“Logic has borrowed, perhaps, the rules of geometry, without comprehending their force”

— Blaise Pascal

The Art of Persuasion
Context: Logic has borrowed, perhaps, the rules of geometry, without comprehending their force... it does not thence follow that they have entered into the spirit of geometry, and I should be greatly averse... to placing them on a level with that science that teaches the true method of directing reason.

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Blaise Pascal 144

French mathematician, physicist, inventor, writer, and Chri… 1623–1662

George Frederick James Temple (1901–1992) British mathematician

100 Years of Mathematics: a Personal Viewpoint (1981)

“What is the true geometry of the plate? …Anyone examining the situation will prefer Poincaré's common-sense solution… to attribute it Euclidean geometry, and to consider the measured deviations… as due to the actions of a force (thermal stresses in the rule). …On employing a brass rule in place of one of steel we would find that the local curvature is trebled—and an ideal rule (c = 0) would… lead to Euclidean geometry.”

Howard P. Robertson (1903–1961) American mathematician and physicist

Geometry as a Branch of Physics (1949)

“Logic cannot comprehend love; so much the worse for logic.”

N.T. Wright (1948) Anglican bishop

Source: Surprised by Hope: Rethinking Heaven, the Resurrection, and the Mission of the Church

“Magic, or rather magical power, comprehends two things, a science and a force: without the force the science is nothing, or rather it is a danger.”

Eliphas Levi (1810–1875) French writer

Miscellaneous Quotes On the Subjects of Magic and Magicians
Source: Dogme et Rituel de la Haute Magi Part I: The Doctrine of Transcendental Magic By Eliphas Levi (Alphonse Louis Constant), Translated by A. E. Waite, England, Rider & Company, England, 1896, Introduction p. 11

“Man is not to be comprehended as a starting-point, or progress as a goal, without those two great forces, Faith and Love. Prayer is sublime.”

Albert Pike book Morals and Dogma of the Ancient and Accepted Scottish Rite of Freemasonry

Source: Morals and Dogma of the Ancient and Accepted Scottish Rite of Freemasonry (1871), Ch. I : Apprentice, The Twelve-Inch Rule and Common Gavel, p. 1

“Neither Aristotelian nor Russellian rules give the exact logic of any expression of ordinary language; for ordinary language has no exact logic.”

P. F. Strawson (1919–2006) British philosopher

Strawson (1950) On Referring p. 27.

“Forgotten were the elementary rules of logic, that extraordinary claims require extraordinary evidence and that what can be asserted without evidence can also be dismissed without evidence.”

Christopher Hitchens (1949–2011) British American author and journalist

2003-10-20
Mommie Dearest
Slate
1091-2339
http://www.slate.com/articles/news_and_politics/fighting_words/2003/10/mommie_dearest.html, quoted in Michael Shermer, "The Skeptic's Skeptic," Scientific American, November 2010, p. 86.
February/March
http://secularhumanism.org/library/fi/hitchens_24_2.html
Less than Miraculous
Free Inquiry
0272-0701
24
"What can be asserted without evidence can also be dismissed without evidence." appears by itself in God Is Not Great: How Religion Poisons Everything (2007).
Translation of the Latin phrase "Quod gratis asseritur, gratis negatur.".
2000s, 2003
Variant: "What can be asserted without proof can be dismissed without proof." in * 2004

“Almost the only persons who may be said to comprehend even approximately the significance, principles, and purposes of Socialism are the chief leaders of the extreme wings of the Socialistic forces, and perhaps a few of the money kings themselves.”

Benjamin Ricketson Tucker (1854–1939) American journalist and anarchist

¶ 2
State Socialism and Anarchism: How Far They Agree, and Wherin They Differ (1888)
Context: Almost the only persons who may be said to comprehend even approximately the significance, principles, and purposes of Socialism are the chief leaders of the extreme wings of the Socialistic forces, and perhaps a few of the money kings themselves. It is a subject of which it has lately become quite the fashion for preacher, professor, and penny-a-liner to treat, and, for the most part, woeful work they have made with it, exciting the derision and pity of those competent to judge. That those prominent in the intermediate Socialistic divisions do not fully understand what they are about is evident from the positions they occupy.

“Euclidean geometry can be easily visualized; this is the argument adduced for the unique position of Euclidean geometry in mathematics. It has been argued that mathematics is not only a science of implications but that it has to establish preference for one particular axiomatic system. Whereas physics bases this choice on observation and experimentation, i. e., on applicability to reality, mathematics bases it on visualization, the analogue to perception in a theoretical science. Accordingly, mathematicians may work with the non-Euclidean geometries, but in contrast to Euclidean geometry, which is said to be "intuitively understood," these systems consist of nothing but "logical relations" or "artificial manifolds". They belong to the field of analytic geometry, the study of manifolds and equations between variables, but not to geometry in the real sense which has a visual significance.”

Hans Reichenbach (1891–1953) American philosopher

The Philosophy of Space and Time (1928, tr. 1957)

“There is no single rule that governs the use of geometry. I don't think that one exists.”

Benoît Mandelbrot (1924–2010) Polish-born, French and American mathematician

New Scientist interview (2004)

“Logic has borrowed, perhaps, the rules of geometry, without comprehending their force”

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Blaise Pascal 144

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