SummaryThe paper presents a paradigmatic part of the logic of magnitudes, an invention of Descartes, different from alethic formal logic, but a proper formal logic sui generis. Descartes' logic consists of corporeal – geometrical and physical – devices that behave like deductive calculi, generating inferences of magnitudes from magnitudes. Its syntactic elements are magnitudes as corporeal entities, whose connections can be characterized by various magnitudinal connectives, distinguished from those of alethic logic. The paper presents two kinds of orthogonal and the (...) congruence connectives applying them to line segments and to physical magnitudes. It describes the value semantics and the interpretative semantics of these connections, the inference rules they take part in, states the conditions for validity and theoremhood, and compares it to model theory. It shows that one of the orthogonal connections displays the ontic and logical properties of Descartes’ideae innatae, whereas the other displays those of Descartes’ideae factae, and shows that the physical law m v =p regarded as an orthogonal connection is an idea innata. (shrink)

This paper is about - cognitive science's claim to obtain an empirically theory of human intelligence by experiments with intelligent machines; - the question, whether simulation yields/is explanation , i.e. whether the theory explaining the behaviour of a thing A, appropriately abstracted, as well explains the behaviour of a thing B, different in type from A, when A's and B's behaviours are indistinguishable; - the question, whether the Aristotelian ontic distinction between the natural and the artificial was in fact extinguished (...) by Descartes' materialistic intensional ontology; this question is denied by evidence of the existence of different theories of artificial and natural magnetism in current physics; - and about the comparison of the current theories of magnetism, of artificial or electromagnetism and of natural or ferromagnetism with the result that there is no uniform theory explaining all kinds of magnetism to be gained out of Maxwell's theory. Thus by counterexample is demonstrated that cognitive science's claim to obtain a theory of natural intelligence by the S:E-strategy is to be refused. Descartes' premise of the ontic indifference of the size of physical magnitudes is introduced as basis of the S:E-claim and its refutation as cause of the partial continuation of the ontic distinction between natural and artificial things in physics. (shrink)