The mental operation by which one achieves new concepts and which one denotes generally by the inadequate name of induction is not a simple but rather a very complicated process. Above all, it is not a logical process although such processes can be inserted as intermediary and auxiliary links. The principle effort that leads to the discovery of new knowledge is due to abstraction and imagination.
Ernst MachRelated topics
above abstraction auxiliary due effort induction intermediary knowledge name operation simple linksRelated quotes
You wish, or rather, have decided, to remove a splinter from someone? Very well, but do not go after it with a stick instead of a lancet for you will only drive it deeper. Rough speech and harsh gestures are the stick, while even-tempered instruction and patient reprimand are the lancet. 'Reprove, rebuke, exhort,' says the Apostle (II Tim. 4:2), not 'batter'.
John Climacus
What is easier to remember, a collection of facts glued together, or a story, something that offers a series of logical links? Causality is easier to commit to memory. ...What is induction exactly? ...It is very handy, as the general takes much less room in onel's memory than a collection of particulars. The effect of such compression is the reduction in the degree of detected randomness.
Nassim Nicholas Taleb
The experience or the vision is the artist's counterpart to the scientific discovery of a principle or law. What the scientist does when he discovers a new law is to give a new ordering to observed facts. The artist is engaged in a similar task. He gives new meaning to our experience and organizes it in a different way due to his perception of subtler qualities in reality.
Sarvepalli Radhakrishnan
Pure mathematics is, in its way, the poetry of logical ideas. One seeks the most general ideas of operation which will bring together in simple, logical and unified form the largest possible circle of formal relationships. In this effort toward logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.
Albert Einstein
When speaking of a "body of knowledge” or of "the results of research,” e. g., we tacitly assign the same cognitive status to inherited knowledge and to independently acquired knowledge. To counteract this tendency a special effort is required to transform inherited knowledge into genuine knowledge by revitalizing its original discovery, and to discriminate between the genuine and the spurious elements of what claims to be inherited knowledge.
Leo Strauss