Abstract
In this paper, I reinterpret Kant’s Transcendental Analytic as a description of a cognitive architecture. I describe a computer implementation of this architecture, and show how it has been applied to two unsupervised learning tasks. The resulting program is very data efficient, able to learn from a tiny handful of examples. I show how the program achieves data-efficiency: the constraints described in the Analytic of Principles are reinterpreted as strong prior knowledge, constraining the set of possible solutions.
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Notes
- 1.
In making this claim, I am assuming a suitably red-blooded notion of “experience”. Of course, for some sufficiently thin notion of “experience”, the thermostat must “experience” the world in order to act at all. But there is a difference between merely responding to a stimulus and making sense of that stimulus: reinterpreting the stimulus as a representation of a coherent external world. The latter is “experience” in the strong sense I am using it.
- 2.
Note that I am not defining intentionality in terms of the activity of counting-as (which would be uninformative). Rather, I am using counting-as to distinguish between original and derivative intentionality. Later, counting-as will itself be explicated in terms of the construction and application of rules.
- 3.
All such references [A, B] are to the A and B editions of the Critique of Pure Reason, (Kant 1781).
- 4.
By “willy-nilly”, I mean without justification from the application of a rule. Kant’s view is that the only mental actions that are justified are actions that result from applying a rule. What leaves room in this stern vision for spontaneity and autonomy is that the rules are not imposed from outside; rather, they are self-legislated.
- 5.
Please note that these Kantian rules do not have to be linguistically articulated or consciously accessible. Rather, the rules that determine the activities of mental combination are implicit and consciously inaccessible, in the same way that the rules of a compiled Prolog program are inaccessible to the executing process.
- 6.
See Kant (1781)(B201n): “the synthesis of a manifold of what does not necessarily belong to each other”.
- 7.
See Kant (1781)(B201n): “the second combination is the synthesis of that which is manifold insofar as they necessarily belong to one another”.
- 8.
See also [A105], [A177, B220].
- 9.
In computational terms, think of a meta-interpreter that is able to construct pieces of code as data, and then execute these new pieces of code.
- 10.
Kant makes the same point in the Metaphysical Deduction: “The same function that gives unity to the different representations in a judgement also gives unity to the mere synthesis of different representations in an intuition, which, expressed generally, is called the pure concept of the understanding. The same understanding, therefore, and indeed by means of the very same actions through which it brings the logical form of a judgement into concepts by means of the analytical unity, also brings a transcendental content into its representations by means of the synthetic unity of the manifold” (Kant 1781)(A79, B104-5). In other words, there is only one process (a process of constructing and applying rules) which explains both how we form judgements and how we form intuitions.
- 11.
Some of the connection rules involved in characterising a concept do more than simply state that one concept is a sub-concept of another, or that one concept excludes another. Some of them relate the concept to another concept only conditionally – dependent on the existence of external factors. For example: “If the weather gets cold, trees lose their leaves”, “If a tree gets no water, it perishes” (Longuenesse 1998). Some of the conceptual inference rules, in Kantian terms, are hypothetical rather than categorical.
- 12.
These activities are described in Kant (1781)(B185, A146) .
- 13.
I use the Kantian term apprehension to denote a time-slice of an enduring object at a particular moment in time. Throughout, I use “apprehension” and “object-slice” interchangeably.
- 14.
Here I assume the stable model semantics (Gelfond and Lifschitz 1988) for negation-as-failure.
- 15.
See Reiter (1980).
- 16.
- 17.
I omit, for reasons of space, discussion of the Second Principle, the Anticipations of Perception. The Fourth Principle does not need its own relation.
- 18.
This is claimed explicitly in a marginal note to the first edition.
- 19.
This is called a “language bias” in the program induction literature.
- 20.
Contrast with Shanahan (2005), who sees perception as a form of abduction.
- 21.
The problem description for finding non-monotonic logic programs from positive and negative examples is actually somewhat more complicated, as there may be multiple models, each with their own positive and negative instances. See Law et al (2014) for details.
- 22.
Hence Kant’s emphasis on spontaneity: the Kantian agent is both less free (because he can only perform actions by applying rules) and more free (because he can construct any set of rules he likes) than the empiricist can possibly imagine.
- 23.
There are two major simplifications in the current implementation. The first is that the spatial framework needed to satisfy the Axioms of Intuition is given in advance, pre-specified, hand-coded. The agent is told that he is operating in a 2-dimensional grid world. The second major simplification is that the constraints involved in the Anticipations of Perception are ignored altogether: in the initial implementation, time is modelled as a series of discrete points, rather than being dense. In future work, I plan to overcome these limitations.
- 24.
One important difference is that your tactile sensations are much more fine-grained: you receive a number of intermediate sensations as the object moves between your four knuckles. The robot just has four discrete boolean sensors (one for each knuckle).
- 25.
We assume, for simplicity, that the alphabet is cyclic, so that the successor of z is a.
- 26.
We need to be careful with notions of “correctness” in sequence induction tasks. There are always infinitely many ways of continuing a finite series, even if some appear more “natural” to us than others. In the case of the “Blackburn Dozen” and the “Hofstadter Fifteen”, the authors specified the intended continuation. I did not use these intended continuations when evaluating correctness. Instead, I gave the questions to 100 people, as an online form, and took the mode as the “correct” continuation. The Kantian constraints provide a way of formally specifying what is “natural” about the “natural” continuations.
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Evans, R. (2019). A Kantian Cognitive Architecture. In: Berkich, D., d'Alfonso, M. (eds) On the Cognitive, Ethical, and Scientific Dimensions of Artificial Intelligence. Philosophical Studies Series, vol 134. Springer, Cham. https://doi.org/10.1007/978-3-030-01800-9_13
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