Quotes about logic
page 7

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George Boole photo

“I presume that few who have paid any attention to the history of the Mathematical Analysis, will doubt that it has been developed in a certain order, or that that order has been, to a great extent, necessary -- being determined, either by steps of logical deduction, or by the successive introduction of new ideas and conceptions, when the time for their evolution had arrived.”

George Boole (1815–1864) English mathematician, philosopher and logician

Source: 1850s, A treatise on differential equations (1859), p. v; cited in: Quotations by George Boole http://www-history.mcs.st-and.ac.uk/Quotations/Boole.html, MacTutor History of Mathematics, August 2010.

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“The war industries in many countries and the enormous trade in weapons of all kinds generate corruption and fuel conflict throughout the world. The existence of an immensely powerful military-industrial complex constitutes a danger to democracy, both internationally and domestically, because it follows its own logic and operates independently of popular participation.”

Alfred de Zayas (1947) American United Nations official

Alfred de Zayas' comments to the remarks made by NGOs and States during the United Nations (UN) Human Rights Council Session http://www.ohchr.org/EN/NewsEvents/Pages/DisplayNews.aspx?NewsID=13713&LangID=E Comments by Alfred de Zayas, Independent Expert on the promotion of a democratic and equitable international order, following the Interactive Dialogue on the presentation of his thematic report.
2013

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“Aristotle (De Anima, I. 1) makes in the first place the general remark that it appears as if the soul must, on the one hand, be regarded in its freedom as independent and as separable from the body, since in thinking it is independent; and, on the other hand, since in the emotions it appears to be united with the body and not separate, it must also be looked on as being inseparable from it; for the emotions show themselves as materialized Notions (λόγοι έννοια), as material modes of what is spiritual. With this a twofold method of considering the soul, also known to Aristotle, comes into play, namely the purely rational or logical view, on the one hand, and, on the other hand, the physical or physiological; these we still see practiced side by side. According to the one view, anger, for instance, is looked on as an eager desire for retaliation or the like; according to the other view it is the surging upward of the heartblood and the warm element in man. The former is the rational, the latter the material view of anger; just as one man may define a house as a shelter against wind, rain, and other destructive agencies, while another defines it as consisting of wood and stone; that is to say, the former gives the determination and the form, or the purpose of the thing, while the latter specifies the material it is made of, and its necessary conditions.”

Georg Wilhelm Friedrich Hegel, Lectures on the Philosophy of History Vol 2 1837 translated by ES Haldane and Francis H. Simson first translated 1894 p. 181
Lectures on the Philosophy of History (1832), Volume 2

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“History knew a midnight, which we may estimate at about the year 1000 A. D., when the human race lost the arts and sciences even to the memory. The last twilight of paganism was gone, and yet the new day had not begun. Whatever was left of culture in the world was found only in the Saracens, and a Pope eager to learn studied in disguise in their unversities, and so became the wonder of the West. At last Christendom, tired of praying to the dead bones of the martyrs, flocked to the tomb of the Saviour Himself, only to find for a second time that the grave was empty and that Christ was risen from the dead. Then mankind too rose from the dead. It returned to the activities and the business of life; there was a feverish revival in the arts and in the crafts. The cities flourished, a new citizenry was founded. Cimabue rediscovered the extinct art of painting; Dante, that of poetry. Then it was, also, that great courageous spirits like Abelard and Saint Thomas Aquinas dared to introduce into Catholicism the concepts of Aristotelian logic, and thus founded scholastic philosophy. But when the Church took the sciences under her wing, she demanded that the forms in which they moved be subjected to the same unconditioned faith in authority as were her own laws. And so it happened that scholasticism, far from freeing the human spirit, enchained it for many centuries to come, until the very possibility of free scientific research came to be doubted. At last, however, here too daylight broke, and mankind, reassured, determined to take advantage of its gifts and to create a knowledge of nature based on independent thought. The dawn of the day in history is know as the Renaissance or the Revival of Learning.”

Carl Gustav Jacob Jacobi (1804–1851) German mathematician

"Über Descartes Leben und seine Methode die Vernunft Richtig zu Leiten und die Wahrheit in den Wissenschaften zu Suchen," "About Descartes' Life and Method of Reason.." (Jan 3, 1846) C. G. J. Jacobi's Gesammelte werke Vol. 7 https://books.google.com/books?id=_09tAAAAMAAJ&pg=PA309 p.309, as quoted by Tobias Dantzig, Number: The Language of Science (1930).

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“As a transitional condition, skepticism is logical insurrection; as a system, it is anarchy. Skeptical method would therefore be much the same as rule by insurgents.”

Karl Wilhelm Friedrich Schlegel (1772–1829) German poet, critic and scholar

Als vorübergehender Zustand ist der Skeptizismus logische Insurrektion; als System ist er Anarchie. Skeptische Methode wäre also ungefähr wie insurgente Regierung.
#97, as translated in Walter Benjamin: Selected Writings (1996), vol. 1, p. 136
Athenäum (1798 - 1800)

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“I will ask of you only the ability to read English and to think logically—no high school mathematics, and certainly no higher mathematics.”

Edmund Landau (1877–1938) German Jewish mathematician

Grundlagen der Analysis [Foundations of Analysis] (1930) Preface for the Student, as quoted by Eli Maor, Trigonometric Delights (2013)

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“VII. Let me call your attention to the recent tragedy in New Orleans, whereof the facts are obtained entirely through Pro-Slavery channels. A considerable body of resolute, able-bodied men, held in Slavery by two Rebel sugar-planters in defiance of the Confiscation Act which you have approved, left plantations thirty miles distant and made their way to the great mart of the South-West, which they knew to be the indisputed possession of the Union forces. They made their way safely and quietly through thirty miles of Rebel territory, expecting to find freedom under the protection of our flag. Whether they had or had not heard of the passage of the Confiscation Act, they reasoned logically that we could not kill them for deserting the service of their lifelong oppressors, who had through treason become our implacable enemies. They came to us for liberty and protection, for which they were willing render their best service: they met with hostility, captivity, and murder. The barking of the base curs of Slavery in this quarter deceives no one--not even themselves. They say, indeed, that the negroes had no right to appear in New Orleans armed (with their implements of daily labor in the cane-field); but no one doubts that they would gladly have laid these down if assured that they should be free. They were set upon and maimed, captured and killed, because they sought the benefit of that act of Congress which they may not specifically have heard of, but which was none the less the law of the land which they had a clear right to the benefit of--which it was somebody's duty to publish far and wide, in order that so many as possible should be impelled to desist from serving Rebels and the Rebellion and come over to the side of the Union, They sought their liberty in strict accordance with the law of the land--they were butchered or re-enslaved for so doing by the help of Union soldiers enlisted to fight against slaveholding Treason. It was somebody's fault that they were so murdered--if others shall hereafter stuffer in like manner, in default of explicit and public directions to your generals that they are to recognize and obey the Confiscation Act, the world will lay the blame on you. Whether you will choose to hear it through future History and 'at the bar of God, I will not judge. I can only hope.”

Horace Greeley (1811–1872) American politician and publisher

1860s, The Prayer of the Twenty Millions (1862)

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“I am a plain practical man, not one of your theorists and splitters of hairs and choppers of logic.”

Source: The Golden Bough (1890), Chapter 4, Magic and Religion.

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“.. the classical aesthetic offers us at the same time a method of thinking and a method of wanting to be, a moral and at the same time a psychology... The classical tradition as a whole, by the logic of the effort and the greatness of results, is in some way parallel with the religious tradition of humanity.”

Maurice Denis (1870–1943) French painter

Quote from Denis's essay 'Les Arts a Rome', 1898; as cited on Wikipedia: Maurice Denis https://en.wikipedia.org/wiki/Maurice_Denis - reference [22]
Denis made Jan. 1895 his first visit to Rome, where the works of Raphael and Michaelangelo in the Vatican made a strong impression upon him.
1890 - 1920

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“Modern positivism…expresses criticism against the naïve use of certain terms… by the general postulate that the question whether a given sentence has any meaning… should always be thoroughly and critically examined. This… is derived from mathematical logic. The procedure of natural science is pictured as an attachment of symbols to the phenomena. The symbols can, as in mathematics, be combined according to certain rules… However, a combination of symbols that does not comply with the rules is not wrong but conveys no meaning.
The obvious difficulty in this argument is the lack of any general criterion as to when a sentence should be considered meaningless. A definite decision is possible only when the sentence belongs to a closed system of concepts and axioms, which in the development of natural science will be rather the exception than the rule. In some case the conjecture that a certain sentence is meaningless has historically led to important progress… new connections which would have been impossible if the sentence had a meaning. An example… sentence: "In which orbit does the electron move around the nucleus?"”

Werner Heisenberg (1901–1976) German theoretical physicist

But generally the positivistic scheme taken from mathematical logic is too narrow in a description of nature which necessarily uses words and concepts that are only vaguely defined.
Physics and Philosophy (1958)

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“Formal logic and the logical syllogism encapsulate connectedness in reasoning.”

Marshall McLuhan (1911–1980) Canadian educator, philosopher, and scholar-- a professor of English literature, a literary critic, and a …

1980s, Laws of Media: The New Science (with Eric McLuhan) (1988)

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“The world was created by God and we are always to remember as we deal with the world, what was God’s purpose here, in creating this? But at the same time, while the world was created essentially good, it is fallen and not normative. Thus, perfectionism with regard to nature is anti Christian. Everything has a purpose in creation, but God created man and set him in the garden of Eden with a purpose to use and to develop nature. Thus, while hybridization is forbidden, the improvement of various species is definitely a part of our responsibility. Thus, we do not look back to Eden, we look forward to the kingdom of God. Those who hold to a perfectionism with regard to nature are anti Christian. The logic of this perfectionism with regard to nature, holding nature as normative is to eat raw foods only because you can’t improve on nature, it is to be a nudist because you can’t improve on nature, it is to deny housing because housing is an improvement on nature. This is all very very definitely hostile to scripture because while creation is essentially good, from the biblical perspective, it is to be developed by man. There is to be an improvement in terms of the guidelines laid down by God. Thus, hybridization is not Christian, but improvement is definitely the Christian responsibility. Hybridization and unequal yoking involve a fundamental disrespect for God’s handiwork, and it leads to futile experimentation. But for us as creationists, the fertility and the potentiality of the world rests in his law, in it’s pattern, in it’s fixity.”

Rousas John Rushdoony (1916–2001) American theologian

Audio lectures, Hybridization and the Law (n. d.)

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“If mankind had always been logical and wise, history would not be a long chronicle of folly and crime.”

Source: The Golden Bough (1890), Chapter 29, The Myth of Adonis

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“The instincts of man are so earth-bound that they shrewdly sense it whenever the approach of logic threatens them.”

Source: Irrational Man: A Study in Existential Philosophy (1958), Chapter Five, Christian sources, p. 87

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“Is A=A useful? Does logic come in handy? Is math a magnificent symbolic system with which to comprehend what's around us? And is math based on A=A? Yes. Absolutely. But math and logic are… very, very simplified representations.”

Howard Bloom (1943) American publicist and author

When a Frog is a River? Aristotle Wrestles Heraclitus
The God Problem: How a Godless Cosmos Creates (2012)

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“The two great conceptual revolutions of twentieth-century science, the overturning of classical physics by Werner Heisenberg and the overturning of the foundations of mathematics by Kurt Gödel, occurred within six years of each other within the narrow boundaries of German-speaking Europe. … A study of the historical background of German intellectual life in the 1920s reveals strong links between them. Physicists and mathematicians were exposed simultaneously to external influences that pushed them along parallel paths. … Two people who came early and strongly under the influence of Spengler's philosophy were the mathematician Hermann Weyl and the physicist Erwin Schrödinger. … Weyl and Schrödinger agreed with Spengler that the coming revolution would sweep away the principle of physical causality. The erstwhile revolutionaries David Hilbert and Albert Einstein found themselves in the unaccustomed role of defenders of the status quo, Hilbert defending the primacy of formal logic in the foundations of mathematics, Einstein defending the primacy of causality in physics. In the short run, Hilbert and Einstein were defeated and the Spenglerian ideology of revolution triumphed, both in physics and in mathematics. Heisenberg discovered the true limits of causality in atomic processes, and Gödel discovered the limits of formal deduction and proof in mathematics. And, as often happens in the history of intellectual revolutions, the achievement of revolutionary goals destroyed the revolutionary ideology that gave them birth. The visions of Spengler, having served their purpose, rapidly became irrelevant.”

Freeman Dyson (1923) theoretical physicist and mathematician

The Scientist As Rebel (2006)

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“The mental operation by which one achieves new concepts and which one denotes generally by the inadequate name of induction is not a simple but rather a very complicated process. Above all, it is not a logical process although such processes can be inserted as intermediary and auxiliary links. The principle effort that leads to the discovery of new knowledge is due to abstraction and imagination.”

Ernst Mach (1838–1916) Austrian physicist and university educator

3rd edition, p. 318ff, As quoted by Phillip Frank, Philosophy of Science: The Link Between Science and Philosophy (1957)
20th century, "Erkenntnis und Irrtum: Skizzen zur Psychologie der Forschung" (1905)

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“The Grape that can with Logic absolute
The Two-and-Seventy jarring Sects confute:
The sovereign Alchemist that in a trice
Life's leaden metal into Gold transmute:”

Omar Khayyám (1048–1131) Persian poet, philosopher, mathematician, and astronomer

The Rubaiyat (1120)

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“Implication is thus the very texture of our web of belief, and logic is the theory that traces it.”

Willard van Orman Quine (1908–2000) American philosopher and logician

S. 41
The Web of Belief (1970)

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“How about,” she said, “that you do the logical thing because it’s the logical thing to do?”

Source: Hyperion (1989), Chapter 5 (p. 315)

Herbert Marcuse photo

“If the progressing rationality of advanced industrial society tends to liquidate, as an “irrational rest,” the disturbing elements of Time and Memory, it also tends to liquidate the disturbing rationality contained in this irrational rest. Recognition and relation to the past as present counteracts the functionalization of thought by and in the established reality. It militates against the closing of the universe of discourse and behavior it renders possible the development of concepts which destabilize and transcend the closed universe by comprehending it as historical universe. Confronted with the given society as object of its reflection, critical thought becomes historical consciousness as such, it is essentially judgment. Far from necessitating an indifferent relativism, it searches in the real history of man for the criteria of truth and falsehood, progress and regression. The mediation of the past with the present discovers the factors which made the facts, which determined the war of life, which established the masters and the servants; it projects the limits and the alternatives. When this critical consciousness speaks, it speaks “le langage de la connaissance” (Roland Barthes) which breaks open a closed universe of discourse and its petrified structure. The key terms of this language are not hypnotic nouns which evoke endlessly the same frozen predicates. They rather allow of an open development; they even unfold their content in contradictory predicates. The Communist Manifesto provides a classical example. Here the two key terms, Bourgeoisie and Proletariat, each “govern” contrary predicates. The “bourgeoisie” is the subject of technical progress, liberation, conquest of nature, creation of social wealth, and of the perversion and destruction of these achievements. Similarly, the "proletariat” carries the attributes of total oppression and of the total defeat of oppression. Such dialectical relation of opposites in and by the proposition is rendered possible by the recognition of the subject as an historical agent whose identity constitutes itself in and against its historical practice, in and against its social reality. The discourse develops and states the conflict between the thing and its function, and this conflict finds linguistic expression in sentences which join contradictory predicates in a logical unit—conceptual counterpart of the objective reality. In contrast to all Orwellian language, the contradiction is demonstrated, made explicit, explained, and denounced.”

Source: One-Dimensional Man (1964), p. 99-100

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“The Protestant churches generally hold that the elements of the sacrament are flesh and blood only in a tropical sense; they nourish our souls as meat and the juice of it would our bodies. But the Catholics maintain that they are literally just that; although they possess all the sensible qualities of wafer-cakes and diluted wine. But we can have no conception of wine except what may enter into a belief, either —
# That this, that, or the other, is wine; or,
# That wine possesses certain properties.
Such beliefs are nothing but self-notifications that we should, upon occasion, act in regard to such things as we believe to be wine according to the qualities which we believe wine to possess. The occasion of such action would be some sensible perception, the motive of it to produce some sensible result. Thus our action has exclusive reference to what affects the senses, our habit has the same bearing as our action, our belief the same as our habit, our conception the same as our belief; and we can consequently mean nothing by wine but what has certain effects, direct or indirect, upon our senses; and to talk of something as having all the sensible characters of wine, yet being in reality blood, is senseless jargon. Now, it is not my object to pursue the theological question; and having used it as a logical example I drop it, without caring to anticipate the theologian's reply. I only desire to point out how impossible it is that we should have an idea in our minds which relates to anything but conceived sensible effects of things. Our idea of anything is our idea of its sensible effects; and if we fancy that we have any other we deceive ourselves, and mistake a mere sensation accompanying the thought for a part of the thought itself. It is absurd to say that thought has any meaning unrelated to its only function. It is foolish for Catholics and Protestants to fancy themselves in disagreement about the elements of the sacrament, if they agree in regard to all their sensible effects, here or hereafter.
It appears, then, that the rule for attaining the third grade of clearness of apprehension is as follows: Consider what effects, which might conceivably have practical bearings, we conceive the object of our conception to have. Then, our conception of these effects is the whole of our conception of the object.”

Charles Sanders Peirce (1839–1914) American philosopher, logician, mathematician, and scientist

The final sentence here is an expression of what became known as the Pragmatic maxim, first published in "Illustrations of the Logic of Science" in Popular Science Monthly, Vol. 12 (January 1878), p. 286

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“It is dangerous to attach probability zero to anything other than a logical impossibility.”

Dennis Lindley (1923–2013) British statistician

5. The Rules of Probability. p. 64.
Understanding Uncertainty (2006)

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“.. [to gather] under a new banner.... [that the poets of yesterday's Futurism ] change the means of battle with thought, content, and logic.... advance Alogism after Futurism.”

Kazimir Malevich (1879–1935) Russian and Soviet artist of polish descent

Quote of Malevich, Nov. 1915; as cited by Vasilii Rakitin, in The great Utopia - The Russian and Soviet Avant-Garde, 1915-1932; Guggenheim Museum, New York, 1992, p. 26
1910 - 1920

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“I was introduced to the great philosophical systems of the past to which the Western universities have given their blessing, arranging and classifying them with the delicate care lavished on museum pieces. When once these systems were so handled, it was natural that they should be regarded as monuments of human intellection. And monuments, because they mark achievements at their particular point in history, soon become conservative in the impression which they make on posterity. I was introduced to Plato, Aristotle, Descartes, Kant, Hegel, Schopenhauer, Nietzsche, Marx and other immortals, to whom I should like to refer as the university philosophers. But these titans were expounded in such a way that a student from a colony could easily find his breast agitated by Conflicting attitudes. These attitudes can have effects which spread out over a whole society, should such a student finally pursue a political life. A colonial student does not by origin belong to the intellectual history in which the university philosophers are such impressive landmarks. The colonial student can be so seduced by these attempts to give a philosophical account of the universe, that surrenders his whole personality to them. When he does this, he loses sight of the fundamental social fact that he is a colonial subject. In this way, he omits to draw from his education and from the concern displayed by the great philosophers for human problems, anything which he might relate to the very real problem of colonial domination, which, as it happens, conditions the immediate life of every colonized African. With single-minded devotion, the colonial student meanders through the intricacies of the philosophical systems. And yet these systems did aim at providing a philosophical account ofthe world in the circumstances and conditions of their time. For even philosophical systems are facts of history. By the time, however, that they come to be accepted in the universities for exposition, they have lost the vital power which they had at their first statement, they have shed their dynamism and polemic reference. This is a result of the academic treatment which they are given. The academic treatment is the result of an attitude to philosophical systems as though there was nothing to them hut statements standing in logical relation to one another. This defective approach to scholarship was suffered hy different categories of colonial student. Many of them had heen handpicked and, so to say, carried certificates ofworthiness with them. These were considered fit to become enlightened servants of the colonial administration. The process by which this category of student became fit usually started at an early age, for not infrequently they had lost contact early in life with their traditional background. By reason of their lack of contact with their own roots, they became prone to accept some theory of universalism, provided it was expressed in vague, mellifluous terms. Armed with their universalism, they carried away from their university courses an attitude entirely at variance with the concrete reality of their people and their struggle. When they came across doctrines of a combative nature, like those of Marxism, they reduced them to arid abstractions, to common-room subtleties. In this way, through the good graces oftheir colonialist patrons, these students, now competent in the art of forming not a concrete environmental view of social political problems, but an abstract, 'liberal' outlook, began to fulfil the hopes and expectations oftheir guides and guardians.”

Kwame Nkrumah (1909–1972) Pan Africanist and First Prime Minister and President of Ghana

Source: Consciencism (1964), Introduction, pp. 2-4.

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“Emancipation, not colonization, was the real goal to which the logic of the American Founding was driving the nation.”

Allen C. Guelzo (1953) American historian

2010s, The Logic of Liberty (2014)

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“Logic works, metaphysics contemplates.”

Joseph Joubert (1754–1824) French moralist and essayist
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“Aristotle… a mere bond-servant to his logic, thereby rendering it contentious and well nigh useless.”

Francis Bacon (1561–1626) English philosopher, statesman, scientist, jurist, and author

Rerum Novarum (1605)

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