Nor is it enough to have created the Grand Fetiche (so he actually proposes to call the Earth), and to be able to include it and all concrete existence in our adoration along with the Grand Etre.  It is necessary also to extend Positivist Fetishism to purely abstract existence; to “animate” the laws as well as the facts of nature.  It is not sufficient to have made physics sentimental, mathematics must be made so too.  This does not at first seem easy; but M. Comte finds the means of accomplishing it.  His plan is, to make Space also an object of adoration, under the name of the Grand Milieu, and consider it as the representative of Fatality in general.  “The final unity disposes us to cultivate sympathy by developing our gratitude to whatever serves the Grand Etre.  It must dispose us to venerate the Fatality on which reposes the whole aggregate of our existence.”  We should conceive this Fatality as having a fixed seat, and that seat must be considered to be Space, which should be conceived as possessing feeling, but not activity or intelligence.  And in our abstract speculations we should imagine all our conceptions as located in free Space.  Our images of all sorts, down to our geometrical diagrams, and even our ciphers and algebraic symbols, should always be figured to ourselves as written in space, and not on paper or any other material substance.  M. Comte adds that they should be conceived as green on a white ground.

We cannot go on any longer with this.  In spite of it all, the volume on mathematics is full of profound thoughts, and will be very suggestive to those who take up the subject after M. Comte.  What deep meaning there is, for example, in the idea that the infinitesimal calculus is a conception analogous to the corpuscular hypothesis in physics; which last M. Comte has always considered as a logical artifice; not an opinion respecting matters of fact.  The assimilation, as it seems to us, throws a flood of light on both conceptions; on the physical one still more than the mathematical.  We might extract many ideas of similar, though none perhaps of equal, suggestiveness.  But mixed with these, what pitiable niaiseries!  One of his great points is the importance of the “moral and intellectual properties of numbers.”  He cultivates a superstitious reverence for some of them.  The first three are sacred, les nombres sacres:  One being the type of all Synthesis, Two of all Combination, which he now says is always binary (in his first treatise he only said that we may usefully represent it to ourselves as being so), and Three of all Progression, which not only requires three terms, but as he now maintains, never ought to have any more.  To these sacred numbers all our mental operations must be made, as far as possible, to adjust themselves.  Next to them, he has a great partiality for the number seven; for these whimsical reasons:  “Composed of two progressions followed by a synthesis, or of one progression between