Deductive reasoning

“Robert [Grosseteste] became much interested in science and scientific method … He was conscious of the dual approach by means of induction and deduction (resolution and composition); i.e., from the empirical knowledge one proceeds to probable general principles, and from these as premises one them derives conclusions which constitute verifications or falsifications of the principles. This approach to science was not that far removed from Aristotle ...”

“I cannot see why it is necessary that every deduction from algebra should be bound to certain conventions incident to an earlier stage of mathematical learning, even supposing them to have been consistently used up to the point in question. I should not care if any one thought this treatise unalgebraical, but should only ask whether the premises were admissible and the conclusions logical.”

“The two operations of our understanding, intuition and deduction, on which alone we have said we must rely in the acquisition of knowledge.”

“Descartes was an eminent mathematician, and it would seem that the bent of his mind led him to overestimate the value of deductive reasoning from general principles, as much as Bacon had underestimated it.”

“I may as well say at once that I do not distinguish between inference and deduction. What is called induction appears to me to be either disguised deduction or a mere method of making plausible guesses.”

“The Greeks... discovered mathematics and the art of deductive reasoning. Geometry, in particular, is a Greek invention, without which modern science would have been impossible.”

“But in connection with mathematics the one-sidedness of the Greek genius appears: it reasoned deductively from what appeared self-evident, not inductively from what had been observed. Its amazing successes in the employment of this method misled not only the ancient world, but the greater part of the modern world also.”

“It has only been very slowly that scientific method, which seeks to reach principles inductively from observation of particular facts, has replaced the Hellenic belief in deduction from luminous axioms derived from the mind of the philosopher.”

“It seems that scientists are often attracted to beautiful theories in the way that insects are attracted to flowers — not by logical deduction, but by something like a sense of smell.”