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Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
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Home > Category Index for Science Quotations > Category Index U > Category: Universality

Universality Quotes (22 quotes)

A primâ facie argument in favour of the efficacy of prayer is therefore to be drawn from the very general use of it. The greater part of mankind, during all the historic ages, have been accustomed to pray for temporal advantages. How vain, it may be urged, must be the reasoning that ventures to oppose this mighty consensus of belief! Not so. The argument of universality either proves too much, or else it is suicidal.
'Statistical Inquiries into the Efficacy of Prayer', Fortnightly Review, 1872, 12, 126.
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Among the minor, yet striking characteristics of mathematics, may be mentioned the fleshless and skeletal build of its propositions; the peculiar difficulty, complication, and stress of its reasonings; the perfect exactitude of its results; their broad universality; their practical infallibility.
In Charles S. Peirce, ‎Charles Hartshorne (ed.), ‎Paul Weiss (ed.), Collected Papers of Charles Sanders Peirce (1931), Vol. 4, 197.
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Any opinion as to the form in which the energy of gravitation exists in space is of great importance, and whoever can make his opinion probable will have, made an enormous stride in physical speculation. The apparent universality of gravitation, and the equality of its effects on matter of all kinds are most remarkable facts, hitherto without exception; but they are purely experimental facts, liable to be corrected by a single observed exception. We cannot conceive of matter with negative inertia or mass; but we see no way of accounting for the proportionality of gravitation to mass by any legitimate method of demonstration. If we can see the tails of comets fly off in the direction opposed to the sun with an accelerated velocity, and if we believe these tails to be matter and not optical illusions or mere tracks of vibrating disturbance, then we must admit a force in that direction, and we may establish that it is caused by the sun if it always depends upon his position and distance.
Letter to William Huggins (13 Oct 1868). In P. M. Hannan (ed.), The Scientific Letters and Papers of James Clerk Maxwell (1995), Vol. 2, 1862-1873, 451-2.
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At every major step physics has required, and frequently stimulated, the introduction of new mathematical tools and concepts. Our present understanding of the laws of physics, with their extreme precision and universality, is only possible in mathematical terms.
In Book Review 'Pulling the Strings,' of Lawrence Krauss's Hiding in the Mirror: The Mysterious Lure of Extra Dimensions, from Plato to String Theory and Beyond in Nature (22 Dec 2005), 438, 1081.
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First, [Newton’s Law of Universal Gravitation] is mathematical in its expression…. Second, it is not exact; Einstein had to modify it…. There is always an edge of mystery, always a place where we have some fiddling around to do yet…. But the most impressive fact is that gravity is simple…. It is simple, and therefore it is beautiful…. Finally, comes the universality of the gravitational law and the fact that it extends over such enormous distances…
In The Character of Physical Law (1965, 2001), 33.
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It would be difficult to name a man more remarkable for the greatness and the universality of his intellectual powers than Leibnitz.
In System of Logic, Bk. 2, chap. 5, sect. 6.
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My colleagues in elementary particle theory in many lands [and I] are driven by the usual insatiable curiosity of the scientist, and our work is a delightful game. I am frequently astonished that it so often results in correct predictions of experimental results. How can it be that writing down a few simple and elegant formulae, like short poems governed by strict rules such as those of the sonnet or the waka, can predict universal regularities of Nature?
Nobel Banquet Speech (10 Dec 1969), in Wilhelm Odelberg (ed.),Les Prix Nobel en 1969 (1970).
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No physiologist who calmly considers the question in connection with the general truths of his science, can long resist the conviction that different parts of the cerebrum subserve different kinds of mental action. Localization of function is the law of all organization whatever: separateness of duty is universally accompanied with separateness of structure: and it would be marvellous were an exception to exist in the cerebral hemispheres.
The Principles of Psychology (1855), 607.
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Our ultimate task is to find interpretative procedures that will uncover each bias and discredit its claims to universality. When this is done the eighteenth century can be formally closed and a new era that has been here a long time can be officially recognised. The individual human being, stripped of his humanity, is of no use as a conceptual base from which to make a picture of human society. No human exists except steeped in the culture of his time and place. The falsely abstracted individual has been sadly misleading to Western political thought. But now we can start again at a point where major streams of thought converge, at the other end, at the making of culture. Cultural analysis sees the whole tapestry as a whole, the picture and the weaving process, before attending to the individual threads.
As co-author with Baron Isherwood, The World of Goods: Towards an Anthropology of Consumption (1979, 2002), 41-42.
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Science has hitherto been proceeding without the guidance of any rational theory of logic, and has certainly made good progress. It is like a computer who is pursuing some method of arithmetical approximation. Even if he occasionally makes mistakes in his ciphering, yet if the process is a good one they will rectify themselves. But then he would approximate much more rapidly if he did not commit these errors; and in my opinion, the time has come when science ought to be provided with a logic. My theory satisfies me; I can see no flaw in it. According to that theory universality, necessity, exactitude, in the absolute sense of these words, are unattainable by us, and do not exist in nature. There is an ideal law to which nature approximates; but to express it would require an endless series of modifications, like the decimals expressing surd. Only when you have asked a question in so crude a shape that continuity is not involved, is a perfectly true answer attainable.
Letter to G. F. Becker, 11 June 1893. Merrill Collection, Library of Congress. Quoted in Nathan Reingold, Science in Nineteenth-Century America: A Documentary History (1966), 231-2.
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Scripture and Nature agree in this, that all things were covered with water; how and when this aspect began, and how long it lasted, Nature says not, Scripture relates. That there was a watery fluid, however, at a time when animals and plants were not yet to be found, and that the fluid covered all things, is proved by the strata of the higher mountains, free from all heterogeneous material. And the form of these strata bears witness to the presence of a fluid, while the substance bears witness to the absence of heterogeneous bodies. But the similarity of matter and form in the strata of mountains which are different and distant from each other, proves that the fluid was universal.
The Prodromus of Nicolaus Steno's Dissertation Concerning a Solid Body enclosed by Process of Nature within a Solid (1669), trans. J. G. Winter (1916), 263-4.
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The elementary parts of all tissues are formed of cells in an analogous, though very diversified manner, so that it may be asserted, that there is one universal principle of development for the elementary parts of organisms, however different, and that this principle is the formation of cells.
Mikroskopische Untersuchungen über die Uebereinstimmung in der Struktur und dem Wachsthum der Thiere und Pflanzen (1839). Microscopic Researches into the Accordance in the Structure and Growth of Animals and Plants, trans. Henry Smith (1847), 165.
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The results of systematic symbolical reasoning must always express general truths, by their nature; and do not, for their justification, require each of the steps of the process to represent some definite operation upon quantity. The absolute universality of the interpretation of symbols is the fundamental principle of their use.
In 'The Foundations of Higher Mathematics', The Philosophy of the Inductive Sciences (1847), Part I, Bk. 2, 149.
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The universality of parasitism as an offshoot of the predatory habit negatives the position taken by man that it is a pathological phenomenon or a deviation from the normal processes of nature. The pathological manifestations are only incidents in a developing parasitism. As human beings intent on maintaining man's domination over nature we may regard parasitism as pathological insofar as it becomes a drain upon human resources. In our efforts to protect ourselves we may make every kind of sacrifice to limit, reduce, and even eliminate parasitism as a factor in human life. Science attempts to define the terms on which this policy of elimination may or may not succeed. We must first of all thoroughly understand the problem, put ourselves in possession of all the facts in order to estimate the cost. Too often it has been assumed that parasitism was abnormal and that it needed only a slight force to reestablish what was believed to be a normal equilibrium without parasitism. On the contrary, biology teaches us that parasitism is a normal phenomenon and if we accept this view we shall be more ready to pay the price of freedom as a permanent and ever recurring levy of nature for immunity from a condition to which all life is subject. The greatest victory of man over nature in the physical realm would undoubtedly be his own delivery from the heavy encumbrance of parasitism with which all life is burdened.
Parasitism and Disease (1934), 4.
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There is a finite number of species of plants and animals—even of insects—upon the earth. … Moreover, the universality of the genetic code, the common character of proteins in different species, the generality of cellular structure and cellular reproduction, the basic similarity of energy metabolism in all species and of photosynthesis in green plants and bacteria, and the universal evolution of living forms through mutation and natural selection all lead inescapably to a conclusion that, although diversity may be great, the laws of life, based on similarities, are finite in number and comprehensible to us in the main even now.
Presidential Address (28 Dec 1970) to the American Association for the Advancement of Science. 'Science: Endless Horizons or Golden Age?', Science (8 Jan 1971), 171, No. 3866, 24.
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There is a science which investigates being as being and the attributes which belong to this in virtue of its own nature. Now this is not the same as any of the so-called special sciences; for none of these treats universally of being as being. They cut off a part of being and investigate the attribute of this part; this is what the mathematical sciences for instance do. Now since we are seeking the first principles and the highest causes, clearly there must be some thing to which these belong in virtue of its own nature. If then those who sought the elements of existing things were seeking these same principles, it is necessary that the elements must be elements of being not by accident but just because it is being. Therefore it is of being as being that we also must grasp the first causes.
Aristotle
'Book Gamma (1003a17-1011b23' in Metaphysics, trans. W.D. Ross (1924). Excerpt 'Being Qua Being', in Joseph Margolis and Jacques Catudal, The Quarrel between Invariance and Flux (2001), 18-19.
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There is nothing which Nature so clearly reveals, and upon which science so strongly insists, as the universal reign of law, absolute, universal, invariable law... Not one jot or tittle of the laws of Nature are unfulfilled. I do not believe it is possible to state this fact too strongly... Everything happens according to law, and, since law is the expression of Divine will, everything happens according to Divine will, i.e. is in some sense ordained, decreed.
Lecture 18, 'Predestination and Free-Will', Religion and Science: A Series of Sunday Lectures (1874), 278.
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There must be some bond of union between mass and the chemical elements; and as the mass of a substance is ultimately expressed (although not absolutely, but only relatively) in the atom, a functional dependence should exist and be discoverable between the individual properties of the elements and their atomic weights. But nothing, from mushrooms to a scientific dependence can be discovered without looking and trying. So I began to look about and write down the elements with their atomic weights and typical properties, analogous elements and like atomic weights on separate cards, and soon this convinced me that the properties of the elements are in periodic dependence upon their atomic weights; and although I had my doubts about some obscure points, yet I have never doubted the universality of this law, because it could not possibly be the result of chance.
Principles of Chemistry (1905), Vol. 2, 18.
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Without undervaluing any other human agency, it may be safely affirmed that the Common School, improved and energized, as it can easily be, may become the most effective and benignant of all the forces of civilization. Two reasons sustain this position. In the first place, there is a universality in its operation, which can be affirmed of no other institution whatever... And, in the second place, the materials upon which it operates are so pliant and ductile as to be susceptible of assuming a greater variety of forms than any other earthly work of the Creator.
Twelfth Report of the Secretary of the Massachusetts Board of Education (1948). Life and Works of Horace Mann (1891), Vol. 4, 232-233.
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Yet is it possible in terms of the motion of atoms to explain how men can invent an electric motor, or design and build a great cathedral? If such achievements represent anything more than the requirements of physical law, it means that science must investigate the additional controlling factors, whatever they may be, in order that the world of nature may be adequately understood. For a science which describes only the motions of inanimate things but fails to include the actions of living organisms cannot claim universality.
The Human Meaning of Science (1940), 31.
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You can be sure you are acting in accordance with the designs of nature if what you do is calculated to promote nature's great final purpose: grow and make grow. I am firmly convinced of the universality of this law.
Aphorism 44 in Notebook D (1773-1775), as translated by R.J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 50.
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[The aim of science is] to explain what so far has taken to be an explicans, such as a law of nature. The task of empirical science constantly renews itself. We may go on forever, proceeding to explanations of a higher and higher universality…
"The Aim of Science', Ratio 1 (1958), 26. Quoted in Erhard Scheibe and Brigitte Falkenburg (ed), Between Rationalism and Empiricism: Selected Papers in the Philosophy of Physics (2001), 238
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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