“Questions that pertain to the foundations of mathematics, although treated by many in recent times, still lack a satisfactory solution. Ambiguity of language is philosophy's main source of problems. That is why it is of the utmost importance to examine attentively the very words we use.”
Arithmetices principia, nova methodo exposita [The Principles of Arithmetic, presented by a new method] (1889)
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Giuseppe Peano7
Italian mathematician 1858–1932Related quotes
Alfred Tarski (1901–1983) Polish-American logician
"The Concept of Truth in Formalized Languages" (1931) in Logic, Semantics, Metamathematics: Papers from 1923 to 1938 (1956) Tr. J. H. Woodger.
N. Gregory Mankiw (1958) American economist
N. Gregory Mankiw]], Macroeconomics, Preview ; Cited in: David Colander (2005). 'The Stories Economists Tell. p. 182
2000s -
“Sometimes the government has to answer questions with ambiguous language.”
Jason Kenney (1968) Canadian politician and 18th Premier of Alberta
In an interview with Macleans https://www.macleans.ca/politics/jason-kenney-on-life-after-ottawa-and-uniting-albertas-right/ (28 September 2016) <br class="br">2010s
George Pólya (1887–1985) Hungarian mathematician
Mathematical Methods in Science (1977)
Context: We wish to see... the typical attitude of the scientist who uses mathematics to understand the world around us.... In the solution of a problem... there are typically three phases. The first phase is entirely or almost entirely a matter of physics; the third, a matter of mathematics; and the intermediate phase, a transition from physics to mathematics. The first phase is the formulation of the physical hypothesis or conjecture; the second, its translation into equations; the third, the solution of the equations. Each phase calls for a different kind of work and demands a different attitude.<!--p.164
Abraham Lincoln (1809–1865) 16th President of the United States
1860s, Allow the humblest man an equal chance (1860)
Context: It is easy to demonstrate that "our Fathers, who framed this government under which we live," looked on Slavery as wrong, and so framed it and everything about it as to square with the idea that it was wrong, so far as the necessities arising from its existence permitted. In forming the Constitution they found the slave trade existing; capital invested in it; fields depending upon it for labor, and the whole system resting upon the importation of slave-labor. They therefore did not prohibit the slave trade at once, but they gave the power to prohibit it after twenty years. Why was this? What other foreign trade did they treat in that way? Would they have done this if they had not thought slavery wrong? Another thing was done by some of the same men who framed the Constitution, and afterwards adopted as their own act by the first Congress held under that Constitution, of which many of the framers were members; they prohibited the spread of Slavery into Territories. Thus the same men, the framers of the Constitution, cut off the supply and prohibited the spread of Slavery, and both acts show conclusively that they considered that the thing was wrong. If additional proof is wanting it can be found in the phraseology of the Constitution. When men are framing a supreme law and chart of government, to secure blessings and prosperity to untold generations yet to come, they use language as short and direct and plain as can be found, to express their meaning. In all matters but this of Slavery the framers of the Constitution used the very clearest, shortest, and most direct language. But the Constitution alludes to Slavery three times without mentioning it once! The language used becomes ambiguous, roundabout, and mystical. They speak of the "immigration of persons," and mean the importation of slaves, but do not say so. In establishing a basis of representation they say "all other persons," when they mean to say slaves — why did they not use the shortest phrase? In providing for the return of fugitives they say "persons held to service or labor." If they had said slaves it would have been plainer, and less liable to misconstruction. Why didn't they do it. We cannot doubt that it was done on purpose. Only one reason is possible, and that is supplied us by one of the framers of the Constitution — and it is not possible for man to conceive of any other — they expected and desired that the system would come to an end, and meant that when it did, the Constitution should not show that there ever had been a slave in this good free country of ours!
John Kenneth Galbraith book The Affluent Society
Source: The Affluent Society (1958), Chapter 12, Section VII, p. 145
Naomi Klein (1970) Canadian author and activist
Source: No Logo: Taking Aim at the Brand Bullies 1999, Chapter Eight, "Corporate Censorship"
Friedrich Wilhelm Joseph Schelling (1775–1854) German philosopher (idealism)
System of Transcendental Philosophy (1800)