The Basic Laws of Arithmetic (Grundgesetze der Arithmetik)

„It is not that only a complimentary review could satisfy me; quite the contrary! I would always prefer a critical assault based on a thorough study to praise that indulges in generalities without engaging the heart of the matter.”

„A review based on a superficial reading might easily do more harm than good.”

„Custom exerts great power over the mind.”

„Being true is different from being taken to be true, be it by one, be it by many, be it by all, and is in no way reducible to it. It is no contradiction that something is true that is universally held to be false. By logical laws I do not understand psychological laws of taking to be true, but laws of being true. […] If being true is thus independent of anyone's acknowledgement, then the laws of being true are not psychological laws either but boundary stones which are anchored in an eternal ground, which our thinking may wash over but yet cannot displace.”

„Whoever has once acknowledged a law of being true has thereby also acknowledged a law that prescribes what ought to be judged, wherever, whenever and by whomsoever the judgement may be made.”

„If we could apprehend nothing but what is internal to ourselves, then a conflict of opinion, a mutual understanding would be impossible since a common ground would be lacking, and such a common ground cannot be an idea in the sense of psychology. There would be no logic appointed to be arbiter in a conflict of opinions.”

„I count as an object everything that is not a function, e.g., numbers, truth-values and the value-ranges introduced below. Thus, names of objects, the proper names, do not in themselves carry argument places; like the objects themselves, they are saturated.”