 Kant argues that mathematical reasoning cannot be employed outside the domain of mathematics proper for such reasoning, as he understands it, is necessarily directed at objects that are “determinately given in pure intuition a priori and without any empirical data” (A724/B752). Since only formal mathematical objects (i.e. spatial and temporal magnitudes) can be so given, mathematical reasoning is useless with respect to materially given content (though the truths that result from mathematical reasoning about formal mathematical objects are fruitfully applied to such material content, which is to say that mathematics is applicable to and a priori true of the appearances (Shabel 2005). Consequently, the “thorough grounding” that mathematics finds in its definitions, axioms, and demonstrations cannot be “achieved or imitated” by philosophy or physical sciences (A727/B755).