Chapter II: THE ANTINOMY OF PURE REASON (p.384)

• Antinomy: a pseudo-rational inference directed to the transcendental concept of the absolute totality of the series of conditions for any given appearance. From the fact that my concept of the unconditioned synthetic unity of the series is always self-contradictory, I conclude there really is a unity of the opposite kind although I have no concept of it.
  • Follows the analogy of the hypothetical syllogism.
  • Falls into contradictions, both sides of which seem to be true. (Paralogisms were one-sided.)
• Cosmical Concepts: transcendental ideas, in so far as they refer to absolute totality in the synthesis of appearances.
  • Because this unconditioned totality also underlies the concept of the world-whole (itself only an idea).
  • Because they concern only the synthesis of appearances, therefore only empirical.
• Ideal of pure reason: The absolute totality of the synthesis of the conditions of all possible things in general.

• Two points to remember:
  • Pure and transcendental concepts can issue only from the understanding, not from reason. Reason frees the concept from the limits of empirical experience.
    • It does this by carrying the empirical synthesis as far as the unconditioned according to the principle that if the conditioned is given, the entire sum of conditions, and consequently the absolutely unconditioned is also given.
    • The transcendental ideas are therefore categories extended to the unconditioned.
  • Not all categories are fitted for such employment: only those in which the synthesis constitutes a series.
• Two types of synthesis of a series:
  • Regressive Synthesis: begins from the condition which stands nearest a given appearance and passes to more remote conditions.
  • Progressive Synthesis: begins from first consequence.
• Time is, in itself, a series and is the formal condition of all series.
  • We will only be concerned with past time which is necessarily thought as being given in its entirety.
• Space in itself does not constitute a series.
  • But the synthesis of the manifold parts of space (by means of which we apprehend space) is successive.
  • Reality is space (i.e. matter) is a conditioned: its internal conditions are its parts and thus occurs a regressive series [when we inquire as to the parts of these parts].
  • As to the categories of real relation between appearances:
    • Substance with its accidents is not.
    • The concept of the substantial is not.
    • Community is not.
    • Causality is.
  • The concepts of possible, actual and necessary do not form a series, but, the accidental in existence is conditioned.
• We are left with 4 Cosmological Ideas corresponding to the titles of the categories:
  1. Absolute completeness of the Composition of the given whole of all appearances.
  2. Absolute completeness in the Division of a given whole in the field of appearance.
  3. Absolute completeness in the Origination of an appearance.
  4. Absolute completeness as regards the Dependence of Existence of the alterable in the field of appearance.
• Comments:
  • The idea of absolute totality concerns only the exposition of appearances and is not a pure concept.
  • When dealing with appearance we have a special limitation: we do not know if completeness is possible.
  • What reason is seeking in this regressive series is the unconditioned.
    • Since the unconditioned is necessarily contained in the absolute totality of the regressive synthesis of the manifold in the field of appearance, reason adopts the method of starting from the idea of totality, though what is really has in view is the unconditioned.
  • The unconditioned may be conceived in either of two ways:
    • As consisting of the entire series in which all members are conditioned and only the totality of them is unconditioned, i.e. the series is infinite, i.e. without beginning.
    • Or, the absolute unconditioned is only part of the series, a part to which the rest is subordinated, i.e. there is a first member of the series entitled:
      • In respect to time: the beginning of the world.
        • World: the mathematical sum-total of all appearances and the totality of their synthesis.
        • Nature: the same world considered as a dynamical whole.
      • In respect to space: the limit of the world.
      • In respect to the parts of a given whole: the simple.
      • In respect to causes: absolute self activity (freedom).
        • Freedom: the unconditioned causality in the field of appearance.
        • Natural Cause: conditioned causality in the field of appearance.
      • In respect to the existence of alterable things: absolute natural necessity.
        • Natural Necessity: the unconditioned necessity of appearances.