[10] In giving monadic number a subsistence in opinion, I have followed the distribution of Proclus, in the conclusion of his comment on a point; and, I think, not without sufficient reason. For since monadic numbers are more immaterial than geometrical lines and figures, they must have a more immaterial subsistence. But as they are correspondent to matter, they cannot reside in the essential reasons of the soul; nor can they subsist in the phantasy, because they are superior to geometrical figures. It remains, therefore, that we must place them between διάνοια or cogitation, and the phantasy; and this middle situation is that of opinion. For cogitation, which Plato defines, in his Sophista, to be an inward discourse, without voice, is an energy of the rational soul, extending itself from propositions to conclusions. And, according to Plato, in the same place, opinion is the silent affirmation, or negation of διάνοια, or thought. Hence, says he, “opinion is the conclusion of cogitation; but imagination, the mutual mixture of sense and opinion.” So that opinion may, with great propriety, be said to contain monadic number, to which it bears the proportion of matter. And hence the reason is obvious, why the Pythagoreans called the duad opinion. [11] Ἄτροπον, ἀκαμάτον Δεκάδα κλείουσιν μιν ἁγιὴν, Ἀθάνατοί τε θεοὶ καὶ γηγενέεις ἃνθρωποι. Syrian. in Meta. Aristot. p. 113. Gr. i.e. (According to the Pythagoreans) “the immortal gods and earth-born men, call the venerable decad, immutable and unwearied.” [12] Αυτὸς μὲν Πυθαγόρας ἐν τῷ ἱερῷ λόγῳ διαῤῥηδην μορφῶν καὶ ἰδεῶν κράντορα τὸν ἀριθμόν ἔλεγεν εἶναι. Vid. Syrian. in Arist. Meta. p. 85. Gr. [13] Φιλόλαος δέ, τῆς τῶν κοσμικὼν αἰωνίας διαμονῆς τὴν κρατιστεύουσαν καὶ αὐτογειῆ συνοχὴν εἶναι ἀπεφήνατο τὸν ἀριθμόν. Syrian. in eodem loco. [14] Οἱ δὲ περὶ Ἴππασον ἀκουσματικοὶ, ἀριθμόν εἶπον παράδειγμα πρῶτον κοσμοποιίας. Καὶ πάλιν κριτικὸν κοσμουργοῦ θεοῦ ὄργανον. Jamb. in Nicomach. Arith. p. 11. [15] In his Mathematical Lectures, page 48. [16] In Arithmet. p. 23. [17] In Aristot. Meta. p. 113. Gr. vel 59. b. Lat. [18] For the tetrad contains all numbers within its nature, in the manner of an exemplar; and hence it is, that in monadic numbers, 1, 2, 3, 4, are equal to ten. [19] Notes to Letters on Mind, page 83.