Latour’s revision: objects and “truth”

Over the past week I was reading something that reminded me of Kant’s Critique of Pure Reason, particularly the Kantian problem of a priori and a posteriori knowledge. At its core, the Kantian problem can be framed around the claim that mathematics and logic are based on synthetic a priori judgments – statements that are true independent of experience. At its most basic and simple, the Kantian problem is based on Euclidean geometry (he also uses Newtonian mechanics as an illustration), with Kant’s model derived from the argument that our intuitions of concepts, figures, and other constructions played an essential role in the development or discovery of geometrical theorems. (I will cover this in much more depth, especially from a mathematics and physics point of view, in another essay – or possibly a series of essays, as I’d also like to delve into the history leading up to Kant’s work).

Wanting to refresh my memory on the Kantian problem, in my recent reading I came across a couple of postmodernist attempts at explaining the issue. Some of what I had read reminded me of a past essay on Latour and the postmodern project (linked above).

One will see that in my critique of Latour’s project, I reflected on how constructing the postmodern view requires first splitting apart the relationship between subject and object. The fracture occurs on the side of the subject, at the expense of the object. This rejection of the object – an essential move for postmodern subjectivism – is synonymous with the disposal of any possible recognition that certain methodologies have a stronger claim to truth than others. One epistemological consequence is deep subjectivism and social relativism. In other words, pure subjectivism produces a fragmented landscape of relative worldviews, which then gives rise to extreme forms of identity-based thinking that transcend even archaic tribal structures. And while all of this may seem abstracted from the Kantian problem, the postmodern turn – and its embrace of deep subjectivism -ultimately goes back to Kant.

Historically, the failure of the empiricist and rationalist traditions to resolve the Kantian problem led some to conclude that there is no way to objectively know external reality. But something important happened: first, Gottlob Frege formulated Basic Laws of Arithmetic, which aimed to demonstrate the logical nature of mathematical laws. Frege’s interest had to do with the foundations of mathematics. In contrast to the Kantian view, his motivation was to show that the basic laws of number theory are derivable from analytic truths of logic, which, in the context of the Kantian problem, meant we need only appeal to the human faculty of understanding and not to some faculty of intuition (i.e., the synthetic a priori). However, for reasons I will discuss in a future entry, Frege’s Basic Law V failed to be a logical proposition, and his resulting system proved to be inconsistent; it was subject to Russell’s Paradox.

Thus followed the interventions of the interventions of Bertrand Russell and Alfred North Whitehead, who, like Frege, sought to resolve the Kantian problem through logic rather than synthetic intuition. In their seminal work, Principia Mathematica, Russell and Whitehead demonstrated that mathematics could be derived from a small set of logical axioms and definitions using symbolic logic – eliminating reliance on Kant’s notion of the synthetic a priori. As I will explain in more detail in another entry, to avoid Russell’s Paradox, Whitehead and Russell employed a type of mathematical logic known as type theory (or, what today is known as “the ramified theory of types”). In mathematical terms, they used type theory to define sets in terms of higher-order functions. Ultimately, they were able to constrain the hierarchy of sets such that the paradoxical “Russell set” – i.e., the set of all sets which are not members of themselves, – could be defined by an expression involving functions that will violate the theory of types, and thus effectively gets ruled.

Russell and Whitehead’s interventions are fascinating, and there will be lots of opportunity to delve deeply in the mathematics another time. Part of my interest in developing a separate series of essays is to discuss – proceeding from the interventions of Russell and Whitehead – developments in modern set theory and axiomatic systems (not just ZFC) as well as other general theories at the foundations of mathematics – such as category theory (a topic I’ve started writing about on my research blog) – in the context of the Kantian problem.

Russell and Whitehead, in alignment with Frege, firmly rejected Kant’s synthetic a priori distinction for mathematics, proposing instead that mathematics is reducible to pure logic. This intervention gave new strength to the empiricist program of the time. Through Russell, Whitehead, Frege’s approach, a philosophical resolution of the Kantian problem suddenly seemed possible, with the whole of mathematics to be analytically true. Then also followed Einstein’s interventions in physics, with the discovery of the special and general theories of relativity, which displaced Newtonian mechanics as the fundamental theory (as I mentioned, Kant’s formulation of the problem of a priori and a posteriori knowledge was based partly on Newtonian mechanics, and with Einstein’s interventions that had been overthrown not without deep philosophical significance). In so doing, not only was Einstein responsible for a revolution in physics, he subsequently showed that the foundations of physics require the empiricist epistemology.

This was a significant development. Building on the breakthroughs of Russell, Whitehead, and Frege in symbolic logic, alongside Einstein’s revolution in physics, a new perspective emerged: scientific and mathematical truths came to be viewed as analytical truths. While mathematics may not be directly testable in the strict experimental sense, this does not render it meaningless. On the contrary, as most mathematicians and theoretical physicists would attest, mathematics remains deeply meaningful. Physics, through its reliance on mathematics to describe reality, demonstrates an undeniable connection between mathematical structures and the natural world.

And so it came about, at the heights of the modern project, a key lesson derived from the Kantian problem: the true and correct philosophy – much like surprising new theorems in mathematics and the astounding discoveries in physics – seems, in some sense, to always be there, somewhere and somehow, waiting to be uncovered. Of course, Gödel’s incompleteness theorems later demonstrated that no finite set of axioms could ever capture all mathematical truths, fundamentally undermining parts of the logical project envisioned by Russell, Whitehead, and Frege. Added to this is the challenge still posed by Russell’s paradox – again a topic I would like to explore in a future entry (possibly on my research blog), including how category theory (as it also relates to type theory) enters the picture.

So, this is not to say that the Kantian problem has been entirely resolved. But it is also not true that there is reason, or any logical basis, to throw the whole thing out by rejecting the categories of reason and empiricism altogether. And yet, this is ultimately what postmodernism attempts.

Indeed, in reflecting briefly on the Kantian problem, what I think is striking from this lightning review of the history is how the postmodern project can say nothing of these developments, primarily because it does not have much of a foundation to begin with. Lyotard, Foucault, Derrida, Rorty, Latour, and others, resort simplistically to sweeping rejections of all grand narratives. They argue, simplistically, that mathematics and logic – like all scientific frameworks – are merely forms of language. In other words, mathematics is reduced purely to language. As such, it becomes subject to the same instability, indeterminacy, and cultural contingency as any other linguistic structure. In this view, mathematics and science become historically and culturally situated discourses. While all human knowledge – including scientific knowledge – is obviously historically embedded, postmodernism reduces mathematics completely to the status of just another social discourse. It does so at cost of not being able to recognise the many other intrinsic components and features of mathematics.

The reason they want to make this reduction is because it fits with their rejection of all grand narratives; mathematics, like all of science, gets reduced to narrative influenced by some power structure. Analogously, any claim to pure reason is dismissed as a narrative shaped by power, language, and context. Similarly, universal claims to truth are seen as tools for “regimes of truth.” The postmodern project thus represents an attempt to shift from foundationalism to a type of pragmatism. As I argued in my critique of Latour, truth is reduced to a contingent, functional, and context-dependent concept.

Reflecting on the Kantian problem has reminded me just how incredibly weak postmodernism truly is. In my earlier essay on Latour, I focused primarily on the philosophical notion of the subject-object relation and its severing – an issue that underpins much of postmodernism’s deep subjectivism. Back then, I was already quite dismayed reading some of the postmodern literature. Thinking about it again now, I’m struck by an interesting irony. Postmodernism, at its origins, positioned itself as a philosophy of the subject. Yet, by severing the subject-object relation, it ultimately undermines the subject itself. The result is a subject that becomes pathological in character – a subject trapped in an epistemological void, incapable of knowing truth. This is the postmodern void.

*Cover image: “The postmodern void” generated by DallE.