The present work is meant to serve as the first aid and guide in the acquisition of these comprehensive notions of the external world and the inner life. It is not meant to develop or uphold a "system of philosophy." Through long experience as a teacher the writer has learned that those are the best pupils who soon go their own way. However, it _is_ meant to uphold a certain method, that is, the scientific (or, if you will, the _natural_ scientific), which takes its problems, and endeavors to solve its problems, from experience and for experience. If, as a result, several points of view arise that differ from those of the present day, and consequently demand a different attitude toward important matters in the immediate future, this very fact affords proof that our present natural philosophy does not lead away from life, but aims to form a part of our life, and has a right to. CONTENTS PAGE INTRODUCTION 1 PART I GENERAL THEORY OF KNOWLEDGE 11 1. The Formation of Concepts 11 2. Science 13 3. The Aim of Science 13 4. Concrete and Abstract 16 5. The Subjective Part 17 6. Empirical Concepts 18 7. Simple and Complex Concepts 19 8. The Conclusion 24 9. The Natural Laws 28 10. The Law of Causation 31 11. The Purification of the Causal Relation 34 12. Induction 38 13. Deduction 40 14. Ideal Cases 44 15. The Determinateness of Things 47 16. The Freedom of the Will 50 17. The Classification of the Sciences 53 18. The Applied Sciences 57 PART II LOGIC, THE SCIENCE OF THE MANIFOLD, AND MATHEMATICS 61 19. The Most General Concept 61 20. Association 63 21. The Group 65 22. Negation 68 23. Artificial and Natural Groups 69 24. Arrangement of the Members 75 25. Numbers 78 26. Arithmetic, Algebra, and the Theory of Numbers 79 27. Co-ordination 80 28. Comparison 82