 In geometry, Poincaré supposes the pre-existent category of a group. In mechanics, the categorical tools are the principle of (empirical) induction and differential equations. So, Poincaré’s position represents a hierarchy of elements that, as in Kant, are presupposed as necessary conditions of the possibility of the science on the next level. The scheme of generalization in mechanics appears as follows: Experience provides complex phenomena, i.e., “a confused mass of facts” which we reduce into a number of elementary phenomena by means of experiment. From these elementary phenomena, we generalize (e.g., via the empirical induction principle) to elementary facts and move, by means of differential equations, to laws and verifiable hypotheses whose number should be kept as small as possible (Poincaré 1902: 168–171; 2017: 110–113). Finally, laws can be elevated by decree to the status of principles, thus allowing the basic principles of mechanics to become conventions; not arbitrary conventions however, since “They would be arbitrary [only] if we were to lose sight of the experiments that led the founders of mechanics to adopt the laws and which, as imperfect as these experiments may be, suffice to justify them” (1902: 128; 2017: 82). For Poincaré the principles of mechanics (principle of inertia, law of acceleration, principle of relative motion, etc.) are not hypotheses but rather conventions (Poincaré 1902: 151; 2017: 99), although they are of course of experimental origin. These conventions do not constitute a choice between physical alternatives, but rather must be interpreted as defining the basic terms of a theory. Immune to experimental disconfirmation without being a priori in the classical sense, they are necessary preconditions to the sciences further up in the hierarchy (Poincaré 1902: chap. VI and VII).