On this occasion I would like to revisit the notion of “truth” established by Gottlob Frege in his essay “Der Gedanke” (1918)¹, published in a collaborative volume dedicated to the philosophy of German Idealism, and elaborated in his influential book Begriffsschrift (1869), whose task consists in constructing expressions for complex concepts from primitive signs in such a way that rigorous reasoning is formally secured. With this selection of works, I suggest that the split between a “young Frege” and a “mature Frege” is an artificial interpretive construction². By analyzing the syllogisms of being and thinking that unfold from fragment 3 of Parmenides’ poem—the first treatise of ontology in Western philosophy—it will be argued that the Fregean project proves untenable insofar as it maintains the nonexistence of a distinction between the logical differences internal to thought and the categorical differences internal to the order of what is, failing thereby to resolve the Parmenidean aporia.

I

To address the topic, I begin from the Fregean conception according to which logic is essentially inferential, such that to think a logical content is to articulate it within a network of inferences, and on this basis I reformulate three fundamental notions. Thought (Gedanke) is a logical, non-psychological object, belonging to a third realm distinct from both the physical world and the subjective world; it is the bearer of truth or falsity, constitutes the sense of assertoric sentences, and exists objectively, fixedly, and timelessly, independently of being thought—although it is accessible only through language. Truth (Wahrheit) is a primitive and indefinable concept that orients logic and science; it is not a sensible property nor an addition to the content of thought, but a timeless determination that is not altered by its recognition. By contrast, representation (Vorstellung) designates a strictly psychological content, proper to the subject’s inner life—sensations, images, feelings, or moods—which always requires an individual consciousness in order to exist and is therefore essentially private and incommunicable.

Frege argues that, since logic is concerned with truth rather than with the psychological processes of thinking, that for which the question of truth arises cannot be either a subjective representation or a sentence considered as a sensible object, but must instead be an objective, non-psychological thought that constitutes the sense of the assertoric sentence and belongs to an autonomous third realm; it follows from this that truth is a primitive and timeless determination of thoughts themselves, and that logic investigates the laws of truth rather than those of empirical thinking.

Danielle Macbeth, in Realizing Reason (2014), places Frege at the center of a narrative aimed at elucidating how cognitive access to things themselves is possible, especially in the domain of mathematics. She argues that the full realization of the power of reason is achieved in conceptography, though only at the end of a dialectic of transformation that begins with sense-certainty and the presumed immediacy between perception and reality. Along this historical trajectory, philosophy successively confronts the Greek problem of the being of mathematical objects, the modern problem of the nature and possibility of synthetic a priori judgments, and finally the nineteenth-century problem of the possibility of ampliative deductive proof, whose understanding requires grasping an intelligible unity irreducible to the mere sum of its parts, analogous to the unity proper to Kant’s synthetic a priori judgments.

Against the Kantian division between concepts and intuitions, Frege introduces the distinctions between Sinn and Bedeutung and between concept and object, showing that only through this refinement can ampliative deductive proof be rendered intelligible and, with it, that pure reason ceases to be merely critical and reflective and reveals itself—according to Macbeth—as a faculty capable of knowing things as they are in themselves. By correctly distinguishing, as Frege does, between sense and reference and between concept and object, one attains the standpoint of reason, fully realizes its cognitive power, and clarifies its intentional orientation toward reality and truth.

II

In his enigmatic book Thinking and Being (2019), Irad Kimhi offers the tools to challenge the Fregean project as described by Macbeth. The argument of the work can be summarized as follows:

1. Philosophical logic—the project undertaken by Kimhi—has the task of jointly clarifying language, thought, and being, without splitting these domains into independent levels.
2. The contemporary conception of logic as a metalinguistic study of formal languages divides this task into two distinct operations: the formalization of language and the external assignment of semantic values.
3. Any separation between a formal language and a semantic metalanguage introduces an external standpoint incompatible with the presuppositionless aspiration of philosophical logic.
4. Frege conceives his logical system as a universal language in which all reasoning can and must be expressed without recourse to an external metatheoretical position.
5. In a fully achieved universal language, the logical differences internal to thinking cannot be distinguished from the categorical differences internal to the order of what is.
6. For this reason, within the effective practice of truth-oriented thinking there is no place for semantic notions such as sense, reference, or “truth” understood as objects.³
7. However, a logic that excludes any internal position from which to articulate conditions of truth and falsity lacks an explicit logical foundation for those very notions.

In conclusion, although Frege’s project preserves unity in contrast to contemporary metalinguistic conceptions, it exhibits an internal limit consisting in its inability to ground, from within the very activity of rigorous thinking itself, a properly logical notion of the conditions of truth and falsity.

Against the now-dominant conception of logic as a metalinguistic discipline devoted to the study of formal languages—and, through them, of ordinary language—Kimhi emphasizes a decisive distance from earlier understandings of logic. Contemporary approaches tend to split—this being the second premise of the argument—into two independent operations. In contrast to this fragmentation, Frege remains faithful to the classical demand for a presuppositionless logic, conceived as a universal language in which thinking itself is articulated. The idea of the Begriffsschrift is not designed to be the object of an external semantic theory, but to render transparent, from within, the inferential structure of judgment and the character of logical truth. In a fully realized system of this kind, any distinction between logical differences internal to thought and categorical differences internal to the order of what is disappears, and with it the very possibility of adopting a metatheoretical perspective.

III

The study in Thinking and Being begins with Parmenides’ poem, which is usually regarded as the first treatise of ontology in Western philosophy, understood as the logical study of thought and of what is (being). Kimhi considers different readings of the Greek verb ἐστί, confronting the interpretations of the well-known commentators on the Eleatic, Charles Kahn and Alexander Mourelatos⁴. Focusing on fragment 3 of the poem—to gar auto noein estin te kai einai—Kimhi derives the syllogisms of being and of thinking.

The thesis that being and thinking are the same is distorted when it is made compatible with a conception of truth as correspondence between thought and something external to it. It is also deformed when truth is taken to depend on something that does not belong to the activity of thinking itself. At first glance, negation and falsity seem to become intelligible only by opening a gap between thinking and being, conceiving thought as a representation whose value depends on a reality extrinsic to it. But this representational gap is not a theoretical gain; it invariably corresponds to the abandonment of a basic logical point, disarticulating the regimes of ontology and world. The identity of thinking and being does not express a dispensable metaphysical thesis: it is the very condition under which thinking can be true or false.

There is no hiatus between judging that p and judging that very judgment as true. The evaluation of truth does not rest on the recognition of an additional fact, but is internal to the very act of judging. Conceiving thought as the representation of an external reality, by contrast, introduces a logical gap between the judgment and its evaluation as true. Frege conceives thinking and judging in such a way that the content thought has a logical unity and a mode of being of its own prior to and independent of its being judged true or false. The judgeable content functions as a common factor between thought and judgment, such that one can think a content without yet affirming it as true. On this conception, judgment adds to the previously thought content the recognition of its truth, which implies that the logical unity of the content of thought precedes the logical unity of judgment and, therefore, that the truth or falsity of what is thought is extrinsic to its being as propositional content. The Parmenides–Kimhi puzzle arises when one simultaneously maintains that negation and falsity are intelligible and that there is no logical gap between truly thinking that p and p’s being the case. Accepting both claims requires rejecting the Parmenidean exclusion of negation: the initial task of Kimhi’s philosophical logic, which culminates in a theory of syncategorematic terms, is to account for that identity without eliminating the possibility of falsity.

Parmenidean aporia arises precisely from the conjunction of two trivialities: (i) that the use of negation and the evaluation of a statement as false are fully intelligible, and (ii) that there is no logical gap between truly thinking that something is the case and that very thing’s being the case. However, in order to affirm (i) one must not follow the goddess’s guidance, according to which negation and falsity have no place in serious, truth-oriented discourse, since her point is that the truth of (ii) excludes the possibility of (i). The task of philosophical logic, therefore, is to account for the truth of (ii) without discarding the possibility of (i)—something that proves impossible so long as both appear as separate points that need to be aligned with one another.

Frege seems to offer a straightforward solution to this aporia: on the one hand, he affirms that the truth or falsity of a thought depends on something extrinsic to it, and, on the other, he denies that the predicate “is true” expresses a property—whether intrinsic or relational—of the thought. On this basis, he proposes to dissolve the puzzle by identifying the facts of the world with true thoughts, such that what is the case is nothing other than a thought that is true. But this attempt fails, according to Kimhi, because it rests on a decisive assumption: that something’s being thus-and-so the case can be separated from its being true or false—that is, that the propositional unity of what is the case can be dissociated from its truth or non-truth. In doing so, Frege presupposes that the true or the false can be isolated from the very activity of thinking or saying that something is thus-and-so. Kimhi’s argument maintains that this dissociation is incoherent, and that it is precisely by relying on it that the Fregean maneuver fails to confront the underlying difficulty.

IV

Frege thought that the things we can think or say are not, at the most fundamental level, different from other objects in nature. Like them, the things we can think exist independently of us—of those who think or say them. Contemporary philosophers usually call such items “propositions,” and there are many conceptions of what propositions are, what their constituents are, and how finely they should be individuated. But what almost everyone agrees on is that truly thinking that Antarctica is frozen, or falsely thinking that Antarctica is tropical, consists in a thinker standing in a relation—the relation of thinking—to an object of that kind—a proposition—that is true or false independently of whether anyone stands in that relation to it. Just as an object such as Mount Everest can have the property of being tall, so too the proposition that Antarctica is frozen can have the property of being true, and the proposition that Antarctica is tropical can have the property of being false. That a subject thinks that Antarctica is frozen or that it is tropical consists in her standing in a certain relation to those propositions. Thinking, understood in these terms, is not at all special in kind (even if it differs in its details) any more than sitting in this chair is, insofar as my sitting involves a relation between me and it. Thinking, so understood, is not after all something unique. To really think, then, simply consists in what we find in nature anyway: objects, among them propositions and thinkers; relations, among them those that obtain between thinkers and propositions; and properties, among them truth and falsity.

For a philosopher who inherits this relational conception from Frege, the Parmenidean aporia may seem entirely harmless. For what she will say is that, when I think that Antarctica is tropical, the world does indeed give me something to think: a proposition—one that is false. In this way, although I think what is not, what I think is not nothing. There is something there for me to think: a false proposition.

Fregean propositions can perform this trick, however, only if it is reasonable to suppose that there could be things in themselves. And Kimhi argues that this way of thinking about them is deeply confused. To appreciate his reasoning, consider an image: a line drawing of an erupting volcano. I can use such an image to indicate that the volcano is erupting, by pointing to it and saying: things are as they are in this image. But suppose instead that I wanted to indicate that the volcano is not erupting. It would not suffice simply to show an image of a calm volcano, since this would fail to indicate, specifically, that what is absent is the eruption. Rather, in order to say that the volcano is not erupting, I would have to use the same image (the image of the erupting volcano) and say that things are not as the image represents them. In other words, I would have to use the same image to state a fact and its negation.

The image analogy helps to bring out a strange feature of Frege’s thinking about propositions. Since I have to use the same image both in the case in which I want to say that the volcano is erupting and in the case in which I want to say that it is not, it is natural to conclude that the image itself cannot say anything about how things are. And this, Kimhi maintains, is exactly Frege’s conclusion. For Frege, propositions do not themselves say that things are one way or another; only a thinker can do so when she “asserts” the proposition. This is precisely what Kimhi denies. For, he argues, the very fact that we can use the same image to express both an affirmation and a negation suggests that a proposition already says that things are a certain way. After all, I cannot say “yes” or “no” to a proposal unless something is being proposed. Kimhi’s critique is that Frege imagines that there could be something like an object—a proposition—that in itself says nothing and yet can be used to say how things are or are not. That is to imagine something incoherent. And therefore, there cannot be such things as the propositions Frege defends. This is what we have called logical–semantic collapse.

From this a more far-reaching conclusion follows: ultimately, there is no way to recover what is meaningful from what is not. Thus, if nature—in the sense of what science investigates—consists of objects, properties, and their mutual relations, mere collections of things that signify nothing in themselves, then meaning, whether concerning what is or what is not, cannot be part of nature. Kimhi’s careful elaboration and deployment of this and related arguments destabilizes a deeply entrenched picture of the world and of the place thought occupies within it. Once the foundations have been shaken, reconstruction must now proceed. And once the very idea of propositions independent of thought has collapsed, the ancient Parmenidean argument about falsity and negation comes back to life, providing a point around which to begin anew.

1. Specifically in Beiträge zur Philosophie des deutschen Idealismus I, pp. 58–77. Appearing as the first installment in the series of three philosophical investigations, and together with “Über Sinn und Bedeutung,” it constitutes one of Frege’s two most influential and extensively discussed articles. ↩︎
2. In Frege’s Logic, Danielle Macbeth observes that the German philosopher, logician, and mathematician celebrated at this conference cannot be understood as either an inferentialist or a representationalist, but rather as an unprecedented synthesis of both approaches. ↩︎
3. There are no logical objects, only logical concepts. From this follows the failure of Frege’s logicist program. What undermines logicism is the attempt to introduce logical objects to serve as numbers, since this also leads him to introduce “Basic Law V,” and, as is well known, this axiom gives rise to Russell’s paradox (Macbeth, 2014, 298–299). ↩︎
4. Charles Kahn, “The Greek Verb ‘To Be’, and the Concept of Being”; Alexander Mourelatos, “Some Alternatives in Interpreting Parmenides”.  ↩︎