page 306 note ∗ For example, Meyerson writes: “If the water of the grotto at Lourdes invariably healed all the paralytics who were plunged therein, it would be a law, and we should certainly begin to look in the composition of the water for some characteristic explaining this action. If needed, we should be forced to invent a hypothetical element or an unknown form of energy.” (Identity and Reality, p. 28.) (Italics mine.)

page 306 note † Only recently we have “discovered” electricity, Hertzian waves, Röntgen waves, and radioactive substances; there is no good reason to think that we may not soon have need of assuming the existence of other types of energy.

page 306 note ‡ Duhem's interpretation of the theory would cover both A and B, with A constituting a special case including all other systems: “In every modification of an isolated system the total energy of the system conserves an invariable value.” L'évolution de la méchanique, p. 227.

page 308 note ∗ Though one may take exception to some of his terminology, including the use of the word “proof”, Meyerson has apparently seen this point when he writes: “The discovery of Mayer and of Joule only substituted one concept of constancy for others, already preexisting, which it destroyed by that very fact. Leibniz supposed mechanical energy to be indestructible; and, on the other hand, DeLuc, Black, and Wilke admitted the indestructibility of heat-matter. What we call the principle of the conservation of energy consists in the opposite proof, namely, that heat as well as mechanical energy, taken separately, can be created and destroyed, the disappearance of mechanical energy being accompanied by the appearance of a certain quantity of heat energy and vice versa.” (Identity and Reality, pp. 206-7.)

page 309 note ∗ In denying that added empirical data can increase probability or established truth of theories here discussed, I mean that they are such that anything which happens in the future will fit them. As against other possible assumptions of the same nature, no theory gains added probability from new data which fit it. Under these circumstances superiority of one theory over another will consist, not in ability to cover a wider range of data, but in economy of assumption, fruitfulness for prediction, or possibly some other merit.

page 310 note ∗ Two assumptions are usually used to supplement the theory of convertibility in order to eliminate this possibility: a) it is assumed that if the apparent disappearance of one form of energy in a certain quantity is uniformly and invariably accompanied by the apparent appearance of a certain different quantity of another form of energy, then those two different quantities represent an equivalent amount of energy; b) if this correlation is not fully invariable and uniform in experience, the uniformity is saved by the assumption that inaccuracies of instruments or losses of energy through friction or some other such difficulty is responsible for the variation from uniformity.

page 312 note ∗ Poynting and Thomson: Textbook of Physics, pp. 117-118.

page 312 note † Indeed, in attempts to determine the mechanical equivalent of heat energy by electrical methods scientists have received results higher than those gained by water-friction methods. They account for this by assuming some error in the electrical relations assumed, but it would be possible, though perhaps less convenient, to assume that there is a loss of energy in different proportions when the replacement is direct from water-friction methods and is direct from electrical current methods.

page 313 note ∗ This, of course, need be no occasion for disappointment. We cannot establish the probability of any scientific principles except on the assumption of others as unquestioned. These unquestioned assumptions may be replaced when other assumptions more serviceable to science are invented. By an assumption I mean, not something taken as self-evident or taken as true now and forever; an assumption (as here used) is not a matter of belief; we merely act and organize our experience as if the principle held.

page 314 note ∗ The notion of the uniformity of nature is itself an assumption of the sort mentioned above.

page 314 note † One might add a theory which would bear a relationship to G which would be parallel to that of B to A and F to E: “for every type of energy within an isolated system other than the universe, there is a uniform correlation....”

page 314 note ‡ Textbook of Physics, Volume Three, 1928, p. 116. (Italics mine.)

page 316 note ∗ Certainly the non-creatability of energy is often a part of the conception of the conservation of energy and is included in conception H by implication.

page 316 note † The term “potential energy” may be used now to include other types of energy.

page 317 note ∗ Meyerson: Identity and Reality, pp. 207-208.

page 317 note † Professor Lovejoy has suggested the definition of a physical object as an existent locatable in a common space-time frame of reference, continuing to exist wholly or partially when not perceived, capable of interacting with other physical objects according to causal laws determinable in some degree by investigation, having only one shape and size at any given time and place and not having qualities which as perceived by different senses conflict; in short, the object must be public. In the specification of circumstances under which such an object exhibits characteristic relationships, we can never attain completeness; but this difficulty must be admitted by any position granting our inability to attain perfect knowledge.

page 318 note ∗ The separation of energy-complexes from one another would always be a matter of degree. It is most convenient to take the sharpest discoverable lines of separation as definitive of “objects”.