Thus of the three points in which I placed the originality and value of Vico's first theory of knowledge, two, namely the criterion of knowledge opposed to that of Descartes and the defence of concrete as opposed to abstract sciences, are not only left intact by the inquiries into their sources which I have just described, but are actually reinforced. There remains the third of my points: the Vician theory of the arbitrary nature of mathematics, the originality of which has also been impugned by arguments which seem to me to have even less foundation than those I have examined above. Do we find the doctrine that the fundamental objects of mathematics, the unit of arithmetic and the point of geometry, are unreal or fictitious, propounded before Vico's time? Do we find it--this is the chief point--propounded not as a casual remark or an intuition of a truth, but as a consciously reasoned concept from which legitimate consequences are drawn as to the limitations of mathematics and its inability to furnish real knowledge of mind, nature and history? All through the Middle Ages the Aristotelian theory of mathematics is continually enunciated. According to this theory mathematics is the most certain of the sciences because the simplest; it abstracts from all sensible matter, but not from intelligible matter (ὖλη νοητή) which exists in sensible objects but not qua sensible (ἐν τοῑς ἀἰσθητοῑς ὑπάρχουσα μὴ ᾖ ἀἰσθητά)[38] According to Cassiodorus it constituted the body of _doctrinalis_ as opposed to _naturalis_ (physical) science and _divina._ Albertus Magnus followed Aristotle in defining mathematical entities as separable "in imagination," "in thought" but not "in reality" (_in phantasmate, secundum rationem, non secundum esse_) from the sensible matter to which "they are conjoined by existence" (_per esse sunt coniunctae_); and St. Thomas said that mathematics "though the objects it considers are not separate, yet considers them in so far as they are separate" (_etsi sunt non separata ea quae considerat, tamen considerat ea in quantum sunt separata_).[39] The arbitrary character of its foundations was never suspected. Dante, when he wished to indicate "the things which not being subject to our power we can only contemplate and not create," enumerated "the objects of mathematics, physical science and divinity" (_mathematica, physica et divina_).[40]