II. Solution of the Cosmological Idea of the Totality of Division of a Whole Given in Intuition (p. 459)

• The division of a whole given in intuition is a regress from something conditioned to the conditions of its possibility.
  • The conditions (parts) are contained in the conditioned.
  • Contrast this with first cosmological idea where the conditions were met with outside the conditioned.
• The regress, therefore, proceeds in infinitum.
  • We cannot, however, say of a whole which is divisible to infinity, that it is made up of infinitely many parts. Although the parts are contained in the intuition of the whole, the whole division is not so contained.
• This general statement is applicable to space:
  • Every space intuited as within limits is such a whole, the parts of which are always spaces. Every space is therefore infinitely divisible.
  • Body, which is grounded in the divisibility of space, is therefore infinitely divisible without consisting, however, of infinitely many parts.
• This rule cannot be made to apply to a whole in which, as given, the parts are so distinguished from one another that they constitute a quantum discretum (organized system).

• We have been overlooking the distinction between mathematical and dynamical syntheses of appearance.
  • In the dynamical, there may be a presupposition compatible with the pretensions of reason.
• In the dynamical series of sensible conditions, a heterogeneous condition, not itself a part of the series, but purely intelligible, and as such outside the series, can be allowed.
  • The empirically unconditioned is also non-sensible and therefore can satisfy understanding and reason.

• Causality is either according to nature or arises from freedom.
  • In nature all causes have their cause because they exist in time. Each cause must come into being in time.
  • Freedom: the power of beginning a state spontaneously.
• The practical concept of freedom is the will's independence of coercion through sensuous impulses.
  • It is based on the transcendental idea of freedom.
• The denial of transcendental freedom must involve the elimination of all practical freedom.
• The Dynamical concepts of reason are not concerned with an object considered as magnitude, but only with its existence.

  Possibility of Causality Through Freedom, in Harmony with the Universal Law of Natural Necessity (p. 467)

  • Intelligible: whatever in an object of the senses that is not itself appearance.
  • Character: law of causality, every efficient cause must have a character.
  • An object has an empirical character and an intelligible character.
  • Empirical Character: The uniformity according to which certain appearances follow as effects.
    • Every cause presupposes this rule.
    • This rule is what the concept of cause as a faculty is based.
    • Called empirical because the uniformity must be exhibited by mere appearances.
  • If an appearance has a faculty which is not an object of sensible intuition, but through which it can be the cause of appearances, the causality can be regarded in two ways:
    • Regarded as the causality of an appearance in the world of sense, it is sensible in its effects.
      • This is an empirical concept.
      • Character of the thing in the field of appearance.
    • Regarded as the causality of a thing in itself, it is intelligible in its action.
      • This is an intellectual concept.
      • Character as thing in itself.
  • The acting subject in its intelligible character:
    • Would not stand under any conditions of time.
    • Would not have a place in the series of those empirical conditions through which the event is rendered necessary in the world of sense.
    • Is noumenon, and therefore nothing happens in it.
    • Must in its action be independent of and free from all necessity because natural necessity is to be met with only in the sensible world.
    • No action begins in this active being itself, but we can say the active being of itself begins its effects in the sensible world.
  • In this way freedom and nature can exist together without conflict in the same actions, according as the actions are referred to their intelligible or to their sensible cause.