The fulcrum of this work is knowledge: what it is and how it is generated within the context of a capitalist society. First, Marx’s analysis of the objective labour process is extended to the mental labour process. Then, objective and mental labour processes are defined in terms of objective and mental transformations, with consideration paid to which of the two types of transformation is determinant. This requires a discussion of dialectical logic and formal logic. Within dialectical logic, two types of (...) processes are introduced: open ended and pre-determined. It is argued that computers (both traditional and quantum) and Artificial Intelligence cannot generate new knowledge, because they (a) rely on formal logic, i.e. they cannot engage in open-ended dialectical processes, and (b) are impervious to social determination. Connectedly, Artificial Intelligence systems such as ChatGPT cannot be a substitute for human thought or writing, because of the inevitability of ‘model collapse’. Next, focus is shifted to a specific form of knowledge: the ‘Copenhagen interpretation’ of quantum mechanics. It is shown that this interpretation is steeped in irrationalism and that it is a variant of pro-capitalist ideology. Finally, the social-historical roots of this ideology are revealed. (shrink)

Many historians of the calculus deny significant continuity between infinitesimal calculus of the seventeenth century and twentieth century developments such as Robinson’s theory. Robinson’s hyperreals, while providing a consistent theory of infinitesimals, require the resources of modern logic; thus many commentators are comfortable denying a historical continuity. A notable exception is Robinson himself, whose identification with the Leibnizian tradition inspired Lakatos, Laugwitz, and others to consider the history of the infinitesimal in a more favorable light. Inspite of his Leibnizian sympathies, (...) Robinson regards Berkeley’s criticisms of the infinitesimal calculus as aptly demonstrating the inconsistency of reasoning with historical infinitesimal magnitudes. We argue that Robinson, among others, overestimates the force of Berkeley’s criticisms, by underestimating the mathematical and philosophical resources available to Leibniz. Leibniz’s infinitesimals are fictions, not logical fictions, as Ishiguro proposed, but rather pure fictions, like imaginaries, which are not eliminable by some syncategorematic paraphrase. We argue that Leibniz’s defense of infinitesimals is more firmly grounded than Berkeley’s criticism thereof. We show, moreover, that Leibniz’s system for differential calculus was free of logical fallacies. Our argument strengthens the conception of modern infinitesimals as a development of Leibniz’s strategy of relating inassignable to assignable quantities by means of his transcendental law of homogeneity. (shrink)