CHAP. II. OF THE EXPLICATION OF CONCEPTIONS 30 _Sect._ I. _The Historical Progress._ _Art._ 1. The Explication of Conceptions, 2. Has taken place historically by discussions. {xiv} _Art._ 3. False Doctrines when exposed appear impossible: 4. But were plausible before 5. Men's Minds gradually cleared. _Sect._ II. _Use of definitions._ _Art._ 6. Controversies about Definitions. 7. Not arbitrary Definitions. 8. Attention to Facts requisite. 9. Definition is not essential. 10. The omission of Definition not always blameable. _Sect._ III. _Use of Axioms._ _Art._ 11. Axioms serve to express Ideas. _Sect._ IV. _Clear and appropriate Ideas._ _Art._ 12. We must see the Axioms clearly. 13. Inappropriate Ideas cannot lead to Truth. 14. The fault is in the Conceptions. 15. Rules cannot teach Discovery; 16. But are not useless. 17. Discussion as well as Facts needed. _Sect._ V. _Accidental Discoveries._ _Art._ 18. No Scientific Discovery is accidental. 19. Such accidents do not happen to common Men. 20. Examples. 21. So far Explication of Conceptions. CHAP. III. OF FACTS AS THE MATERIALS OF SCIENCE 50 _Art._ 1. Facts must be true. 2. Facts not separable from Ideas. 3. The Ideas must be distinct. 4. Conceptions of the Intellect only to be admitted. 5. Facts are to be observed with reference to Space and Time: 6. And also to other Ideas. 7. The Decomposition of Facts. {xv} _Art._ 8. This step is not sufficient. 9. It introduces Technical Terms, 10. And Classification. 11. The materials of Science. CHAP. IV. OF THE COLLIGATION OF FACTS 59 _Art._ 1. Facts are colligated by Conceptions. 2. Science begins with common Observation. 3. Facts must be decomposed. 4. What Ideas first give Sciences. 5. Facts must be referred to Ideas. 6. Sagacity needed. 7. Discovery made by Guesses. 8. False Hypotheses preluding to true ones. 9. New Hypotheses not mere modifications of old ones. 10. Hypotheses may have superfluous parts. 11. Hypotheses to be compared with Facts. 12. Secondary Steps.