Abstract

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