Source: Science and Hypothesis (1901), Ch. I: On the Nature of Mathematical Reasoning (1905) Tr. https://books.google.com/books?id=5nQSAAAAYAAJ George Bruce Halstead
Context: The very possibility of the science of mathematics seems an insoluble contradiction. If this science is deductive only in appearance, whence does it derive that perfect rigor no one dreams of doubting? If, on the contrary, all the propositions it enunciates can be deduced one from another by the rules of formal logic, why is not mathematics reduced to an immense tautology? The syllogism can teach us nothing essentially new, and, if everything is to spring from the principle of identity, everything should be capable of being reduced to it. Shall we then admit that the enunciations of all those theorems which fill so many volumes are nothing but devious ways of saying A is A!... Does the mathematical method proceed from particular to the general, and, if so, how can it be called deductive?... If we refuse to admit these consequences, it must be conceded that mathematical reasoning has of itself a sort of creative virtue and consequently differs from a syllogism.<!--pp.5-6
“I see not the shadow of a reason to conclude that their [the sexes'] virtues should differ in respect to their nature. In fact, how can they, if virtue has only one eternal standard? I must therefore, if I reason consequentially, as strenuously maintain that they must have the same simple direction as that there is a God.”
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A Vindication of the Rights of Woman (1792)
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Mary Wollstonecraft 44
British writer and philosopher 1759–1797Related quotes
1840s, Essays: First Series (1841), History
The Titmouse http://www.readbookonline.net/readOnLine/1176/, st. 5
1860s, May-Day and Other Pieces (1867)
“Reason, in fact, is a thing of God, inasmuch as there is nothing which God the Maker of all has not provided, disposed, ordained by reason — nothing which He has not willed should be handled and understood by reason. All, therefore, who are ignorant of God, must necessarily be ignorant also of a thing which is His, because no treasure-house at all is accessible to strangers. And thus, voyaging all the universal course of life without the rudder of reason, they know not how to shun the hurricane which is impending over the world.”
Quippe res dei ratio quia deus omnium conditor nihil non ratione providit disposuit ordinavit, nihil [enim] non ratione tractari intellegique voluit. [3] Igitur ignorantes quique deum rem quoque eius ignorent necesse est quia nullius omnino thesaurus extraneis patet. Itaque universam vitae conversationem sine gubernaculo rationis transfretantes inminentem saeculo procellam evitare non norunt.
De Paenitentia (On Repentance), 1.2-3
Source: 1840s, The Sickness unto Death (July 30, 1849), pp. 114 - 115
“Virtue is reason which has become energy.”
Tugend ist zur Energie gewordne Vernunft.
“Selected Ideas (1799-1800)”, Dialogue on Poetry and Literary Aphorisms, Ernst Behler and Roman Struc, trans. (Pennsylvania University Press:1968) #23