The original work as planned by Clifford was to have been entitled The First Principles of the Mathematical Sciences Explained to the Non-Mathematical and to have contained six chapters on Number, Space, Quantity, Position, Motion, and Mass respectively. ...Shortly before his death he expressed a wish that the book should only be published after very careful revision and that its title should be changed to [our title]. Upon Clifford's death the labour of revision and completion was entrusted to Mr. R. C. Rowe... On the sad death of Professor Rowe... I was requested... to take up the... editing thus left incomplete. ...For the latter half of Chapter III and for the whole of Chapter IV... I am alone responsible. Yet whatever there is in them of value I owe to Clifford; whatever is feeble or obscure is my own. ...With Chapter V. my task has been by no means light. ... I felt it impossible to rewrite the whole without depriving the work of its right to be called Clifford's, and yet at the same time it was absolutely necessary to make considerable changes. ...Without any notice of mass or force it seemed impossible to close a discussion on motion; something I felt must be added. I have accordingly introduced a few pages on the laws of motion [and] since found that Clifford intended to write a concluding chapter on mass. How to express the laws of motion in a form of which Clifford would have approved was indeed an insoluble riddle... because I was unaware of his having written on the subject. I have accordingly expressed... my own views on the subject [i.e.,] a strong desire to see the terms matter and force, together with the ideas associated with them, entirely removed from scientific terminology—to reduce, in fact, all dynamic to kinematic. I should hardly have ventured to put forward these views had I not recently discovered that they have... the weighty authority of Professor Mach... But since writing these pages I have also been referred to a discourse delivered by Clifford at the Royal Institution in 1873, some... of which appeared in Nature June 10, 1880 [pp. 122-123.<nowiki>]</nowiki> Therein it is stated that 'no mathematician can give any meaning to the language about matter, force, inertia used in current text-books of mechanics.' This fragmentary account of the discourse undoubtedly proves that Clifford held on the categories of matter and force as clear and original ideas as on all subjects of which he has treated; only, alas! they have not been preserved.
<small>Footnote: Mr. R. Tucker who... searched Clifford's note books... sends me... the following... in Clifford's handwriting: 'Force is not a fact at all, but an idea embodying what is approximately the fact.'</small>

A distinguished writer (Siméon Denis Poisson) has thus stated the fundamental definitions of the science:

Our understanding of the four basic concepts of Physics -- space, time, matter and force -- has undergone radical change in the course of work on unification, starting with Maxwell's unification of electricity with magnetism, all the way to present day string theory. What started as four independent concepts, with space and time postulated and the possible forms of matter and force arbitrarily chosen, now appear as different aspects of a rich and novel dynamically determined structure.

The Greek philosophers thought of static forms and found them in the regular solids. Modern science, however, has from its beginning in the sixteenth and seventeenth centuries started from the dynamic problem. The constant element in physics since Newton is not a configuration or a geometrical form, but a dynamic law.

The Great Gotama gave to the world a complete Teaching of the perfect construction of life. Each attempt to make a god of the great revolutionist, leads to absurdity. Previous to Gotama there was, of course, a whole succession of those who bore the common welfare, but their teachings crumbled to dust in the course of millenniums. Therefore the Teaching of Gotama should be accepted as the first teaching of the laws of matter and the evolution of the world. Contemporary understanding of the community permits a wondrous bridge from Gotama Buddha up to the present time. We pronounce this formula neither for extolling nor for demeaning, but as an evident and immutable fact.

Before a science can develop principles, it must possess concepts. Before a law of gravitation could be formulated, it was necessary to have the notions of “acceleration” and “weight.”

The ancient Greek philosopher, Democritus, propounded an hypothesis of the constitution of matter, and gave the name of atoms to the ultimate unalterable parts of which he imagined all bodies to be constructed. In the 17th century, Gassendi revived this hypothesis, and attempted to develope it, while Newton used it with marked success in his reasonings on physical phenomena; but the first who formed a body of doctrine which would embrace all known facts in the constitution of matter, was Roger Joseph Boscovich, of Italy, who published at Vienna, in 1759, a most important and ingenious work, styled Theoria Philosophiæ Naturalis ad unicam legem virium, in Natura existentium redacta. This is one of the most profound contributions ever made to science; filled with curious and important information, and is well worthy of the attentive perusal of the modern student. In more recent days, the theory of Boscovich has received further confirmation and extension in the researches of Dalton, Joule, Thomson, Faraday, Tyndall, and others.

There is another kind of studies which distinguished from the sometimes opposed to comparative grammar. It is known under the name of general or philosophical grammar , whose principles and observations were articulated by Port Royal and which deals with the relation of the form of language to the operations of the mind.

Anything more hopelessly illogical than the statements with regard to force and matter current in elementary text-books of science, it is difficult to imagine; and the author, as a result of some ten years' teaching and examining, has been forced to the conclusion that these works possess little, if any, educational value; they neither encourage the growth of logical clearness nor form any exercise in scientific method.

Indeed, I think we may concede to our Academician, without flattery, his claim that in the principle [principio, i. e., accelerated motion] laid down in this treatise he has established a new science dealing with a very old subject. Observing with what ease and clearness he deduces from a single principle the proofs of so many theorems, I wonder not a little how such a question escaped the attention of Archimedes, Apollonius, Euclid and so many other mathematicians and illustrious philosophers, especially since so many ponderous tomes have been devoted to the subject of motion. (Galileo referred to himself as the/our Academician in his dialogue)

In March 1879 Clifford died at Madeira; six years afterwards a posthumous work is for the first time placed before the public. ...The original work as planned by Clifford was to have been entitled The First Principles of the Mathematical Sciences Explained to the Non-Mathematical, and to have contained six chapters, on Number, Space, Quantity, Position, Motion, and Mass respectively. Of the projected work Clifford in the year 1875 dictated the chapters on Number and Space completely, the first portion of the chapter on Quantity, and somewhat later nearly the entire chapter on Motion. The first two chapters were afterwards seen by him in proof, but never finally revised. Shortly before his death he expressed a wish that the book should only be published after very careful revision and that its title should be changed to The Common Sense of the Exact Sciences.

Upon Clifford's death the labour of revision and completion was entrusted to Mr. R. C. Rowe, then Professor of Pure Mathematics at University College, London. ...On the sad death of Professor Rowe, in October 1884, I was requested... to take up the task of editing... For the latter half of Chapter III. and for the whole of Chapter IV. ...I am alone responsible. Yet whatever there is in them of value I owe to Clifford; whatever is feeble or obscure is my own. ...With Chapter V. my task has been by no means light. ...Without any notice of mass or force it seemed impossible to close a discussion on motion; something I felt must be added. I have accordingly introduced a few pages on the laws of motion. I have since found that Clifford intended to write a concluding chapter on mass. How to express the laws of motion in a form of which Clifford would have approved was indeed an insoluble riddle to me, because I was unaware of his having written anything on the subject. I have accordingly expressed, although with great hesitation, my own views on the subject; these may be concisely described as a strong desire to see the terms matter and force, together with the ideas associated with them, entirely removed from scientific terminology—to reduce, in fact, all dynamic to kinematic. I should hardly have ventured to put forward these views had I not recently discovered that they have (allowing for certain minor differences) the weighty authority of Professor Mach, of Prag. But since writing these pages I have also been referred to a discourse delivered by Clifford at the Royal Institution in 1873, some account of which appeared in Nature, June 10, 1880. Therein it is stated that <nowiki>'</nowiki>no mathematician can give any meaning to the language about matter, force, inertia used in current text-books of mechanics.' This fragmentary account of the discourse undoubtedly proves that Clifford held on the categories of matter and force as clear and original ideas as on all subjects of which he has treated; only, alas! they have not been preserved.

The first clear expression of the idea of an element occurs in the teachings of the Greek philosophers. ...Aristotle ...who summarized the theories of earlier thinkers, developed the view that all substances were made of a primary matter... On this, different forms could be impressed... so the idea of the transmutation of the elements arose. Aristotle's elements are really fundamental properties of matter... hotness, coldness, moistness, and dryness. By combining these in pairs, he obtained what are called the four elements, fire, air, earth and water... a fifth, immaterial, one was added, which appears in later writings as the quintessence. This corresponds with the ether. The elements were supposed to settle out naturally into the earth (below), water (the oceans), air (the atmosphere), fire and ether (the sky and heavenly bodies).

With the respectability of the senses and feelings established, textbooks written by the Scottish philosophers began to include such topics as perception, memory, imagination, association, attention, language, and thinking. Such a textbook was written by Dugald Stewart (1753–1828), titled Elements of the Philosophy of the Human Mind (1792), and was used at Yale University in 1824.