Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy
Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy
Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
If it be requisite, however, to speak concerning the difference<br />
of these monads, and their privation of difference, we must say<br />
that the monads which subsist in quantity, are by no means to<br />
be extended to essential numbers; but when we call essential<br />
numbers monads, we must assert that all of them mutually<br />
differ from each other by difference itself, and that they possess<br />
a privation of difference from sameness. It is evident also,<br />
that those which are in the same order, are contained through<br />
mutual comparison, in sameness rather than in difference, but<br />
that those which are in different orders are conversant with<br />
much diversity, through the dominion of difference.<br />
Again, the Pythagoreans asserted that nature produces sensible~<br />
by numbers; but then these numbers were not mathematical<br />
but physical; and as they spoke symbolically, it is not improbable<br />
that they demonstrated every property of sensibles by<br />
mathematical names. However, says Syrianus, to ascribe to<br />
them a knowledge of sensible numbers alone, is not only ridiculous,<br />
but highly impious. For they received indeed, from the<br />
theology of Orpheus, the principles of intelligible and intellectual<br />
numbers, they assigned them an abundant progression,<br />
and extended their dominion as far as to sensibles themselves.<br />
Hence that proverb was peculiar to the Pythagoreans, that all<br />
things are assimilated to number. Pythagoras, therefore, in<br />
THE SACRED DISCOURSE, clearly says, that "number is the ruler<br />
of forms and ideas, and is the cause of gods and daemons."<br />
He also supposes that "to the most ancient and artificial1.y<br />
rulz'ng deity, number is the canon, the artificial reason, the intellect<br />
also, and the most undevirrting balance of the composition<br />
and generation of all things." ~ U ~ OPCV S X.J~QYOPQS, 6~ 79<br />
ctpq, ~oyy, %rappq8qv popqov xat tBcwv xpavsopa rov ap:Opov ~hsyiv<br />
rtvat, xac 0oov xar Gatpovov atstova xat 79 zrpc~~u~arq, xac xpx-<br />
rtorcuov.rr q v t q Bey xavova, xoc hoyov ssxvrxov, vouv .re xat<br />
oraopav axhtvto~a~av sov ap tepov .~;rctxc oooraotoG xat yevsuco~ ror