Indubitable Quotes
...nor have I found occasion to depart from the plan... the rejection of the whole doctrine of series in the establishment of the fundamental parts both of the Differential and Integral Calculus. The method of Lagrange... had taken deep root in elementary works; it was the sacrifice of the clear and indubitable principle of limits to a phantom, the idea that an algebra without limits was purer than one in which that notion was introduced. But, independently of the idea of limits being absolutely necessary even to the proper conception of a convergent series, it must have been obvious enough to Lagrange himself, that all application of the science to concrete magnitude, even in his own system, required the theory of limits.
Augustus De Morgan
I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. But I discovered that many mathematical demonstrations, which my teachers expected me to accept, were full of fallacies, and that, if certainty were indeed discoverable in mathematics, it would be in a new field of mathematics, with more solid foundations than those that had hitherto been thought secure. But as the work proceeded, I was continually reminded of the fable about the elephant and the tortoise. having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was no more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.
Bertrand Russell
Government is, or ought to be instituted for the common benefit, protection, and security of the people, nation, or community; of all the various modes and forms of government, that is best which is capable of producing the greatest degree of happiness and safety, and is most effectually secured against the danger of maladministration and [...] when any government shall be found inadequate or contrary to these purposes, a majority of the community hath an indubitable, inalienable, and indefeasible right to reform, alter, or abolish it, in such manner as shall be judged most conducive to the public weal.
George Mason
Aesthetic theories arose one hundred fifty years ago among the wealthy classes of the Christian European world. ...And notwithstanding its obvious insolidity, nobody else's theory so pleased the cultured crowd or was accepted so readily and with such absence of criticism. It so suited the people of the upper classes that to this day, notwithstanding its entirely fantastic character and the arbitrary nature of its assertions, it is repeated by the educated and uneducated as though it were something indubitable and self-evident.
Leo Tolstoy
To a lesser degree, a secret ressentiment underlies every way of thinking which attributes creative power to mere negation and criticism. Thus modern philosophy is deeply penetrated by a whole type of thinking which is nourished by ressentiment. I am referring to the view that the "true” and the "given” is not that which is self-evident, but rather that which is "indubitable” or "incontestable,” which can be maintained against doubt and criticism.
Max Scheler
There are, in fact, as I began to say above, not a few principles which are the special property of mathematics, such principles as are discovered by the common light of nature, require no demonstration, and which concern quantities primarily; then they are applied to other things, so far as the latter have something in common with quantities. Now there are more of these principles in mathematics than in the other theoretical sciences because of that very characteristic of the human understanding which seems to be such from the law of creation, that nothing can be known completely except quantities or by quantities. And so it happens that the conclusions of mathematics are most certain and indubitable.
Johannes Kepler
Gärtner by the results of these transformation experiments, was led to oppose the opinion of those naturalists who dispute the stability of plant species and believe in a continuous evolution of vegetation. He perceives in the complete transformation of one species into another an indubitable proof that species are fixed within limits beyond which they cannot change.
Although this opinion cannot be unconditionally accepted, we find on the other hand in Gartner's experiments a noteworthy confirmation of that supposition regarding variability of cultivated plants which has already been expressed.
Gregor Mendel
