CONCEPTION OF THE SCIENCE.1. Philosophy, as the science which embraces the principles of the universe or world, is only a logical, which may perhaps conduct us to the real, conception.2. The universe or world is the reality of mathematical ideas, or, in simpler language, of mathematics.3. Philosophy is the recognition of mathematical ideas as constituting the world, or the repetition of the origin of the world in consciousness.4, 5. Spirit is the motion of mathematical ideas. Nature, their manifestation.6. The philosophy of Spirit is the representation of the movements of ideas in consciousness.7. The philosophy of Nature that of the phenomena or manifestations of ideas in consciousness.8. The world consists of two parts: of one apparent, real, or material; and one non-apparent, ideal, spiritual, in which the material is not present, or which is naught in relation to the material.9. There are, accordingly, two parts or divisions of Philosophy, viz. Pneumato-and Physio-philosophy.10. Physio-philosophy has to show how, and in accordance indeed with what laws, the Material took its origin; and, therefore, how something derived its existence from nothing. It has to portray the first periods of the world's development from nothing; how the elements and heavenly bodies originated; in what method by self-evolution into higher and manifold forms, they separated into minerals, became finally organic, and in Man attained self-consciousness.11. Physio-philosophy is, therefore, the generative history of the world, or, in general terms, the History of Creation, a name under which it was taught by the most ancient philosophers, viz. as Cosmogony. From its embracing the universe, it is plainly the Genesis of Moses.12. Man is the summit, the crown of nature's development, and must comprehend everything that has preceded him, even as the fruit includes within itself all the earlier developed parts of the plant. In a word, Man must represent the whole world in miniature.13. Now since in Man are manifested self-consciousness or spirit, Physio-philosophy has to show that the laws of spirit are not different from the laws of nature; but that both are transcripts or likenesses of each other.14. Physio-and Pneumato-philosophy range, therefore, parallel to each other.15. Physio-philosophy, however, holds the first rank, Pneumato-philosophy the second: the former, therefore, is the ground and foundation of the latter, for nature is antecedent to the human spirit.16. Without Physio-philosophy, therefore, there is no Pneumato-philosophy, any more than a flower is present without a stem, or an edifice without foundation.17. The whole of philosophy depends, consequently, upon the demonstration of the parallelism that exists between the activities of Nature and of Spirit.

DIVISION OF THE SCIENCE.18. It will be shown in the sequel that the Spiritual is antecedent to nature. Physio-philosophy must, therefore, commence from the spirit.19. It will also be shown in the sequel that the whole Animal Kingdom, e. g. is, none other than the representation of the several activities or organs of Man; naught else than Man disintegrated. In like manner nature is none other than the representation of the individual activities of the spirit. As, therefore, Zoology can be termed the Science of the Conversion of Man into the Animal Kingdom, so may Physio-philosophy be called the Science of the Conversion of Spirit into Nature.20. Physio-philosophy is divisible, therefore, into three parts. The first of these treats of spirit and its activities; the second, of the individual phenomena, or things of the world; the third, of the continuous operation of spirit in the individual things.

The first division is the doctrine of the Whole (de Toto)—Mathesis.

The second, that of Singulars (de Entibus)—Ontology.

The third, that of the Whole in the Singulars (de Toto in Entibus)—Biology.21. The Science of the Whole must divide into two doctrines; into that of immaterial totalities—Pneumatogeny; and into that of material totalities—Hylogeny.

Ontology teaches us the phenomenon of matter. The first phenomenon of this are the heavenly bodies comprehended by Cosmogony; these develop themselves further, and divide into the elements—Stochiogeny.

From these elements the Earth element develops itself still further, and divides into minerals—Mineralogy; these minerals unite into one collective body, and this is Geogeny.

The Whole in Singulars is the living or Organic, which again divides into plants and animals.

Biology, therefore, divides into Organogeny, Phytosophy and Zoosophy.

After this division of the subject the question first of all arises, what is science, provided there is one.

TRUTH.22. Science is a series of necessarily inter-dependent and consecutive propositions, which rest upon a certain fundamental proposition.23. Now, if anything be certain it can only be one in number. If, then, there be only one certainty, there can also be only one science, from which all the rest must be derived.24. The Mathematical is certain, and, by virtue of this character, it stands also alone. Mathematics is the only true science, and thus the primary science, the Mathesis, or Knowledge simply, as it was called by the ancients. The fundamental propositions of mathematics must, therefore, be fundamental propositions for all other sciences also.25. Physio-philosophy is only a science when it is reducible to, i. e. can be placed upon an equal footing with, mathematics. Mathematics is the universal science; so also is Physio-philosophy, although it is only a part, or rather but a condition of the universe; both are one, or mutually congruent.26. Mathematics is, however, a science of mere forms without substance. Physio-philosophy is, therefore, Mathematics endowed with substance.27. The substance of Physio-philosophy must be of one kind with the form of Mathematics.28. The certainty of mathematical propositions depends upon no proposition being essentially different from another. Though there may be much that is diversified or heterogeneous, there is nothing new in Mathematics.

For to prove a mathematical proposition is to show (or demonstrate) that it is equivalent, i. e. of the same kind with another proposition. All mathematical propositions must, consequently, resemble a first proposition.29. Physio-philosophy must also show that all its propositions, or that all things, resemble each other, and, finally, some first proposition or thing.30. These natural propositions or natural things must, however, resemble also mathematical propositions, and depend, after all, upon the primary proposition of mathematics or the axiom.

Now then comes the question, what is the first principle of Mathematics?