In reflecting on the sort of progression Aristotle envisages, some commentators have charged him with an epistemological optimism bordering on the naïve; others contend that it is rather the charge of naïveté which is itself naïve, betraying as it does an unargued and untenable alignment of the necessary and the a priori.[7] Not all rigorous reasoning qualifies as scientific.
Gottlieb has got Hume's geniality down to a T. "Every philosopher likes to think he has reached his conclusions via rigorous reasoning," he says, with a collusive wink to his readers; in the 17th century, indeed, "falling in love with geometry seems almost to have been an occupational hazard".
Anton chose the following quote: "Rigorous reasoning is crucial in mathematics, and insight plays an important secondary role these days.
It's not as if habits of deep reflection, thorough research and rigorous reasoning ever came naturally to people.
We are only told it involves rigorous reasoning about some kind of formal objects.
What is needed is not dogmatism, posturing and self-righteous declarations of outrage (on either side of the debate), but careful, rigorous reasoning and scrutiny.
Through guided group interactions and feedback, and, more important, through a rigorous process of deductive reasoning and self-honesty, these deeply embedded beliefs begin to give up the ghost, so to speak, and reveal themselves.
Our purpose was (1) to provide a rigorous and reliable diagnosis reasoning process for guiding an early and targeted management susceptible to modify the prognosis and (2) to identify factors associated with ICU- and 90-day mortality.
From the outset, Bernoulli wished for his work to demonstrate that combinatorics and probability theory would have numerous real-world applications in all facets of society in the line of Graunt's and de Witt's work— and would serve as a rigorous method of logical reasoning under insufficient evidence, as used in courtrooms and in moral judgements.
For a more rigorous mathematical reasoning of this threshold choice, see [ 20].
