which falls under that concept. Generally, no strong distinction is made between concept and individual. ‘The horse’ can denote a single creature; it can also denote a species… Finally, ‘horse’ can denote a concept.”[8]
Three years earlier, Frege had already concluded in his Begriffsschrift that the reduction of arithmetic to logic demanded first of all a reform of logic itself and a break with the limitations of the Aristotelian theory and that it required secondly the replacement of ordinary language with an appropriate formal symbolism modeled on that of mathematics. When he had first sought to prove that arithmetic could be derived from pure logic, Frege wrote, “I found an obstacle in the inadequacy of language… Out of this came the idea of the present Begriffsschrift.”[9] He hoped to have invented in this way, he added, also “a useful tool for philosophers” which would help them “to break the power of words over the human mind, by uncovering the illusions that through the use of language often almost unavoidably arise concerning the relations of concepts, by freeing thought from the taint of ordinary linguistic means of expression.”[10]
There are, of course, other ways to think about ordinary language and its relation to a symbolic notation. Thus Wittgenstein wrote in his Tractatus that ordinary language is, in fact, perfectly all right but hides its logical structure under its grammatical surface. The logical symbolism cannot improve on ordinary language but only makes the logic of ordinary language more visible when it considers both syntax of language and the complexities of its use. This picture of the relation of language and logical symbolism can draw now also on the work of structural linguistics with its distinction between surface and deep structure. But the thought that ordinary language is perfectly all right has also led to a very different conception of the relation of language and symbolism – one to which Wittgenstein veered in his later work and which is fully developed in the Oxford Ordinary-Language Philosophy of the 1950’s and 60’s. This view emphasizes that ordinary language is the only language we initially have, and that any new idiom or notation will eventually have to be explained in the terms of ordinary language. There is, thus, no escape from the assumptions built into our language. The symbolic notations of modern logic can only be thought of as extensions for our old ways of speaking not as a replacement for them. As Wittgenstein put it once: “Our language can be seen as an ancient city: a maze of little streets and squares, of old and new houses with additions from various periods; and this surrounded by a multitude of new boroughs with straight regular streets and uniform houses.”[11]
Under the influence of Trendelenburg, Frege saw ordinary language, however, in a more negative light and thus also understood the relation between ordinary language and the symbolism in different terms. I will come back to the question what kinds of considerations drove Trendelenburg, Frege, and other nineteenth century thinkers to speak so vividly of the imperfections of ordinary language. Whatever the reasons for this belief, it motivated, in any case, Frege’s subsequent reflections on the concept of truth. How those reflections are related to his thoughts on the imperfection of language still needs to be considered further and that consideration motivates once more a look at the historical context.
Frege and Nietzsche on the imperfection of language
Frege seems, at first sight, to have little in common with Nietzsche. They were admittedly part of the same generation (being born only four years apart) and they grew up in the same part of the world and of Germany and were thus exposed to the same cultural influences, to somewhat the same education, and to the same general set of ideas. But apart from these biographical circumstances the two seem to share very little. Nietzsche was, after all, a philologist by training, Frege a mathematician. The one derided logic while the other sought to reform it. One wrote on questions of history, metaphysics, and morals, the other on mathematics and meaning. They lived in different social spheres and certainly never got to know of each other. If the historian of philosophy finds it, nevertheless, illuminating to put them side by side it can only be to highlight the extraordinary range of philosophy in their period.
Nonetheless, there are certain affinities between them. Characteristic of both of them is their intense concern with the question of truth. They are both, moreover, highly critical of the correspondence conception of truth. And they both convinced that our language is imperfect. We need to look only Beyond Good and Evil in order to appreciate how strongly Nietzsche concerned himself with the problem of truth. He speaks there of truth as a mystery, a sphinx which our philosophers have hardly begun to decipher. What is truth? Are there certain, indubitable, philosophical truths? Why do we want truth at all? What stands in the way of obtaining it? The way we think is, in fact, deeply determined by our grammatical categories and distinctions and these are, in turn, historical and psychological in origin. The philosopher says “I think” but “what gives me the right to speak of an ‘I’, and even of an ‘I’ as cause, and finally of an ‘I’ as cause of thought?”[12] We would be better advised to say, “it thinks,” but even that would mislead us. “This ‘it’ already contains an interpretation of the event and does not belong to the event itself. The inference here is in accordance with the habit of grammar: thinking is an activity, to every activity pertains one who acts, consequently –‘.”[13] Philosophers speak of the will, as of it were the best-known thing in the world. But willing is “a unity only as a word – and it is precisely in this one word that the popular prejudice resides which has overborne the always inadequate caution of the philosophers.”[14]
What stands in the way of truth for Nietzsche is first of all our language and secondly human psychology. I will try to explain this in sequence. In section 20 of Beyond Good and Evil Nietzsche speaks more generally of a family resemblance “between all Indian, Greek, and German philosophizing” which he considers to be due to a “language affinity” and thus to “the unconscious domination and directing by similar functions.” It is, in particular, the subject-object distinction but also the subject-predicate distinction that seem him built into the grammar of Indo-European languages. He writes: “Philosophers of the Ural-Altaic languages (in which the concept of the subject is least developed) will in all probability look ‘into the world’ differently and be found on different paths from the Indo-Germans and Moslems.” That our language says “Lightning strikes” may suggest to the philosopher a distinction between a substance and its action and thus generate in him a linguistically induced metaphysical picture.
Nietzsche expounds on this further in the essay-fragment “On Truth and Lie in a Nonmoral Sense” of which part one of Beyond Good and Evil can be considered a revised version. He speaks there of our concepts as arising out of the recognition of similarity of different things. “Every word instantly becomes a concept precisely insofar as it is not supposed to serve as a reminder of the unique and entirely individual original experience.”[15] But this demands at the same time a transformation of our perceptual metaphors into schemata, a great edifice of concepts which displays rigid regularity and “exhales in logic that strength and coolness which is characteristic of mathematics.”[16] How we schematize these concepts will, however, differ from language to language and from language-group to language-group. Hence, the variations between the Indo-European and the Ural-Altaic languages. These schematic forms are, however, not entirely arbitrary. “The spell of grammatical functions is in the last resort the spell of physiological value-judgments and racial conditions,” or to speak more cautiously of psychological factors. Where Nietzsche’s remarks about the variability of grammatical forms refers us to the nineteenth century rise of philology and its recognition of the variability of human languages, his explanation of these variations as grounded in physiological and psychological facts refers us to the emergence of physiology, psychology, and anthropology in the same period. When I speak here of a psychological explanation of the linguistic forms, we must think, however, not only of empirical psychology in the modern sense but just as much of the philosophical psychology of the Kantian system. Nietzsche is explicit on this. He allows provisionally that Kant may be right in suggesting that our judgments are shaped by the pure concepts of the understanding and that synthetic a priori judgments depend on our intuition of space and time. But he concludes from this, in contrast to Kant, that we have no reason to regard those judgments as true. “Synthetic judgments a priori should not ‘be possible’ at all; we have no right to them; in our mouths they are nothing but false judgments.”[17]
Nietzsche’s conclusions from all this were, as we realize, ultra-radical. In the essay fragment “On Truth and Lies” he asks dramatically: “What then is truth?” and answers himself: “A movable host of metaphors, metonymies, and anthropomorphisms: in short… truths are illusions which we have forgotten are illusions.”[18] We are not wrong in concluding that Nietzsche whole philosophizing is ultimately based on this particular conception of truth. The conclusions he draws from his observations on language, its grammatical forms, and their psychological foundation is surely different from anything we find in Frege’s work, but the remarkable thing is that Frege shared with Nietzsche a belief in the unreliability and untrustworthiness of language.
But why does that theme work itself out so differently in Frege and how does he account for the notion of “truth?” The answer is that, like Leibniz and Trendelenburg, Frege thinks we can overcome the imperfections of language by constructing a new symbolic, adequate notation. We will not, however, be able to preserve our usual grammatical categories in that notation. Frege writes in his Begriffsschrift: “In my first draft of a formula language I was misled by the example of ordinary language into constructing judgments out of subject and predicate.”[19] Instead he sets out to construct a formal notation in which “everything that is necessary for valid inference is fully expressed; but what is not necessary id mostly not even indicated.” (Ibid.)
References
Michael Dummett, Frege. Philosophy of Language, Duckworth, London 1973
Michel Foucault, “Truth and Power,” in Power/Knowledge, edited by Colin Gordon, Pantheon Books, New York 1980,
Wilhelm Windelband, Die Philosophie im Geistesleben des XIX. Jahrhunderts, J. C. B. Mohr, Tübingen 1909
Hermann Lotze, Logic, translated by Bernard Bosanquet, Clarendon Press, Oxford 1888,
Gottlob Frege, The Frege Reader, edited by Michael Beaney,
Gottlob Frege, Conceptual Notation, translated and edited by Terrell Ward Bynum, Clarendon Press, Oxford 1972,
Hans Sluga, “Frege and the Indefinability of Truth,” in From Frege to Wittgenstein, edited by Erich Reck, Oxford University Press, Oxford 2001
Hans Sluga, “Freges These von der Undefinierbarkeit der Wahrheit,” in Das Wahre und das Falsche. Studien zu Freges Auffassung der Wahrheit, edited by Dirk Greimann, Olms, Hildesheim 2006.
Bernard Bolzano, Wissenschaftslehre, 2nd ed., ed. by Wolfgang Schultz, Felix Meiner, Leipzig 1929, vol.
Gottlob Frege, “Vorlesungen über Begriffsschrift“, History and Philosophy of Logic, vol. 17, 1996.
Notes
[1] There are no references to Bolzano and his Wissenschaftslehre to be found in Frege’s writings. While he engaged in debate with two of Bolzano’s followers, Benno Kerry and Alwin Korselt, he seems not have read Bolzano’s Wissenschaftslehre and he makes no reference to its author. Where Frege’s and Bolzano’s ideas overlap that may be due to their common source in Herbart (with whom both Bolzano and Frege were certainly familiar) though Lotze is the more likely source of those Fregean doctrines that appear similar to Bolzano’s.
[2] He knows, for instance, that Sextus Empiricus interpreted the Greek word “aletheia” to mean the unhidden, “to me lethon” thus anticipating Heidegger’s controversial interpretation of that term. (Sect. 24, p. 111) He also draws attention to the principle omne ens est verum asserted by some modern writers (Locke, Wolff, and Baumgarten among them) who sought to make “metaphysical truth” into a property of beings. But in agreement with Leibniz he dismisses such alternatives as “utterly useless and devoid of sense.” (Sect. 29, p. 143)
[3] Immanuel Kant, Critique of Pure Reason, B82-84.
[4] offer a succinct survey of these phases.
[5] We may wonder at this point why Frege would have looked at Trendelenburg’s work in the first instance since it concerns mostly matters far removed from his own mathematical interests. The answer is probably that the relevant third volume in which the essay on Leibniz appeared contained also an attack on Cuno Fischer’s thesis that the synthetic a priori character of mathematical statements implied transcendental idealism. According to Trendelenburg, the Kantian doctrine was fully compatible with a realist conception of space and time. Frege would presumably have been familiar with the Fischer-Trendelenburg controversy from the second edition of Fischer’s Kant book and possibly also from Fischer’s lectures at Jena. The debate between the two may for be important for understanding Frege’s thesis in his Foundations of Arithmetic that geometrical truths are synthetic a priori.
[6] Gottlob Frege, “On the Scientific Justification of a Conceptual Notation,” in p. 84.
[7] Ibid., pp. 84 and 86.
[8] Ibid., p. 84
[9] Gottlob Frege, Begriffsschrift, loc.cit., p. 48.
[10] Ibid., pp. 50-51.
[11] Ludwig Wittgenstein, Philosophical Investigations, section 18.
[12] Fridrich Nietzsche, Beyond Good and Evil, section 16.
[13] Ibid., section 17.
[14] Ibid. section 19.
[15] Friedrich Nietzsche, “On Truth and Lie in a Nonmoral Sense,” p. 83.
[16] Ibid., p. 85.
[17] Beyond Good and Evil, section 11.
[18] “Truth and Lie,” p. 84.
[19] Begriffsschrift, p. 54.
