“The laws of thermodynamics, as empirically determined, express the approximate and probable behavior of systems of a great number of particles, or, more precisely, they express the laws of mechanics for such systems as they appear to beings who have not the fineness of perception to enable them to appreciate quantities of the order of magnitude of those which relate to single particles, and who cannot repeat their experiments often enough to obtain any but the most probable results.”

— Josiah Willard Gibbs

From the preface to Elementary Principles in Statististical Mechanics (1902), p. viii. Full book https://archive.org/details/elementaryprinc00gibbgoog

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Josiah Willard Gibbs 11

physicist 1839–1903

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“Those skilled in mathematical analysis know that its object is not simply to calculate numbers, but that it is also employed to find the relations between magnitudes which cannot be expressed in numbers and between functions whose law is not capable of algebraic expression.”

Antoine Augustin Cournot Researches into the Mathematical Principles of the Theory of Wealth

Source: Researches into the Mathematical Principles of the Theory of Wealth, 1897, p. 3 ; Cited in: Robert Edouard Moritz. Memorabilia mathematica; or, The philomath's quotation-book https://archive.org/stream/memorabiliamathe00moriiala#page/198/mode/2up, (1914) p. 33: About the nature of mathematics

“Science Of Energetics. Although the mechanical hypothesis just mentioned may be useful and interesting as a means of anticipating laws, and connecting the science of thermodynamics with that of ordinary mechanics, still it is to be remembered that the science of thermodynamics is by no means dependent for its certainty on that or any other hypothesis, having been now reduced, to a system of principles, or general facts, expressing strictly the results of experiment as to the relations between heat and motive power. In this point of view the laws of thermodynamics may be regarded as particular cases of more general laws, applicable to all such states of matter as constitute Energy, or the capacity to perform work, which more general laws form the basis of the science of energetics, — a science comprehending, as special branches, the theories of motion, heat, light, electricity, and all other physical phenomena.”

William John Macquorn Rankine (1820–1872) civil engineer

Source: A Manual of the Steam Engine and Other Prime Movers (1859), p. 31

“Law is an order of human behavior. An “order” is a system of rules. Law is not, as it is sometimes said, a rule. It is a set of rules having the kind of unity we understand by a system. It is impossible to grasp the nature of law if we limit our attention to the single isolated rule.”

Hans Kelsen (1881–1973) Austrian lawyer

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“The classical concept of 'physical entity', be it particle, wave, field or system, has become a problematic concept since the advent of relativity theory and quantum mechanics. The recent developments in modern quantum mechanics, with the performance of delicate and precise experiments involving single quantum entities, manifesting explicit non-local behavior for these entities, brings essential new information about the nature of the concept of entity.”

Diederik Aerts (1953) Belgian theoretical physicist

Aerts, D. (1998). " The entity and modern physics: the creation-discovery view of reality. http://www.vub.ac.be/CLEA/aerts/publications/1998EntModPhys.pdf" In E. Castellani (Ed.), Interpreting Bodies: Classical and Quantum Objects in Modern Physics (pp. 223-257). Princeton: Princeton University Press.

“It is not simply that a clear understanding is acquired of the movements of the great bodies which we regard as the system of the world, but it is that we are introduced to a perception of laws governing the motion of all matter, from the finest particle of dust to the largest planet or sun, with a degree of uniformity and constancy, which otherwise we could hardly have conceived. Astronomy is pre-eminently the science of order.”

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“It appeared to me that, although Logic might be viewed with reference to the idea of quantity, it had also another and a deeper system of relations. If it was lawful to regard it from without, as connecting itself through the medium of Number with the intuitions of Space and Time, it was lawful also to regard it from within, as based upon facts of another order which have their abode in the constitution of the Mind.”

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Source: 1840s, The Mathematical Analysis of Logic, 1847, p. i: Lead paragraph of the Preface; cited in: R. H. Hutton, " Professor Boole http://books.google.com/books?id=pfMEAAAAQAAJ&pg=PA157," (1866), p. 157
Context: In presenting this Work to public notice, I deem it not irrelevant to observe, that speculations similar to those which it records have, at different periods, occupied my thoughts. In the spring of the present year my attention was directed to the question then moved between Sir W. Hamilton and Professor De Morgan; and I was induced by the interest which it inspired, to resume the almost-forgotten thread of former inquiries. It appeared to me that, although Logic might be viewed with reference to the idea of quantity, it had also another and a deeper system of relations. If it was lawful to regard it from without, as connecting itself through the medium of Number with the intuitions of Space and Time, it was lawful also to regard it from within, as based upon facts of another order which have their abode in the constitution of the Mind. The results of this view, and of the inquiries which it suggested, are embodied in the following Treatise.

“You could not have evolved a complex system like a city or an organism - with an enormous number of components - without the emergence of laws that constrain their behavior in order for them to be resilient.”

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“General systems theory is a series of related definitions, assumptions, and postulates about all levels of systems from atomic particles through atoms, molecules, crystals, viruses, cells, organs, individuals, small groups, societies, planets, solar systems, and galaxies. General behavior systems theory is a subcategory of such theory, dealing with living systems, extending roughly from viruses through societies. A significant fact about living things is that they are open systems, with important inputs and outputs. Laws which apply to them differ from those applying to relatively closed systems.”

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“Now it is one great object of this work, to shew the importance and advantage of ascertaining the relative weights of the ultimate particles, both of simple and compound bodies, the number of simple elementary particles which constitute one compound particle, and the number of less compound particles which enter into the formation of one more compound particle.”

John Dalton book A New System of Chemical Philosophy

Source: A New System of Chemical Philosophy (1808), Ch. III. On Chemical Synthesis

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Josiah Willard Gibbs 11

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