Lacuria: Occultist Philosopher and Theologian in the 19th Century (vol. I)

From Mathematical Science to the Science of Numbers

If any “science disappears with the number and reappears with it”, mathematics, “where the number is exercised on itself”, constitutes a “pure science”, namely: “distinction related to unity”. Coming out “entirely from unity, [mathematics] can always be brought back to it”. For Lacuria, thus, “unity being at the center of intelligence, mathematics therefore constitutes an exact relationship with the center, that is why they are infallible”. It is also because mathematics, geometry and algebra, contain shapes and numbers which, if they are, strictly speaking, only negative limits to realities which remain inaccessible to them, are also symbols allowing access to them. Hence, for Lacuria, the role of numbers is not limited to quantitative abstraction and descriptive equations of physical laws, they are as many ancestral and universal symbols, qualitative, bequeathed by history—including pre-Christian—and present in biblical revelation.

This double meaning of numbers characterizes the difference between Plato and Aristotle, according to the mathematician Abraham Fraenkel (1891-1965): for the first “the existence of mathematical beings is independent of human thought”, for the second it is “abstract ideas of human activity”; and this same difference would exist between Leibniz and Kant: for the first there exists a “mathematica universalis, symbolic and formal, which goes beyond everything that is within the reach of human constructions and intuitions”, for the second, geometry and even the arithmetic “are linked to the forms of human intuition: space and time”. If it were necessary to choose, and Gödel will have done so explicitly, it is necessary to distinguish two problems beforehand: one of an ontological nature where realism and idealism clash, the other of an epistemological nature, on which lies the controversy between empiricism and idealism (Bouveresse). Therefore, Lacuria’s position is clear: we must not believe that numbers are cause or substance, a trap into which Pythagoras fell, he explains, when they are only form and limit. Moreover, he specifies, it is in this same trap that Fourier fell: although he was a “penetrating genius having felt the deep harmony with the being which was in mathematics”, but he falsely “proclaimed this great law that the mathematical laws were the very laws of being”. This is because, Lacuria makes it clear, “strictly speaking, it is not unity, but the idea of ​​unity that generates the idea of ​​numbers”.

Thus “mathematical certainty is always conscious, it does not add an atom to our positive knowledge”; we are anticipating here a famous formula: “Insofar as the propositions of mathematics relate to reality, they are not certain, and insofar as they are certain, they do not relate to reality” (Einstein). Moreover, Lacuria extends this same criticism to any science calling upon mathematics, which endows them with a double limit: “Astronomy, physics, chemistry are certain where they can be expressed by precise numbers, in all the rest, they are reduced to conjecture”.