The Palætiological Sciences depend upon the Idea of Cause; but the leading conception which they involve is that of 'historical cause', not mechanical cause.

'Natural History' ought to form a part of intellectual education, in order to correct certain prejudices which arise from cultivating the intellect by means of mathematics alone and in order to lead the student to see that the division of things into kinds, and the attribution and use of names, are processes susceptible of great precision.

The Methods of Observation of Quantity in general, are 'Numeration', which is precise by the nature of Number; the 'Measurement of Space' and 'of Time', which are easily made precise; the 'Conversion of Space and Time', by which each aids the measurement of the other. The Idea of Space becomes more clear by studying 'Geometry'; the Idea of Force, by studying 'Mechanics'; the Ideas of Likeness, of Kind, of subordination of Classes, by studying 'Natural History'.

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.

[W]e can ascend to remote periods by a chain of causes, but in none can we ascend to a 'beginning' of the chain.

The Catastrophist constructs theories, the Uniformitarian Demolishes them.

There are, in the Palætiological Sciences, two antagonist doctrines: 'Catastrophes' and 'Uniformity'. The doctrine of a 'uniform course of nature' is tenable only when we extend the notion of uniformity so far that it shall include catastrophes.

The Process of Induction may be resolved into three steps ; the 'Selection of the Idea', the 'Construction of the Conception', and the 'Determination of the Magnitudes'. These three steps correspond to the determination of the 'Independent Variable', the 'formula', and the 'coefficients', in mathematical investigations; or to the 'Argument', the 'Law', and the 'Numerical Data', in a Table of an Inequality. The conceptions involved in scientific truths have attained the requisite degree of clearness by means of the Discussions respecting ideas which have taken place among discoverers and their followers. Such discussions are very far from being unprofitable

The Construction of the Conception very often includes, in a great measure, the Determination of the Magnitudes. The true construction of the conception is frequently suggested by some hypothesis; and in these cases, the hypothesis may be useful, though containing superfluous parts.

'The Law of Continuity' is this:-that a quantity cannot pass from one amount to another by any change of conditions, without passing through all intermediate magnitudes according to the intermediate conditions. It may often be employed to disprove distinctions which have no real foundation. 'The Method of Gradation' consists in taking a number of stages of a property in question, intermediate between two extreme cases which appear to be different. It is employed to determine whether the extreme cases are really distinct or not. 'The Method of Gradation', applied to decide the question, whether the existing phenomena arise from existing causes, leads to this result:-That the phenomena do appear to arise from existing causes, but that the action of existing causes have transgressed their recorded Limits of Intensity. 'The Method of Natural Classification' consists in classing cases, not according to any assumed definition, but according to the connexion of the facts themselves.

When alterations in technical terms become necessary, it is desirable that the new term should contain in its form some memorial of the old one.

Philological analogies are to be preserved if possible, but modified according to scientific convenience.

In forming a Terminology, words may be invented when necessary, but they cannot be conveniently borrowed from casual or arbitrary circumstances.

The fundamental terms of a system of Nomenclature may "be conveniently borrowed from casual or arbitrary circumstances.

If terms are systematically good, they are not to be rejected because they are etymologically inaccurate.

Terms which imply theoretical views are admissible, as far as the theory is proved.

New terms and changes of terms, which are not needed in order to express truth, are to be avoided.

Terms must be constructed and appropriated so as to be fitted to enunciate simply and clearly true general propositions.

It is better to form new words as technical terms, than to employ old ones in which the last three Aphorisms cannot be complied with.

In the 'Induction of Causes' the principal maxim is, that we must be careful to possess, and to apply, with perfect clearness, the Fundamental Idea on which the Induction depends. The Induction of Substance, of Force, of Polarity, go beyond mere laws of phenomena, and may be considered as the Induction cf Causes. The Cause of certain phenomena being inferred, we are led to inquire into the Cause of this Cause, which inquiry must be conducted in the same manner as the previous one; and thus we have the Induction of Ulterior Causes.

In the Ancient Period of Science, Technical Terms were formed in three different ways:-by appropriating common words and fixing their meaning;-by constructing terms containing a description;-by constructing terms containing reference to a theory.

In framing scientific terms, the appropriation of old words is preferable to the invention of new ones.

When common words are appropriated as technical terms, their meaning and relations in common use should be retained as far as can conveniently be done.

When common words are appropriated as technical terms, their meaning may be modified, and must be rigorously fixed.

When common words are appropriated as technical terms, this must be done so that they are not ambiguous in their application.

All hypotheses respecting the manner in which the elements of inorganic bodies are arranged in space, must be constructed with regard to the general facts of crystallization.

Life is a System of Vital Forces ; and the conception of such Forces involves a peculiar Fundamental Idea.

Mechanical, chemical, and vital Forces form an ascending progression, each including the preceding. Chemical Affinity includes in its nature Mechanical Force, and may often be practically resolved into Mechanical Force. (Thus the ingredients of gunpowder, liberated from their chemical union, exert great mechanical Force : a galvanic battery acting by chemical process does the like.) Vital Forces include in their nature both chemical Affinities and mechanical Forces: for Vital Powers produce both chemical changes, (digestion,) and motions which imply considerable mechanical force, (as the motion of the sap and of the blood.)

In 'voluntary' motions, Sensations produce Actions, and the connexion is made by means of Ideas: in 'reflected' motions, the connexion neither seems to be nor is made by means of Ideas: in 'instinctive' motions, the connexion is such as requires Ideas, but we cannot believe the Ideas to exist.

The assumption of a Final Cause in the structure of each part of animals and plants is as inevitable as the assumption of an Efficient Cause for every event. The maxim that in organized bodies nothing is 'in vain', is as necessarily true as the maxim that nothing happens 'by chance'.

The idea of living beings as subject to 'disease' includes a recognition of a Final Cause in organization; for disease is a state in which the vital forces do not attain their 'proper ends'.

The Sensations are the 'Objective', the Ideas the 'Subjective' part of every act of perception or knowledge.

It has been proved by the biological speculations of past time, that organic Life cannot rightly be resolved into mechanical or chemical forces, or the operation of a vital fluid, or of a soul.

The basis of all Natural Systems of Classification is the Idea of Natural Affinity. The Principle which this Idea involves is this:-Natural arrangements, obtained from 'different' sets of characters, must 'coincide' with each other.

Truths obtained by Induction are made compact and permanent by being expressed in 'Technical Terms'.

In Deductive Reasoning, we cannot have any truth in the conclusion which is not virtually contained in the premises.

In order to acquire any exact and solid knowledge, the student must possess with perfect precision the ideas appropriate to that part of knowledge: and this precision is tested by the student's 'perceiving' the axiomatic evidence of the 'axioms' belonging to each 'Fundamental Idea'.

'Form' or 'figure' is space limited by boundaries. Space has necessarily 'three' dimensions, length, breadth, depth; and no ethers which cannot be resolved into these.

The Perception of Time involves a constant and latent kind of memory, which may be termed a 'Sense of Succession'. The Perception of Number also involves this Sense of Succession, although in small numbers we appear to apprehend the units simultaneously and not successively.

'Intuitive' is opposed to 'discursive' reason. In intuition, we obtain our conclusions by dwelling upon 'one' aspect of the fundamental Idea; in discursive reasoning, we combine several aspects of the Idea

Among the foundations of the Higher Mathematics is also the 'Idea of a Limit'. The Idea of a Limit cannot be superseded by any other definitions or Hypotheses.