Rigor Quotes - page 2
A new fundamental science, pure phenomenology, has developed within philosophy: This is a science of a thoroughly new type and endless scope. It is inferior in methodological rigor to none of the modern sciences. All philosophical disciplines are rooted in pure phenomenology, through whose development, and through it alone, they obtain their proper force.
Edmund Husserl
The function just found cannot, it is true, express rigorously the probabilities of the errors: for since the possible errors are in all cases confined within certain limits, the probability of errors exceeding those limits ought always to be zero, while our formula always gives some value. However, this defect, which every analytical function must, from its nature, labor under, is of no importance in practice, because the value of our function decreases so rapidly... that it can safely be considered as vanishing. Besides, the nature of the subject never admits of assigning with absolute rigor the limits of error.
Carl Friedrich Gauss
It is known that Whistler when asked how long it took him to paint one of his "nocturnes" answered: "All of my life." With the same rigor he could have said that all of the centuries that preceded the moment when he painted were necessary. From that correct application of the law of causality it follows that the slightest event presupposes the inconceivable universe and, conversely, that the universe needs even the slightest of events.
Jorge Luis Borges
Mathematics is so useful because physical scientists and engineers have the good sense to largely ignore the "religious" fanaticism of professional mathematicians, and their insistence on so-called rigor, that in many cases is misplaced and hypocritical, since it is based on "axioms" that are completely fictional, i.e. those that involve the so-called infinity.
Doron Zeilberger
Conscience is the most dangerous thing you possess. If you wake it up, it may destroy you. To live a life of total moral rigor is not necessarily the way to go. It's the path for very few people. Most people need to come up with some kind of middle ground that satisfies their practical, moral, and philosophical esthetic needs.
John Patrick Shanley
Ascetic rigor? This doesn't mean something like ‘renounce' or even a ‘lack' of something. No, it means, in philosophical manner (and especially in the historic Greek sense of ‘Askesis'), a special kind of internal yearning, a special power wherein, despite all depressions, defeats, and failures you develop a new power to ‘keep' to something, to create something. It's something like an obsession. Bach, Mozart, Schubert, they all (and their oeuvre) are filled from this phenomenon, and it's this spirit which keeps this music so vivid and alive – and fashioned for all times and generations.
Burkard Schliessmann
Yet in a relatively short creative life of twenty years or so, Chopin redrew the boundaries of Romantic music, and his self-imposed restriction to the 88 keys of the piano keyboard sublimated nothing less than the aesthetic essence of piano music. It was his total identification with the instrument which, in its radical regeneration of the lyric and the dramatic, fantasy and passion and their unique fusion, shaped a tonal language which united an aristocratic sense of style and formal Classical training and intuition with an ascetic rigor. Chopin's precisely marshaled trains of thought permitted no experiments, and so he did not ‘wander about' within his stylistic points of reference as Scriabin was to do. Chopin's works may seem light and improvisatory, but they are planned in meticulous details, exactly and well calculated.
Burkard Schliessmann
The idea of a liberal elite is not intellectually robust. It's never been enunciated with anything approaching scholarly rigor, it has been refuted countless times, and it falls apart under any sort of systematic scrutiny.Yet the idea persists. It did not die with Richard Nixon or peter out with the busing controversy or depart the national scene with the wily Bill Clinton. Indeed, it has greater currency on the street today than do twenty years' worth of blue-ribbon studies and a lifetime of responsible sociology.
Thomas Frank