We could present spatially an atomic fact which contradicted the laws of physics, but not one which contradicted the laws of geometry.

Mathematics is a logical method ... Mathematical propositions express no thoughts. In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics.

*Tractatus Logico Philosophicus,* (New York 1922).

Whereof one cannot speak, thereof one must be silent.

*Tractatus Logico Philosophicus,* (New York 1922).

There can never be surprises in logic.

Quoted in J R Newman, *The World of Mathematics* (New York 1956).

The riddle does not exist. If a question can be put at all, then it can also be answered.

*Tractatus Logico Philosophicus* (New York 1922).

Everything that can be said, can be said clearly.

All mathematics is tautology.

Quoted in D MacHale, *Comic Sections * (Dublin 1993)

The process of calculating brings about just this intuition. Calculation is not an experiment.

*Tractatus Logico Philosophicus*

A mathematical proof must be perspicuous.

*Remarks on the Foundations of Mathematics*

... mathematics is a *motley* of techniques and proofs.

*Remarks on the Foundations of Mathematics*

There is no religious denomination in which the misuse of metaphysical expressions has been responsible for so much sin as it has in mathematics.

*Culture and Value*

With my full philosophical rucksack I can only climb slowly up the mountain of mathematics.

*Culture and Value*

With my full philosophical rucksack I can only climb slowly up the mountain of mathematics.

(1929)

No one can think a thought for me in the way that no one can don my hat for me.

(1929)

Telling someone something he does not understand is pointless, even if you add that he will not be able to understand it.

(1930)

What Copernicus really achieved was not the discovery of a true theory but of a fertile new point of view.

(1931)

The mathematician Pascal admires the beauty of a theorem in number theory; it's as though he were admiring a beautiful natural phenomenon. Its marvellous, he says, what wonderful properties numbers have. It's as though he were admiring the regularities in a kind of crystal.

(1941)

Genius is what makes us forget the master's talent.

(1942)

The popular scientific books by our scientists aren't the outcome of hard work, but are written when they are resting on their laurels.

(1942)

The quarrel [between Newton and Leibniz] is simply the expression of evil weaknesses and fostered by vile people. Just what would Newton have lost if he had acknowledged Leibniz's originality? Absolutely nothing! He would have gained a lot. And yet how hard it is to acknowledge something of this sort: someone who tries it feels as though he were confessing his own incapacity. ... It's a question of envy of course. And anyone who experiences it ought to keep on telling himself: "It's a mistake! It's a mistake! -- "

(1947)

We could present spatially an atomic fact which contradicted the laws of physics, but not one which contradicted the laws of geometry.

*Tractatus Logico Philosophicus* (1922).

Death is not an event in life; we do not experience death.

Quoted in Des MacHale, *Wisdom* (London, 2002).

Even when all the possible scientific questions have been answered, the problems of life remain completely untouched.

Quoted in Des MacHale, *Wisdom* (London, 2002).

What is your aim in philosophy? To show the fly the way out of the fly-bottle.

Quoted in Des MacHale, *Wisdom* (London, 2002).

JOC/EFR February 2006

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