Gottlob Frege > Quotes

“Every good mathematician is at least half a philosopher, and every good philosopher is at least half a mathematician.”
― Gottlob Frege

“[..] I do not begin with concepts and put them together to form a thought or judgement; I come by the parts of a thought by analysing the thought.”
― Gottlob Frege, Posthumous Writings

“A scientist can hardly encounter anything more desirable than, just as a work is completed, to have its foundation give way.”
― Gottlob Frege

“Thus the thought, for example, which we expressed in the Pythagorean theorem is timelessly true, true independently of whether anyone takes it to be true. It needs no bearer. It is not true for the first time when it is discovered, but is like a planet which, already before anyone has seen it, has been in interaction with other planets.”
― Gottlob Frege

“If anyone tried to contradict the statement that what is true is true independently of our recognizing it as such, he would by his very assertion contradict what he had asserted; he would be in a similar position to the Cretan who said that all Cretans are liars.”
― Gottlob Frege, Logical Investigations

“Die Gedanken sind weder Dinge der Außenwelt noch Vorstellungen.
Ein drittes Reich muß anerkannt werden. Was zu diesem gehört, stimmt mit den Vorstellungen darin überein, daß es nicht mit den Sinnen wahrgenommen werden kann, mit den Dingen aber darin, daß es keines Trägers bedarf, zu dessen Bewußtseinsinhalte es gehört.”
― Gottlob Frege, Logical Investigations

“If number were an idea, then Arithmetic would be Psychology.”
― Gottlob Frege

“What is it, in fact, that we are supposed to abstract from, in order to get, for example, from the moon to the number 1? By abstraction we do indeed get certain concepts, viz. satellite of the Earth, satellite of a planet, non-self-luminous heavenly body, heavenly body, body, object. But in this series 1 is not to be met with; for it is no concept that the moon could fall under. In the case of 0, we have simply no object at all from which to start our process of abstracting. It is no good objecting that 0 and 1 are not numbers in the same sense as 2 and 3. What answers the question How many? is number, and if we ask, for example, "How many moons has this planet?", we are quite as much prepared for the answer 0 or 1 as for 2 or 3, and that without having to understand the question differently. No doubt there is something unique about 0, and about 1000; but the same is true in principle of every whole number, only the bigger the number the less obvious it is. To make out of this a difference in kind is utterly arbitrary. What will not work with 0 and 1 cannot be essential to the concept of number.”
― Gottlob Frege

“[I]t is here that geometry and philosophy come closest together. In fact they belong to one another. A philosopher who has nothing to do with geometry is only half a philosopher, and a mathematician with no element of philosophy in him is only half a mathematician. These disciplines have estranged themselves from one another to the detriment of both.”
― Gottlob Frege

“[I]t is evident that sense perception can yield nothing infinite. However many stars we may include in our inventories, there will never be infinitely many. […] For this we need a special source of knowledge, and one such is the geometrical.”
― Gottlob Frege

“The question why and with what right we acknowledge a law of logic to be true, logic can answer only by reducing it to another law of logic. Where that is not possible, logic can give no answer.”
― Gottlob Frege, Grundgesetze Der Arithmetik - Begriffsschriftlich Abgeleitet: In Moderne Formelnotation Transkribiert Und Mit Einem Ausführlichen Sachregister Versehen. Band I Und II

“From the geometrical source of knowledge flows the infinite in the genuine and strictest sense of this word. […] We have infinitely many points on every interval of a straight line. […] We cannot imagine the totality of these. […] One man may be able to imagine more, another less. But here we are not in the domain of psychology, of the imagination, of what is subjective, but in the domain of the objective, of what is true.”
― Gottlob Frege

“Um nur das hier zunächst Liegende zu berühren, sehe ich ein großes Verdienst Kants darin, daß er die Unterscheidung von synthetischen und analytischen Urteilen gemacht hat. (Grundlagen der Arithmetik, §89)”
― Gottlob Frege

“In order to produce it [an infinite series] we would need an infinitely long blackboard, an infinite supply of chalk, and an infinite length of time. We may be censured as too cruel for trying to crush so high a flight of the spirit by such a homely objection; but this is no answer.”
― Gottlob Frege, Basic Laws of Arithmetic: Exposition of the System

“The more I have thought the matter over, the more convinced I have become that arithmetic and geometry have developed on the same basis —a geometrical one in fact— so that mathematics in its entirety is really geometry.”
― Gottlob Frege