Four Forms Make a Universe


Since Immanuel Kant’s Inaugural Dissertation of 1770 we assume that the concepts of space and time are not abstracted from sensations of external things. But outer experience is considered possible at all only through an inner representation of space and time within the cognitive system. In this work we describe a representation which is both inner and outer. We add to the Kantian imagination that “forms of nature, matter, space and time are intelligible, perceivable and comprehensible”, the idea that these four are indeed intelligent, perceiving, grasping and clear. They are active systems with their own intelligence. In this paper on the mind-matter interface we create the mathematical prerequisites for an appropriate system representation. We show that there is an oriented logic core within the space–time algebra. This logic core is a commutative subspace from which not only binary logic, but syntax with arbitrary real and complex truth classifiers can be derived. Space–time algebra too is obtained from this inner grammar by two rearrangements of four basic forms of connectives. When we conceive the existence of a few features like polarity between two appearances, identification and rearrangement of the latter as basic and primordial to human cognition and construction, the intelligence of space–time is prior to cognition, as it contains within its representation the basic self-reference necessary for the intelligible de-convolution of space–time. Thus the process of nature extends into the inner space.

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Schmeikal, B. Four Forms Make a Universe. Adv. Appl. Clifford Algebras 26, 889–911 (2016).

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Mathematics Subject Classification

  • Primary 02.10.Ab
  • Secondary 03.65.Fd
  • 02.10.−v
  • 03.67.−a
  • 04.62.+ v
  • 11.30.−j


  • Logic
  • Algebraic logic
  • Clifford algebra
  • Geometric algebra
  • Iterant algebra
  • Quantum information
  • Space–time-logic