The Birth of Logic

Kant, Schopenhauer, Nietzsche, and Durkheim

Last week I wrote about Émile Durkheim (1858–1917), the French founder of the academic discipline of sociology, and Marcel Mauss (1872–1950), his nephew and the “father of French ethnology.”

As a reminder, Durkheim and Mauss, at the start of their book Primitive Classification (1903), write about the mental “faculties of definition, deduction, and induction.” In particular, they argue that these apparently basic acts — acts like defining a word, drawing logical conclusions, and drawing principles from evidence — are neither innate nor universal.

The classical view is that classical logic has not changed over time, even if we have gotten better at applying it. Logic, in this view, is securely grounded, and has made no progress since it was first articulated by Aristotle (384–323 BC), sometime before 323 BC — but neither has it needed any amendments. Logic, in this telling, burst fully formed from Aristotle’s head, not unlike Athena from the forehead of Zeus.

The idea of logic being born in Aristotle’s head is as upsetting to me as the idea of Athena’s being born from Zeus’ head. From black-figure vase painting, Athena’s birth from Zeus’ head, cleaved by Hephaestus, Phrynos (signed), c. 560 BC, British Museum, London.

Over the course of the 19th Century, however, the idea that logic is unchanging, the idea that logic holds everywhere, and the idea that logic was built on faculties that are innate and stable all came into question.

In my opinion, a decisive blow was dealt to both the classical view of the history of logic, and to classical logic itself, in 1903 with Primitive Classification, which we’ve been discussing, and which relied on anthropological fieldwork.

Five years later, in 1908, L.E.J. Brouwer’s “The Unreliability of Logical Principles” dealt another blow from quite another quarter, during an abstract debate about the foundations of mathematics. In other words, classical logic faced assaults on two fronts: the experiential, and the theoretical.

Before we go into that, let’s take a closer look at the classical view. Here’s Immanuel Kant (1724–1804), expressing exactly this sentiment, in his Preface to the second edition of the Critique of Pure Reason (1787, emphasis his):

That from the earliest times logic has travelled this secure course can be seen from the fact that since the time of Aristotle it has not had to go a single step backwards, unless we count the abolition of a few dispensable subtleties or the more distinct determination of its presentation, which improvements belong more to the elegance than to the security of that science. What is further remarkable about logic is that until now it has also been unable to take a single step forward, and therefore seems to all appearance to be finished and complete. For if some moderns have thought to enlarge it by interpolating psychological chapters about our different cognitive powers (about imagination, wit), or metaphysical chapters about the origin of cognition or the different kinds of certainty in accordance with the diversity of objects' (about idealism, skepticism, etc.), or anthropological chapters about our prejudice (about their causes and remedies), then this proceeds only from their ignorance of the peculiar nature of this science. It is not an improvement but a deformation of the sciences when their boundaries are allowed to run over into one another; the boundaries of logic, however, are determined quite precisely by the fact that logic is the science that exhaustively presents and strictly proves nothing but the formal rules of all thinking (whether this thinking be empirical or a priori, whatever origin or object it may have, and whatever contingent or natural obstacles it may meet with in our minds). (B viii)

Logic ends with Aristotle, who rendered it “finished and complete.” This is precisely the position that Durkheim wishes to question. But let’s first take a look at some intermediate steps.

An earlier argument against the idea that logic bursts forth fully formed from the mind of Aristotle comes from Schopenhauer, who was a great admirer of Kant’s, but who does part ways with him in certain significant regards.

Although Schopenhauer might agree that the laws of logic had not changed from Aristotle to the 19th Century, he at least sees the historicity of logic in Plato’s dialogues (~400–347 BC) and in Sextus Empiricus’ Against the Mathematicians (~200). In other words, he sees logic as developing and having a human history.¹

Here’s Schopenhauer (1788–1860), World as Will and Representation (1818), vol. I, §9. He argues that the certain rules were first explicitly agreed and “jointly acknowledged” at the start of every debate. Originally, these propositions were specific to each debate. But over time, they grew in generality and in repetition. Eventually, over a process lasting centuries, the “logical principles” came to be codified (emphasis mine):

These propositions were at first concerned only with the material of the inquiry. It was soon observed that, even in the way in which the debaters went back to the jointly acknowledged truth, and sought to deduce their assertions from it, certain forms and laws were followed, about which, although without any previous agreement, there was never any dispute. From this it was seen that these must be the peculiar and essentially natural method of reason itself, the formal way of investigating. Now although this was not exposed to doubt and disagreement, some mind, systematic to the point of pedantry, nevertheless hit upon the idea that it would look fine, and would be the completion of methodical dialectic, if this formal part of all debating, this procedure of reason itself always conforming to law, were also expressed in abstract propositions. These would then be put at the head of the inquiry, just like those propositions jointly acknowledged and concerned with the material of the inquiry, as the fixed canon of debate, to which it would always be necessary to look back and to refer. In this way, what had hitherto been followed as if by tacit agreement or practised by instinct would be consciously recognized as law, and given formal expression. Gradually, more or less perfect expressions for logical principles were found, such as the principles of contradiction, of sufficient reason, of the excluded middle […] and so on. That all this came about only slowly and very laboriously, and, until Aristotle, remained very incomplete, is seen in part from the awkward and tedious way in which logical truths are brought out in many of Plato’s dialogues, and even better from what Sextus Empiricus tells us of the controversies of the Megarics concerning the easiest and simplest logical laws, and the laborious way in which they made such laws plain and intelligible.

So what was once tacit and implicit came to be made explicit through a difficult and painful process. Notice also that the concern is not only pedantic but aesthetic: “it would look fine” if the basic principles of reason were expressed abstractly. This sense of a long, arduous struggle for the establishment of logic permeates both Durkheim’s work as well as another enemy of the classical view: Friedrich Nietzsche (1844–1900).

By the 1880s, Nietzsche was famously mounting an assault on the idea that concepts like good and evil are basic and innate categories that exist independently of human history and culture (Beyond Good and Evil, 1886) and that morality itself is simple and straightforward (On the Genealogy of Morality, 1887). Schopenhauer’s sense that apparently simple mental constructs actually come about through a complex and painful struggle over long periods of time is everywhere evident in Nietzsche’s works.

But in the decade before, Nietzsche, influenced by Schopenhauer, had already developed a structurally similar critique of logic itself. Just as he would later show how moral categories emerge from complex historical processes rather than from eternal truths, he had in the 1870s shown how logical thinking depends on abstraction which ignores the uniqueness of experience — and abstractions which therefore presuppose the structure of reality. Note especially the use of the word “presupposition,” which will later become a central feature of Gilles Deleuze’s (1925–1995) critique of Western philosophy.

Both philosophy and logic depend on concepts. In the most classical deductive syllogism, “All humans are mortal” and “Socrates is a human.” Therefore “Socrates is mortal.” But this reasoning assumes not only the rules of inference, but more fundamentally that “human” is a stable conceptual category in both premises. If this seems obviously true, remember that this feeling of obviousness is exactly what we’re trying to dismantle.

Here’s Nietzsche, Human, All Too Human (1878), I, §11:

Logic too depends on presuppositions with which nothing in the real world corresponds, for example on the presupposition that there are identical things, that the same thing is identical at different points of time: but this science came into existence through the opposite belief (that such conditions do obtain in the real world).

While Schopenhauer uses historicity to contextualize logic, Nietzsche mounts a more direct attack on the act of conceptual groupings themselves.

Even earlier, Nietzsche had called stable concepts into question. From On Truth and Lies in a Nonmoral Sense (1873):

Every word immediately becomes a concept, in as much as it is not intended to serve as a reminder of the unique and wholly individualized original experience to which it owes its birth, but must at the same time fit innumerable, more or less similar cases — which means, strictly speaking, never equal — in other words, a lot of unequal cases. Every concept originates through our equating what is unequal.

Let us now return to Durkheim, who seeks to answer precisely this question through sociological evidence. His introduction to Primitive Classification (1903) continues:

Admittedly, it has been known for a long time that, in the course of history, men have learned to use these diverse functions better and better. But it is thought that there have been no important changes except in the way of employing them; that in their essential features they have been fully formed as long as mankind has existed.

In other words, Durkheim is responding to Kant’s ahistorical view, which sees the operations of the mind as stable, universal, and unchanging. For Kant, reason has both a fixed character and fixed capacities — and he thinks its fixed character is to seek past its fixed capacities.² Durkheim instead regards reason as evolving. So though he does not name him, he is arguing directly against Kant.³

Durkheim argues, therefore, that mental functions have a history. This history is not just about using the same faculties in new and improved ways; instead, the faculty itself changes over time and across cultures.

The idea that the mind can change is contra Kant, who, though he critiques pure reason as a source of knowledge of the “thing-in-itself,” still thinks that reason itself, is stable, universal, and unchanging. Reason is always seeking things it can’t know (e.g., metaphysics), but in this seeking its nature is unchanging. Moreover, Kant regards what he calls the forms of the intuition of time and space, and the achievement he himself was most proud of, the list of categories, which include attributes of the objects of perception. These are: unity, plurality, totality, reality, negation, limitation, substance-accident, cause-effect, community (reciprocal causation), possibility/impossibility, existence/non-existence, and necessity/coningency. These are pure concepts of the understanding which, Kant thinks, structure all possible experience. These are precisely the categories that Nietzsche, and later Deleuze, will critique. Notice that several of them, especially unity, plurality, totality are required for concepts to function, and reality, negation, and limitation are required for logic to function.

Durkheim continues:

It has not even been imagined that [these functions] might have been formed by a painful combination of elements borrowed from extremely different sources, quite foreign to logic, and laboriously organized. And this conception of the matter was not at all surprising so long as the development of logical faculties was thought to belong simply to individual psychology, so long as no one had the idea of seeing in these methods of scientific thought veritable social institutions whose origin sociology alone can retrace and explain.

So far, we’ve covered three major critiques of logic. Schopenhauer showed its historical development — logic was not born complete but emerged through centuries of debate. Nietzsche revealed its dependencies — before we can even begin doing logic, we must accept presuppositions about identity, stability, abstraction, and non-contradiction. Finally, Durkheim has brought in anthropological evidence for an idea nascent in Nietzsche: that all concepts emerge from social interactions. This is because concepts are built upon language, and language is built upon social interactions.

If you object that concepts simply reflect reality, you have presupposed precisely what requires proof. Because, as Durkheim will demonstrate, our very notion of “reality” is itself socially constructed. And Brouwer will start to show that assuming the reality of numbers has limitations too.

As always, I’d love to hear from you,

Bryan

1. Charles Sanders Peirce (1839–1914), another great admirer of Kant’s, also thinks that logic has a history: “[The] history of logic is not altogether without an interest as a branch of history. For so far as the logic of an age adequately represents the methods of thought of that age, its history is a history of the human mind in its most essential relation — that is to say with reference to its power of investigating truth.” (CP 1.28)

2. Kant, the beginning of Preface to the first edition of the Critique of Pure Reason (1781):

Human reason has the peculiar fate in one species of its cognitions that it is burdened with questions which it cannot dismiss, since they are given to it as problems by the nature of reason itself, but which it also cannot answer, since they transcend every capacity of human reason. (A vii)

3. I felt that although Durkheim names Aristotle, he’s actually arguing against Kant. Steven Collins came to the same conclusion in “Categories, concepts, or predicaments?” in The Category of the Person (1985):

In fact, as we shall see, it is not Aristotle but Kant — mediated in a particular way by certain French philosophers of Durkheim's own day — whose notion of ‘categories of thought’ lies behind Durkheim’s approach to these problems. Durkheim has often been taken, in a famous phrase, to have ‘sociologised Kant’.