On Phenomena (1875-1899)

"There is a maxim which is often quoted, that ‘The same causes will always produce the same effects.’ To make this maxim intelligible we must define what we mean by the same causes and the same effects, since it is manifest that no event ever happens more that once, so that the causes and effects cannot be the same in all respects. [...] There is another maxim which must not be confounded with that quoted at the beginning of this article, which asserts ‘That like causes produce like effects’. This is only true when small variations in the initial circumstances produce only small variations in the final state of the system. In a great many physical phenomena this condition is satisfied; but there are other cases in which a small initial variation may produce a great change in the final state of the system, as when the displacement of the ‘points’ causes a railway train to run into another instead of keeping its proper course." (James C Maxwell, "Matter and Motion", 1876)

"You may read any quantity of books, and you may be almost as ignorant as you were at starting, if you don’t have, at the back of your minds, the change for words in definite images which can only be acquired through the operation of your observing faculties on the phenomena of nature." (Thomas H Huxley, "Science and Education", 1877)

"As long as the training of a naturalist enables him to trace the action only of a particular material system, without giving him the power of dealing with the general properties of all such systems, he must proceed by the method so often described in histories of science - he must imagine model after model of hypothetical apparatus, till he finds one which will do the required work. If this apparatus should afterwards be found capable of accounting for many of the known phenomena, and not demonstrably inconsistent with any of them, he is strongly tempted to conclude that his hypothesis is a fact, at least until an equally good rival hypothesis has been invented." (James C Maxwell, "Tait’s Thermodynamics", Nature Vol. XVII (431), 1878)

"Purely mechanical phenomena do not exist […] are abstractions, made, either intentionally or from necessity, for facilitating our comprehension of things. The science of mechanics does not comprise the foundations, no, nor even a part of the world, but only an aspect of it." (Ernst Mach, "The Science of Mechanics", 1883)

"While all that we have is a relation of phenomena, a mental image, as such, in juxtaposition with or soldered to a sensation, we can not as yet have assertion or denial, a truth or a falsehood. We have mere reality, which is, but does not stand for anything, and which exists, but by no possibility could be true. […] the image is not a symbol or idea. It is itself a fact, or else the facts eject it. The real, as it appears to us in perception, connects the ideal suggestion with itself, or simply expels it from the world of reality. […] you possess explicit symbols all of which are universal and on the other side you have a mind which consists of mere individual impressions and images, grouped by the laws of a mechanical attraction." (Francis H Bradley, "Principles of Logic", 1883)

"The steps to scientific as well as other knowledge consist in a series of logical fictions which are as legitimate as they are indispensable in the operations of thought, but whose relations to the phenomena whereof they are the partial and not unfrequently merely symbolical representations must never be lost sight of." (John Stallo, "The Concepts and Theories of Modern Physics", 1884)

"Most surprising and far-reaching analogies revealed themselves between apparently quite disparate natural processes. It seemed that nature had built the most various things on exactly the same pattern; or, in the dry words of the analyst, the same differential equations hold for the most various phenomena. (Ludwig Boltzmann, "On the methods of theoretical physics", 1892)

"It is certainly true that all physical phenomena are subject to strictly mathematical conditions, and mathematical processes are unassailable in themselves. The trouble arises from the data employed. Most phenomena are so highly complex that one can never be quite sure that he is dealing with all the factors until the experiment proves it. So that experiment is rather the criterion of mathematical conclusions and must lead the way." (Amos E Dolbear, "Matter, Ether, Motion", 1894)

"The aim of research is the discovery of the equations which subsist between the elements of phenomena." (Ernst Mach, 1898)

"[…] no theory can be objective, actually coinciding with nature, but rather that each theory is only a mental picture of phenomena, related to them as sign is to designatum. From this it follows that it cannot be our task to find an absolutely correct theory but rather a picture that is, as simple as possible and that represents phenomena as accurately as possible. One might even conceive of two quite different theories both equally simple and equally congruent with phenomena, which therefore in spite of their difference are equally correct." (Ludwig Boltzmann, "On the development of the methods of theoretical physics", 1899)

"All our ideas and concepts are only internal pictures, or if spoken, combinations of sounds. The task of our thinking is so to use and combine them that by their means we always most readily hit upon the correct actions and guide others likewise. In this, metaphysics follows the most down-to-earth and practical point of view, so that extremes meet. The conceptual signs that we form thus exist only within us, we cannot measure external phenomena by the standard of our ideas. We can therefore pose such formal questions as whether only matter exists and force is a property of it, or whether force exists independently of matter or conversely whether matter is a product of force but none of these questions are significant since all these concepts are only mental pictures whose purpose is to represent phenomena correctly." (Ludwig Boltzmann, 1899)