# The Fifth Horseman 13

I thought this was an interesting pre-rebuttal to Peter Boghossian’s unconvincing attempt to redefine faith. Consider Oswald Spengler’s explicit linking of faith and mathematics in The Decline of the West:

The symbol of the West is an idea of which no other Culture gives even a hint, the idea of Function. The function is anything rather than an expansion of, it is complete emancipation from, any pre-existent idea of number. With the  function, not only the Euclidean geometry (and with it the common human geometry of children and laymen, based on everyday experience) but also the Archimedean arithmetic, ceased to have any value for the really significant mathematic of Western Europe. Henceforward, this consisted solely in abstract analysis. For Classical man geometry and arithmetic were self-contained and complete sciences of the highest rank, both phenomenal and both concerned with magnitudes that could be drawn or numbered. For us, on the contrary, those things are only practical auxiliaries of daily life. Addition and multiplication, the two Classical methods of reckoning magnitudes, have, like their sister geometrical-drawing, utterly vanished in the infinity of functional processes. Even the power, which in the beginning denotes numerically a set of multiplications (products of equal magnitudes), is, through the exponential idea (logarithm) and its employment in complex, negative and fractional forms, dissociated from all connexion with magnitude and transferred to a transcendent relational world which the Greeks, knowing only the two positive whole-number powers that represent areas and volumes, were unable to approach.

Think, for instance, of expressions like e~~ x , /x, al m

Every one of the significant creations which succeeded one another so rapidly from the Renaissance onward — imaginary and complex numbers, introduced by Cardanus as early as 1550; infinite series, established theoretically by Newton’s great discovery of the binomial theorem in 1666; the differential geometry, the definite integral of Leibniz; the aggregate as a new number-unit, hinted at even by Descartes; new processes like those of general integrals; the expansion of functions into series and even into infinite series of other functions— is a victory over the popular and sensuous number-feeling in us, a victory which the new mathematic had to win in order to make the new world-feeling actual.

In all history, so far, there is no second example of one Culture paying to another Culture long extinguished such reverence and submission in matters of science as ours has paid to the Classical. It was very long before we found courage to think our proper thought. But though the wish to emulate the Classical was constantly present, every step of the attempt took us in reality further away from the imagined ideal. The history of Western knowledge is thus one of progressive emancipation from Classical thought, an emancipation never willed but enforced in the depths of the unconscious. And so the development of the new mathematic consists of a long, secret and finally victorious battle against the notion of magnitude.(1)

(1) Thus Bishop Berkeley’s Discourse addressed to an infidel mathematician (1735) shrewdly asked whether the mathematician were in a position to criticize the divine for proceeding on the basis of faith.

It underlines the New Atheists’ lack of not only historical knowledge, but basic scholarship, when century-old writings by long-dead authors are sufficient to highlight the holes in their arguments. Peter Boghossian isn’t merely a bad anti-apologist, he’s an inept logician and philosopher. Then again, Portland State University isn’t exactly Oxford.