All these pretty little things are therefore not only not "axiomatically decided", as prescribed, but are merely imported from outside, that is to say, from Hegel's Logic. And in fact in such a form that in the whole chapter there is not even the semblance of any internal coherence unless borrowed from Hegel, and the whole question finally trickles out in a meaningless subtilising about space and time, inertness and change.
From being Hegel passes to essence, to dialectics. Here he deals with the determinations of reflection, their internal antagonisms and contradictions, as for example, positive and negative; he then comes to causality or the relation of cause and effect and ends with necessity. Not otherwise Herr Dühring. What Hegel calls the doctrine of essence Herr Dühring translates into "logical properties of being" {D. Ph.
29}. These, however, consist above all in the "antagonism of forces" {31}, in opposites. Contradiction, however, Herr Dühring absolutely denies; we will return to this point later. Then he passes over to causality , and from this to necessity. So that when- Herr Dühring says of himself:
"We, who do not philosophise out of a cage " {41}, he apparently means that he philosophises in a cage, namely, the cage of the Hegelian schematism of categories.
V.
PHILOSOPHY OF NATURE.
TIME AND SPACE W e now come to philosophy of nature. Here again Herr Dühring has every cause for dissatisfaction with his predecessors.
Natural philosophy "sank so low that it became an arid, spurious doggerel founded on ignorance", and "fell to the prostituted philosophistics of a Schelling and his like, rigging themselves out in the priesthood of the Absolute and hoodwinking the public". Fatigue has saved us from these "deformities";but up to now it has only given place to "instability"; "and as far as the public at large is concerned, it is well known that the disappearance of a great charlatan is often only the opportunity for a lesser but commercially more experienced successor to put out again, under another signboard; the products of his predecessor". Natural scientists themselves feel little "inclination to make excursions into the realm of world-encompassing ideas", and consequently jump to "wild and hasty conclusions" in the theoretical sphere {D. Ph. 56-57}.
The need for deliverance is therefore urgent, and by a stroke of good luck Herr Dühring is at hand.
In order properly to appreciate the revelations which now follow on the development of the world in time and its limitations in space, we must turn back again to certain passages in "world schematism" {15}.
Infinity -- which Hegel calls bad infinity -- is attributed to being also in accordance with Hegel (Encyclopaedia , § 93) , and then this infinity is investigated.
"The clearest form of an infinity which can be conceived without contradiction is the unlimited accumulation of numbers in a numerical series {18} ... As we can add yet another unit to any number, without ever exhausting the possibility of further numbers, so also to every state of being a further state succeeds, and infinity consists in the unlimited begetting of these states. This exactly conceived infinity has consequently only one single basic form with one single direction. For although it is immaterial to our thought whether or not it conceives an opposite direction in the accumulation of states, this retrogressing infinity is nevertheless only a rashly constructed thought-image. indeed, since this infinity would have to be traversed in reality in the reverse direction, it would in each of its states have an infinite succession of numbers behind itself.
But this would involve the impermissible contradiction of a counted infinite numerical series, and so it is contrary to reason to postulate any second direction in infinity" {19}.
The first conclusion drawn from this conception of infinity is that the chain of causes and effects in the world must at some time have had a beginning:
"an infinite number of causes which assumedly already have lined up next to one another is inconceivable, just because it presupposes that the uncountable has been counted" {37}.
And thus a final cause is proved.
The second conclusion is "the law of definite number: the accumulation of identities of any actual species of independent things is only conceivable as forming a definite number". Not only must the number of celestial bodies existing at any point of time be in itself definite, but so must also the total number of all, even the tiniest independent particles of matter existing in the world.
This latter requisite is the real reason why no composition can be conceived without atoms. All actual division has always a definite limit, and must have it if the contradiction of the counted uncountable is to be avoided.
