KANT'S CRITIQUE OF TELEOLOGY IN BIOLOGICAL EXPLANATION

Concept of Infinity 93
difference between "mental regress" and "real progress," but in
doing so he maintains that Kant confuses the two. Russell notes
quite correctly: 43
When Kant says that an infinite series can 'never' be completed by successive
synthesis, all that he has even conceivably a right to say is that it
cannot be completed in a finite time. Thus what he really proves is, at most,
that if the world had no beginning, it must have already existed for an
infinite time.
Russell simply assumes that Kant was unaware of this and ventures
some speculations as to the reasons why he did not see this.
Owing to the inveterate subjectivism of his mental habits, he failed to notice
that he had reversed the sense of the series by substituting backward synthesis
for forward happening, and thus he supposed that it was necessary to
identify the mental series, which had no end with the physical series, which
had an end but no beginning. It was this mistake, I think, which, operating
unconsciously, led him to attribute validity to a singularly flimsy piece of
fallacious reasoning.
Instead of examining Kant's objection, that the world could
not "have already existed for an infinite time," Russell assumes that
Kant has ascribed the end of the progress to the regress and has
thus simply made a trivial mistake. Consequently he does not discuss
any philosophical grounds that might have moved Kant to take
up this particular position offering instead psychological speculations
about mental habits and unconscious operations.
Kant rejected the notion of an infinite past. The reason for this
lies however not in a confusion of progress and regress. The reason
lies in Kant's belief that if the world had already existed for an infinite
time, then an infinite amount or set of discrete successive
events would already have occurred. If the regress (mental series)
back in time can be carried on to infinity, that is, if it represents an
infinite task, then the real history of the world (physical series) has
already completed an equally great task forwards. An infinite task
can be carried out forever, but it cannot be sensibly said to be completed.
While there is no difficulty in imagining a task which has a
beginning but no end, it quite questionable whether we can conceive
of completing a task which has no beginning, especially if we
assume (as Kant obviously does) that what is completed is also
given. In a paper on the "logic" of this problem Fred Dretske4 4
43 Russell, Knowledge, p. 161.
44 Dretske, "Counting to Infinity," p. 100.