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

Being true is different from being taken as true, whether by one or by many or everybody, and in no case is it to be reduced to it. There is no contradiction in something's being true which everybody takes to be false. I understand by 'laws of logic' not psychological laws of takings-to-be-true, but laws of truth. ...If being true is thus independent of being acknowledged by somebody or other, then the laws of truth are not psychological laws: they are boundary stones set in an eternal foundation, which our thought can overflow, but never displace. It is because of this that they have authority for our thought if it would attain truth. They do not bear the relation to thought that the laws of grammar bear to language; they do not make explicit the nature of our human thinking and change as it changes.

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.

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?