Quotes About Logic

From a drop of water a logician could infer the possibility of an Atlantic or a Niagara without having seen or heard of one or the other.

When you have eliminated all which is impossible, then whatever remains, however improbable, must be the truth.

Rationalism is the enemy of art, though necessary as a basis for architecture.

saw logic as the buttress of theology and his faith, not a substitute for them. If this earns him impatience from later skeptics and freethinkers, it does fit him into his own time and place. Peter Abelard's Aristotle points down the road to Thomas Aquinas, not the Enlightenment.

All the same, Abelard opened the mind of the Middle Ages in new and startling ways. He gave the name of Aristotle and Aristotle's logic an edgy glamour it never entirely lost. Aristotle had said: All men desire to know. Abelard now added: All men need to question and doubt in order to know. These were important signposts for the future. For now, medieval civilization was about to swing down another path, one emblazoned by the Neoplatonist imagination.

Dialectic teaches us that contradiction is the essence of the false, just as consistency with first principles is the essence of the true.

Why use two (or more) when one (or fewer) will do, is the principle that William of Ockham introduced into the medieval thought process. It grew out of his refinement of Aristotle's logic and set off a revolution not only in philosophy, but in politics and religion. Before he died, Ockham's razor would undercut the foundations of the medieval Church.

Ockham didn't use the term fiction to suggest that what we say about the world isn't true; just the opposite. Science deals with real life; and logic is the language of science. But we shouldn't mistake the logical gymnastics going on inside our heads for the reality going on outside. Science is about real things; logic, surprisingly perhaps, is not.

Any appeal to reason is hopeless, since "reason is, and ought to be, the slave of the passions": and the passions are the root of the problem.

The universe, Galileo wrote, "is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is humanly impossible to understand a single world of it." Without mathematics, he concluded, "one wanders about in a dark labyrinth"—or what Plato might have called a cave.

The classic deductive inference (actually taken from Aristotle's Categories) is "All men are mortal; Socrates is a man; therefore Socrates is mortal." Usually a good deductive inference goes from greater generalities to lesser ones:

By contrast, inductive logic usually (though not always) goes from the lesser to the greater. "I have five friends who have white beards; all five are over fifty years of age; therefore all men with white beards are over fifty years of age.

Aristotle called these true deductive inferences syllogisms. All syllogisms follow the same basic structure as the "Socrates is mortal" example. Each contains two premises or assumptions (called major and minor) and the inescapable conclusion we have to draw from them.

Aristotle showed (or seemed to show) that by linking one valid syllogism to another regarding a single subject, such as biology or ethics or even the nature of God, one could build a conceptual chain of reasoning that would inevitably lead, link by link, from one set of necessary truths to another, all the way to the highest truths of all.

In effect, Aristotle's logic offered the possibility of creating a universally true science out of anything—or of deconstructing claims of being a science.

Not everything that makes deductive sense may be true.b But if it doesn't fit into a syllogism, Aristotle concluded, then don't bother asking if it's true or not.

Thanks to Boethius, Aristotle's logic was now available to apply the same test to Christianity's weightiest assertions about God, heaven and hell, and the Church's most cherished views about human beings and nature.

was Gerbert who made Boethius "the schoolmaster of medieval Europe" and made Aristotle's logic the centerpiece of an education based on the seven liberal arts.15 The idea of the "liberal arts" (so called because it was the education fit for liberi, or free men, as opposed to slaves) was a late Roman invention.c16

Gerbert's first loves were the subjects of the trivium, especially rhetoric and logic. His insistence that students learn the rules of logic before embarking on anything else made Aristotle the founder of the medieval university curriculum.18

To fall for the notion of a 'double truth' and argue there was one set of truths for reason and another for faith and never the two shall meet made nonsense of the idea of truth itself.

Anyone who failed to apply the test of reasoned logic to the assertions of religious dogma was denying his own nature, Berengar said, "for it is by his reason that man resembles God.

All of Aristotle's works point out, however, that the most vital knowledge we have comes a posteriori, meaning "after the fact" or from experience, as we link up a given visible effect to its preceding cause.

Aristotle insisted, the source of that justice is always the same: observation of the underlying order of nature.

Aristotle is the true father of science and scientific method, by which we still mean a methodical process of observation, classification, and discovery.