Gottlob Frege citáty

Friedrich Ludwig Gottlob Frege byl německý matematik, logik a filosof, dlouholetý profesor univerzity v Jeně.

Frege kritizoval psychologismus, tj. názor, že matematické objekty mají psychologický původ a že logika je „věda o správném myšlení“. Je pokládán za „druhého zakladatele logiky“, která až do jeho doby byla závislá na Aristotelově sylogistice. Sestavil také predikátový kalkul a věnoval se konstrukci formálního jazyka a formalizaci důkazů. Jeho filosofie jazyka stála na počátku celého směru analytické filosofie 20. století. Wikipedia  

✵ 8. listopad 1848 – 26. červenec 1925   •   Další jména Friedrich Ludwig Gottlob Frege
Gottlob Frege foto
Gottlob Frege: 23   citátů 2   lajky

Gottlob Frege citáty a výroky

„Každý dobrý matematik, je přinejmenším z poloviny filozof, a každý dobrý filozof je minimálně poloviční matematik.“

Originál: (en) Every good mathematician is at least half a philosopher, and every good philosopher is at least half a mathematician.
Zdroj: [Sibley, Thomas Q., 2008, The Foundations of Mathematics, John Wiley & Sons, 21, angličtina]

Gottlob Frege: Citáty anglicky

“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.”

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.
Grundgesetze der Arithmetik, 1893 and 1903

“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.”

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 paradox.
Grundgesetze der Arithmetik, 1893 and 1903

“Is it always permissible to speak of the extension of a concept, of a class? And if not, how do we recognize the exceptional cases? Can we always infer from the extension of one concept's coinciding with that of a second, that every object which falls under the first concept also falls under the second?”

Vol. 2, p. 127. Replying to Bertrand Russell's letter about Russell's Paradox; quoted in The Stanford Encyclopedia of Philosophy http://plato.stanford.edu/entries/russell-paradox/
Grundgesetze der Arithmetik, 1893 and 1903

“A judgment, for me is not the mere grasping of a thought, but the admission of its truth.”

Gottlob Frege Sense and reference

Gottlob Frege (1892). On Sense and Reference, note 7.
Über Sinn und Bedeutung, 1892

“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)

“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 [1884]). p. 73

“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

“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)

“Equality gives rise to challenging questions which are not altogether easy to answer… a = a and a = b are obviously statements of differing cognitive value; a = a holds a priori and, according to Kant, is to be labeled analytic, while statements of the form a = b often contain very valuable extensions of our knowledge and cannot always be established a priori.”

Gottlob Frege Sense and reference

The discovery that the rising sun is not new every morning, but always the same, was one of the most fertile astronomical discoveries. Even to-day the identification of a small planet or a comet is not always a matter of course. Now if we were to regard equality as a relation between that which the names 'a' and 'b' designate, it would seem that a = b could not differ from a = a (i.e. provided a = b is true). A relation would thereby be expressed of a thing to itself, and indeed one in which each thing stands to itself but to no other thing.
As cited in: M. Fitting, Richard L. Mendelsoh (1999), First-Order Modal Logic, p. 142. They called this Frege's Puzzle.
Über Sinn und Bedeutung, 1892

“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.”

Gottlob Frege kniha The Foundations of Arithmetic

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 [1884]). The Foundations of Arithmetic. p. 99.

“A philosopher who has no connection to geometry is only half a philosopher, and a mathematician who has no philosophical vein is only half a mathematician.”

Originál: (de) Ein Philosoph, der keine Beziehung zur Geometrie hat, ist nur ein halber Philosoph, und ein Mathematiker, der keine philosophische Ader hat, ist nur ein halber Mathematiker.

Gottlob Frege: Erkenntnisquellen der Mathematik und der mathematischen Naturwissenschaften, 1924/1925, submitted to Wissenschaftliche Grundlagen; posthumously published in: Frege, Gottlob: Nachgelassene Schriften und Wissenschaftlicher Briefwechsel. Felix Meiner Verlag, 1990, p. 293

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