What are numbers? What is the nature of arithmetical truth? Gottlob Frege More Quotes by Gottlob Frege More Quotes From Gottlob Frege Every good mathematician is at least half a philosopher, and every good philosopher is at least half a mathematician. Gottlob Frege analysis philosophy science '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 mind men science ...one can hardly deny that mankind has a common store of thoughts which is transmitted from one generation to another. Gottlob Frege generations mind knowledge The thought: A logical inquiry Gottlob Frege inquiry logical 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 technique roots tree 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 judgement judging science Having visual impressions is, of course, necessary for seeing things, but it is not sufficient. What must be added is not anything sensible. And it is precisely this that unlocks the outer world for us; for without this non-sensible something, each of us would remain locked up in his inner world. Gottlob Frege locked-up impression world 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 growing-up tree heaven It really is worth the trouble to invent a new symbol if we can thus remove not a few logical difficulties and ensure the rigour of the proofs. But many mathematicians seem to have so little feeling for logical purity and accuracy that they will use a word to mean three or four different things, sooner than make the frightful decision to invent a new word. Gottlob Frege decision science mean A scientist can hardly meet with anything more undesirable than to have the foundations give way just as the work is finished. I was put in this position by a letter from Mr. Bertrand Russell when the work was nearly through the press. Gottlob Frege foundation math giving 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 names knowledge thinking Your discovery of the contradiction caused me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build my arithmetic. Gottlob Frege serious loss discovery Arithmetic has began to totter. Gottlob Frege arithmetic
