Kant's Critique of Pure Reason
TRANSCENDENTAL LOGIC, SECOND DIVISION:
BOOK II: THE DIALECTICAL INFERENCES OF PURE REASON
Chapter II: THE ANTINOMY OF PURE REASON
Section 8: THE REGULATIVE PRINCIPLE OF PURE REASON IN ITS APPLICATION TO THE COSMOLOGICAL IDEAS (p. 449)
Section 9: THE EMPIRICAL EMPLOYMENT OF THE REGULATIVE PRINCIPLE OF REASON, IN RESPECT OF ALL COSMOLOGICAL IDEAS (p. 454)
- The principle of reason is properly only a regulative rule.
- No maximum of the series of conditions in a sensible world is given through the cosmological principle of totality, but can only be set as a task.
- It is not a principle of the understanding because it is not a principle of empirical knowledge.
- It is not a constitutive principle of reason which would allow us to extend our concept of the sensible world beyond experience.
- It does not tell us what the object is, but only how the empirical
regress is to be carried out.
- To determine how the synthesis is to be carried out when the synthesis is never complete:
- Progressus in indefinitum: you produce the series as far as you please.
- Progressus in infinitum: you must never cease producing
- When the whole is empirically given, it is possible to proceed back in the series of its inner conditions in infinitum.
- The division of a body proceeds in infinitum because further members of the series are given empirically.
- We necessarily find further members.
- When the whole is not given (i.e. only a member is given), but has to be found through empirical regress, we can only say that the search for still higher conditions of the series is possible in infinitum.
- The series of ancestors of any given man is not given in its absolute totality in any given possible experience, so no empirical limit is ever met, therefore you produce the series in indefinitum, i.e. search for additional members indefinitely far.
- Since no experience is absolutely necessary, the necessity is that we enquire for them.
I. Solution of the Cosmological Idea of the Totality of the Composition of the Appearances of a Cosmic Whole.
- We need to establish the validity of the principle of reason as a rule for the continuation and magnitude of possible experience.
Back to Section 7: Critical Solution Of The Cosmological Conflict Of Reason With Itself
- For the solution we have to decide whether, in the regress to the unconditioned magnitude of the universe in time and space, the regress should be to infinity or only indeterminately continued.
- The most we can ever know of this empirical regress is that from every given member of the series of conditions we have always to advance empirically to a higher member.
- The magnitude is not determined in any absolute manner so we cannot say the regress proceeds to infinity.
- We cannot say, therefore, anything at all in regard to the magnitude of the world, not even that there is in it a regress in infinitum.
- We cannot say, therefore, that the world is infinite in space or time.
- I also cannot say the regress is finite.
- The answer, therefore, is that the world has no first beginning in time and no outermost limit in space.
- An absolute limit of the world in impossible empirically, and therefore also absolutely.
- This proof is different from that of the antithesis where we
regarded the sensible world as a thing given in itself, in its totality, prior
to any regress, and asserted that unless it occupies all time and all places,
it cannot have any determinate position whatsoever in them.
- This answer does not mean that we will never reach the outermost edge of the universe, all it says is that we must continue the advance.
- While appearances in the world are conditionally limited, the world itself is neither conditionally nor unconditionally limited.
- The regress consists only in the determining of the magnitude, and does not give any determinate concept.
Forward to III. Solution of the Cosmological Idea of Totality in the Derivation of Cosmical Events from their Causes
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