Gottlob Frege: Quotes about knowledge

“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

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

Knowledge , Effort

“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. 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.”

Gottlob Frege Sense and reference

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

Question , Knowledge , Sun

“We suppose, it would seem, that concepts grow in the individual mind like leaves on a tree, and we think to discover their nature by studying their growth; we seek to define them psychologically, in terms of the human mind. But this account makes everything subjective, and if we follow it through to the end, does away with truth. What is known as the history of concepts is really a history either of our knowledge of concepts or of the meanings of words.”

Gottlob Frege

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

Truth , History , Nature , Knowledge

“The historical approach, with its aim of detecting how things began and arriving from these origins at a knowledge of their nature, is certainly perfectly legitimate; but it also has its limitations. If everything were in continual flux, and nothing maintained itself fixed for all time, there would no longer be any possibility of getting to know about the world, and everything would be plunged into confusion.”

Gottlob Frege

Translation J. L. Austin (Oxford, 1950) as quoted by Stephen Toulmin, Human Understanding: The Collective Use and Evolution of Concepts (1972) Vol. 1, p. 55.
Grundgesetze der Arithmetik, 1893 and 1903

World , Nature , Knowledge , Time

“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

Knowledge , Question