(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.
Now for the arguments from evidence.
The arguments from evidence against Natural Selection come under three main heads:—
(1) Within humanly recorded historical experience no trace of such permanent progressive action is observable. There is no doubt of individual differences; there is also plenty of proof of slight changes swinging round the normal. There is manifest to every one differentiation of type: Negroes and Mongols among men for instance. But the main types are fixed. Negro and Mongol are both men. Man and other mature types are, within historical record, fixed. They are not on their way to becoming something else.
It is true that humanly recorded historical experience covers but a very brief fraction of the total time allowed for even the shortest estimates of the past of this world. None the less, it is sufficient to prove that types once achieved are permanent. Call it five thousand years (perhaps man-made prehistoric pictures may extend that limit), even that short period is enough to prove the existence of stable types. For if during five million years some animal form existing at the moment has been forever slowly changing by a process such that its present apparent fixity is an illusion, and is still proceeding to further slow changes indefinitely, then five thousand years ought to show a perceptible fraction of the movement; only a thousandth of it, no doubt, but one in a thousand is measurable: tiny, but measurable. Yet no fundamental change, still less any progressive change, is apparent. During all the historical epoch fixity of type is invariable.
(2) The geological record, so far from showing types perpetually in a state of flux, presents us with Fixed Types and Nothing but Fixed Types. A Fixed Type does not mean a Type which had no other Type for its ancestors; nor one which never passed through immature stages before reaching maturity. Nor does it mean a type without collaterals. It means a type which, when mature, is repeated indefinitely.
(3) The geological record does not as a fact show gradually progressive change by imperceptible degrees like an inclined plane, but on the contrary, a series of leaps, like a number of steps.