Among those conceptions of the history of science which deal with the formation of theories is the concept of the unity of science. This unity is in turn based on the unity of scientific method, the unity of scientific laws and the unity of the language of science. After a systematic explication of modern approaches, historical conceptions of the unity of the language of science are described and analyzed. To these belong first of all the idea of a mathesis universalis (...) and the so called Leibniz program, which leads to the architecture of a Leibniz world. (shrink)

In his 1763 Prize Essay, Kant is thought to endorse a version of formalism on which mathematical concepts need not apply to extramental objects. Against this reading, I argue that the Prize Essay has sufficient resources to explain how the objective reference of mathematical concepts is secured. This account of mathematical concepts’ objective reference employs material from Wolffian philosophy. On my reading, Kant's 1763 view still falls short of his Critical view in that it does not explain the universal, unconditional (...) applicability of mathematical concepts. (shrink)

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)