John Locke - Collected Quotes

"Abstraction involves perceiving something, relating it to other things, grasping some common trait of those things, and conceiv­ing of the common trait as to it can be related not only to those things but also to other similar things."  (John Locke, "An Essay Concerning Human Understanding", 1689)

"And thus many are ignorant of mathematical truths, not out of any imperfection of their faculties, or uncertainty in the things themselves, but for want of application in acquiring, examining, and by due ways comparing those ideas." (John Locke, "An Essay Concerning Human Understanding", 1689)

“Probability is likeliness to be true, the very notation of the word signifying such a proposition, for which there be arguments or proofs to make it pass, or be received for true. […] The grounds of probability are two: conformity with our own experience, or the testimony of others' experience. Probability then, being to supply the defect of our knowledge and to guide us where that fails, is always conversant about propositions whereof we have no certainty, but only some inducements to receive them for true.”  (John Locke, “An Essay Concerning Human Understanding”, 1689)

“Probability is the appearance of agreement upon fallible proofs. As demonstration is the showing the agreement or disagreement of two ideas by the intervention of one or more proofs, which have a constant, immutable, and visible connexion one with another; so probability is nothing but the appearance of such an agreement or disagreement by the intervention of proofs, whose connexion is not constant and immutable, or at least is not perceived to be so, but is, or appears for the most part to be so, and is enough to induce the mind to judge the proposition to be true or false, rather than the contrary.” (John Locke, “An Essay Concerning Human Understanding”, 1689)

“Sometimes the mind perceives the agreement or disagreement of two ideas immediately by themselves, without the intervention of any other; and this, I think, we may call intuitive knowledge. [...] Intuitive knowledge needs no probation, nor can have any, this being the highest of all human certainty.” (John Locke, “An Essay Concerning Human Understanding”, 1689)

“They that are ignorant of Algebra cannot imagine the wonders in this kind are to be done by it: and what further improvements and helps advantageous to other parts of knowledge the sagacious mind of man may yet find out, it is not easy to determine. This at least I believe, that the ideas of quantity are not those alone that are capable of demonstration and knowledge; and that other, and perhaps more useful, parts of contemplation, would afford us certainty, if vices, passions, and domineering interest did not oppose and menace such endeavors.” (John Locke, “An Essay Concerning Human Understanding”, 1689)

“Knowledge being to be had only of visible and certain truth, error is not a fault of our knowledge, but a mistake of our judgment, giving assent to that which is not true.” (John Locke, “An Essay Concerning Human Understanding”, 1690)

“Mathematics in gross, it is plain, are a grievance in natural philosophy, and with reason: for mathematical proofs, like diamonds, are hard as well as clear, and will be touched with nothing but strict reasoning. Mathematical proofs are out of the reach of topical arguments; and are not to be attacked by the equivocal use of words or declaration, that make so great a part of other discourses, - nay, even of controversies.” (John Locke, “An Essay Concerning Human Understanding”, 1690)

“[…] for the saving the long progression of the thoughts to remote and first principles in every case, the mind should provide itself several stages; that is to say, intermediate principles, which it might have recourse to in the examining those positions that come in its way. These, though they are not self-evident principles, yet, if they have been made out from them by a wary and unquestionable deduction, may be depended on as certain and infallible truths, and serve as unquestionable truths to prove other points depending upon them, by a nearer and shorter view than remote and general maxims. […] And thus mathematicians do, who do not in every new problem run it back to the first axioms through all the whole train of intermediate propositions. Certain theorems that they have settled to themselves upon sure demonstration, serve to resolve to them multitudes of propositions which depend on them, and are as firmly made out from thence as if the mind went afresh over every link of the whole chain that tie them to first self-evident principles.” John Locke, “The Conduct of the Understanding”, 1706)

“Algebra is a way to bring us to certainty in mathematics; but must it be presently condemned as an ill way, because there are some questions in mathematics, which a man cannot come to certainty in by the way of Algebra?” (John Locke)

“But of all other ideas, it is number, which I think furnishes us with the clearest and most distinct idea of infinity we are capable of.” (John Locke)

“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)

“The business of education is not to make the young perfect in any one of the sciences, but so to open their minds as may best make them capable of any, when they shall apply themselves to it.” (John Locke)