Regulative Employment of the Ideas of Pure Reason (p. 532)

• Reason has a natural tendency to transgress its limits and transcendental ideas are as natural to it as the categories are to the understanding.
  • We are entitled to suppose that transcendental ideas have their own good, proper and therefore immanent use.
• Just as the understanding unifies the manifold in the object by means of concepts, so reason unifies the manifold of concepts by means of ideas.
  • Reason does not create concepts, but only orders them.
• Transcendental ideas have regulative employment which is necessary to understanding.
  • They direct the understanding towards a certain goal upon which the routes marked out by all its rules converge.
  • They serve to give to concepts the greatest possible unity combined with the greatest possible extension.
• Reason prescribes the systematization of the knowledge obtained by the understanding.
  • It seeks to exhibit the connection of its parts in conformity with a single principle.
  • It presupposes the idea of the form of a whole knowledge which is prior to the determinate knowledge of the parts and contains the conditions that determine a priori for every part its position and relation to other parts.
  • These concepts of reason are not derived from nature, we interrogate nature with these ideas.
• Apodeictic Use of Reason: Where reason is the faculty of deducing the particular from the universal and:
  • Where the universal is already certain in itself and given.
  • And judgment only is required to execute the subsumption.
  • And the particular is thereby determined in a necessary manner.
• Hypothetical Use of Reason: Where the universal is admitted as problematic only and is a mere idea.
  • The particular is still certain, but the universality of the rule of which it is a consequence is still a problem.
  • It is regulative only. Its aim is to approximate the rule to universality, i.e. to bring systematic unity, so far as possible, into the body of our detailed knowledge.
    • This unity is the criterion of the truth of its rules.
    • The systematic unity is only a projected unity.
    • The systematic unity is a logical principle
• To secure an empirical criterion, we must presuppose the systematic unity of nature as objectively valid and necessary.
  • This is the logical Principle of Homogeneity (genera), which postulates identity among appearances.
  • This principle gives us the extent (universality) of concepts.
  • Aims at the unity of knowledge.
  • Reason demands that no genera be the highest.
  • The law of reason which requires us to seek for systematic unity is a necessary law, since without it we should have no reason at all, and without reason no coherent employment of the understanding, and in the absence of this, no sufficient criterion of empirical truth.
  • In other words we must assume our rules conform to nature.
  • If the appearances which present themselves were of so great a variety that understanding could never by comparison detect the slightest similarity, we would not have any universal concept and the understanding itself would not exist.
• The logical principle of genera is balanced by the Principle of Species which prescribes to the understanding that it attend to diversity no less than to identity.
  • This principle gives us the content (determinateness) of concepts in respect of the multiplicity of species.
  • Aims at the systematic completeness of knowledge.
  • Reason demands that no species be the lowest.
  • This law cannot be derived from experience.
  • It is also only on the assumption of differences in nature that we can have any faculty of understanding.
• In order to complete the systematic unity, reason has another law, the Principle of Continuity which prescribes that we proceed from each species to every other by a gradual increase in the diversity.
  • Arises from the union of the other two by prescribing that even amidst the utmost manifoldness we observe homogeneity in the gradual transition from one species to another and thus recognize a relationship of the different branches all springing from the same stem.
  • No difference is the smallest.
  • This law cannot be derived from experience.
  • This continuity of forms is a mere idea to which no congruent object can be discovered in experience because:
    • First, the species in nature are actually divided and constitute a quantum discretum.
    • Second, we could not make any determinate empirical use of this law since it instructs us only in quite general terms that we are to seek for grades of affinity.
• These principles are transcendental ideas and although they contain mere ideas for the guidance of the empirical employment of reason, they yet possess, as synthetic a priori propositions, objective but indeterminate validity, and serve as rules for possible experience.
• These are dynamical laws which are constitutive in respect to experience since they render the concepts, without which there can be no experience, possible a priori.
  • But dynamical principles can be merely regulative per Transcendental Analytic.
  • There is no schema of sensibility corresponding to them so they can never have an object given in concreto.
• If, then we disallow empirical employment of them as constitutive principles, how are we to secure for them a regulative employment, and some sort of objective validity?
  • Every principle which prescribes unity in its employment also holds, although only indirectly, of the object of experience.
  • Therefore, the principles of pure reason must also have objective reality in respect of that object.
  • Not, however, in order to determine anything in it, but only to indicate the procedure whereby the empirical and determinate employment of the understanding can be brought into complete harmony with itself.
  • They are more properly called maxims of reason than principles.
• When merely regulative principles are treated as constitutive, and are therefore employed as objective principles, the may come into conflict with each other.
  • But when they are treated as maxims, there is no real conflict, but merely those differences in the interest of reason that give rise to differing modes of thought.
• The unity of reason is, in itself, undetermined, as regards the conditions under which, and the extent to which, the understanding ought to combine its concepts in systematic fashion.
  • We cannot find in intuition a schema for the complete systematic unity of all concepts of the understanding.
  • However, an analogon of such a schema must necessarily allow of being given.
    • The analogon is the idea of the maximum in the division and unification of the knowledge of the understanding under one principle.
    • What is greatest and absolutely complete can be determinately thought.
  • Thus the idea of reason is an analogon of a schema of sensibility; but with this difference, that the application of the concepts of the understanding to the schema of reason does not yield knowledge of the object itself, but only a rule or principle.

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