On Proofs (1800 - 1849)

"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 half proof = 0, and it is demanded for proof that every doubt becomes impossible." (Carl Friedrich Gauss)

"Mathematical proofs, like diamonds, are hard and clear, and will be touched with nothing but strict reasoning." (John Locke, 1824)

"Mathematics in gross, it is plain, are a grievance in natural philosophy, and with reason. […] Mathematical proofs are out of the reach of topical arguments, and are not to be attacked by the equivocal use of words or declamation, that make so great a part of other discourses; nay, even of controversies." (John Locke, 1824)

"Logic does not pretend to teach the surgeon what are the symptoms which indicate a violent death. This he must learn from his own experience and observation, or from that of others, his predecessors in his peculiar science. But logic sits in judgment on the sufficiency of that observation and experience to justify his rules, and on the sufficiency of his rules to justify his conduct. It does not give him proofs, but teaches him what makes them proofs, and how he is to judge of them." (John Stuart Mill, "A System of Logic, Ratiocinative and Inductive: Being a Connected View of the Principles of Evidence, and the Methods of Scientific Investigation", 1843)