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We must never assume that which is incapable of proof.
--
The Physiology of Common Life (1859-60; repr. New York: D. Appleton, 1867) vol. 2, p. 349

 

George Henry Lewes

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The most difficult thing is to know what we do know, and what we do not know.
Therefore, desiring to know anything, we shall before all else determine WHAT we accept as given, and WHAT as demanding definition and proof; that is, determine WHAT we know already, and WHAT we wish to know.
In relation to the knowledge of the world and of ourselves, the conditions would be ideal could we venture to accept nothing as given, and count all as demanding definition and proof. In other words, it would be best to assume that we know nothing, and make this our point of departure.
But unfortunately such conditions are impossible to create. Knowledge must start from some foundation, something must be recognized as known; otherwise we shall be obliged always to define one unknown by means of another.

 

P. D. Ouspensky

 

Like the majority of men who are born to a given belief they demand the most rigorous proof of any adverse belief but assume that their own needs none.

 

Herbert Spencer

 

I shall, without further discussion of the other theories, attempt to contribute something towards the understanding and appreciation of the Utilitarian or Happiness theory, and towards such proof as it is susceptible of. It is evident that this cannot be proof in the ordinary and popular meaning of the term. Questions of ultimate ends are not amenable to direct proof. Whatever can be proved to be good, must be so by being shown to be a means to something admitted to be good without proof.

 

John Stuart Mill

 

I am obliged to interpolate some remarks on a very difficult subject: proof and its importance in mathematics. All physicists, and a good many quite respectable mathematicians, are contemptuous about proof. I have heard Professor Eddington, for example, maintain that proof, as pure mathematicians understand it, is really quite uninteresting and unimportant, and that no one who is really certain that he has found something good should waste his time looking for proof.

 

G. H. Hardy

 

I mean the word proof not in the sense of the lawyers, who set two half proofs equal to a whole one, but in the sense of a mathematician, where ? proof = 0, and it is demanded for proof that every doubt becomes impossible.

 

Carl Friedrich Gauss