Quotations from the writings of Gottlob Frege
Grundgesetze der Arithmetik
Scientific Method in Mathematics

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:

It cannot be required that we should prove everything, for that is impossible; but we can demand that all propositions used without proof should be expressly mentioned as such, so that we can see distinctly what the whole construction rests upon.

We should accordingly strive to reduce the number of these fundamental laws as much as possible, by proving everything which can be proved.

Furthermore I demand --- and in this I go beyond Euclid --- that all the methods of inference used should be specified in advance. Otherwise is it impossible to ensure satisfying the first demand.

From the preface to Grundgesetze der Arithmetik Volume I frege1893. Translation to English from frege1952.

Die Grundlagen der Arithmetik
Three Fundamental Principles
In the enquiry which follows I have kept to three fundamental principles:
  • always to separate sharply the psychological from the logical, the subjective from the objective
  • never to ask for the meaning of a word in isolation, but only in the context of a proposition
  • never to lose sight of the distinction between concept and object

From the introduction to The Foundations of Arithmetic frege1884.

2. Analyticity and A Priority
Now these distinctions between a priori and a posteriori, synthetic and analytic, concern, as I see it, not the content of the judgement but the justification for making the judgement... When a proposition is called a posteriori or analytic in my sense, this is not a statement about the conditions, psychological, physiological, and physical, which have made it possible to form the content of the proposition in our consciousness; nor is it a judgement about how some other man has come, perhaps erroneously, to believe it true; rather, it is a judgement about the ultimate ground on which rests the justification for holding it to be true.

The Foundations of Arithmetic frege1884, §3.

87. The Analyticity of Arithmetic
I hope I may claim in the present work to have made it probable that the laws of arithmetic are analytic judgements 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.

The Foundations of Arithmetic frege1884, §87.

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