Quotes about proposition
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John Napier photo

“28 Proposition. The image of the Beast, is these degenerate Princes, that in name onely were called Roman Emporours, and were neither Romans of blood, nor Emperours of Magnanimitie.”

John Napier (1550–1617) Scottish mathematician

A Plaine Discovery of the Whole Revelation of St. John (1593), The First and Introductory Treatise

Moritz Schlick photo
Thomas Robert Malthus photo
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George Boole photo

“Let x represent an act of the mind by which we fix our regard upon that portion of time for which the proposition X is true; and let this meaning be understood when it is asserted that x denote the time for which the proposition X is true. (...) We shall term x the representative symbol of the proposition X.”

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

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 165; As cited in: James Joseph Sylvester, ‎James Whitbread Lee Glaisher (1910) The Quarterly Journal of Pure and Applied Mathematics. p. 350

Augustus De Morgan photo

“In order to see the difference which exists between… studies,—for instance, history and geometry, it will be useful to ask how we come by knowledge in each. Suppose, for example, we feel certain of a fact related in history… if we apply the notions of evidence which every-day experience justifies us in entertaining, we feel that the improbability of the contrary compels us to take refuge in the belief of the fact; and, if we allow that there is still a possibility of its falsehood, it is because this supposition does not involve absolute absurdity, but only extreme improbability.
In mathematics the case is wholly different… and the difference consists in this—that, instead of showing the contrary of the proposition asserted to be only improbable, it proves it at once to be absurd and impossible. This is done by showing that the contrary of the proposition which is asserted is in direct contradiction to some extremely evident fact, of the truth of which our eyes and hands convince us. In geometry, of the principles alluded to, those which are most commonly used are—
I. If a magnitude is divided into parts, the whole is greater than either of those parts.
II. Two straight lines cannot inclose a space.
III. Through one point only one straight line can be drawn, which never meets another straight line, or which is parallel to it.
It is on such principles as these that the whole of geometry is founded, and the demonstration of every proposition consists in proving the contrary of it to be inconsistent with one of these.”

Augustus De Morgan (1806–1871) British mathematician, philosopher and university teacher (1806-1871)

Source: On the Study and Difficulties of Mathematics (1831), Ch. I.

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Alexander Osterwalder photo

“Business models and value propositions expire like a yogurt in the fridge.”

Alexander Osterwalder (1974) Austrian business theorist

Alexander Osterwalder in foreword to: Stefanie Auge-Dickhut, ‎Bernhard Koye, ‎Axel Liebetrau (2015), Customer Value Generation in Banking: The Zurich Model of Customer-Centricity. p. ix

Aristarchus of Samos photo

“Proposition 2. If a sphere be illuminated by a sphere greater than itself, the illuminated portion of the former sphere will be greater than a hemisphere.”

Aristarchus of Samos ancient Greek astronomer and mathematician

p, 125
On the Sizes and Distances of the Sun and the Moon (c. 250 BC)

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Salman Rushdie photo

“The fundamentalist seeks to bring down a great deal more than buildings. Such people are against, to offer just a brief list, freedom of speech, a multi-party political system, universal adult suffrage, accountable government, Jews, homosexuals, women's rights, pluralism, secularism, short skits, dancing, beardlessness, evolution theory, sex. There are tyrants, not Muslims. United Nations Secretary-General Kofi Annan has said that we should now define ourselves not only by what we are for but by what we are against. I would reverse that proposition, because in the present instance what we are against is a no brainer. Suicidist assassins ram wide-bodied aircraft into the World Trade Center and Pentagon and kill thousands of people: um, I'm against that. But what are we for? What will we risk our lives to defend? Can we unanimously concur that all the items in the preceding list — yes, even the short skirts and the dancing — are worth dying for? The fundamentalist believes that we believe in nothing. In his world-view, he has his absolute certainties, while we are sunk in sybaritic indulgences. To prove him wrong, we must first know that he is wrong. We must agree on what matters: kissing in public places, bacon sandwiches, disagreement, cutting-edge fashion, literature, generosity, water, a more equitable distribution of the world's resources, movies, music, freedom of thought, beauty, love. These will be our weapons. Not by making war but by the unafraid way we choose to live shall we defeat them. How to defeat terrorism? Don't be terrorized. Don't let fear rule your life. Even if you are scared.”

Salman Rushdie (1947) British Indian novelist and essayist

Step Across This Line: Collected Nonfiction 1992–2002

Aristarchus of Samos photo

“Proposition 8. When the sun is totally eclipsed, the sun and the moon are then comprehended by one and the same cone which has its vertex at our eye.”

Aristarchus of Samos ancient Greek astronomer and mathematician

p, 125
On the Sizes and Distances of the Sun and the Moon (c. 250 BC)

John Napier photo

“31 Proposition. The visible marks of the Beast, are the abused characters, of λρς and crosses of all kindes, taken out of the number of the first beasts name.”

John Napier (1550–1617) Scottish mathematician

A Plaine Discovery of the Whole Revelation of St. John (1593), The First and Introductory Treatise

John Napier photo

“27 Proposition. The image, marke, name, and number of the beast: are of the first great Romane beast, and whole Latine impyre universallie, and not of the second beaste, or Antichrist alone in particular.”

John Napier (1550–1617) Scottish mathematician

A Plaine Discovery of the Whole Revelation of St. John (1593), The First and Introductory Treatise

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“Argument is to me the air I breathe. Given any proposition, I cannot help believing the other side and defending it.”

Gertrude Stein (1874–1946) American art collector and experimental writer of novels, poetry and plays

"Form and Intelligibility," from The Radcliffe Manuscripts (1949); written in 1895 as an undergraduate at Radcliffe College

William John Macquorn Rankine photo

“Reengineering cannot be planned meticulously and accomplished in small and cautious steps. It’s an all-or-nothing proposition with an uncertain result.”

Michael Hammer (1948–2008) American academic

Source: "Reengineering work: don't automate, obliterate," 1990, p. 105

John Napier photo

“16 Proposition. The 42. moneths, 1260 propheticall daies, three great daies and a halfe: And a time, times and halfe a time, signifieth everie one of them, 1260 Julliane yeares.”

John Napier (1550–1617) Scottish mathematician

A Plaine Discovery of the Whole Revelation of St. John (1593), The First and Introductory Treatise

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Herbert Spencer photo

“As a corollary to the proposition that all institutions must be subordinated to the law of equal freedom, we cannot choose but admit the right of the citizen to adopt a condition of voluntary outlawry. If every man has freedom to do all that he wills, provided he infringes not the equal freedom of any other man, then he is free to drop connection with the state — to relinquish its protection, and to refuse paying towards its support.”

Pt. III, Ch. 19 : The Right to Ignore the State, § 1 http://oll.libertyfund.org/titles/273#lf0331_label_200
Social Statics (1851)
Context: As a corollary to the proposition that all institutions must be subordinated to the law of equal freedom, we cannot choose but admit the right of the citizen to adopt a condition of voluntary outlawry. If every man has freedom to do all that he wills, provided he infringes not the equal freedom of any other man, then he is free to drop connection with the state — to relinquish its protection, and to refuse paying towards its support. It is self-evident that in so behaving he in no way trenches upon the liberty of others; for his position is a passive one; and whilst passive he cannot become an aggressor. It is equally selfevident that he cannot be compelled to continue one of a political corporation, without a breach of the moral law, seeing that citizenship involves payment of taxes; and the taking away of a man’s property against his will, is an infringement of his rights. Government being simply an agent employed in common by a number of individuals to secure to them certain advantages, the very nature of the connection implies that it is for each to say whether he will employ such an agent or not. If any one of them determines to ignore this mutual-safety confederation, nothing can be said except that he loses all claim to its good offices, and exposes himself to the danger of maltreatment — a thing he is quite at liberty to do if he likes. He cannot be coerced into political combination without a breach of the law of equal freedom; he can withdraw from it without committing any such breach; and he has therefore a right so to withdraw.

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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““Organization theory,” a term that appeared in the middle of the twentieth century, has multiple meanings. When it first emerged, the term expressed faith in scientific research as a way to gain understanding of human beings and their interactions. Although scientific research had been occurring for several centuries, the idea that scientific research might enhance understanding of human behavior was considerably newer and rather few people appreciated it. Simon (1950, 1952-3, 1952) was a leading proponent for the creation of “organization theory”, which he imagined as including scientific management, industrial engineering, industrial psychology, the psychology of small groups, human-resources management, and strategy. The term “organization theory” also indicated an aspiration to state generalized, abstract propositions about a category of social systems called “organizations,” which was a very new concept. Before and during the 1800s, people had regarded armies, schools, churches, government agencies, and social clubs as belonging to distinct categories, and they had no name for the union of these categories. During the 1920s, some people began to perceive that diverse kinds of medium-sized social systems might share enough similarities to form a single, unified category. They adopted the term “organization” for this unified category.”

Philippe Baumard (1968) French academic

William H. Starbuck and Philippe Baumard (2009). "The seeds, blossoming, and scant yield of organization theory," in: Jacques Rojot et. al (eds.) Comportement organisationnel - Volume 3 De Boeck Supérieur. p. 15

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Jerry Coyne photo

“After all, by what lights can you see atheism as a “leap of faith”? What is the “faith” there? Failure to accept gods is no more a leap of faith than is doubting the existence of the Loch Ness Monster, Bigfoot, or Santa Claus. It’s not “faith” when you refuse to accept a proposition for which there’s no evidence.”

Jerry Coyne (1949) American biologist

" Self-abasing atheist at the Guardian calls atheism is a “leap of faith” https://whyevolutionistrue.wordpress.com/2015/10/29/self-abasing-atheist-at-the-guardian-says-that-atheism-is-a-leap-of-faith/" October 29, 2015

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“The First Proposition. In propheticall dates of daies, weekes, moneths, and yeares, everie common propheticall day is taken for a yeare.”

John Napier (1550–1617) Scottish mathematician

A Plaine Discovery of the Whole Revelation of St. John (1593), The First and Introductory Treatise

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“The whole world knows that virtue consists in the subjugation of one's passions, or in self-renunciation. It is not just the Christian world, against whom Nietzsche howls, that knows this, but it is an eternal supreme law towards which all humanity has developed, including Brahmanism, Buddhism, Confucianism, and the ancient Persian religion. And suddenly a man appears who declares that he is convinced that self-renunciation, meekness, submissiveness and love are all vices that destroy humanity (he has in mind Christianity, ignoring all the other religions).

One can understand why such a declaration baffled people at first. But after giving it a little thought and failing to find any proof of the strange propositions, any rational person ought to throw the books aside and wonder if there is any kind of rubbish that would not find a publisher today. But this has not happened with Nietzsche´s books. The majority of pseudo-enlightened people seriously look into the theory of the Übermensch, and acknowledge its author to be a great philosopher, a descendant of Descartes, Leibniz and Kant. And all this has come about because the majority of pseudo-enlightened men of today object to any reminder of virtue, or to its chief premise: self-renunciation and love—virtues that restrain and condemn the animal side of their life. They gladly welcome a doctrine, however incoherently and disjointedly expressed, of egotism and cruelty, sanctioning the idea of personal happiness and superiority over the lives of others, by which they live.”

Leo Tolstoy (1828–1910) Russian writer

Source: What is Religion, of What does its Essence Consist? (1902), Chapter 11

“The philosopher considering the Universe in its entirety is led to admit that there is only one necessary, absolute being, God. All other beings are contingent; this is why Pascal said of himself: "I feel that I might not have been… therefore I am not a necessary being" (Pensées, No. 597). The proposition applies equally to every living thing.”

Pierre-Paul Grassé (1895–1985) French zoologist

Grassé, Pierre Paul (1977); Evolution of living organisms: evidence for a new theory of transformation. Academic Press, p. 172
Evolution of living organisms: evidence for a new theory of transformation (1977)
Original: Le philosophe, considérant l'univers dans son intégralité, est conduit à n'admettre qu'un seul être nécessaire, absolu, Dieu. Tous les autres sont contingents; c'est pour cela que Pascal disait de lui-même : « Je sens que je puis n'avoir pas été... donc je ne suis pas un être nécessaire » (Pensées, 597). Cette proposition s'applique avec autant de justesse à tout être

James Bradley photo

“Hitherto we have considered the apparent motion of the star about its true place, as made only in a plane parallel to the ecliptic, in which case it appears to describe a circle in that plane; but since, when we judge of the place and motion of a star, we conceive it to be in the surface of a sphere, whose centre is our eye, 'twill be necessary to reduce the motion in that plane to what it would really appear on the surface of such a sphere, or (which will be equivalent) to what it would appear on a plane touching such a sphere in the star's true place. Now in the present case, where we conceive the eye at an indefinite distance, this will be done by letting fall perpendiculars from each point of the circle on such a plane, which from the nature of the orthographic projection will form an ellipsis, whose greater axis will be equal to the diameter of that circle, and the lesser axis to the greater as the sine of the star's latitude to the radius, for this latter plane being perpendicular to a line drawn from the centre of the sphere through the star's true place, which line is inclined to the ecliptic in an angle equal to the star's latitude; the touching plane will be inclined to the plane of the ecliptic in an angle equal to the complement of the latitude. But it is a known proposition in the orthographic projection of the sphere, that any circle inclined to the plane of the projection, to which lines drawn from the eye, supposed at an infinite distance, are at right angles, is projected into an ellipsis, having its longer axis equal to its diameter, and its shorter to twice the cosine of the inclination to the plane of the projection, half the longer axis or diameter being the radius.
Such an ellipse will be formed in our present case…”

James Bradley (1693–1762) English astronomer; Astronomer Royal

Miscellaneous Works and Correspondence (1832), Demonstration of the Rules relating to the Apparent Motion of the Fixed Stars upon account of the Motion of Light.

“Are there mathematical propositions for which there is a considerable amount of computational evidence, evidence that is so persuasive that a physicist would regard them as experimentally verified?”

Gregory Chaitin (1947) Argentinian mathematician and computer scientist

Thoughts on the Riemann hypothesis http://link.springer.com/article/10.1007/BF02985392 The Mathematical Intelligencer (December 2004) vol. 26, issue 1, pp. 4–7, quote on p. 4

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“In my Inaugural I laid down the simple proposition that nobody is going to starve in this country. It seems to me to be equally plain that no business which depends for existence on paying less than living wages to its workers has any right to continue in this country. By "business" I mean the whole of commerce as well as the whole of industry; by workers I mean all workers, the white collar class as well as the men in overalls; and by living wages I mean more than a bare subsistence level-I mean the wages of decent living.”

Franklin D. Roosevelt (1882–1945) 32nd President of the United States

Franklin Roosevelt's Statement on the National Industrial Recovery Act (16 June 1933) http://docs.fdrlibrary.marist.edu/odnirast.html
1930s
Source: [Tritch, Teresa, F.D.R. Makes the Case for the Minimum Wage, http://takingnote.blogs.nytimes.com/2014/03/07/f-d-r-makes-the-case-for-the-minimum-wage/, March 7, 2014, New York Times, March 7, 2014]

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“The Pennsylvania legislature, who, on a proposition to make the belief in God a necessary qualification for office, rejected it by a great majority, although assuredly there was not a single atheist in their body. And you remember to have heard, that when the act for religious freedom was before the Virginia Assembly, a motion to insert the name of Jesus Christ before the phrase, "the author of our holy religion," which stood in the bill, was rejected, although that was the creed of a great majority of them.”

Thomas Jefferson (1743–1826) 3rd President of the United States of America

Letter to Albert Gallatin (16 June 1817). Published in The Works of Thomas Jefferson in Twelve Volumes http://oll.libertyfund.org/ToC/0054.php, Federal Edition, Paul Leicester Ford, ed., New York: G. P. Putnam's Sons, 1904, Vol. 12 http://oll.libertyfund.org/Texts/Jefferson0136/Works/0054-12_Bk.pdf, p. 73
1810s

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“36 Proposition. The 1260 years of the Antichrists universal raign over Christians, begins about the year of Christ 300. or 316. at the farthest.”

John Napier (1550–1617) Scottish mathematician

A Plaine Discovery of the Whole Revelation of St. John (1593), The First and Introductory Treatise

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John Napier photo

“19 Proposition. The foure beasts are the foure Evangelles with all the true writers and professors thereof.”

John Napier (1550–1617) Scottish mathematician

A Plaine Discovery of the Whole Revelation of St. John (1593), The First and Introductory Treatise

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“The respondents in this case insist that a difficult question of public policy must be taken from the reach of the voters, and thus removed from the realm of public discussion, dialogue, and debate in an election campaign. Quite in addition to the serious First Amendment implications of that position with respect to any particular election, it is inconsistent with the underlying premises of a responsible, functioning democracy. One of those premises is that a democracy has the capacity—and the duty—to learn from its past mistakes; to discover and confront persisting biases; and by respectful, rationale deliberation to rise above those flaws and injustices. That process is impeded, not advanced, by court decrees based on the proposition that the public cannot have the requisite repose to discuss certain issues. It is demeaning to the democratic process to presume that the voters are not capable of deciding an issue of this sensitivity on decent and rational grounds. The process of public discourse and political debate should not be foreclosed even if there is a risk that during a public campaign there will be those, on both sides, who seek to use racial division and discord to their own political advantage. An informed public can, and must, rise above this. The idea of democracy is that it can, and must, mature. Freedom embraces the right, indeed the duty, to engage in a rational, civic discourse in order to determine how best to form a consensus to shape the destiny of the Nation and its people.”

Anthony Kennedy (1936) Associate Justice of the Supreme Court of the United States

Schuette v. Coalition to Defend Affirmative Action, 572 U. S. ____, (2016), plurality opinion.

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“3. Proposition. The Star and locusts of the fift trumpet, are not the greate Antichrist and his Cleargie, but the Dominator of the Turkes and his armie, who began their dominion in anno Christi 1051.”

John Napier (1550–1617) Scottish mathematician

A Plaine Discovery of the Whole Revelation of St. John (1593), The First and Introductory Treatise

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“Philosophy rests on a proposition that whatever is is right. Preaching begins by assuming that whatever is is wrong.”

Elbert Hubbard (1856–1915) American writer, publisher, artist, and philosopher fue el escritor del jarron azul

The Philistine http://books.google.com/books?id=AoxHAAAAYAAJ&q="Philosophy+rests+on+a+proposition+that+whatever+is+is+right+preaching+begins+by+assuming+that+whatever+is+is+wrong"&pg=PA130#v=onepage (October 1897).

John Napier photo

“25 Proposition. The two horned Beast, is the Antichrist and his kingdome, it alone.”

John Napier (1550–1617) Scottish mathematician

A Plaine Discovery of the Whole Revelation of St. John (1593), The First and Introductory Treatise

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“34 Proposition. The thousand yeares that Sathan was bound (Revel. 20.) began in Anno Christi 300. or thereabout.”

John Napier (1550–1617) Scottish mathematician

A Plaine Discovery of the Whole Revelation of St. John (1593), The First and Introductory Treatise

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“Secularization theory is a term that was used in the fifties and sixties by a number of social scientists and historians. Basically, it had a very simple proposition. It could be stated in one sentence. Modernity inevitably produces a decline of religion.”

Peter L. Berger (1929–2017) Austrian-born American sociologist

Peter L. Berger, Gregor Thuswaldner. " A Conversation with Peter L. Berger "How My Views Have Changed http://thecresset.org/2014/Lent/Thuswaldner_L14.html," at thecresset.org, Lent 2014, Vol LXXVII, No. 3, pp 16-21

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“The term 'fundamentalist', which was coined in 1920, derives from the title of a series of tracts - The Fundamentals - published in the United States from 1910 to 1915. It has since been implicitly defined as meaning a person who believes that, since The Bible is the Word of God, every proposition in it must be true; a belief which, notoriously, is taken to commit fundamentalist Christians to defending the historicity of the accounts of the creation of the Universe given in the first two chapters of Genesis. On this understanding a fully believing Christian does not have to be fundamentalist. Instead it is both necessary and sufficient to accept the Apostles' and/or The Nicene Creed. In Islam, however, the situation is altogether different. For, whereas only a very small proportion of all the propositions contained in the Old and New Testaments are presented as statements made directly by God in any of the three persons of the Trinity, The Koran consists entirely and exclusively of what are alleged to be revelations from Allah (God). Therefore, with regard to The Koran, all Muslims must be as such fundamentalists; and anyone denying anything. asserted in The Koran ceases, ipso facto, to be properly accounted a Muslim. Those whom the media call fundamentalists would therefore better be described as revivalists. This conceptual truth not only places a tight limitation upon the possibilities of developmental change within Islam, as opposed to the tacit or open abandonment of one or more of its original particular claims, but also opens up the theoretical possibility of falsifying the Islamic system as a whole by presenting some known fact which is inconsistent with a Koranic assertion.”

Antony Flew (1923–2010) British analytic and evidentialist philosopher

Turning away from Mecca (The Salisbury Review, Spring 1996) quoted from Goel, Sita Ram (editor) (1998). Freedom of expression: Secular theocracy versus liberal democracy. https://web.archive.org/web/20171026023112/http://www.bharatvani.org:80/books/foe/index.htm

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“Philosophy is not a system of propositions, and not a science.”

Source: Allgemeine Erkenntnislehre, 1925, p. 157 ; As cited in: Thomas Uebel (2012). Empiricism at the Crossroads: The Vienna Circle's Protocol-Sentence. p. 78

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“Art before the modern period is as much art as Neanderthal man is man'. It is for this reason that around the same time I replaced the term "work" for art proposition. Because a conceptual work of art in the traditional sense, is a contradiction in terms.”

Joseph Kosuth (1945) American conceptual artist

Joseph Kosuth. (1969), as cited in: Claude Gintz, ‎Musée d'Art Moderne Paris (1989). L'Art conceptuel, une perspective: exposition au Musée d'art moderne de la Ville de Paris, 22 nov. 1989 - 18 fév. 1990. p. 42

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“My campaign is based upon the proposition that the answers to the problems which currently plague our cities, our towns, and our homes, are not to be found in the decisions in Washington. They are instead to be found in the hearts, minds and resources of our own people here at home.”

Jerry Springer (1944) American television presenter, former lawyer, politician, news presenter, actor, and musician

from a speech given circa 1970 to citizens in Cincinnati Ohio.
This American Life http://www.thislife.org/pages/descriptions/04/258.html, Ep. 258, 01/30/04, Leaving the Fold; Act One.

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“That is the naked, undisguised proposition of the Democratic Party in the year of grace 1860.”

Benjamin Stanton (1809–1872) American politician

Speech (1860)

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“24 Proposition. The great ten-horned beast, is the whole bodie of the Latine Empire, whereof the Antichrist is a part.”

John Napier (1550–1617) Scottish mathematician

A Plaine Discovery of the Whole Revelation of St. John (1593), The First and Introductory Treatise

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“A finished or even a competent reasoner is not the work of nature alone… education develops faculties which would otherwise never have manifested their existence. It is, therefore, as necessary to learn to reason before we can expect to be able to reason, as it is to learn to swim or fence, in order to attain either of those arts. Now, something must be reasoned upon, it matters not much what it is, provided that it can be reasoned upon with certainty. The properties of mind or matter, or the study of languages, mathematics, or natural history may be chosen for this purpose. Now, of all these, it is desirable to choose the one… in which we can find out by other means, such as measurement and ocular demonstration of all sorts, whether the results are true or not.
.. Now the mathematics are peculiarly well adapted for this purpose, on the following grounds:—
1. Every term is distinctly explained, and has but one meaning, and it is rarely that two words are employed to mean the same thing.
2. The first principles are self-evident, and, though derived from observation, do not require more of it than has been made by children in general.
3. The demonstration is strictly logical, taking nothing for granted except the self-evident first principles, resting nothing upon probability, and entirely independent of authority and opinion.
4. When the conclusion is attained by reasoning, its truth or falsehood can be ascertained, in geometry by actual measurement, in algebra by common arithmetical calculation. This gives confidence, and is absolutely necessary, if… reason is not to be the instructor, but the pupil.
5. There are no words whose meanings are so much alike that the ideas which they stand for may be confounded.
…These are the principal grounds on which… the utility of mathematical studies may be shewn to rest, as a discipline for the reasoning powers. But the habits of mind which these studies have a tendency to form are valuable in the highest degree. The most important of all is the power of concentrating the ideas which a successful study of them increases where it did exist, and creates where it did not. A difficult position or a new method of passing from one proposition to another, arrests all the attention, and forces the united faculties to use their utmost exertions. The habit of mind thus formed soon extends itself to other pursuits, and is beneficially felt in all the business of life.”

Augustus De Morgan (1806–1871) British mathematician, philosopher and university teacher (1806-1871)

Source: On the Study and Difficulties of Mathematics (1831), Ch. I.

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