Gottlob Frege quotes

Gottlob Frege was a German philosopher, logician, and mathematician, regarded as a founder of modern logic and analytic philosophy. His pioneering work laid the foundations for much of twentieth-century philosophy and influenced figures such as Russell and Wittgenstein. He is remembered for his groundbreaking contributions to the philosophy of language and the development of predicate logic. Here are 24 of his quotes:

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 my arithmetic.

Gottlob Frege

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

Gottlob Frege

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

Facts, facts, facts,' cries the scientist if he wants to emphasize the necessity of a firm foundation for science. What is a fact? A fact is a thought that is true. But the scientist will surely not recognize something which depends on men's varying states of mind to be the firm foundation of science.

Gottlob Frege

It really is worth the trouble to invent a new symbol if we can thus remove not a few logical difficulties and ensure the rigour of the proofs. But many mathematicians seem to have so little feeling for logical purity and accuracy that they will use a word to mean three or four different things, sooner than make the frightful decision to invent a new word.

Gottlob Frege

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

If I compare arithmetic with a tree that unfolds upward into a multitude of techniques and theorems while its root drives into the depths, then it seems to me that the impetus of the root.

Gottlob Frege

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

The ideal of strictly scientific method in mathematics which I have tried to realise here, and which perhaps might be named after Euclid I should like to describe in the following way... The novelty of this book does not lie in the content of the theorems but in the development of the proofs and the foundations on which they are based... With this book I accomplish an object which I had in view in my Begriffsschrift of 1879 and which I announced in my Grundlagen der Arithmetik. I am here trying to prove the opinion on the concept of number that I expressed in the book last mentioned.

Gottlob Frege

What are numbers? What is the nature of arithmetical truth?

Gottlob Frege

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

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

Without some affinity in human ideas art would certainly be impossible; but it can never be exactly determined how far the intentions of the poet are realized.

Gottlob Frege

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

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

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

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

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.

Gottlob Frege

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?

Gottlob Frege

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

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