Ludwig Wittgenstein vs. Gottlob Frege: Between Logic and Language

How do Wittgenstein and Frege attempt to grapple with a similar problem—that of thinking clearly – and yet draw such opposite conclusions about the nature of and best available solutions to that problem? This article begins by exploring some of the personal differences between Frege and Wittgenstein: between the lives they led, their temperaments, and how both are of relevance when understanding their intellectual differences. We will then discuss the disagreement between the two in earnest, with a particular focus on their attempted definitions of logic, thought, and the relationship between the two.

It is worth saying something about each of our two protagonists in turn, before discussing the philosophical basis of their dispute. Both of them are understood by philosophers in the English-speaking world to be two of the most influential figures in the development of modern-day philosophy. Indeed, they both have a strong claim to be the most important figure in that story. Yet they were demonstrably of entirely different temperaments.

According to those who knew him best, Wittgenstein was erratic, often consumed by periods of serious depression, aggressive and moralistic. Although he found great acclaim from many of the greatest philosophers of his time early in life, he retained a strictly iconoclastic disposition throughout his life.

Frege, by all accounts, was the epitome of a mild-mannered professor, who showed little aggressive intent even towards those who were critical of his work, and even in spite of the only modest interest garnered by his work. Indeed, as with many philosophers, little of general interest appears to have happened to Frege, and he lived the vast majority of his life in a way entirely characteristic of German academics of the period.

Wittgenstein, on the other hand, lived what was in many ways a restless life. Perhaps it is always a mistake to attempt to understand a philosopher’s work through the lives they lived, but it seems similarly erroneous to attempt to divorce our understanding of their intellectual output from them.

Life and Work, Continued 

Indeed, if there isn’t a relationship between a philosopher’s life and their work, this only speaks ill of their commitment to philosophy, and both Frege and Wittgenstein were, in their different ways, exceptionally committed.

Even though Frege’s work constituted a radical break with what came before him philosophically—indeed, it was so against the grain that it garnered little attention during his lifetime—he was not disposed to putting things in Wittgenstein’s confrontational terms. The idea that whole swathes of seemingly productive and intelligible discourse were in need not of clarification, but could be categorized as nonsensical and dismissed, would have been anathema to him.

Though this interpretation of Wittgenstein is not the only way of understanding his early work, it is not at all out of keeping with his general disposition. He was polemical, his prose is exciting and demanding and self-consciously paradoxical. He conceived of himself not as building a system, but as generating a new approach to philosophy—one which produces no results at all, in fact, and defines itself not in terms of the doctrine it generates but in terms of how it changes us and affects the way we think going forward.

This is all to say that it is difficult not to conflate the personal and intellectual differences between Wittgenstein and Frege, and it is probably necessary to bear some of the former differences in mind as we explore their disagreement.

This article focuses on the early work of Ludwig Wittgenstein and its relationship to that of Gottlob Frege, who Wittgenstein greatly admired and who was a serious influence on Wittgenstein’s philosophical development as a younger man. In particular, it focuses on how Wittgenstein’s early work—which culminated in the production of a short book, known as the Tractatus Logico-Philosophicus—functions as a critique of Frege’s conception of logic and language.

The element of Wittgenstein’s philosophy which can be taken to be critical of Frege lies in his conception of logic. Frege developed a conception of logic that radically departed from the established conception of logic, which was first developed by Aristotle.

Wittgenstein conceives of logic simply as that which is true or false in all circumstances—there is no possibility of a logical statement being anything other than its determined truth valuation. On Wittgenstein’s view, this is equivalent to saying that logic statements have no content in the sense that they do not express a genuine thought.

A brief précis of Wittgenstein’s project in the Tractatus is probably necessary here to make the point clearer here. Wittgenstein describes the Tractatus as an attempt to define that which can be said and that which cannot, to clarify our thinking, and to figure out which of the things we pre-reflectively think make sense and which ones are nonsense.

The criteria for something making sense lies in our ability to picture the thing about which a certain statement is made, to be able to represent it. Wittgenstein is attempting to characterize the world of facts—that is, the world as it is understood—above the world as it is (consisting of a-representational “things”). Logical statements cannot be pictured in this way, and therefore it is true to say that logical statements are not “sense” in the specific way Wittgenstein is interested in.

What in Frege’s work could Wittgenstein be taken to be responding to? As we had to give a summary of Wittgenstein’s project in order to achieve an approximate definition of his conception of logic, so we need to give a general account of Frege’s philosophy to do the same.

The complication is that whereas Wittgenstein’s intellectual output was, for the most part, at least nominally or apparently either philosophical or unclassifiable, Frege was, by training and by profession, a mathematician, not a philosopher. Explaining Frege’s intellectual project, even in quite a general way, is therefore extremely difficult.

The best we can say is that Frege, like Wittgenstein, was greatly concerned with the inconsistency, inadequacy, and muddle which characterizes ordinary language; that is, how people actually tend to speak spontaneously.

As a result, Frege was interested in constructing an artificial, logical language that could eradicate such inadequacies and represent thought in a way that was entirely clear, precise, and unambiguous. Part of the difference between Wittgenstein and Frege stems from their differing conceptions of the epistemic status of logic.

For Wittgenstein, logic does not produce facts, and the propositions must be strictly distinguished from those of other disciplines. Consider:

“[When a] logical proposition acquires all the characteristics of a proposition of natural science … this is a sure sign that it has been construed wrongly”.

In contrast, Frege appears at various points to conceive of the “findings” of logic as comparable to those of other fields of investigation. Given that logic for Frege captures that which we are able to think of, consider Adrian Moore’s analysis of this conflation:

“When he contrasted the domain of what is thinkable and therefore subject to the former laws with the domain of what is actual and therefore subject to the latter laws—as indeed he did both of these with the domain of what is intuitable and therefore subject to the laws of geometry—he did so by treating them simply as wider or narrower domains and by calling the first ‘the widest domain of all’.”

To summarize what we’ve established so far: the tension between Wittgenstein’s early thought and Fregean philosophy arises in spite of their shared concern with the clarity of thought and the problems with our ordinary way of speaking.

On what basis does Wittgenstein draw such a stringent distinction between the domain of logic and other areas? In other words, what’s so special about logic? Following Moore again, there is a sense in which logical analysis has no content. Logic is not just the “widest domain” for thought, but it rather constitutes the space in which we start to draw the distinction between different domains. Logic is not a limit to what can be thought (which, for Wittgenstein, means what can be pictured and, therefore, what can be represented in a language).

As Wittgenstein puts it himself: “In order to be able to draw a limit to thought [understood as a limitation of thought], we should have to find both sides of the limit thinkable.” This seems paradoxical, and indeed Wittgenstein breezily adds that “we should have to be able to think what cannot be thought.”

Wittgenstein is defining thought in a relatively narrow sense—that of being liable to representation—and thinking in a broader sense—that of gesturing towards both thought in the narrow sense, and what is not thought. The crux of the dispute between Wittgenstein and Frege, therefore, comes down to a conception of logic and what it does. For Frege, logical analysis produces knowledge, and for Wittgenstein, logic tells us nothing new and does not produce anything but the ground or the conditions for further investigations.