Frases de Gottlob Frege

Gottlob Frege Foto
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Gottlob Frege

Fecha de nacimiento: 8. Noviembre 1848
Fecha de muerte: 26. Julio 1925
Otros nombres: Friedrich Ludwig Gottlob Frege

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Friedrich Ludwig Gottlob Frege fue un matemático, lógico y filósofo alemán, padre de la lógica matemática y la filosofía analítica. Frege es ampliamente reconocido como el mayor lógico desde Aristóteles.[cita requerida]

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Frases Gottlob Frege

„Todo buen matemático es, al menos, la mitad de un filósofo, y todo buen filósofo es, al menos, la mitad de un matemático.“

—  Gottlob Frege
Source: Atribuido a Frege en: A.A.B. Aspeitia (2000) Mathematics as grammar: 'Grammar' in Wittgenstein's philosophy of mathematics during the Middle Period. Universidad de Indiana. pág. 25

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„El realismo, por tanto, es el punto de vista que sostiene que la matemática es la ciencia de los números, conjuntos, funciones, etc., tal y como la física es el estudio de los objetos físicos ordinarios, cuerpos astronómicos y partículas subatómicas entre otros. Esto es, la matemática trata acerca de esos objetos, y es el modo en que tales objetos son lo que hace a los enunciados de la matemática verdaderos o falsos.“

—  Gottlob Frege
Source: Maddy, Penélope. Realism in mathematics. Pg. 2 ‘Realism, then, is the view that mathematics is the science of numbers, sets, functions, etc., just as physical science is the study of ordinary physical objects, astronomical bodies, subatomic particles, and so on. That is, mathematics is about these things, and the way these things are is what makes mathematical statements true or false.’

„Cada enunciado que tenemos por verdadero, es conocido o bien por medio de la experiencia o en razón de su significado. No hay más fuentes de conocimiento que el dato de los sentidos o el significado que le damos al enunciado.“

—  Gottlob Frege
Source: Lewis, C. I. The modes of meaning. pág 15-16 ‘Every statement we know to be true is so known either by reason of experience or by reason of what the statement itself means. There are no other sources of knowledge than on the one hand data of sense and on the other hand our own intended meanings.’

„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, libro Los fundamentos de la aritmética
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.

„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
Über Sinn und Bedeutung, 1892, 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.

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„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.“

—  Gottlob Frege
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.

„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.“

—  Gottlob Frege
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 paradox.

„Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam egestas wisi a erat. Morbi imperdiet, mauris ac auctor dictum.“

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