Gottlob Frege

numbers arithmetical truth

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

—Gottlob Frege (1848-1925)

compute figure mechanically parrot thinking

"It is possible, of course, to operate with figures mechanically, just as it is possible to speak like a parrot: but that hardly deserves the names of thought. It only becomes possible at all after the mathematical notation has, as a result of genuine thought, been so developed that it does the thinking for us, so to speak."

—Gottlob Frege (1848-1925)

numerical sequence indefinite danger heaven

"There is more danger of numerical sequences continued indefinitely than of trees growing up to heaven. Each will some time reach its greatest height."

—Gottlob Frege (1848-1925)

science truth judge assert

"The aim of scientific work is truth. While we internally recognise something as true, we judge, and while we utter judgements, we assert."

—Gottlob Frege (1848-1925)

arithmetic tree technique theorem root depth

"I compare arithmetic with a tree that unfolds upwards in a multitude of techniques and theorems while the root drives into the depths."

—Gottlob Frege (1848-1925)

fact science thought true foundation

"'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 (1848-1925)

Pythagorean theorem bearer planet interaction

“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 (1848-1925)

begin concept part thought analyse construct

“[..] 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 (1848-1925)

scientist work completed foundation

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

—Gottlob Frege (1848-1925)

good mathematician philosopher half

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

—Gottlob Frege (1848-1925)