- In I An. Post. l. 42 n. 8: "For these ["first things," e.g., axioms, demonstrations, definitions, constructions, etc.] are understood in virtue of themselves; and such knowledge of these things is more certain than any science, because it is from such knowledge that science acquires its certitude."
- In II De Anima l. 3 n. 245: "In…mathematics…what is the more knowable is such both in itself and relatively to us." (Mathematics is thus most "co-natural" to the human intellect.)
- In I An. Post. l. 1 n. 8: "Of these (demonstrations) the best are the mathematical sciences because of their most certain manner of demonstrating."
- In II Met. l. 5 n. 336: "[T]he things with which mathematics deals are abstracted from matter, they do not surpass our understanding; and therefore in their case most certain reasoning is demanded."
- In I Eth. l. 3 n. 36: "Mathematics is concerned with matter in which perfect certitude is found."
- In X Eth. l. 7 n. 2043: "[G]eometricians who take pleasure in the study of geometry can grasp more clearly each problem of this science because their mind is detained longer by that which is pleasant." (Thus, mathematics is beautiful because of its certitude.)
Saturday, November 23, 2013
St. Thomas Aquinas attests to mathematics's certitude:
(cf. "Cap. XII. La certeza matematica" of the excellent Filosofía de las Matemáticas en Santo Tomás, pp. 125 ff., by José Alvarez Laso, C.M.F.)