Gottlob Frege Quotes
Friedrich Ludwig Gottlob Frege was a 19th and early 20th-century German mathematician, logician, and philosopher, regarded as the founder of modern formal logic and one of the founders of analytic philosophy. His 1879 work Begriffsschrift introduced the system of formal predicate logic that has been the foundation of subsequent logic in mathematics, philosophy, computer science, and linguistics. The quotes below are attributed to Gottlob Frege, organized by topic.
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Gottlob Frege on Death
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“Nur im Zusammenhange eines Satzes bedeuten die Wörter etwas. Es wird also darauf ankommen, den Sinn eines Satzes zu erklären, in dem ein Zahlwort vorkommt.”
Since it is only in the context of a proposition that words have any meaning, our problem becomes this: To define the sense of a proposition in which a number-word occurs. | Gottlob Frege (1950 ). p. 73
Gottlob Frege on Freedom
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“This ideography is a "formula language", that is, a lingua characterica , a language written with special symbols, "for pure thought", that is, free from rhetorical embellishments, "modeled upon that of arithmetic", that is, constructed from specific symbols that are manipulated according to definite rules.”
paraphrasing Frege's Begriffsschrift, a formula language, modeled upon that of arithmetic, for pure thought (1879) in Jean Van Heijenoort ed., in From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931 (1967)
Gottlob Frege on Justice
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“I hope I may claim in the present work to have made it probable that the laws of arithmetic are analytic judgments and consequently a priori . Arithmetic thus becomes simply a development of logic, and every proposition of arithmetic a law of logic, albeit a derivative one. To apply arithmetic in the physical sciences is to bring logic to bear on observed facts; calculation becomes deduction.”
Gottlob Frege (1950 ). The Foundations of Arithmetic . p. 99. -
“A scientist can hardly meet with anything more undesirable than to have the foundations give way just as the work is finished. I was put in this position by a letter from Mr. Bertrand Russell when the work was nearly through the press.”
Grundgesetze der Arithmetik, 1893 and 1903 | Note in the appendix of Grundlagen der Arithmetik (Vol. 2) after Frege had received a letter of Bertrand Russell in which Russell had explained his discovery of, what is now known as, Russell's parado
Gottlob Frege on Knowledge
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“Every good mathematician is at least half a philosopher, and every good philosopher is at least half a mathematician.”
Attributed to Frege in: A. A. B. Aspeitia (2000), Mathematics as grammar: 'Grammar' in Wittgenstein's philosophy of mathematics during the Middle Period , Indiana University, p. 25 -
Attributed to Gottlob Frege:
“Never ask for the meaning of a word in isolation, but only in the context of a proposition.”
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Attributed to Gottlob Frege:
“A statement of number contains an assertion about a concept.”
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Attributed to Gottlob Frege:
“An arithmetician finds the rules for the calculation of numbers, but he does not invent them.”
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“Begriffsschrift (1879) Preface to the Begriffsschrift”
If the task of philosophy is to break the domination of words over the human mind [...], then my concept notation, being developed for these purposes, can be a useful instrument for philosophers [...] I believe the cause of logic has been advanced already by the invention of this concept notation. -
“Gottlob Frege (1950 ). The Foundations of Arithmetic . p. 99.”
I hope I may claim in the present work to have made it probable that the laws of arithmetic are analytic judgments and consequently a priori . Arithmetic thus becomes simply a development of logic, and every proposition of arithmetic a law of logic, albeit a derivative one. To apply arithmetic in the physical sciences is to bring logic to bear on observed facts; calculation becomes deduction. -
“Since it is only in the context of a proposition that words have any meaning, our problem becomes this: To define the sense of a proposition in which a number-word occurs.”
Nur im Zusammenhange eines Satzes bedeuten die Wörter etwas. Es wird also darauf ankommen, den Sinn eines Satzes zu erklären, in dem ein Zahlwort vorkommt. -
“Gottlob Frege (1950 ). p. 73”
Nur im Zusammenhange eines Satzes bedeuten die Wörter etwas. Es wird also darauf ankommen, den Sinn eines Satzes zu erklären, in dem ein Zahlwort vorkommt. -
“Your discovery of the contradiction caused me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build arithmetic.”
Letter to Bertrand Russel " (1902) in J. van Heijenoort, ed., From Frege to Godel: A Source Book in Mathematical Logic, 1879-1931 (1967) -
“Often it is only after immense intellectual effort, which may have continued over centuries, that humanity at last succeeds in achieving knowledge of a concept in its pure form, by stripping off the irrelevant accretions which veil it from the eye of the mind.”
Grundgesetze der Arithmetik, 1893 and 1903 | Translation J. L. Austin (Oxford, 1950) as quoted by Stephen Toulmin , Human Understanding: The Collective Use and Evolution of Concepts (1972) Vol. 1, p. 56.
Gottlob Frege on Mind
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Attributed to Gottlob Frege:
“Thoughts are objective; they are neither things in the external world nor ideas in the mind.”
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“If the task of philosophy is to break the domination of words over the human mind [...], then my concept notation, being developed for these purposes, can be a useful instrument for philosophers [...] I believe the cause of logic has been advanced already by the invention of this concept notation.”
Begriffsschrift (1879) Preface to the Begriffsschrift -
“paraphrasing Frege's Begriffsschrift, a formula language, modeled upon that of arithmetic, for pure thought (1879) in Jean Van Heijenoort ed., in From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931 (1967)”
This ideography is a "formula language", that is, a lingua characterica , a language written with special symbols, "for pure thought", that is, free from rhetorical embellishments, "modeled upon that of arithmetic", that is, constructed from specific symbols that are manipulated according to definite rules.
Gottlob Frege on Truth
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Attributed to Gottlob Frege:
“The laws of truth are not psychological laws.”
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“A judgment, for me is not the mere grasping of a thought, but the admission of its truth.”
Über Sinn und Bedeutung, 1892 | Gottlob Frege (1892). On Sense and Reference , note 7.