ABSTRACT
In a number of places, Aristotle seems to state unequivocally that no science can make use of the principles of any other science in its demonstrations. Elsewhere, however, he seems not only to countenance such borrowings, but on occasion to make them an essential feature of the construction of scientific explanations. This chapter offers an interpretation of Aristotle’s views on the issues that tries at least to minimize the tensions involved. The axioms of a science Aristotle calls ‘principles’, and scientific understanding, or episteme in its dispositional sense, consists in seeing why the predicates hold of their subjects in the conclusions of the syllogisms. Aristotle draws the following conclusion from the argument of T4: T5. Aristotle’s first example is that of the impossibility of proving anything in geometry by way of arithmetic–and geometry and arithmetic did indeed seem distinct to the Greeks, in spite of their habit of representing certain arithmetical features in geometrical terms.
