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

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

'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.

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

Coexistent polarities are fundamentally identical.

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 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 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.

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 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.

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.

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.

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

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.

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

'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.

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'.

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

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'.

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.

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'.

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.

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

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.)

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.

Our assent to the hypothesis implies that it is held to be true of all particular instances. That these cases belong to past or to future times, that they have or have not already occurred, makes no difference in the applicability of the rule to them. Because the rule prevails, it includes all cases.

Natural Groups are best described, not by any definition which marks their boundaries, but by a 'Type' which marks their centre. The Type of any natural group is an example which possesses in a marked degree all the leading characters of the class.

The Idea of Cause is expressed for purposes of science by these three Axioms:-'Every Event must have a Cause':-'Causes are measured by their Effects':-'Reaction is equal and opposite to Action'.

And so no force however great can stretch a cord however fine into an horizontal line which is accurately straight.

We collect individuals into 'kinds' by applying to them the Idea of Likeness.

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

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 Sight cannot decompose a compound colour into simple colours, or distinguish a compound from a simple colour

The system becomes more coherent as it is further extended. The elements which we require for explaining a new class of facts are already contained in our system. Different members of the theory run together, and we have thus a constant convergence to unity. In false theories, the contrary is the case.

A Natural Group is steadily fixed, though not precisely limited; it is given in position, though not circumscribed; it is determined, not by a boundary without, but by a central point within; -not by what it strictly excludes, but by what it eminently includes; - by a Type, not by a Definition.

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.

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.

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.

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

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.

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.

'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.'

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 " 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.