The Apoptosis of Reason

Against Ontology

Here I defend two connected theses. The first is Logical Nihilism. This view is that there is no single, global, topic-neutral relation of logical consequence that governs all correct reasoning. Once we fix a language, a class of models, and a practical goal, we can define local consequence relations that work well for that setting, but there is no framework-independent fact of what follows from what. The second thesis is a kind of Instrumental Finitism. I treat mathematics as a finite, resource-bounded technology of symbol manipulation rather than as a window onto a realm of abstract objects or actual infinities. Mathematics is indispensable as a tool, yet dispensable as ontology.

I arrive at these positions by extending a line of eliminative thinking that runs from Sellars and Quine through the Churchlands and contemporary predictive processing accounts of cognition, and that receives a particularly stark expression in Ray Brassier’s nihilistic reading of the scientific image. I suggest that the same apoptotic pressure that dissolves the folk psychological subject also undermines the idea of a universal logic that binds all rational agents. At the same time, I draw on work by Russell, Cotnoir, Wyatt, Payette, Field, Maddy, and others to argue that both logic and mathematics are better understood as engineered instruments inside finite practices than as metaphysical structures that thought must mirror. I then sketch a picture of scientific rationality that relies on robustness, model building, and social objectivity rather than on transcendental logical or mathematical guarantees. I will close by proposing a stance of onto-suspension, a kind of modern Pyrrhonism. But instead of replacing old metaphysics with a new skepticism, I refuse the demand that successful practices be underwritten by any ontology at all, while acknowledging that they are bounded by the finite and possibly terminal character of our cognitive lives.

I. From the Apoptosis of Belief to the Apoptosis of Logic

I want to begin from a thought that has become increasingly difficult to evade in contemporary philosophy of mind and science. The conceptual framework through which I ordinarily understand myself is not sacrosanct. The categories of belief, desire, intention, and experience do not arrive with the authority of timeless structures of reason. They are theoretical posits that have grown up within a particular historical form of life, and they are vulnerable to replacement by more powerful explanatory schemes.

Sellars taught me to distrust the supposed immediacy of the given. On his account, even the simplest perceptual awareness is already articulated within a conceptual framework. The manifest image, as he calls it, is not a mere report of what is there. It is a sophisticated pattern of classificatory and normative practices. When I say that someone believes that it is raining, I am not pointing to a primitive mental glow. I am applying a theory-laden concept that helps explain and evaluate their behavior.

Once I accept this, eliminative materialism becomes a live option rather than a caricature. If folk psychological talk of beliefs and desires is theoretical, then in principle it can be replaced. The Churchlands take that possibility seriously. They suggest that a mature neuroscience may have no real use for belief and desire at all. Instead, it will traffic in neural activation patterns, vector coding, or whatever structure turns out to do the actual explanatory work. In that case, my current self-image as a belief-bearing subject would resemble the phlogiston theorist’s self-image as an observer of fiery exhalations. It would have done valuable work for a time, then quietly it would die via the apoptotic process.

Recent work in cognitive science only sharpens this trajectory. Predictive processing and free energy accounts depict the brain as a hierarchically organized prediction error minimizer. In this picture, the nervous system does not passively receive data and then reason about it in a classical logical sense. It generates probabilistic predictions, compares them with sensory input, and adjusts its generative models in order to keep expected surprise within viable bounds. What I call a belief, on this view, is at best a rough way of talking about a relatively stable high-level component of such a generative model, and at worst a social tool for coordinating behavior, what some authors call mindshaping rather than mindreading. The brain computes, but it does not obviously implement the inferential structure of textbook logic.

Ray Brassier takes this line of thought very seriously. He reads the scientific image as progressively dismantling the manifest image. In his work, the disenchantment that results does not end with the loss of comforting metaphysical pictures. It eventually reveals the indifference of cosmological and thermodynamic processes to the existence of any rational subject at all. Extinction becomes the strict horizon of thought. Brassier calls this a kind of transcendental nihilism. Thought discovers, by its own lights, that it is neither necessary nor central to what there is.

I share much of this nihilistic diagnosis, but I want to push it in a different direction. I want to apply the same apoptotic pressure not only to folk psychology, but to logic itself. My target is not just the image of the human subject as a belief holder, but the image of logic as a universal law that binds that subject. Call this the logical image. It is the idea that there exists a set of topic-neutral, exceptionless rules, often codified under names such as modus ponens or the law of non-contradiction, that any rational agent must implicitly acknowledge whenever they think.

In the background of much philosophy of logic lies what Wyatt and Payette call logical generalism. According to the generalist, logical validity is a property of certain forms of argument that holds regardless of subject matter. If an inference is logically valid, then its premises cannot be true and its conclusion false in any possible circumstance. Generalists then disagree over which logic captures that notion, and whether there is exactly one correct logic or several, but they tend to agree that there is something in the world or in the space of possibilities that answers to the idea of a single core consequence relation.

My first claim is that this entire picture is unsustainable. When we look closely at how logical systems actually function in mathematics, computer science, law, natural language semantics and so on, we do not find convergence on a unique logical skeleton. We find a proliferation of incompatible logics, each designed to handle particular kinds of problems. More importantly, we find that the very standards that were supposed to pick out a universal logic, such as topic neutrality and exceptionlessness, drive us toward this fragmentation rather than away from it. If we insist that an alleged law of logic must hold across all domains, then we rapidly discover that every familiar candidate runs into serious counterpressure somewhere. We can salvage it by restricting its range, or we can devise a new logic that behaves better in that domain, but in doing so we give up the idea that we are describing one single universal relation. This is the core of Logical Nihilism as I understand it.

Logical Nihilism is not the claim that there is no difference between good and bad reasoning. It is the claim that there is no single, global, topic neutral consequence relation that all good reasoning instantiates. Once we fix a language, a model class, and a set of practical aims, we can define a consequence relation that works well within that framework. We can then prove formally that certain inferences preserve truth in the intended models, or that certain sets of constraints are jointly unsatisfiable. All of that is legitimate and important. What I deny is that there is any fact of the matter, independent of such framework choices, about which arguments are logically valid in general. Logical consequence, with a capital L and a capital C, does not name a natural kind.

The second claim I want to defend is Instrumental Finitism about mathematics. Here my target is the idea that mathematics reveals to us an independently existing realm of abstract objects, such as sets, numbers, and functions, including actual infinities. On my view, we can understand mathematical practice as the development and deployment of a finite, resource bounded symbolic technology. We adopt concepts such as the real numbers or uncountable sets because they make certain forms of reasoning tractable, and because treating them as if they were genuine objects simplifies our models and proofs. We do not need to believe that these entities exist in any robust metaphysical sense for the technology to do its work.

Instrumental Finitism does not require me to adopt an extreme ultrafinitist position that denies the meaningfulness of all large numbers, although I will draw on finitist arguments as a useful source of pressure. It requires only that I take seriously the fact that all mathematical activity is implemented by finite agents with limited computational resources in a physically finite environment. From that observation, together with work by Hartry Field on the conservativeness of mathematics over nominalistic physics, and practice oriented accounts of mathematics by authors such as Penelope Maddy, I conclude that mathematical indispensability in science supports only an instrumental reading of mathematical discourse, not a commitment to a realm of abstracta.

What results from combining Logical Nihilism with Instrumental Finitism is a strongly deflationary picture of rationality. I do not possess a universal logic written into the fabric of thought. I do not have access to a mathematical realm that underwrites my most successful physical theories. Instead, I have a growing, revisable toolkit of inferential and representational devices that have proven useful within the limits of my finite projects. Logic and mathematics, on this view, are like measuring instruments or experimental protocols. They are crucial, but they are also historically contingent and subject to replacement. They can undergo apoptosis when they outlive their usefulness.

A natural worry at this point is that I have undermined scientific rationality rather than clarified it. If there is no universal logic and no mathematical ontology, how can I claim that science has any special authority? Part of my task in what follows is to show that this worry is misplaced. I will argue that scientific practice gains its robustness not from correspondence to an independent logical or mathematical structure of the world, but from features such as model pluralism, error correction, social criticism, and robustness analysis. These do not presuppose a universal logic or mathematical ontology.

The final ingredient in my picture is a stance I call onto-suspension. I do not want to replace the old idea that reality has a logical or mathematical form with the equally heavy idea that reality is void, chaotic, or intrinsically illogical. Instead I want to stop demanding that my best practices be grounded in any ontology at all. Extinction and cosmological eschatology play a role here, but not as revelations of the essence of being. They function as reminders that my cognitive tools are finite and may eventually cease to be used. That finitude is enough to motivate humility about the reach of my inferential frameworks, without forcing me to erect a new metaphysical barrier around what reality is really like.

I will develop each of these themes in detail over the course of the month. In the next section, I state and defend Logical Nihilism, and distinguish it carefully from both logical monism and logical pluralism. I then illustrate the toolkit character of logic by discussing substructural, non-monotonic, paraconsistent, and probabilistic logics as engineered responses to different constraints. After that, I turn to Instrumental Finitism about mathematics, drawing on finitist concerns, Field’s nominalism, and practice-based philosophy of mathematics. I then show how scientific rationality can be reconstructed in terms of robustness and social objectivity, without appealing to a universal logic or a mathematical realm. Finally, I return to the theme of extinction and articulate onto-suspension as an appropriate attitude for a finite, scientifically informed rational agent who has accepted the apoptosis of both belief and logic.