The deep paradox uncovered by AI research: the only way to deal efficiently with very complex problems is to move away from pure logic.... Most of the time, reaching the right decision requires little reasoning.... Expert systems are, thus, not about reasoning: they are about knowing.... Reasoning takes time, so we try to do it as seldom as possible. Instead we store the results of our reasoning for later reference.
I would call the attention of the reader to the difference between "reason" and "reasoning." Reason is a light, reasoning a process. Reason is a faculty, reasoning an exercise of that faculty. Reasoning proceeds from one truth to another by means of argumentation. This generally involves the whole mind in labor and complexity. But reason does not exist merely in order to engage in reasoning. The process is a means to an end. The true fulfillment of reason as a faculty is found when it can embrace the truth simply and without labor in the light of single intuition.
I begin the chapter and book on very elementary reasoning and a simple description: this description of relationships developed naturally and socially; this reasoning that such relationships have long-existed and are very important-even eternal to those called 'special people'. My own freedom to choose this elementary reasoning has something to do with firsthand experience as one whose role has been reduced to the realm of illegal... with all the punishment. Such reasoning has consumed me in moments and has prevailed for as long as my role has been at risk.
H. Kirk Rainer
... if you insist that the inference is made by a chain of reasoning, I desire you to produce that reasoning. The connection between the two is not intuitive. There is required a medium, which may enable the mind to draw such an inference, if indeed it be drawn by reasoning and argument. What that medium is, I must confess, passes my comprehension; and it is incumbent on those to produce it, who assert that it really exists, and is the origin of all our conclusions concerning matter of fact.
It is difficult to distinguish deduction from what in other circumstances is called problem-solving. And concept learning, inference, and reasoning by analogy are all instances of inductive reasoning. (Detectives typically induce, rather than deduce.) None of these things can be done separately from each other, or from anything else. They are pseudo-categories.
Chelan had acted as imprudently for Julien as he had for himself. He had given him the habit of reasoning correctly, and of not being put off by empty words, but he had neglected to tell him that this habit was a crime in the person of no importance, since every piece of logical reasoning is offensive.
Religion is a subject which, if the believers used the same "reasoning" to address problems at work as they use to defend their beliefs, they'd soon find themselves unemployed. And if they found their child applying that kind of "reasoning" on a homework assignment they'd wonder what the hell was the wrong with their child.
The great mathematician fully, almost ruthlessly, exploits the domain of permissible reasoning and skirts the impermissible. That his recklessness does not lead him into a morass of contradictions is a miracle in itself: certainly it is hard to believe that our reasoning power was brought, by Darwin's process of natural selection, to the perfection which it seems to possess.
The inability of Darwinian psychology to account for human reasoning is devastating to its pretensions to be a science. The prestige of science depends on the application of highly advanced practical and theoretical reason. A 'science' that is incompatible with such reasoning is therefore at odds with the very essence of scientific activity.
Since reasoning , or inference, the principal subject of logic, is an operation which usually takes place by means of words , and in complicated cases can take place in no other way: those who have not a thorough insight into both the signification and purpose of words, will be under chances, amounting almost to certainty, of reasoning or inferring incorrectly.
John Stuart Mill
When all actions are used for feedback, the consequence of making mistakes will be a corrective and appropriate response, because everything everybody does matters. ... The more selective you are in the feedback you accept, the more insane your reasoning will become as you will necessarily reject corrective feedback that would have led to better reasoning.
A woman anticipates danger by instinct, rather than inductive reasoning. Due to this, when faced with danger due to passionate feelings related to their basic needs, women are impelled by reasoning, conditioned by instincts acquired from family traditions and the conventions of her social stratum, much more than men are.
The Reader may here observe the Force of Numbers, which can be successfully applied, even to those things, which one would imagine are subject to no Rules. There are very few things which we know, which are not capable of being reduc'd to a Mathematical Reasoning, and when they cannot, it's a sign our Knowledge of them is very small and confus'd; and where a mathematical reasoning can be had, it's as great folly to make use of any other, as to grope for a thing in the dark when you have a Candle standing by you.
There are two modes of acquiring knowledge, namely by reasoning and experience. Reasoning draws a conclusion and makes us grant the conclusion, but does not make the conclusion certain, nor does it remove doubt so that the mind may rest on the intuition of truth, unless the mind discovers it by the path of experience.
Facts are certainly the solid and true foundation of all sectors of nature study ... Reasoning must never find itself contradicting definite facts; but reasoning must allow us to distinguish, among facts that have been reported, those that we can fully believe, those that are questionable, and those that are false. It will not allow us to lend faith to those that are directly contrary to others whose certainty is known to us; it will not allow us to accept as true those that fly in the face of unquestionable principles.
Rene Antoine Ferchault de Reaumur
For most problems found in mathematics textbooks, mathematical reasoning is quite useful. But how often do people find textbook problems in real life? At work or in daily life, factors other than strict reasoning are often more important. Sometimes intuition and instinct provide better guides; sometimes computer simulations are more convenient or more reliable; sometimes rules of thumb or back-of-the-envelope estimates are all that is needed.
There are also two kinds of truths, those of reasoning and those of fact. Truths of reasoning are necessary and their opposite is impossible: truths of fact are contingent and their opposite is possible. When a truth is necessary, reason can be found by analysis, resolving it into more simple ideas and truths, until we come to those which are primary.
Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity. The activity of the intuition consists in making spontaneous judgements which are not the result of conscious trains of reasoning... The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings.
Reasoning is compared to understanding as movement is to rest, or acquisition to possession.... Since movement always proceeds from something immovable, and ends in something at rest, hence it is that human reasoning, in the order of inquiry and discovery, proceeds from certain things absolutely understood--namely, the first principles; and, again, in the order of judgment, returns by analysis to first principles, in the light of which it examines what it has found. Now it is clear that rest and movement are not to be referred to different powers, but to one and the same.
Mathematics is a form of poetry which transcends poetry in that it proclaims a truth; a form of reasoning which transcends reasoning in that it wants to bring about the truth it proclaims; a form of action, of ritual behavior, which does not find fulfilment in the act but must proclaim and elaborate a poetic form of truth.
It is not at all coincidental that Darwinian psychology has the same difficulty explaining the unity and integration of human reasoning as Darwinian biology has explaining the unity and integration of irreducibly complex functions. Practical and theoretical reasoning is often irreducibly complex. A given argument has several well-matched, interacting reasons, and the removal of any one of them makes the argument break down.
Any man who stands for progress has to criticize, disbelieve and challenge every item of the old faith. Item by item he has to reason out every nook and corner of the prevailing faith. If after considerable reasoning one is led to believe in any theory or philosophy, his faith is welcomed. His reasoning can be mistaken, wrong, misled and sometimes fallacious. But he is liable to correction because reason is the guiding star of his life. But mere faith and blind faith is dangerous: it dulls the brain, and makes a man reactionary.
Eternity. —Thy name Or glad, or fearful, we pronounce, as thoughts Wandering in darkness shape thee. Thou strange being, Which art and must be, yet which contradict'st All sense, all reasoning, —thou, who never wast Less than thyself, and who still art thyself Entire, though the deep draught which Time has taken Equals thy present store —No line can reach To thy unfathomed depths. The reasoning sage Who can dissect a sunbeam, count the stars, And measure distant worlds, is here a child, And, humbled, drops his calculating pen.
Anna Letitia Barbauld
Our moral reasoning is plagued by two illusions. The first illusion can be called the wag-the-dog illusion: We believe that our own moral judgment (the dog) is driven by our own moral reasoning (the tail). The second illusion can be called the wag-theother-dog's-tail illusion: In a moral argument, we expect the successful rebuttal of an opponent's arguments to change the opponent's mind. Such a belief is like thinking that forcing a dog's tail to wag by moving it with your hand will make the dog happy.
our moral reasoning is plagued by two illusions. The first illusion can be called the wag-the-dog illusion: We believe that our own moral judgment (the dog) is driven by our own moral reasoning (the tail). The second illusion can be called the wag-theother-dog's-tail illusion: In a moral argument, we expect the successful rebuttal of an opponent's arguments to change the opponent's mind. Such a belief is like thinking that forcing a dog's tail to wag by moving it with your hand will make the dog happy.