Rosen Lutskanov

The design of the following paper is to establish an interpretative link between Kant’s transcendental philosophy and Hilbert’s foundational program. Through a regressive reading of Kant’s Critique of Pure Reason (1781), we can see the motivation of his philosophical project as bound with the task to expose the a priori presuppositions which are the grounds for the possibility of actual knowledge claims. Moreover, according to him the sole justification for such procedure is the (informal) proof of consistency and (architectonical) completeness. Hilbert tried to strip Kant’s philosophy of its last anthropomorphic vestiges which led to the formulation of his “finite standpoint” and the prooftheoretical methods for axiomatic reconstruction of classical mathematics. Therefore, contrary to the received view, the proofs of consistency and completeness which were envisaged as part of his metamathematical program were not conceived as a means to secure to epistemic basis of mathematical knowledge. Accordingly, the program itself was not confuted by Gödel’s theorems and remains as viable as ever.

The paper explores the intricate interplay of two parallel developments: on the one hand, the Socratic turn in epistemology with its shifting focus on information retrieval, evidence-based reasoning, and the cognitive relevance of questions; and the advance of dynamic epistemic logic with its accent on knowledge-acquisition. Both are relevant for any realistic model of knowledge which pays due attention to learning. It is argued that the formal models are still wanting in some key respects, but the development of alternative and mutually complementing logical systems marks a promising trend for re-establishing the close links between epistemology and epistemic logic.

The paper develops a semi-formal model of learning which modifies the traditional paradigm of artificial neural networks, implementing deep learning by means of a key insight borrowed from the works of Marvin Minsky: the so-called Principle of Non-Compromise. The principle provides a learning mechanism which states that conflicts in the processing of data to be integrated are a mark of unreliability or irrelevance; hence, lower-level conflicts should lead to higher-level weight-adjustments. This internal mechanism augments the external mechanism of weight adjustment by back-propagation, which is typical for the standard models of machine learning. The text is structured as follows: (§1) opens the discussion by providing an informal overview of real-world decision-making and learning; (§2) sketches a typology of decision architectures: the individualistic approach of classical decision theory, the general aggregation mechanism of social choice theory, the local aggregation mechanism of agent-based modeling, and the intermediate hierarchical model of Marvin Minsky's “Society of Mind”; (§3) sketches the general outline of ANIMA – a new model of decision-making and learning that borrows insights from Minsky's informal exposition; (§4) is the bulk of the paper; it provides a discussion of a toy exemplification of ANIMA which lets us see the Principle of Non-Compromise at work; (§5) lists some possible scenarios for the evolution of a model of this kind; (§6) is the closing section; it discusses some important differences between the way ANIMA was construed here and the typical formal rendering of learning by means of artificial neural networks and deep learning.