“We invent by intuition, though we prove by logic.”

— Sarvepalli Radhakrishnan

Eminent Indians (1947)

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Sarvepalli Radhakrishnan 84

Indian philosopher and statesman who was the first Vice Pre… 1888–1975

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“The art of discovery is confused with the logic of proof and an artificial simplification of the deeper movements of thought results. We forget that we invent by intuition though we prove by logic.”

Sarvepalli Radhakrishnan (1888–1975) Indian philosopher and statesman who was the first Vice President and the second President of India

Internet Encyclopedia of Philosophy

“It is by logic that we prove, but by intuition that we discover. To know how to criticize is good, to know how to create is better.”

Henri Poincaré book Science and Method

C'est par la logique qu'on démontre, c'est par l'intuition qu'on invente.
Part II. Ch. 2 : Mathematical Definitions and Education, p. 129
Science and Method (1908)

“It is through science that we prove, but through intuition that we discover.”

Henri Poincaré (1854–1912) French mathematician, physicist, engineer, and philosopher of science

“Invention is not the product of logical thought, even though the final product is tied to a logical structure.”

Albert Einstein (1879–1955) German-born physicist and founder of the theory of relativity

From his "Autobiographische Skizze" (18 April 1955), original German version here http://philoscience.unibe.ch/documents/kursarchiv/WS99/Skizze.pdf. Translation from Subtle is the Lord: The Science and the Life of Albert Einstein by Abraham Pais (1982), p. 131 http://books.google.com/books?id=U2mO4nUunuwC&lpg=PP1&pg=PA131#v=onepage&q&f=false. Pais notes that when he said "during that year", he was referring to some time between October 1895 and early fall 1896.
Variant: "Innovation is not the product of logical thought, even though the final product is tied to a logical structure."
Original German version: Während dieses Jahres in Aarau kam mir die Frage: Wenn man einer Lichtwelle mit Lichtgeschwindigkeit nachläuft, so würde man ein zeitunabhängiges Wellenfeld vor sich haben. So etwas scheint es aber doch nicht zu geben! Dies war das erste kindliche Gedanken-Experiment, das mit der speziellen Relativitätstheorie zu tun hat. Das Erfinden ist kein Werk des logischen Denkens, wenn auch das Endprodukt an die logische Gestalt gebunden ist. ("Autobiographische Skizze", p. 10)
1950s
Context: During that year in Aarau the question came to me: If one runs after a light wave with [a velocity equal to the] light velocity, then one would encounter a time-independent wavefield. However, something like that does not seem to exist! This was the first juvenile thought experiment which has to do with the special theory of relativity. Invention is not the product of logical thought, even though the final product is tied to a logical structure.

“Even if all life on our planet is destroyed, there must be other life somewhere which we know nothing of. It is impossible that ours is the only world; there must be world after world unseen by us, in some region or dimension that we simply do not perceive. Even though I can't prove that, even though it isn't logical — I believe it.”

Philip K. Dick book The Man in the High Castle

The Man in the High Castle (1962)

“Our intuition gets obscured by the fears and beliefs that we have erected in front of it. When we lose trust in our intuitive knowledge, we begin to close down that channel of information by ignoring it. The good news is, though we may shut out the messages we receive from the higher self, the higher self continues to give them, so it is impossible to completely lose the ability to be intuitive.”

Teal Swan (1984) American spiritual teacher

“We are confident that the Islamic logic, culture, and discourse can prove their superiority in all fields over all schools of thought and theories.”

Mahmoud Ahmadinejad (1956) 6th President of the Islamic Republic of Iran

Ahmadinejad on His Proposal for a Jewish State in Europe and on Iran's Nuclear Energy http://www.memritv.org/Transcript.asp?P1=987 Jan. 2006.
2006

“Until writing was invented, we lived in acoustic space: boundless, directionless, horizonless, the dark of the mind, the world of emotion, primordial intuition, terror. Speech is a social chart of this bog.”

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

Variant: Until writing was invented, we lived in acoustic space: boundless, directionless, horizonless, the dark of the mind, the world of emotion, primordial intuition, terror. Speech is a social chart of this bog. (p. 13)
Source: 1960s, Counterblast (1969), p. 13

“It really is worth the trouble to invent a new symbol if we can thus remove not a few logical difficulties and ensure the rigour of the proofs. But many mathematicians seem to have so little feeling for logical purity and accuracy that they will use a word to mean three or four different things, sooner than make the frightful decision to invent a new word.”

Gottlob Frege (1848–1925) mathematician, logician, philosopher

Gottlob Frege in: Dagobert David Runes (1962). Readings in epistemology, theory of knowledge and dialectics. p. 334

“The construction of hypotheses is a creative act of inspiration, intuition, invention; its essence is the vision of something new in familiar material. The process must be discussed in psychological, not logical, categories; studied in autobiographies and biographies, not treatises on scientific method; and promoted by maxim and example, not syllogism or theorem.”

Milton Friedman (1912–2006) American economist, statistician, and writer

"The Methodology of Positive Economics" (1953)

“We invent by intuition, though we prove by logic.”

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Sarvepalli Radhakrishnan 84

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