So great was his intellectual authority and his fame as a teacher that he was the subject of a popular quip: "Pragam videre, Arriagam audire"—"To see Prague, to hear Arriaga.

Among the attempts made in the course of the seventeenth century to revive and reinvigorate medieval scholasticism, the Cursus Philosophicus of Arriaga, scholastic alike in contents, in arrangement, and in form, is one of the most skilful.

Arriaga had studied with attention the recent writings of the anti-Aristotelians; and, giving effect to many of the opinions advanced by them, he endeavoured by modifications and concessions to adapt to modern use the logic and metaphysics, but still more the physical hypotheses, of his scholastic masters.

In his own day, as a Jesuit teaching the doctrines then approved by his order, he was indeed safe from any serious charge of heterodoxy; but his position as an innovator laid him open to many attacks from the uncompromising adherents of the Aristotelian school.

He claimed that “ex Philosophia” there was no reason to postulate quantity distinct from prime matter and that this opinion had sufficient supporters both ancient and modern who provided very strong arguments.

Arriaga admitted that it was impossible to determine whether something was impenetrable by having something added to it or by its essence, but then he drew the typically Ockhamist conclusion that when we do not have positive arguments for proving a plurality of entities (i.e., quantity being something additional to the thing itself), we must deny that they exist.

Arriaga displays an original approach to natural philosophy, interest in the critical scientific spirit of the time, and familiarity with the new experimental science, quite unusual among the scholastics.

[24] Arriaga exerted a strong influence on the Czech physician Jan Marek Marci, on the Italian scholar Valeriano Magni and on the Spanish philosopher and scientist Juan Caramuel y Lobkowitz.

This doctrine, which asserted that quantity consisted of points, had been repeatedly and strenuously rejected by the revisers general as incompatible with the orthodox account of Eucharist.

However, the routine reissuing of such injunctions and the unflagging efforts of the censors to expunge such a doctrine from Jesuit books attest to the continued dissemination of zenonism within the Order.

His work Tratado sobre las leyes (1647) stands out for addressing the interpretation of laws within the context of the Catholic Iberian legal culture of the Early Modern period.

As part of the probabilist tradition, Arriaga argued that, in the face of moral or legal doubts, one could follow a probable opinion, even if less certain, as long as it was based on solid arguments.