I decided to give this a go with the new Gemini 2.5 model. I’ll present the output first and my comments below:
Prompt: Write a Wittgenstenian critique of John Wentworth’s natural abstraction hypothesis.
Answer: Okay, let’s approach John Wentworth’s Natural Abstraction Hypothesis (NAH) from a Wittgensteinian perspective. This requires setting aside the search for a definitive “theory” of abstraction and instead focusing on how we use the concept of “abstraction” and related terms, and the philosophical confusions that might arise.
NAH posits that abstractions aren’t just convenient human constructs but reflect “natural” structural properties of the world. Certain high-level summaries (abstractions) of low-level physical systems are robustly useful for prediction and control because the underlying causal dynamics “clump” or “factorize” in particular ways. Different intelligent systems, interacting with the same reality, will likely converge on similar abstractions because these summaries capture real, objective features of the system’s causal architecture. Examples might include concepts like “object,” “temperature,” or “pressure.”
A Wittgensteinian Critique:
A Wittgensteinian critique wouldn’t necessarily deny the phenomena NAH points to (e.g., that different models often converge on similar high-level variables like temperature). Instead, it would focus on the philosophical interpretation and the language used, highlighting potential conceptual confusions:
The Grammar of “Abstraction”:
NAH’s Picture: NAH seems to treat “abstraction” as a noun referring to a thing or structure that exists “out there” in the world, waiting to be “discovered” (like a new particle). It speaks of abstractions being “natural” or “objective.”
Wittgenstein’s Approach: Wittgenstein would urge us to look at how we use the word “abstraction” and related terms (“summary,” “level of description”). We use it in diverse contexts (mathematics, art, science, everyday life). Is there one single essence? Unlikely. Instead, “abstraction” functions within specific language games. In science, an abstraction (like “temperature”) is a concept embedded within a practice of measurement, prediction, theory-building, and instrument use. Its meaning arises from this use, not from mirroring a pre-existing “natural abstraction.”
Critique: NAH risks reifying the concept of abstraction, turning a feature of our representational practices into an independent feature of the world. The “naturalness” might simply reflect the success and inter-subjective agreement achieved within certain scientific or engineering language games, driven by shared goals (prediction, control) and interaction with the world.
“Discovery” vs. “Invention” or “Utility”:
NAH’s Picture: The language of “discovery” implies finding something pre-existing and independent of the observer.
Wittgenstein’s Approach: Wittgenstein often dissolved such dichotomies. Are mathematical theorems discovered or invented? The question might be misleading. We develop concepts and rules within a system (a language game, a calculus). An abstraction like “temperature” wasn’t simply “found.” It was developed alongside practices of thermometry, theories of thermodynamics, and specific technological needs. Its “objectivity” lies in its role within this established, rule-governed practice and its reliable utility for interacting with the world in ways we care about.
Critique: Calling abstractions “natural discoveries” obscures the role of human (or agent) purpose, criteria, and methods. We select summaries that are useful for our purposes. The causal structure of the world certainly constrains what summaries are useful, but it doesn’t uniquely determine the abstraction. Different agents with different goals or sensory apparatus might find different “summaries” useful, yet NAH seems to privilege a particular kind based on physical causality relevant to prediction/control.
The Lure of the Causal/Physical Picture:
NAH’s Picture: NAH grounds abstraction in the “causal structure of reality.” This gives it a pleasingly objective, scientific feel.
Wittgenstein’s Approach: Wittgenstein was wary of “craving for generality” and the tendency to be held captive by a particular picture (e.g., the scientific picture of everything being reducible to physics). While physics describes the world, our concepts (including abstractions) are part of our form of life, our way of navigating and making sense of the world. “Causality” itself is a complex concept whose grammar needs careful examination, not just taken as a bedrock feature onto which abstractions are mapped.
Critique: NAH might be overly influenced by the physicist’s view. Why should physical causal structure be the sole arbiter of what constitutes a “natural” abstraction? Biological abstractions (like “species,” notoriously fuzzy), social abstractions (“justice”), or computational abstractions (“function”) operate under different criteria and within different language games. Grounding all “natural” abstraction solely in low-level causal summaries seems like an over-extension of one successful, but specific, language game (physics/engineering).
Levels of Description and Usefulness:
NAH’s Picture: Abstractions are useful summaries because they discard irrelevant low-level detail while preserving predictive power.
Wittgenstein’s Approach: This description of usefulness is fine, but Wittgenstein would ask: Useful for whom? Useful for what purpose? Criteria for “relevance” are not inherent in the low-level details themselves; they are imposed by the agent interacting with the system based on its goals and context. A thermostat needs “temperature.” A Maxwell’s Demon (hypothetically) might operate better using individual particle kinetics. Which abstraction is “natural”? The question dissolves when we see that the abstraction is defined by its role within a particular system of practice and purpose.
Critique: NAH’s focus on the objective “summarizing” power risks downplaying the constitutive role of the user and their context in determining what counts as a salient or useful abstraction. The “naturalness” seems less about the world in itself and more about a robust relationship between certain world structures and the predictive/control goals of certain kinds of agents.
Conclusion from a Wittgensteinian Standpoint:
A Wittgensteinian wouldn’t necessarily say NAH is “wrong” about the empirical observation that similar high-level descriptions often emerge. However, they would be deeply skeptical of the philosophical framing. NAH appears to take concepts deeply embedded in our practices (“abstraction,” “summary,” “level”) and project them onto the world as independent, discoverable entities (“natural abstractions”).
The critique would suggest that:
NAH reifies “abstraction” and seeks a general theory where a careful description of use in different contexts is needed.
The language of “discovery” obscures the role of criteria, purpose, and practice in forming and validating abstractions.
The grounding in “physical causal structure” might be an over-generalization from one successful scientific picture, neglecting the diversity of ways we form and use abstractions.
The “naturalness” likely points to the robust utility of certain conceptual tools within specific forms of life or goal-oriented practices, rather than to observer-independent structures waiting to be found.
Instead of seeking the “objective basis” of abstraction in the world’s causal structure, Wittgenstein might suggest we investigate the grammar of how we use abstractions as tools to navigate, predict, and simplify our interactions with a complex reality, acknowledging that these tools are shaped by our needs, goals, and shared practices. The convergence NAH seeks to explain might be better understood through shared environments, shared problems, and the constraints these place on effective action and representation, rather than through discovering pre-packaged “natural abstractions.”
This seems to be significantly higher quality than when I tried ChatGPT approximately two years ago. For a start, the answer is now good enough to post, without me having to prompt it to make edits. Secondly, its reasoning feels much less fuzzy. It illustrates its points with examples and engages more closely with the kinds of things that folks might say.
I decided to give this a go with the new Gemini 2.5 model. I’ll present the output first and my comments below:
This seems to be significantly higher quality than when I tried ChatGPT approximately two years ago. For a start, the answer is now good enough to post, without me having to prompt it to make edits. Secondly, its reasoning feels much less fuzzy. It illustrates its points with examples and engages more closely with the kinds of things that folks might say.