The Grammar of Science

• the relativity of motion to a frame of reference,
• the equivalence of "matter" and energy,
• physics as geometry,
• the non-existence of the ether,
• the importance of creative imagination rather than mere fact-gathering,
• antimatter,
• fourth dimension,
• wrinkles in space,
• molecular relative position and motion, and
• motion of corpuscles as relative motion in a field.

  Chapter I

1. The scope of science is to ascertain truth in every possible branch of knowledge. There is no sphere of inquiry which lies outside the legitimate field of science. To draw a distinction between the scientific and philosophical fields is obfuscation.
2. The scientific method has the following distinctive features:
3. The claims of science to our support depend on:

   Chapter II

1. Immediate sense-impressions form permanent impresses in the brain which psychically correspond to memory. The union of immediate sense-impressions with associated stored impressions leads to the formation of "constructs," which we project "outside ourselves," and term phenomena or appearances. The real world lies for us in such phenomenal constructs and not in shadowy things-in-themselves. "Outside" and "inside" oneself are alike ultimately based on sense-impressions; but from these sense-impressions by association, mechanical and mental, we form conceptions and draw inferences. These are the facts of science, and its field is essentially the contents of the mind.
2. When an interval elapses between sense-impression and muscular exertion, and the interval contains cerebral activity marking the revival and combination of past sense-impresses, we are said to think or be conscious. Consciousness of something external is an inference which, not yet having been verified by immediate sense-impression, we term an "eject;" it is conceivable, however, that it could become an object. Consciousness has no meaning other than to nervous systems akin to our own; it is illogical to assert that all matter is conscious, still more that consciousness or will can exist outside matter.
3. The term knowledge is meaningless when extended beyond the sphere in which we may legitimately infer consciousness, or when applied to things outside the area of thought, i.e., to metaphysical terms dignified by the name of conceptions although they do not ultimately flow from sense-impressions.

   Chapter III

1. Scientific Law is of a totally different nature from civil law; it does not involve an intelligent lawgiver, a command and a corresponding duty. It is a brief description in mental shorthand of as wide a range as possible of the sequences of our sense-impressions.
2. There are two distinct meanings to natural law: the mere routine of perception, and the scientific law or formula describing the field of nature. The "reason" in natural law is only obvious when we speak of law in the latter sense, and then it is really placed there by the human mind. Thus the supposed reason behind natural law does not enable us to pass from the routine of perceptions to anything of the nature of reason behind the world of sense-impression.
3. The fact that the human reflective faculty is able to express the routine of perceptions in mental formulae may be due to this routine being a product of the perceptive faculty itself. The perceptive faculty appears to be selective and to have developed in co-ordination with the reflective faculty. Of the world outside sensation science can only logically infer chaos, or the absence of the conditions of knowledge; no human concept, such as order, reason, or consciousness, can be logically projected into it.

   Chapter IV

1. Cause is scientifically used to denote an antecedent stage in a routine of perceptions. In this sense, "force" as a cause is meaningless. First cause is only a limit, permanent or temporary, to knowledge. No instance, certainly not "will," occurs in our experience of an arbitrary first cause in the popular sense of the word.
2. There is no inherent necessity in the routine of perceptions, but the permanent existence of rational beings necessitates a routine of perceptions; the possibility of a thinking being ceases with the cessation of routine. The only necessity we are acquainted with exists in the sphere of conceptions; routine in perceptions may possibly be due to the constitution of the perceptive faculty.
3. Proof in the field of perceptions is the demonstration of overwhelming probability. Logically we ought to use the word know only of conceptions, and reserve the word believe for perceptions. "I know that the angle at the circumference on any diameter of a circle is right," but "I believe that the sun will rise tomorrow." The proof that a breach of routine will not occur for a finite future depends upon the solid experience that we are ignorant only in areas in which, statistically, all constitutions of the unknown are found to be equally probable.

   Chapter V

1. Routine in perceptions is a relative term; the idea of causation is extracted by conceptual processes from phenomena, it is neither a logical necessity, nor an actual experience. We can merely classify things as like; we cannot reproduce sameness, but we can only measure how relatively like follows relatively like. The wider view of the universe sees all phenomena as correlated, but not causally related.
2. Whether phenomena are qualitative or quantitative, a classification leads to a contingency table. From such a table we can measure the degree of dependence between any two phenomena. Causation is the limit to such a table, when it contains an indefinitely large number of "cells," but in each array only one such cell is occupied. Mathematical function arises when the belt of dots which are the actual result of all experience shrivels up into a curve. It is a purely conceptual limit which is just as much a conceptual limit to actual experience when we use a multiplicity of "causes."
3. The intellectual gain of this contingency category lies in the fact that it sees variation as the fundamental factor in phenomena. Determinatism is the result of supposing "sameness" instead of a mere classificatory "likeness" in phenomena. Variation and correlation include causation and determinatism as special cases, if indeed they have any actual existence in regard to phenomena. No experience we have at present justifies us, however, in assuming them to be anything but conceptual limits created by human need for economy of thought, and as little inherent in phenomena themselves as geometrical surfaces or centres of force.

   Chapter VI

1. Space and time are not realities in the phenomenal world, but the modes under which we perceive things apart. They are not infinitely large nor infinitely divisible, but are essentially limited by the contents of our perception.
2. Scientific concepts are, as a rule, limits drawn in conception to processes which can be started but not carried to a conclusion in perception. The historical origin of the concepts of geometry and physics can thus be traced. Concepts such as geometrical surface, atom, and ether, are not asserted by science to have a real existence in or behind phenomena, but are valid as shorthand methods of describing the correlation and sequence of phenomena. From this standpoint conceptual space and time can be easily appreciated, and the danger avoided of projecting their ideal infinities and eternities into the real world of perception.

   Chapter VII

1. All the notions by aid of which we describe and measure change are geometrical, and thus are not real perceptual limits. They are forms distinguishing and classifying the contents of our personal experience under the mixed mode of motion. The principal forms are point-motion, spin of a rigid body, and strain. Motion is found to be relative, never absolute; for example, it is meaningless to speak of the motion of a point without reference to what system is related to the motion of the point.
2. An analysis of point-motion leads us to the conceptions of velocity and acceleration. Velocity is a proper measure of the manner in which position is instantaneously changing. Acceleration is a proper measure of how velocity itself is an increased change. It is found that a motion is fully determined. Theoretically, a complete description of the path and position at each instant of time may be deduced when the velocity in any one position and the acceleration for all positions is given.
3. The parallelogram law as the general rule for combining motions is the foundation of the synthesis by which complex motions are constructed out of simple motions.

   Chapter VIII

Chapter IX

Chapter X

Editions in print

• The Grammar of Science, Dover Publications 2004 edition,

  Editions online

• A. and C. Black.
• A. and C. Black.