The reason that people rightly and necessarily supplement _a priori_ reason in practical affairs by the experimental method is that _a priori_ conclusions depend for their value on the rigid certitude of their premises. E.g. a man who died on the 16th cannot have died of poison bought on the 20th. But are we sure that the 16th is really the date of his death? To test that we require actual evidence. One can conclude absolutely against a false theory by either of these two methods of reasoning. But when they concur, when you find the theory to be false both _a priori_ and from the available evidence as well, then certitude could not be more certain: the combination of both methods of proof is overwhelming. Now we shall see that this is exactly what happens in the case of this false theory of Evolution called Natural Selection. There are four crushing _a priori_ arguments disposing of it, and, after that, there is overwhelming positive evidence against it, of which the main divisions are three in number. The four conclusive _a priori_ arguments are these:— (1) Variations in nearly every case must continue to accumulate. Variations more and more advantageous must appear successively, Generation after Generation. This is not logically essential in every conceivable case, e.g. particoloured animals could grow whiter against snow. But in the vast majority of cases such accumulation is essential: e.g. to produce a taller type or to produce horns or to lengthen a tail. Now the chances of such a regular series appearing by accident even in one case, let alone in millions, clearly approximate to zero. (2) The advantageous differences making for survival are not of one kind in any particular case, but of an indefinitely large number (e.g. climate getting colder needs not only warmer coat, but power to digest new food, protective colouring so as not to show dark against snow, etc. An indefinitely large number of qualities). Now the chance of _all_ being combined (and co-ordinated) in a single individual, _without design, accidentally_—let alone of their thus appearing in many individuals _accidentally and without design_—approximates to zero. On the same line of reasoning the chances of co-ordination between all the vastly numerous parts of one complex creature by accident approximate to zero. (3) The chances of _each_ very slight change being an advantageous one over the last in a series indefinitely prolonged of myriads or millions approximate to zero. (4) Where more than one specially favoured progenitor is necessary to the production of an organism (e.g. among mammals, two, a male and female: with many plants three, a male and female and an insect go-between) the chance combination of such favoured progenitors _accidentally and without design_ diminishes with each generation in geometrical ratio and rapidly approximates to zero. The decisive character of these _a priori_ arithmetical arguments will appear later.