"Mathematics is not the discoverer of laws, for it is not induction; neither is it the framer of theories, for it is not hypothesis; but it is the judge over both, and it is the arbiter to which each must refer its claims; and neither law can rule nor theory explain without the sanction of mathematics." (Benjamin Peirce,"Linear Associative Algebra", American Journal of Mathematics, Vol. 4, 1881)
"As is known, scientific physics dates its existence from the discovery of the differential calculus. Only when it was learned how to follow continuously the course of natural events, attempts, to construct by means of abstract conceptions the connection between phenomena, met with success. To do this two things are necessary: First, simple fundamental concepts with which to construct; second, some method by which to deduce, from the simple fundamental laws of the construction which relate to instants of time and points in space, laws for finite intervals and distances, which alone are accessible to observation" (can be compared with experience)." (Bernhard Riemann,"Die partiellen Differentialgleichungen der mathematischen Physik", 1882)
"The object of pure Physic is the unfolding of the laws of the intelligible world; the object of pure Mathematic that of the unfolding the laws of human intelligence." (James J Sylvester, "On a Theorem Connected with Newton’s Rule", cca. 1870-1883)
"[…] the process of evolution on this earth, so far as we can judge, has been carried out neither with intelligence nor truth, but entirely through the routine of various sequences, commonly called 'laws', established or necessitated we know not how." (Sir Francis Galton, "Inquiries into Human Faculty and Its Development", 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)
"I hope I may claim in the present work to have made it probable that the laws of arithmetic are analytic judgments and consequently a priori. Arithmetic thus becomes simply a development of logic, and every proposition of arithmetic a law of logic, albeit a derivative one. To apply arithmetic in the physical sciences is to bring logic to bear on observed facts; calculation becomes deduction." (Gottlob Frege, "The Foundations of Arithmetic", 1884)
"The basis of arithmetic lies deeper, it seems, than that of any of the empirical sciences, and even than that of geometry. The truths of arithmetic governs all that is numerable. This is the widest domain of all; for to it belongs not only the existent, not only the intuitable, but everything thinkable. Should not the laws of number, then, be connected very intimately with the laws of thought? " (Gottlob Frege, "The Foundations of Arithmetic", 1884)
"To apply arithmetic in the physical sciences is to bring logic to bear on observed facts, calculation becomes deduction. The laws of number, therefore, are not really applicable to external things, they are not laws of nature. They are, however, applicable to judgements holding good of things in the external world they are laws of the laws of nature. They assert not connections between phenomena, but connections between judgements, and among judgements are included the laws of nature." (Gottlob Frege,"The Foundations of Arithmetic", 1884)
"Plasticity, then, in the wide sense of the word, means the possession of a structure weak enough to yield to an influence, but strong enough not to yield all at once. Each relatively stable phase of equilibrium in such a structure is marked by what we may call a new set of habits." (William James, "The Laws of Habit", 1887)
"In calling arithmetic" ("Mathematics is not the discoverer of laws, for it is not induction; neither is it the framer of theories, for it is not hypothesis; but it is the judge over both, and it is the arbiter to which each must refer its claims; and neither law can rule nor theory explain without the sanction of mathematics." (Benjamin Peirce,"Linear Associative Algebra", American Journal of Mathematics, Vol. 4, 1881)
"As is known, scientific physics dates its existence from the discovery of the differential calculus. Only when it was learned how to follow continuously the course of natural events, attempts, to construct by means of abstract conceptions the connection between phenomena, met with success. To do this two things are necessary: First, simple fundamental concepts with which to construct; second, some method by which to deduce, from the simple fundamental laws of the construction which relate to instants of time and points in space, laws for finite intervals and distances, which alone are accessible to observation" (can be compared with experience)." (Bernhard Riemann,"Die partiellen Differentialgleichungen der mathematischen Physik", 1882)
"The object of pure Physic is the unfolding of the laws of the intelligible world; the object of pure Mathematic that of the unfolding the laws of human intelligence." (James J Sylvester, "On a Theorem Connected with Newton’s Rule", cca. 1870-1883)
"[…] the process of evolution on this earth, so far as we can judge, has been carried out neither with intelligence nor truth, but entirely through the routine of various sequences, commonly called 'laws', established or necessitated we know not how." (Sir Francis Galton, "Inquiries into Human Faculty and Its Development", 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)
"I hope I may claim in the present work to have made it probable that the laws of arithmetic are analytic judgments and consequently a priori. Arithmetic thus becomes simply a development of logic, and every proposition of arithmetic a law of logic, albeit a derivative one. To apply arithmetic in the physical sciences is to bring logic to bear on observed facts; calculation becomes deduction." (Gottlob Frege, "The Foundations of Arithmetic", 1884)
"The basis of arithmetic lies deeper, it seems, than that of any of the empirical sciences, and even than that of geometry. The truths of arithmetic governs all that is numerable. This is the widest domain of all; for to it belongs not only the existent, not only the intuitable, but everything thinkable. Should not the laws of number, then, be connected very intimately with the laws of thought? " (Gottlob Frege, "The Foundations of Arithmetic", 1884)
"To apply arithmetic in the physical sciences is to bring logic to bear on observed facts, calculation becomes deduction. The laws of number, therefore, are not really applicable to external things, they are not laws of nature. They are, however, applicable to judgements holding good of things in the external world they are laws of the laws of nature. They assert not connections between phenomena, but connections between judgements, and among judgements are included the laws of nature." (Gottlob Frege,"The Foundations of Arithmetic", 1884)"
"Plasticity, then, in the wide sense of the word, means the possession of a structure weak enough to yield to an influence, but strong enough not to yield all at once. Each relatively stable phase of equilibrium in such a structure is marked by what we may call a new set of habits." (William James, "The Laws of Habit", 1887)
"In calling arithmetic (algebra, analysis) just a part of logic, I declare already that I take the number-concept to be completely independent of the ideas or intuitions of space and time, that I see it as an immediate product of the pure laws of thought." (Richard Dedekind, "Was sind und was sollen die Zahlen?", 1888)
"In science nothing capable of proof ought to be accepted without proof. Though this demand seems so reasonable yet I cannot regard it as having been met even in […] that part of logic which deals with the theory of numbers. In speaking of arithmetic (algebra, analysis) as a part of logic I mean to imply that I consider the number concept entirely independent of the notions of intuition of space and time, that I consider it an immediate result from the laws of thought." (Richard Dedekind, "Was sind und was sollen die Zahlen?", 1888)
"One should not understand this compulsion to construct concepts, species, forms, purposes, laws" ('a world of identical cases') as if they enabled us to fix the real world; but as a compulsion to arrange a world for ourselves in which our existence is made possible - we thereby create a world which is calculable, simplified, comprehensible, etc., for us." (Friedrich Nietzsche, "The Will to Power", 1883-1888)
"Pure mathematics proves itself a royal science both through its content and form, which contains within itself the cause of its being and its methods of proof. For in complete independence mathematics creates for itself the object of which it treats, its magnitudes and laws, its formulas and symbols." (Eduard Dillmann, "Die Mathematik die Fackelträgerin einer neuen Zeit", 1889)
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