The distinction of Fact and Theory is only relative. Brute animals have a practical knowledge of relations of space and force; but they have no knowledge of Geometry or Mechanicks.

The Logic of Induction is the 'Criterion of Truth' inferred from Facts, as the Logic of Deduction is the 'Criterion of Truth' deduced from necessary Principle. In Art, Truth is a means to an end; in Science, it is the only end.

The 'Logic of Induction' consists in stating the Facts and the Inference in such a manner, that the evidence of the Inference is manifest; just as the Logic of Deduction consists in stating the Premises and the Conclusion in such a manner that the Evidence of the Conclusion is manifest.

'Induction' is a term applied to describe the 'process' of a true Colligation of Facts by means of an exact and appropriate Conception. 'An Induction' is also employed to denote the 'proposition' which results from this process. An Induction is not the mere sum of the Facts which are colligated. The Facts are not only brought together, but seen in a new point of view. 'The Consilience of Inductions' takes place when an Induction, obtained from one class of facts, coincides with an Induction, obtained from another different class.

When a series of progressive numbers is given as the result of observation, it may generally be reduced to law by combinations of arithmetical and geometrical progressions. A true formula for a progressive series of numbers cannot commonly be obtained from a narrow range of observations.

The resolution of complex Facts into precise and measured partial Facts, we call the 'Decomposition of Facts'. This process is requisite for the progress of science, but does not necessarily lead to progress. The Conceptions by which Facts are bound together, are suggested by the sagacity of discoverers. But a supply of appropriate hypotheses cannot be constructed by rule, nor without inventive talent. The truth of tentative hypotheses must be tested by their application to facts. The discoverer must be ready, carefully to try his hypotheses in this manner, and to reject them if they will not bear the test, in spite of indolence and vanity.

Facts are the materials of science, but all Facts involve Ideas. Since, in observing Facts, we cannot exclude Ideas, we must, for the purposes of science, take care that the Ideas are clear and rigorously applied.

Discovery depends upon the previous cultivation or natural clearness of the appropriate Idea, and therefore no discovery is the work of accident.

The two processes by which Science is constructed are the 'Explication of Conceptions' and the 'Colligation of Facts'.

The Palaetiological Sciences point backwards with lines which are broken, but which all converge to the 'same' invisible point: and this point is the Origin of the Moral and Spiritual, as well as of the natural world.