"It may be observed of mathematicians that they only meddle with such things as are certain, passing by those that are doubtful and unknown. They profess not to know all things, neither do they affect to speak of all things. What they know to be true, and can make good by invincible arguments, that they publish and insert among their theorems. Of other things they are silent and pass no judgment at all, choosing rather to acknowledge their ignorance, than affirm anything rashly." (Isaac Barrow, "Mathematical Lecture", 1734)
"Though there be no such thing as Chance in the world, our ignorance of the real cause of any event has the same influence on the understanding, and begets a like species of belief or opinion." (David Hume, "An Enquiry Concerning Human Understanding", 1748)
"[…] chance, that is, an infinite number of events, with respect to which our ignorance will not permit us to perceive their causes, and the chain that connects them together. Now, this chance has a greater share in our education than is imagined. It is this that places certain objects before us and, in consequence of this, occasions more happy ideas, and sometimes leads us to the greatest discoveries […]" (Claude A Helvetius, "On Mind", 1751)
"I find a frank acknowledgment of one’s ignorance is not only the easiest way to get rid of a difficulty, but the likeliest way to obtain information, and therefore I practice it: I think it an honest policy. Those who affect to be thought to know everything, and so undertake to explain everything, often remain long ignorant of many things that others could and would instruct them in, if they appeared less conceited." (Benjamin Franklin, [letter to John Lining", 1755)
"By the word simplicity, is not always meant folly or ignorance; but often, pure and upright Nature, free from artifice, craft or deceitful ornament." (Benjamin Franklin, Poor Richard's Almanack, 1733-1758)
"But ignorance of the different causes involved in the production of events, as well as their complexity, taken together with the imperfection of analysis, prevents our reaching the same certainty about the vast majority of phenomena. Thus there are things that are uncertain for us, things more or less probable, and we seek to compensate for the impossibility of knowing them by determining their different degrees of likelihood. So it was that we owe to the weakness of the human mind one of the most delicate and ingenious of mathematical theories, the science of chance or probability." (Pierre-Simon Laplace, "Recherches, 1º, sur l'Intégration des Équations Différentielles aux Différences Finies, et sur leur Usage dans la Théorie des Hasards", 1773)
"Ignorance is preferable to error; and he is less remote from the truth who believes nothing, than he who believes what is wrong." (Thomas Jefferson, "Notes on the State of Virginia", 1781)
"The word ‘chance’ then expresses only our ignorance of the causes of the phenomena that we observe to occur and to succeed one another in no apparent order. Probability is relative in part to this ignorance, and in part to our knowledge." (Pierre-Simon Laplace, "Mémoire sur les Approximations des Formules qui sont Fonctions de Très Grands Nombres", 1783)
"It is of the utmost importance to your real advancement in science, to avoid every source of error, or whatever may lead you to form an erroneous judgment. Now a true judgment can only be obtained by a profound view of nature, and a strict examination into the mutual connections and dependencies of things; you will hence see the necessity of strict and accurate examination, of time to acquire the requisite knowledge, and of attention to comprehend it: for among the various sources of error, we may reckon the precipitation of our judgment and a presumptuous ignorance as the principal." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 1, 1794)
"The natural propensity of the human mind to know the cause of every effect often leads men into errors, and makes them satisfied with a word which does not remove their ignorance." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 1, 1794)
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