15 Apr 2009

The Beginning of Time according to Eugene Dühring

by Corry Shores
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Nietzsche refers to Eugene Dühring's theory of infinity in §1066 of The Will to Power.

Dühring argues that at some point, the flow of time began. So there is not an infinite stretch of time going backwards through the past without end.

His argument is essentially this:
1) we can only conceive infinity clearly as being a series of numerical units to which we may continually add a new unit. There is no end to this series, because you can always add another unit to a collection of numerical values. [This is the "spurious infinite" that Hegel calls a progressive infinite, see his Science of Logic, §§552-562]
2) Even though this infinity continues without end, it had to begin with its base step.
3) If we claim there is an infinity of time leading up to now, then it had to have a beginning, just as infinities starting now have their beginning in this moment.
4) Thus time has a beginning.

Below we take from the Burns translation of Engels' Anti-Dühring:

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}.

Here are the Dühring pages that Engels cites [click image for an enlargement]:

Dühring, Eugen. Cursus der Philosophie, als streng wissenschaftlicher Weltschauung und Lebensgestaltung. Leipzig: Verlag, 1875.

Engels, Frederick. Anti-Dühring: Herr Eugen Dühring's Revolution in Science. Transl. Emile Burns.
Available online at [cited section]:

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