"The mathematics are the friends to religion, inasmuch as they charm the passions, restrain the impetuosity of the imagination, and purge the mind from error and prejudice. Vice is error, confusion and false reasoning; and all truth is more or less opposite to it. Besides, mathematical truth may serve for a pleasant entertainment for those hours which young men are apt to throw away upon their vices; the delightfulness of them being such as to make solitude not only easy but desirable." (John Arbuthnot, "An Essay on the Usefulness of Mathematical Learning", 1701)
"[…] even if someone refuses to admit infinite and infinitesimal lines in a rigorous metaphysical sense and as real things, he can still use them with confidence as ideal concepts" (notions ideales) which shorten his reasoning, similar to what we call imaginary roots in the ordinary algebra, for example, v-2." (Gottfried W Leibniz, [letter to Varignon], 1702)
“It is easy to perceive that the prodigious variety which appears both in the works of nature and in the actions of men, and which constitutes the greatest part of the beauty of the universe, is owing to the multitude of different ways in which its several parts are mixed with, or placed near, each other. But, because the number of causes that concur in producing a given event, or effect, is oftentimes so immensely great, and the causes themselves are so different one from another, that it is extremely difficult to reckon up all the different ways in which they may be arranged, or combined together, it often happens that men, even of the best understandings and the greatest circumspection, ale guilty of that fault in reasoning which the writers on logic call the insufficient, or imperfect enumeration of parts, or cases: insomuch that I will venture to assert, that this is the chief, and almost the only, source of the vast number of erroneous opinions, and those too very often in matters of great importance, which we are apt to form on all the subjects we reflect upon, whether they relate to the knowledge of nature, or the merits and motives of human actions. It must therefore be acknowledged, that that art which affords a cure to this weakness, or defect, of our understandings, and teaches us so to enumerate all the possible ways in which a given number of things may be mixed and combined together, that we may be certain that we have not omitted any one arrangement of them that can lead to the object of our inquiry, deserves to be considered as most eminently useful and worthy of our highest esteem and attention. And this is the business of the art, or doctrine of combinations." (Jakob Bernoulli,"Ars Conjectandi" [“The Art of Conjecturing"], 1713)
"[...] this subject] has a relation to almost every species of useful knowledge that the mind of man can be employed upon." (Jacob Bernoulli,"Ars Conjectandi"[“The Art of Conjecturing"], 1713)
"There are two kinds of truths: those of reasoning and those of fact. The truths of reasoning are necessary and their opposite is impossible; the truths of fact are contingent and their opposites are possible." (Gottfried W Leibniz, "Monadology", 1714)
“Reasoning will never make a Man correct an ill Opinion, which by Reasoning he never acquired." ( Jonathan Swift,"A Letter to a Young Gentleman, Lately Enter’d Into Holy Orders by a Person of Quality", 1721)
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