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'.

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'.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

'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.'

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.

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.

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.

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

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'.

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.

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.

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.

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

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.

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.

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

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'.

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.

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

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

Coexistent polarities are fundamentally identical.

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.

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