Gottlob Frege Quotes on Knowledge
Frege founded modern logic and the analytic tradition with the Begriffsschrift (1879) — the first complete formalization of predicate logic, with quantifiers binding variables — and the Foundations of Arithmetic (1884), which sought to derive arithmetic from logic via the analysis of cardinal number as the extension of a concept. The 1892 paper On Sense and Reference distinguished the sense of an expression (the mode of presentation through which it picks out its reference) from its reference itself (the object so picked out), supplying the framework that Russell, Wittgenstein, Carnap, and the entire subsequent analytic tradition would inherit. The logicist program collapsed when Russell's paradox revealed an inconsistency in the underlying set theory, but the conceptual apparatus survives intact.
Quotes
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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:
“The laws of truth are not psychological laws.”
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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.