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.

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

The Catastrophist constructs theories, the Uniformitarian Demolishes them.

'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.

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

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.

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.

[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 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

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

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

Mechanical Science depends on the Conception of Force; and is divided into 'Statics', the doctrine of Force preventing motion, and 'Dynamics', the doctrine of Force producing motion.

A whale is not a fish in natural history, but it is a fish in commerce and law. A plea that human laws which mention fish do not apply to whales, would be rejected at once by an intelligent judge.

We cannot observe external things without some degree of Thought; nor can we reflect upon our Thoughts, without being influenced in the course of our reflection by the Things which we have observed.

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'.

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'.

The solution is, that we do not see the image on the retina at all, we only see by means of it.

The 'Diagnosis', or Scheme of the Characters, comes, in the order of philosophy, after the Classification. The characters do not 'make' the classes, they only enable us to 'recognize' them. The Diagnosis is an Artificial Key to a Natural System.

Man, servant and interpreter of Nature, does and understands only as much as he has observed of the order of Nature, either in reality or in mind; he neither knows nor can do more.

'When two equal weights are supported on the middle point between them, the pressure on the fulcrum is equal to the sum of the weights.'

The " Five Words," 'genus', 'species', 'difference', 'property', 'accident', were used by the Aristotelians, in order to express the subordination of kinds, and to describe the nature of definitions and propositions. In modern times, these technical expressions have been more referred to by Natural Historians than by Metaphysicians.

Every failure is a step to success. Every detection of what is false directs us towards what is true: every trial exhausts some tempting form of error. Not only so; but scarcely any attempt is entirely a failure; scarcely any theory, the result of steady thought, is altogether false; no tempting form of Error is without some latent charm derived from Truth.

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'.

'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.

Coexistent polarities are fundamentally identical.

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.

The antithesis of 'Sense' & 'Ideas' is the foundation of the Philosophy of Science. No knowledge can exist without the union, no philosophy without the separation, of these two elements.

The Science of Hydrostatics depends upon the Fundamental Principle that 'fluids press equally in all directions'. This Principle necessarily results from the conception of a Fluid, as a body of which the parts are perfectly moveable in all directions. For since the Fluid is a body, it can transmit pressure; and the transmitted pressure is equal to the original pressure, in virtue of the Axiom that Reaction is equal to Action. That the Fundamental Principle is not derived from experience, is plain both from its evidence and from its history.

The Plan of the System, may aim at a Natural or an Artificial System. But no classes can be absolutely artificial, for if they were, no assertions could be made concerning them.

According to the technical language of old writers, a thing and its qualities are described as subject and attributes; and thus a man's faculties and acts are attributes of which he is the subject. The mind is the subject in which ideas inhere. Moreover, the man's faculties and acts are employed upon external objects; and from objects all his sensations arise. Hence the part of a man's knowledge which belongs to his own mind, is subjective: that which flows in upon him from the world external to him, is objective.

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.

Attractions take place between bodies, affinities between the particles of a body. The former may be compared to the alliances of states, the latter to the ties of family.

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

We necessarily perceive bodies as 'without' us: the Idea of 'Externality' is one of the conditions of perception.

An 'Artificial System' is one in which the 'smaller' groups (the Genera) are 'natural'; and in which the 'wider' divisions (Classes, Orders) are constructed by the 'peremptory' application of selected Characters

We unfold out of the Idea of Space the propositions of geometry, which are plainly truths of the most rigorous necessity and universality. But if the idea of space were merely collected from observation of the external world, it could never enable or entitle us to assert such propositions: it could never authorize us to say that not merely some lines, but all lines, not only have, but must have, those properties which geometry teaches. Geometry in every proposition speaks a language which experience never dares to utter; and indeed of which she but half comprehends the meaning.

'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

The governing principles of chemical affinity are, that it is elective ; that it is definite ; that it determines the properties of the compound; and that analysis is possible.

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

Truths once obtained by legitimate Induction are Facts: these Facts may be again connected, so as to produce higher truths: and thus we advance to 'Successive Generalizations'.

Secondary Qualities are not 'extended' but 'intensive'; their effects are not augmented by addition of parts, but by increased operation of the medium. Hence they are not measured directly, but by 'scales'; not by 'units', but by 'degrees'.

A 'Natural System' is one which attempts to make 'all' the divisions natural, the widest as well as the narrowest; and therefore applies 'no' characters 'peremptorily'.

By speaking of space as an Idea, I intend to imply the apprehension of objects as existing in space, and of the relations of position prevailing among them, is not a consequence of experience but a result of a peculiar constitution and activity of the mind which is independent of all experience in its origin, though constantly combined with experience in its exercise.

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.

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.

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.)

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

We perceive by 'means' of a medium and 'by means' of impressions on the nerves: but we do not (by our senses,) perceive either the medium or the impressions on the nerves.