Deductive Reasoning Quotes

What a lovely thing a rose is!" He walked past the couch to the open window and held up the drooping stalk of a moss-rose, looking down at the dainty blend of crimson and green. It was a new phase of his character to me, for I had never before seen him show any keen interest in natural objects. "There is nothing in which deduction is so necessary as religion," said he, leaning with his back against the shutters. "It can be built up as an exact science by the reasoner. Our highest assurance of the goodness of Providence seems to me to rest in the flowers. All other things, our powers, our desires, our food, are all really necessary for our existence in the first instance. But this rose is an extra. Its smell and its color are an embellishment of life, not a condition of it. It is only goodness which gives extras, and so I say again that we have much to hope from the flowers.

There is nothing in which deduction is so necessary as in religion," said he, leaning with his back against the shutters. "It can be built up as an exact science by the reasoner. Our highest assurance of the goodness of Providence seems to me to rest in the flowers. All other things, our powers, our desires, our food, are all really necessary for our existence in the first instance. But this rose is an extra. Its smell and its colour are an embellishment of life, not a condition of it. It is only goodness which gives extras, and so I say again that we have much to hope from the flowers.

Where did I get it from? Was it by reason that I attained to the knowledge that I must love my neighbour and not throttle him? They told me so when I was a child, and I gladly believed it, because they told me what was already in my soul. But who discovered it? Not reason! Reason has discovered the struggle for existence and the law that I must throttle all those who hinder the satisfaction of my desires. That is the deduction reason makes. But the law of loving others could not be discovered by reason, because it is unreasonable.

What do you want to swear to?" she asks. "Science? Deductive reasoning? The ghost of Friedrich Nietzsche?

You often show yourself without any faculty of deductive reasoning.

The sensible man,' Crow had said (to Sherlock Holmes), 'don't look to confirm what he already knows -- he looks to deny it. Finding evidence that backs up your theories ain't useful, but finding evidence that your theories are wrong is priceless. Never try to prove yourself right -- always try to prove yourself wrong instead.

When I am high I couldn’t worry about money if I tried. So I don’t. The money will come from somewhere; I am entitled; God will provide. Credit cards are disastrous, personal checks worse. Unfortunately, for manics anyway, mania is a natural extension of the economy. What with credit cards and bank accounts there is little beyond reach. So I bought twelve snakebite kits, with a sense of urgency and importance. I bought precious stones, elegant and unnecessary furniture, three watches within an hour of one another (in the Rolex rather than Timex class: champagne tastes bubble to the surface, are the surface, in mania), and totally inappropriate sirenlike clothes. During one spree in London I spent several hundred pounds on books having titles or covers that somehow caught my fancy: books on the natural history of the mole, twenty sundry Penguin books because I thought it could be nice if the penguins could form a colony. Once I think I shoplifted a blouse because I could not wait a minute longer for the woman-with-molasses feet in front of me in line. Or maybe I just thought about shoplifting, I don’t remember, I was totally confused. I imagine I must have spent far more than thirty thousand dollars during my two major manic episodes, and God only knows how much more during my frequent milder manias. But then back on lithium and rotating on the planet at the same pace as everyone else, you find your credit is decimated, your mortification complete: mania is not a luxury one can easily afford. It is devastating to have the illness and aggravating to have to pay for medications, blood tests, and psychotherapy. They, at least, are partially deductible. But money spent while manic doesn’t fit into the Internal Revenue Service concept of medical expense or business loss. So after mania, when most depressed, you’re given excellent reason to be even more so.

In the study of ideas, it is necessary to remember that insistence on hard-headed clarity issues from sentimental feeling, as if it were a mist, cloaking the perplexities of fact. Insistence on clarity at all costs is based on sheer superstition as to the mode in which human intelligence functions. Our reasoning grasps at straws for premises and float on gossamer for deductions.

Children are rarely taught critical thinking anymore, and society has become so antirational that basic reason and evidence are the new counterculture: thought is the new punk.

It’s abductive reasoning, not deductive. Working from observation to theory is abduction, not deduction.’ ‘But

Your powers of deductive reasoning are stunning," spits Tobias. "Consider me awed.

If I sound as if I'm always predicting ominous things, it's because I'm a pragmatist. I use deductive reasoning to generalize, and I suppose this sometimes ends up sounding like unlucky prophecies. You know why? Because reality's just the accumulation of ominous prophecies come to life. You have to only open a newspaper on any given day and weigh the good news versus the bad, and you'll see what I mean.

Mathematics is not a deductive science - that's a cliche. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.

All people, whether Aspie or neuro-typical are predisposed by their society to make guesses, jump to conclusions and then seek to defend those conclusions, regardless of logic or changing circumstance. This is sloppy, illogical thinking which may not hinder your life too much, under normal circumstances. But if you want to be a great detective, then such thinking will absolutely ruin your chances.

You," she says,pointing at me. "I expected. All the trouble with your aptitude test results made me suspicious from the beginning.But you..." She shakes her had as she sifts her eyes to Tobias. "You, Tobias-or should I call you Four?-managed to elude me," she says quietly. "Everything about you checked out: test results, initiation simulations, everything. But here you are nonetheless." She folds her hands and sets her chin on top of them. "Perhaps you could explain to me how that is?" "You're the genius," he says coolly. "Why don't you tell me?" Her mouth curls into a smile. "My theory is that you really do belong in Abnegation. That your Divergence is weaker." She smiles wider. Like she's amused. I grit my teeth and consider lunging across the table and strangling her. If I didn't have a bullet in my shoulder, I might. "Your powers of deductive reasoning are stunning," spits Tobias. "Consider me awed." I look sideways at him. I had always forgotten about this side of him-the part that is more likely to explode than to lie down and die." "Now that your intelligence has been verified, you might want to get on with killing us." Tobias closes his eyes. "You have a lot of Abnegation leaders to murder, after all.

The very notion of nature as a closed system entirely sufficient to itself is plainly one that cannot be verified, deductively or empirically, from within the system of nature. It is a metaphysical (which is to say “extra-natural”) conclusion regarding the whole of reality, which neither reason nor experience legitimately warrants.

I said that he was my superior in observation and deduction. If the art of the detective began and ended in reasoning from an armchair, my brother would be the greatest criminal agent that ever lived. But he has no ambition and no energy. He will not even go out of his way to verify his own solutions, and would rather be considered wrong than take the trouble to prove himself right.

It is apparent that inductive reasoning knows circumstance and seeks the law, while deductive reasoning knows the law and seeks the circumstance. The parallel can be seen immediately. Man knows circumstance and seeks the law. The Universal Subconscious Mind knows the law and seeks the circumstance.

Exposition is a mode of thought, a method of learning, and a means of expression. Almost all of the characteristics we associate with mature discourse were amplified by typography, which has the strongest possible bias toward exposition: a sophisticated ability to think conceptually, deductively and sequentially; a high valuation of reason and order; an abhorrence of contradiction; a large capacity for detachment and objectivity; and a tolerance for delayed response.

I don't know why dogs always go for postmen, I'm sure," continued our guide. "It's a matter of reasoning," said Poirot. "The dog, he argues from reason. He is intelligent; he makes his deductions according to his point of view. There are people who may enter a house and there are people who may not - that a dog soon learns. Eh bien, who is the person who most persistently tries to gain admission, rattling on the door twice or three times a day - and who is never by any chance admitted? The postman. Clearly, then, an undesirable guest from the point of view of the master of the house. He is always sent about his business, but he persistently returns and tries again. Then a dog's duty is clear, to aid in driving this undesirable man away, and to bite him if possible. A most reasonable proceeding.

For better or for worse, I don't have that kind of power. If I sound as if I'm always predicting ominous things, it's because I'm a pragmatist. I use deductive reasoning to generalise, and I suppose this sometimes ends up sounding like unlucky prophecies. You know why? Because reality's just the accumulation of ominous prophecies come to life.

Apply reason and evidence to the problems around you. Reach conclusions, then test them. See if your deductions stand up to testing. Only then will you know real truth.

Was it by reason that I attained to the knowledge that I must love my neighbor and not to throttle him?. They told me so when I was a child, and I gladly believed it, because they told me what was already in my soul. But who discovered it? Not reason! Reason has discovered the struggle for existence and the law that I must throttle all those who hinder the satisfaction of my desires. That is the deduction reason makes. But the law of loving others couldn't be discovered by reason, because it is unreasonable.

The real purpose of the scientific method is to make sure Nature hasn't misled you into thinking you know something you don't actually know. There's not a mechanic or scientist or technician alive who hasn't suffered from that one so much that he's not instinctively on guard. That's the main reason why so much scientific and mechanical information sounds so dull and so cautious. If you get careless or go romanticizing scientific information, give it a flourish here and there, Nature will soon make a complete fool out of you. It does it often enough anyway even when you don't give it opportunities. One must be extremely careful and rigidly logical when dealing with Nature: one logical slip and an entire scientific edifice comes tumbling down. One false deduction about the machine and you can get hung up indefinitely.

It was a good answer that was made by one who when they showed him hanging in a temple a picture of those who had paid their vows as having escaped shipwreck, and would have him say whether he did not now acknowledge the power of the gods, — ‘Aye,’ asked he again, ‘but where are they painted that were drowned after their vows?’ And such is the way of all superstition, whether in astrology, dreams, omens, divine judgments, or the like; wherein men, having a delight in such vanities, mark the events where they are fulfilled, but where they fail, though this happens much oftener, neglect and pass them by.

In a well-balanced, reasoning mind there is no such thing as an intuition - an inspired guess! You can guess, of course - and a guess is either right or wrong. If it is right you can call it an intuition. If it is wrong you usually do not speak of it again. But what is often called an intuition is really impression based on logical deduction or experience. When an expert feels that there is something wrong about a picture or a piece of furniture or the signature on a cheque he is really basing that feeling on a host of a small signs and details. He has no need to go into them minutely - his experience obviates that - the net result is the definite impression that something is wrong. But it is not a guess, it is an impression based on experience.

Prayer—the art of believing what is denied by the senses—deals almost entirely with the subconscious. Through prayer, the subconscious is suggested into acceptance of the wish fulfilled, and, reasoning deductively, logically unfolds it to its legitimate end.

But in life you have to take lots of deductions and if you don't take decisions you would never do anything because you would spend all your time choosing between things you could do.So it is good to have a reason why you hate some things and why you like others.

Puedes reconocer a un viejo maestro por el trayecto de su pincel.

The metaphysician reasons deductively out of his own subjectivity. The scientist reasons inductively from the facts of experience.

Only an idiot guesses or reasons or deduces,’ the Professor said, patiently.

Emotional speculation is to deductive reasoning what weeds are to a garden – at first sight they appear to belong, but eventually they obscure that which one hopes will come into bud.

But who discovered it? Not reason. Reason discovered the struggle for existence, and the law that requires us to oppress all who hinder the satisfaction of our desires. That is the deduction of reason. But loving one's neighbor reason could never discover, because it's irrational.

Theologians, and religionists in general, start with a fantasy premise and then proceed to apply rigorous formal logic to tease out its implications. Stark himself points out that “theology consists of formal reasoning about God.” This is admirably exact. Theologians, beginning with a wished-for creation of their own minds, analyze that creation’s characteristics by rigorous application of the principles of formal—that is, deductive—logic.

Fancy what a game of chess would be if all the chessmen had passions and intellects, more or less small and cunning; if you were not only uncertain about your adversary's men, but a little uncertain also about your own; if your knight could shuffle himself on to a new square by the sly; if your bishop, at your castling, could wheedle your pawns out of their places; and if your pawns, hating you because they are pawns, could make away from their appointed posts that you might get checkmate on a sudden. You might be the longest-headed of deductive reasoners, and yet you might be beaten by your own pawns. You would be especially likely to be beaten, if you depended arrogantly on your mathematical imagination, and regarded your passionate pieces with contempt. Yet this imaginary chess is easy compared with the game a man has to play against his fellow-men with other fellow-men for his instruments.

I have the advantage of knowing your habits, my dear Watson," said he. "When your round is a short one you walk, and when it is a long one you use a hansom. As I perceive that your boots, although used, are by no means dirty, I cannot doubt that you are at present busy enough to justify the hansom." "Excellent!" I cried. "Elementary," said he. "It is one of those instances where the reasoner can produce an effect which seems remarkable to his neighbour, because the latter has missed the one little point which is the basis of the deduction. The same may be said, my dear fellow, for the effect of some of these little sketches of yours, which is entirely meretricious, depending as it does upon your retaining in your own hands some factors in the problem which are never imparted to the reader.

reason Amazon can take on such a slow, inefficient workforce,” noted one itinerant worker on her blog, Tales from the Rampage. “Since they are getting us off government assistance for almost three months of the year, we are a tax deduction for them.

In many cases it is not one series of consequences will serve the turn, but many different and opposite deductions must be examined and laid together, before a man can come to make a right judgment of the point in question. What then can be expected from men that neither see the want of any such kind of reasoning as this, nor, if they do, know they how to set about it, or could perform it?

To engage the written word means to follow a line of thought, which requires considerable powers of classifying, inference-making and reasoning. It means to uncover lies, confusions, and overgeneralizations, to detect abuses of logic and common sense. It also means to weigh ideas, to compare and contrast assertions, to connect one generalization to another. To accomplish this, one must achieve a certain distance from the words themselves, which is, in fact, encouraged by the isolated and impersonal text. That is why a good reader does not cheer an apt sentence or pause to applaud even an inspired paragraph. Analytic thought is too busy for that, and too detached.

It’s abductive reasoning, not deductive. Working from observation to theory is abduction, not deduction.’ ‘But I thought—’ ‘Yes, you and so many other people. We know who to blame, of course, and I’ve written to him more than once care of his publisher, but he takes no notice.

reasonings on this subject can only be drawn from effects to causes; and that every argument, deducted from causes to effects, must of necessity be a gross sophism; since it is impossible for you to know anything of the cause, but what you have antecedently, not inferred, but discovered to the full, in the effect.

I was disappointed. Voice analysis can tell a lot about the caller: gender, most of the time, national and regional roots, illnesses, even reasonable morphological deductions can be made about the shape of the nose, mouth and throat. But at least we had a confirmed spelling of the principal’s name, which was a plus.

The metaphysician reasons deductively out of his own subjectivity. The scientist reasons inductively from the facts of experience. The metaphysician reasons from theory to facts, the scientist reasons from facts to theory. The metaphysician explains the universe by himself, the scientist explains himself by the universe.

Pythagoras also established the principle of deductive reasoning, which is the step-by-step process of starting with self-evident axioms (such as “2 + 2 = 4”) to build toward a new conclusion or fact. Deductive reasoning was later refined by Euclid, and it formed the basis of mathematical thinking into medieval times and beyond.

It’s abductive reasoning, not deductive. Working from observation to theory is abduction, not deduction.

When a fact appears to be opposed to a long train of deductions, it invariably proves to be capable of bearing some other interpretation. (Sherlock)

If reasoning is a set of deductions, then tact consists in omitting the workings.

Logical reasoning may be a most convenient means of mental communication for covering short distances, but the curvature of the earth, alas, is reflected even in logic: an ideally rational progression of thought will finally bring you back to the point of departure where you return aware of the simplicity of genius, with a delightful sensation that you have embraced truth, while actually you have merely embraced your own self... anything you might term a deduction already exposes the flaw: logical development inexorably becomes an envelopment.

I look at things and think about them,' Folly replied. 'And use my intuition, of course, and deduction and induction, as well as any historical or theoretical models that seem to apply.

The discovery of geometry had intoxicated them, and its a priori deductive method appeared capable of universal application. They would prove, for instance, that all reality is one, that there is no such thing as change, that the world of sense is a world of mere illusion; and the strangeness of their results gave them no qualms because they believed in the correctness of their reasoning.

The rigorousness of restraint is other than the one of the “exactitude” of a loose, indifferent “reasoning” which belongs equally to everyone and whose results are compelling within the sphere of its own claims to certainty. Such results are compelling, however, only because the claim to truth is content with the correctness that comes from deduction and from insertion into a regulated and calculable order.

No discussion of logic is complete without a refresher course in the difference between inductive and deductive reasoning. By its strictest definition, inductive reasoning proves a general principle—your idea worth spreading—by highlighting a group of specific events, trends, or observations. In contrast, deductive reasoning builds up to a specific principle—again, your idea worth spreading—through a chain of increasingly narrow statements.

Reason is itself a matter of faith. It is an act of faith to assert that our thoughts have any relation to reality at all. If you are merely a sceptic, you must sooner or later ask yourself the question, “Why should anything go right; even observation and deduction? Why should not good logic be as misleading as bad logic? They are both movements in the brain of a bewildered ape?” The young sceptic says, “I have a right to think for myself.” But the old sceptic, the complete sceptic, says, “I have no right to think for myself. I have no right to think at all...Man, by a blind instinct, knew that if once things were wildly questioned, reason could be questioned first. The authority of priests to absolve, the authority of popes to define the authority, even of inquisitors to terrify: these were all only dark defences erected round one central authority, more undemonstrable, more supernatural than all—the authority of a man to think. We know now that this is so; we have no excuse for not knowing it. For we can hear scepticism crashing through the old ring of authorities, and at the same moment we can see reason swaying upon her throne. In so far as religion is gone, reason is going. For they are both of the same primary and authoritative kind. They are both methods of proof which p 60 cannot themselves be proved. And in the act of destroying the idea of Divine authority we have largely destroyed the idea of that human authority by which we do a long-division sum. With a long and sustained tug we have attempted to pull the mitre off pontifical man; and his head has come off with it.

It's a matter of reasoning," said Poirot. "The dog, he argues from reason. He is intelligent, he makes his deductions according to his point of view. There are people who may enter a house and there people who may not - that a dog soon learns. Eh bien, who is the person who most persistently tries to gain admission, rattling on the door twice or three times a day - and who is never by any chance admitted? The postman. Clearly, then, an undesirable guest from the point of view of the master of the house. He is always sent about his business, but he persistently returns and tries again. Then the dog's duty is clear, to aid in driving this undesirable man away, and to bite him if possible. A most reasonable proceeding.

Not reason. Reason discovered the struggle for existence, and the law that requires us to oppress all who hinder the satisfaction of our desires. That is the deduction of reason. But loving one's neighbor reason could never discover, because it's irrational.

However, though the request is reasonable and the citizenry is better off paying taxes as their price for maintaining a stable and efficient government, they are nevertheless reluctant to do so. In order to overcome this reluctance, governments must make it appear that they are not taking too many credits, and that they are considering each citizen’s rights and benefits. In other words, they must lower the percentage taken out of low incomes; they must allow deductions of various kinds to be made before the tax is assessed, and so on.

One of the reasons the rich get richer is that they buy more investments by taking advantage of the tax laws. In essence, the money that would have been paid in taxes is used to buy additional assets, which provide another deduction against income, which reduces the taxes due, legally.

The word 'proof' should strictly only be used when we are dealing with deductive inferences.... Popper claimed that scientists only need to use deductive inferences.... So if a scientist is only interested in demonstrating that a given theory is false, she may be able to accomplish her goal without the use of inductive inferences.... When a scientist collects experimental data, her aim might be to show that a particular theory...is false. She will have to resort to inductive reasoning.... So Popper's attempt to show that science can get by without induction does not succeed.

Not even the intercourse of the sexes is exempt from the despotism of positive institution. Law pretends even to govern the indisciplinable wanderings of passion, to put fetters on the clearest deductions of reason, and, by appeals to the will, to subdue the involuntary affects of our nature. Love is inevitably consequent upon the perception of loveliness. Love withers under constraint: its very essence is liberty: it is compatible neither with obedience, jealously, nor fear: it is there most pure, perfect, and unlimited, where its votaries live in confidence, equality, and unreserve.

Our society’s almost doctrinal emphasis upon deductive reasoning, convergent thinking and selective retention perversely excludes divergent thinking, approximation and, importantly, guessing. If we are truly to understand the adolescent mind and develop effective ways to minimize the effects of risk-taking behaviour, we really need to understand these processes and engage with them. There is no logic involved with drug-taking and gambling. Adults can learn, too; understanding these mechanisms will also allow us to encourage creativity and value the spontaneity so characteristic of the adolescent mind.

Deductive reasoning goes from the general to the specific – Socrates is mortal – because that is what predators do. If you were to program a lion with syllogisms, it might come out something like this: I am hungry. My hunger is satisfied with meat. All zebras are made of meat. The slowest zebras are the easiest to catch. I will stalk and chase the slowest zebra. This zebra is the slowest zebra; I will stalk and chase this one. You see how this works? The lion is going from the general to the specific – from all zebras to one particular zebra that satisfies the criterion for appeasing the lion’s hunger.

It is idle to talk always of the alternative of reason and faith. Reason is itself a matter of faith. It is an act of faith to assert that our thoughts have any relation to reality at all. If you are merely a sceptic, you must sooner or later ask yourself the question, "Why should ANYTHING go right; even observation and deduction? Why should not good logic be as misleading as bad logic? They are both movements in the brain of a bewildered ape?" The young sceptic says, "I have a right to think for myself." But the old sceptic, the complete sceptic, says, "I have no right to think for myself. I have no right to think at all.

All right,” she said. “Inductive reasoning. It’s what those so-called detectives on CSI, SVU, LMNOP and all the rest of them call deductive reasoning, which is wrong and they should know better. It’s inductive reasoning, a tool you will use frequently in geometry as well as calculus and trigonometry, assuming you get that far and that certainly won’t be you, Jacquon. Stop messing with that girl’s hair and pay attention. Your grade on that last test was so low I had to write it on the bottom of my shoe.” Mrs. Washington glared at Jacquon until his face melted. She began again: “Inductive reasoning is reasoning to the most likely explanation. It begins with one or more observations, and from those observations we come to a conclusion that seems to make sense. All right. An example: Jacquon was walking home from school and somebody hit him on the head with a brick twenty-five times. Mrs. Washington and her husband, Wendell, are the suspects. Mrs. Washington is five feet three, a hundred and ten pounds, and teaches school. Wendell is six-two, two-fifty, and works at a warehouse. So who would you say is the more likely culprit?” Isaiah and the rest of the class said Wendell. “Why?” Mrs. Washington said. “Because Mrs. Washington may have wanted to hit Jacquon with a brick twenty-five times but she isn’t big or strong enough. Seems reasonable given the facts at hand, but here’s where inductive reasoning can lead you astray. You might not have all the facts. Such as Wendell is an accountant at the warehouse who exercises by getting out of bed in the morning, and before Mrs. Washington was a schoolteacher she was on the wrestling team at San Diego State in the hundred-and-five-to-hundred-and-sixteen-pound weight class and would have won her division if that blond girl from Cal Northridge hadn’t stuck a thumb in her eye. Jacquon, I know your mother and if I tell her about your behavior she will beat you ’til your name is Jesus.” The

Reason is itself a matter of faith. It is an act of faith to assert that our thoughts have any relation to reality at all. If you are merely a sceptic, you must sooner or later ask yourself the question, "Why should anything go right; even observation and deduction? Why should not good logic be as misleading as bad logic? They are both movements in the brain of a bewildered ape?" The young sceptic says, "I have a right to think for myself." But the old sceptic, the complete sceptic, says, "I have no right to think for myself. I have no right to think at all." There is a thought that stops thought. That is the only thought that ought to be stopped.

His signature was not the smoking six-shooter; instead, like Sherlock Holmes, he relied upon the startling powers of reason and deduction, the ability to observe what the Watsons of the world merely saw. He found order in a scramble of clues and, as one author put it, “turned brutal crimes—the vestiges of the beast in man—into intellectual puzzles.

There is, after all, nothing inherently reasonable in the conviction that all of reality is simply an accidental confluence of physical causes, without any transcendent source or end. Materialism is not a fact of experience or a deduction of logic; it is a metaphysical prejudice, nothing more, and one that is arguably more irrational than almost any other.

It is devastating to have the illness and aggravating to have to pay for medications, blood tests, and psychotherapy. They, at least, are partially deductible. But money spent while manic doesn’t fit into the Internal Revenue Service concept of medical expense or business loss. So after mania, when most depressed, you’re given excellent reason to be even more so.

Free will is an idealization of human beings that makes the ethics game playable. Euclidean geometry requires idealizations like infinite straight lines and perfect circles, and its deductions are sound and useful even though the world does not really have infinite straight lines or perfect circles. The world is close enough to the idealization that the theorems can usefully be applied. Similarly, ethical theory requires idealizations like free, sentient, rational, equivalent agents whose behavior is uncaused, and its conclusions can be sound and useful even though the world, as seen by science, does not really have uncaused events. As long as there is no outright coercion or gross malfunction of reasoning, the world is close enough to the idealization of free will that moral theory can meaningfully be applied to it.

In the history of philosophy, the term “rationalism” has two distinct meanings. In one sense, it signifies an unbreached commitment to reasoned thought in contrast to any irrationalist rejection of the mind. In this sense, Aristotle and Ayn Rand are preeminent rationalists, opposed to any form of unreason, including faith. In a narrower sense, however, rationalism contrasts with empiricism as regards the false dichotomy between commitment to so-called “pure” reason (i.e., reason detached from perceptual reality) and an exclusive reliance on sense experience (i.e., observation without inference therefrom). Rationalism, in this sense, is a commitment to reason construed as logical deduction from non-observational starting points, and a distrust of sense experience (e.g., the method of Descartes). Empiricism, according to this mistaken dichotomy, is a belief that sense experience provides factual knowledge, but any inference beyond observation is a mere manipulation of words or verbal symbols (e.g., the approach of Hume). Both Aristotle and Ayn Rand reject such a false dichotomy between reason and sense experience; neither are rationalists in this narrow sense. Theology is the purest expression of rationalism in the sense of proceeding by logical deduction from premises ungrounded in observable fact—deduction without reference to reality. The so-called “thinking” involved here is purely formal, observationally baseless, devoid of facts, cut off from reality. Thomas Aquinas, for example, was history’s foremost expert regarding the field of “angelology.” No one could match his “knowledge” of angels, and he devoted far more of his massive Summa Theologica to them than to physics.

FANCY what a game at chess would be if all the chessmen had passions and intellects, more or less small and cunning: if you were not only uncertain about your adversary’s men, but a little uncertain also about your own; if your knight could shuffle himself on to a new square by the sly; if your bishop, in disgust at your castling, could wheedle your pawns out of their places; and if your pawns, hating you because they are pawns, could make away from their appointed posts that you might get checkmate on a sudden. You might be the longest-headed of deductive reasoners, and yet you might be beaten by your own pawns. You would be especially likely to be beaten, if you depended arrogantly on your mathematical imagination, and regarded your passionate pieces with contempt. Yet this imaginary chess is easy compared with the game a man has to play against his fellow-men with other fellow-men for his instruments.

and that simpler principle remains intact. All physical reality is logically contingent, and the existence of the contingent requires the Absolute as its source. Why the Absolute produces the contingent may be inconceivable for us; but that the contingent can exist only derivatively, receiving its existence from the Absolute, is a simple deduction of reason. Alternatively, reality is essentially absurd: absolute contingency, unconditional conditionality, an uncaused effect.

That peril is that the human intellect is free to destroy itself. Just as one generation could prevent the very existence of the next generation, by all entering a monastery or jumping into the sea, so one set of thinkers can in some degree prevent further thinking by teaching the next generation that there is no validity in any human thought. It is idle to talk always of the alternative of reason and faith. Reason is itself a matter of faith. It is an act of faith to assert that our thoughts have any relation to reality at all. If you are merely a sceptic, you must sooner or later ask yourself the question, “Why should anything go right; even observation and deduction? Why should not good logic be as misleading as bad logic? They are both movements in the brain of a bewildered ape?” The young sceptic says, “I have a right to think for myself.” But the old sceptic, the complete sceptic, says, “I have no right to think for myself. I have no right to think at all.” There

It's all over, it's all over,' I muttered to myself. My grief resembled that of a fainthearted student who has failed an examination: I made a mistake! I made a mistake! Simply because I didn't solve that X, everything was wrong. If only I'd solved that X at the beginning, everything would have been all right. If only I had used deductive methods like everyone else to solve the mathematics of life. To be half-clever was the worst thing I could have done. I alone depended upon the inductive method, and for the simple reason I failed.

The influence of geometry upon philosophy and scientific method has been profound. Geometry, as established by the Greeks, starts with axioms which are (or are deemed to be) self-evident, and proceeds, by deductive reasoning, to arrive at theorems that are very far from self-evident. The axioms and theorems are held to be true of actual space, which is something given in experience. It thus appeared to be possible to discover things about the actual world by first noticing what is self-evident and then using deduction. This view influenced Plato and Kant, and most of the intermediate philosophers. When the Declaration of Independence says 'we hold these truths to be self-evident', it is modelling itself on Euclid. The eighteenth-century doctrine of natural rights is a search for Euclidean axioms in politics.8 The form of Newton's Principia, in spite of its admittedly empirical material, is entirely dominated by Euclid. Theology, in its exact scholastic forms, takes its style from the same source. Personal religion is derived from ecstasy, theology from mathematics; and both are to be found in Pythagoras.

But then back on lithium and rotating on the planet at the same pace as everyone else, you find your credit is decimated, your mortification complete: mania is not a luxury one can easily afford. It is devastating to have the illness and aggravating to have to pay for medications, blood tests, and psychotherapy. They, at least, are partially deductible. But money spent while manic doesn't fit into the Internal Revenue Service concept of medical expense or business loss. So after mania, when most depressed, you're given excellent reason to be even more so.

All the same,” I said, “when you read the prints in the snow and the evidence of the branches, you did not yet know Brunellus. In a certain sense those prints spoke of all horses, or at least all horses of that breed. Mustn’t we say, then, that the book of nature speaks to us only of essences, as many distinguished theologians teach?” “Not entirely, dear Adso,” my master replied. “True, that kind of print expressed to me, if you like, the idea of ‘horse,’ the verbum mentis, and would have expressed the same to me wherever I might have found it. But the print in that place and at that hour of the day told me that at least one of all possible horses had passed that way. So I found myself halfway between the perception of the concept ‘horse’ and the knowledge of an individu?al horse. And in any case, what I knew of the universal horse had been given me by those traces, which were singular. I could say I was caught at that moment between the singularity of the traces and my ignorance, which assumed the quite diaphanous form of a univer?sal idea. If you see something from a distance, and you do not understand what it is, you will be content with defining it as a body of some dimension. When you come closer, you will then define it as an animal, even if you do not yet know whether it is a horse or an ass. And finally, when it is still closer, you will be able to say it is a horse even if you do not yet know whether it is Brunellus or Niger. And only when you are at the proper distance will you see that it is Brunellus (or, rather, that horse and not another, however you decide to call it). And that will be full knowledge, the learning of the singular. So an hour ago I could expect all horses, but not because of the vastness of my intellect, but because of the paucity of my deduction. And my intellect’s hunger was sated only when I saw the single horse that the monks were leading by the halter. Only then did I truly know that my previous reasoning, had brought me close to the truth. And so the ideas, which I was using earlier to imagine a horse I had not yet seen, were pure signs, as the hoofprints in the snow were signs of the idea of ‘horse’; and sins and the signs of signs are used only when we are lacing things.

All right,” she said. “Inductive reasoning. It’s what those so-called detectives on CSI, SVU, LMNOP and all the rest of them call deductive reasoning, which is wrong and they should know better. It’s inductive reasoning, a tool you will use frequently in geometry as well as calculus and trigonometry, assuming you get that far and that certainly won’t be you, Jacquon. Stop messing with that girl’s hair and pay attention. Your grade on that last test was so low I had to write it on the bottom of my shoe.” Mrs. Washington glared at Jacquon until his face melted. She began again: “Inductive reasoning is reasoning to the most likely explanation. It begins with one or more observations, and from those observations we come to a conclusion that seems to make sense. All right. An example: Jacquon was walking home from school and somebody hit him on the head with a brick twenty-five times. Mrs. Washington and her husband, Wendell, are the suspects. Mrs. Washington is five feet three, a hundred and ten pounds, and teaches school. Wendell is six-two, two-fifty, and works at a warehouse. So who would you say is the more likely culprit?” Isaiah

All knowledge of reality starts from experience and ends in it.” But he immediately proceeded to emphasize the role that “pure reason” and logical deductions play. He conceded, without apology, that his success using tensor calculus to come up with the equations of general relativity had converted him to a faith in a mathematical approach, one that emphasized the simplicity and elegance of equations more than the role of experience. The fact that this method paid off in general relativity, he said, “justifies us in believing that nature is the realization of the simplest conceivable mathematical ideas.”45

That there was no God was a given, as far as Hope was concerned, and being nice to people and making the most of your life struck her as a reasonable enough conclusion to draw from it, and in any case what she wanted to do. But besides the spires of theology and the watch-towers of ideology, it seemed a very shaky hut indeed, and not one that offered her much shelter or would stand up in court. She couldn't see a way to make her objection to the fix a deduction from any body of thought. It came from a body of flesh, her own, and that was enough for her. She doubted that this would be enough for anyone else.

Part of what kept him standing in the restive group of men awaiting authorization to enter the airport was a kind of paralysis that resulted from Sylvanshine’s reflecting on the logistics of getting to the Peoria 047 REC—the issue of whether the REC sent a van for transfers or whether Sylvanshine would have to take a cab from the little airport had not been conclusively resolved—and then how to arrive and check in and where to store his three bags while he checked in and filled out his arrival and Post-code payroll and withholding forms and orientational materials then somehow get directions and proceed to the apartment that Systems had rented for him at government rates and get there in time to find someplace to eat that was either in walking distance or would require getting another cab—except the telephone in the alleged apartment wasn’t connected yet and he considered the prospects of being able to hail a cab from outside an apartment complex were at best iffy, and if he told the original cab he’d taken to the apartment to wait for him, there would be difficulties because how exactly would he reassure the cabbie that he really was coming right back out after dropping his bags and doing a quick spot check of the apartment’s condition and suitability instead of it being a ruse designed to defraud the driver of his fare, Sylvanshine ducking out the back of the Angler’s Cove apartment complex or even conceivably barricading himself in the apartment and not responding to the driver’s knock, or his ring if the apartment had a doorbell, which his and Reynolds’s current apartment in Martinsburg most assuredly did not, or the driver’s queries/threats through the apartment door, a scam that resided in Claude Sylvanshine’s awareness only because a number of independent Philadelphia commercial carriage operators had proposed heavy Schedule C losses under the proviso ‘Losses Through Theft of Service’ and detailed this type of scam as prevalent on the poorly typed or sometimes even handwritten attachments required to explain unusual or specific C-deductions like this, whereas were Sylvanshine to pay the fare and the tip and perhaps even a certain amount in advance on account so as to help assure the driver of his honorable intentions re the second leg of the sojourn there was no tangible guarantee that the average taxi driver—a cynical and ethically marginal species, hustlers, as even their smudged returns’ very low tip-income-vs.-number-of-fares-in-an-average-shift ratios in Philly had indicated—wouldn’t simply speed away with Sylvanshine’s money, creating enormous hassles in terms of filling out the internal forms for getting a percentage of his travel per diem reimbursed and also leaving Sylvanshine alone, famished (he was unable to eat before travel), phoneless, devoid of Reynolds’s counsel and logistical savvy in the sterile new unfurnished apartment, his stomach roiling in on itself in such a way that it would be all Sylvanshine could do to unpack in any kind of half-organized fashion and get to sleep on the nylon travel pallet on the unfinished floor in the possible presence of exotic Midwest bugs, to say nothing of putting in the hour of CPA exam review he’d promised himself this morning when he’d overslept slightly and then encountered last-minute packing problems that had canceled out the firmly scheduled hour of morning CPA review before one of the unmarked Systems vans arrived to take him and his bags out through Harpers Ferry and Ball’s Bluff to the airport, to say even less about any kind of systematic organization and mastery of the voluminous Post, Duty, Personnel, and Systems Protocols materials he should be receiving promptly after check-in and forms processing at the Post, which any reasonable Personnel Director would expect a new examiner to have thoroughly internalized before reporting for the first actual day interacting with REC examiners, and which there was no way in any real world that Sylvanshine could expect

It’s a matter of reasoning,’ said Poirot. ‘The dog, he argues from reason. He is intelligent, he makes his deductions according to his point of view. There are people who may enter a house and there are people who may not—that a dog soon learns. Eh bien, who is the person who most persistently tries to gain admission, rattling on the door twice or three times a day—and who is never by any chance admitted? The postman. Clearly, then, an undesirable guest from the point of view of the master of the house. He is always sent about his business, but he persistently returns and tries again. Then a dog’s duty is clear, to aid in driving this undesirable man away, and to bite him if possible. A most reasonable proceeding.

Romance is the deepest thing in life; romance is deeper even than reality. For even if reality could be proved to be misleading, it still could not be proved to be unimportant or unimpressive. Even if the facts are false, they are still very strange. And this strangeness of life, this unexpected and even perverse element of things as they fall out, remains incurably interesting. ... People wonder why the novel is the most popular form of literature; people wonder why it is read more than books of science or books of metaphysics. The reason is very simple; it is merely that the novel is more true than they are. Life may sometimes legitimately appear as a book of science. Life may 102 sometimes appear, and with a much greater legitimacy, as a book of metaphysics. But life is always a novel. Our existence may cease to be a song; it may cease even to be a beautiful lament. Our existence may not be an intelligible justice, or even a recognizable wrong. But our existence is still a story. In the fiery alphabet of every sunset is written, “to be continued in our next.” If we have sufficient intellect, we can finish a philosophical and exact deduction, and be certain that we are finishing it right. With the adequate brain-power we could finish any scientific discovery, and be certain that we were finishing it right. But not with the most gigantic intellect could we finish the simplest or silliest story, and be certain that we were finishing it right.

The real purpose of scientific method is to make sure Nature hasn’t misled you into thinking you know something you don’t actually know. There’s not a mechanic or scientist or technician alive who hasn’t suffered from that one so much that he’s not instinctively on guard. That’s the main reason why so much scientific and mechanical information sounds so dull and so cautious. If you get careless or go romanticizing scientific information, giving it a flourish here and there, Nature will soon make a complete fool out of you. It does it often enough anyway even when you don’t give it opportunities. One must be extremely careful and rigidly logical when dealing with Nature: one logical slip and an entire scientific edifice comes tumbling down. One false deduction about the machine and you can get hung up indefinitely.

In every system of morality, which I have hitherto met with, I have always remark’d, that the author proceeds for some time in the ordinary ways of reasoning, and establishes the being of a God, or makes observations concerning human affairs; when all of a sudden I am surpriz’d to find, that instead of the usual copulations of propositions, is, and is not, I meet with no proposition that is not connected with an ought, or an ought not. This change is imperceptible; but is however, of the last consequence. For as this ought, or ought not, expresses some new relation or affirmation, ‘tis necessary that it shou’d be observ’d and explain’d; and at the same time that a reason should be given; for what seems altogether inconceivable, how this new relation can be a deduction from others, which are entirely different from it.

What a lovely thing a rose is!’ He walked past the couch to the open window, and held up the drooping stalk of a moss rose, looking down at the dainty blend of crimson and green. It was a new phase of his character to me, for I had never before seen him show any keen interest in natural objects. ‘There is nothing in which deduction is so necessary as in religion,’ said he, leaning with his back against the shutters. ‘It can be built up as an exact science by the reasoner. Our highest assurance of the goodness of Providence seems to me to rest in the flowers. All other things, our powers our desires, our food, are all really necessary for our existence in the first instance. But this rose is an extra. Its smell and its color are an embellishment of life, not a condition of it. It is only goodness which gives extras, and so I say again that we have much to hope from the flowers.

governed by definite laws, you ultimately have to combine the partial theories into a complete unified theory that will describe everything in the universe. But there is a fundamental paradox in the search for such a complete unified theory. The ideas about scientific theories outlined above assume we are rational beings who are free to observe the universe as we want and to draw logical deductions from what we see. In such a scheme it is reasonable to suppose that we might progress ever closer toward the laws that govern our universe. Yet if there really is a complete unified theory, it would also presumably determine our actions. And so the theory itself would determine the outcome of our search for it! And why should it determine that we come to the right conclusions from the evidence? Might it not equally well determine that we draw the wrong conclusion? Or no conclusion at all?

But as the cause of perturbations is now discovered, 162for all of them arise from the judgment or opinion, or volition, I shall put an end to this discourse. But we ought to be assured, since the boundaries of good and evil are now discovered, as far as they are discoverable by man, that nothing can be desired of philosophy greater or more useful than the discussions which we have held these four days. For besides instilling a contempt of death, and relieving pain so as to enable men to bear it, we have added the appeasing of grief, than which there is no greater evil to man. For though every perturbation of mind is grievous, and differs but little from madness, yet we are used to say of others when they are under any perturbation, as of fear, joy, or desire, that they are agitated and disturbed; but of those who give themselves up to grief, that they are miserable, afflicted, wretched, unhappy. So that it doth not seem to be by accident, but with reason proposed by you, that I should discuss grief, and the other perturbations separately; for there lies the spring and head of all our miseries; but the cure of grief, and of other disorders, is one and the same in that they are all voluntary, and founded on opinion; we take them on ourselves because it seems right so to do. Philosophy undertakes to eradicate this error, as the root of all our evils: let us therefore surrender ourselves to be instructed by it, and suffer ourselves to be cured; for while these evils have possession of us, we not only cannot be happy, but cannot be right in our minds. We must either deny that reason can effect anything, while, on the other hand, nothing can be done right without reason, or else, since philosophy depends on the deductions of reason, we must seek from her, if we would be good or happy, every help and assistance for living well and happily.

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 observations of particular facts, has replaced the Hellenic belief in deduction from luminous axioms derived from the mind of the philosopher. For this reason, apart from others, it is a mistake to treat the Greeks with superstitious reverence. Scientific method, though some few among them were the first men who had an inkling of it, is, on the whole, alien to their temper of mind, and the attempt to glorify them by belittling the intellectual progress of the last four centuries has a cramping effect upon modern thought.

Parmenides was offering a rational deduction. He starts from a basic principle—that you can have “is,” but you can’t have “is not”—and then proceeds to explore the consequences, whatever they might be. Whatever we make of his argument, this is a real quantum leap in the history of philosophy. Parmenides is not just offering explanations of what he can see around him, though he goes on to do that in the way of opinion. Rather, he puts all his trust in reason itself, and trusts the power of argument more than he trusts the evidence of his own eyes and ears. This is not to say that Parmenides is the first Pre-Socratic to offer arguments. Already with Thales, I suggested that he may have had implicit arguments for his views on water and the claim that everything is full of gods. Nonetheless Parmenides does represent something new. He tries to settle an abstract philosophical issue—the nature of being itself—with an explicit and complex deductive argument.

The very possibility of the science of mathematics seems an insoluble contradiction. If this science is deductive only in appearance, whence does it derive that perfect rigor no one dreams of doubting? If, on the contrary, all the propositions it enunciates can be deduced one from another by the rules of formal logic, why is not mathematics reduced to an immense tautology? The syllogism can teach us nothing essentially new, and, if everything is to spring from the principle of identity, everything should be capable of being reduced to it. Shall we then admit that the enunciations of all those theorems which fill so many volumes are nothing but devious ways of saying A is A! ...Does the mathematical method proceed from particular to the general, and, if so, how can it be called deductive? ...If we refuse to admit these consequences, it must be conceded that mathematical reasoning has of itself a sort of creative virtue and consequently differs from a syllogism.

When I am high I couldn’t worry about money if I tried. So I don’t. The money will come from somewhere; I am entitled; God will provide. Credit cards are disastrous, personal checks worse. Unfortunately, for manics anyway, mania is a natural extension of the economy. What with credit cards and bank accounts there is little beyond reach....During one spree in London I spent several hundred pounds on books having titles or covers that somehow caught my fancy: books on the natural history of the mole, twenty sundry Penguin books because I thought it could be nice if the penguins could form a colony..... But then back on lithium and rotating on the planet at the same pace as everyone else, you find your credit is decimated, your mortification complete: mania is not a luxury one can easily afford. It is devastating to have the illness and aggravating to have to pay for medications, blood tests, and psychotherapy. They, at least, are partially deductible. But money spent while manic doesn’t fit into the Internal Revenue Service concept of medical expense or business loss. So after mania, when most depressed, you’re given excellent reason to be even more so.

From Smith's principle that labor is the true measure of price—or, as Warren phrased it, that cost is the proper limit of price—these three men (Josiah Warren, Pierre-Joseph Proudhon and Karl Marx) made the following deductions: that the natural wage of labor is its product; that this wage, or product, is the only just source of income (leaving out, of course, gift, inheritance, etc.); that all who derive income from any other source abstract it directly or indirectly from the natural and just wage of labor; that this abstracting process generally takes one of three forms, interest, rent, and profit; that these three constitute the trinity of usury, and are simply different methods of levying tribute for the use of capital; that, capital being simply stored-up labor which has already received its pay in full, its use ought to be gratuitous, on the principle that labor is the only basis of price; that the lender of capital is entitled to its return intact, and nothing more; that the only reason why the banker, the stockholder, the landlord, the manufacturer, and the merchant are able to exact usury from labor lies in the fact that they are backed by legal privilege, or monopoly; and that the only way to secure to labor the enjoyment of its entire product, or natural wage, is to strike down monopoly.

The fact that at first glance a theory appears reasonable should not lead us hastily to accept it, and to attempt to twist the Bible into harmony with it. In a thousand ways we have proved the Bible, and know beyond peradventure that it contains a superhuman wisdom which makes its statements unerring. We should remember, too, that while scientific research is to be commended, and its suggestions considered, yet its conclusions are by no means infallible. And what wonder that it has proven its own theories false a thousand times, when we remember that the true scientist is merely a student attempting, under many unfavorable circumstances, and struggling against almost insurmountable difficulties, to learn from the great Book of Nature the history and destiny of man and his home. We would not, then, either oppose or hinder scientific investigation; but in hearing suggestions from students of the Book of Nature, let us carefully compare their deductions, which have so often proved in part or wholly erroneous, with the Book of Divine Revelation, and prove or disprove the teachings of scientists by 'the law and the testimony. If they speak not according to this word, it is because there is no light in them' (Isa 8:20). And accurate knowledge of both books will prove them to be harmonious; but until we have such knowledge, God's Revelation must take precedence, and must be the standard among the children of God, by which the supposed findings of fallible fellow-men shall be judged.

Rule by decree has conspicuous advantages for the domination of far-flung territories with heterogeneous populations and for a policy of oppression. Its efficiency is superior simply because it ignores all intermediary stages between issuance and application, and because it prevents political reasoning by the people through the withholding of information. It can easily overcome the variety of local customs and need not rely on the necessarily slow process of development of general law. It is most helpful for the establishment of a centralized administration because it overrides automatically all matters of local autonomy. If rule by good laws has sometimes been called the rule of wisdom, rule by appropriate decrees may rightly be called the rule of cleverness. For it is clever to reckon with ulterior motives and aims, and it is wise to understand and create by deduction from generally accepted principles. Government by bureaucracy has to be distinguished from the mere outgrowth and deformation of civil services which frequently accompanied the decline of the nation-state—as, notably, in France. There the administration has survived all changes in regime since the Revolution, entrenched itself like a parasite in the body politic, developed its own class interests, and become a useless organism whose only purpose appears to be chicanery and prevention of normal economic and political development. There are of course many superficial similarities between the two types of bureaucracy, especially if one pays too much attention to the striking psychological similarity of petty officials. But if the French people have made the very serious mistake of accepting their administration as a necessary evil, they have never committed the fatal error of allowing it to rule the country—even though the consequence has been that nobody rules it. The French atmosphere of government has become one of inefficiency and vexation; but it has not created and aura of pseudomysticism. And it is this pseudomysticism that is the stamp of bureaucracy when it becomes a form of government. Since the people it dominates never really know why something is happening, and a rational interpretation of laws does not exist, there remains only one thing that counts, the brutal naked event itself. What happens to one then becomes subject to an interpretation whose possibilities are endless, unlimited by reason and unhampered by knowledge. Within the framework of such endless interpretive speculation, so characteristic of all branches of Russian pre-revolutionary literature, the whole texture of life and world assume a mysterious secrecy and depth. There is a dangerous charm in this aura because of its seemingly inexhaustible richness; interpretation of suffering has a much larger range than that of action for the former goes on in the inwardness of the soul and releases all the possibilities of human imagination, whereas the latter is consistently checked, and possibly led into absurdity, by outward consequence and controllable experience.

Where has logic originated in men’s heads? Undoubtedly out of the illogical, the domain of which must originally have been immense. But numberless beings who reasoned otherwise than we do at present, perished; albeit that they may have come nearer to truth than we! Whoever, for example, could not discern the "like" often enough with regard to food, and with regard to animals dangerous to him, whoever, therefore, deduced too slowly, or was too circumspect in his deductions, had smaller probability of survival than he who in all similar cases immediately divined the equality. The dominant tendency however, to treat as equal that which is merely similar - an illogical tendency for there is nothing equal - is what first created the whole basis for logic. It was just so (in order that the conception of substance should originate, this being indispensable to logic, although in the strictest sense nothing actual corresponds to it) that for a long period the changing process in things had to be overlooked, and remain unperceived; the beings not seeing correctly had an advantage over those who saw everything "in flux" In itself every high degree of circumspection in conclusions, every skeptical inclination, is a great danger to life. No living being might have been preserved unless the contrary inclination to affirm rather than suspend judgment, to mistake and fabricate rather than wait, to assent rather than deny, to decide rather than be in the right had been cultivated with extra ordinary assiduity. The course of logical thought and reasoning in our modern brain corresponds to a process and struggle of impulses, which singly and in themselves are all very illogical and unjust; we experience usually only the result of the struggle, so rapidly and secretly does this primitive mechanism now operate in us.

Origin of the Logical. Where has logic originated in men’s heads? Undoubtedly out of the illogical, the domain of which must originally have been immense. But numberless beings who reasoned otherwise than we do at present, perished; albeit that they may have come nearer to truth than we! Whoever, for example, could not discern the "like" often enough with regard to food, and with regard to animals dangerous to him, whoever, therefore, deduced too slowly, or was too circumspect in his deductions, had smaller probability of survival than he who in all similar cases immediately divined the equality. The preponderating inclination, however, to deal with the similar as the equal - an illogical inclination, for there is no thing equal in itself - first created the whole basis of logic. It was just so (in order that the conception of substance should originate, this being indispensable to logic, although in the strictest sense nothing actual corresponds to it) that for a long period the changing process in things had to be overlooked, and remain unperceived; the beings not seeing correctly had an advantage over those who saw everything "in flux." In itself every high degree of circumspection in conclusions, every sceptical inclination, is a great danger to life. No living being might have been preserved unless the contrary inclination - to affirm rather than suspend judgment, to mistake and fabricate rather than wait, to assent rather than deny, to decide rather than be in the right - had been cultivated with extraordinary assiduity. - The course of logical thought and reasoning in our modern brain corresponds to a process and struggle of impulses, which singly and in themselves are all very illogical and unjust; we experience usually only the result of the struggle, so rapidly and secretly does this primitive mechanism now operate in us.

Origin of the Logical. — Where has logic originated in men's heads? Undoubtedly out of the illogical, the domain of which must originally have been immense. But numberless beings who reasoned otherwise than we do at present, perished; albeit that they may have come nearer to truth than we! Whoever, for example, could not discern the “like” often enough with regard to food, and with regard to animals dangerous to him, whoever, therefore, deduced too slowly, or was too circumspect in his deductions, had smaller probability of survival than he who in all similar cases immediately divined the equality. The preponderating inclination, however, to deal with the similar as the equal — an illogical inclination, for there is no thing equal in itself — first created the whole basis of logic. It was just so (in order that the conception of substance should originate, this being indispensable to logic, although in the strictest sense nothing actual corresponds to it) that for a long period the changing process in things had to be overlooked, and remain unperceived; the beings not seeing correctly had an advantage over those who saw everything “in flux.” In itself every high degree of circumspection in conclusions, every sceptical inclination, is a great danger to life. No living being might have been preserved unless the contrary inclination — to affirm rather than suspend judgment, to mistake and fabricate rather than wait, to assent rather than deny, to decide rather than be in the right — had been cultivated with extraordinary assiduity. — The course of logical thought and reasoning in our modern brain corresponds to a process and struggle of impulses, which singly and in themselves are all very illogical and unjust; we experience usually only the result of the struggle, so rapidly and secretly does this primitive mechanism now operate in us.

theory. “The development of the general theory of relativity introduced Einstein to the power of abstract mathematical formalisms, notably that of tensor calculus,” writes the astrophysicist John Barrow. “A deep physical insight orchestrated the mathematics of general relativity, but in the years that followed the balance tipped the other way. Einstein’s search for a unified theory was characterized by a fascination with the abstract formalisms themselves.”44 In his Oxford lecture, Einstein began with a nod to empiricism: “All knowledge of reality starts from experience and ends in it.” But he immediately proceeded to emphasize the role that “pure reason” and logical deductions play. He conceded, without apology, that his success using tensor calculus to come up with the equations of general relativity had converted him to a faith in a mathematical approach, one that emphasized the simplicity and elegance of equations more than the role of experience. The fact that this method paid off in general relativity, he said, “justifies us in believing that nature is the realization of the simplest conceivable mathematical ideas.”45 That is an elegant—and also astonishingly interesting—creed. It captured the essence of Einstein’s thought during the decades when mathematical “simplicity” guided him in his search for a unified field theory. And it echoed the great Isaac Newton’s declaration in book 3 of the Principia: “Nature is pleased with simplicity.” But Einstein offered no proof of this creed, one that seems belied by modern particle physics.46 Nor did he ever fully explain what, exactly, he meant by mathematical simplicity. Instead, he merely asserted his deep intuition that this is the way God would make the universe. “I am convinced that we can discover by means of purely mathematical constructions the concepts and the laws connecting them with each other,” he claimed.

At this point, the cautious reader might wish to read over the whole argument again, as presented above, just to make sure that I have not indulged in any 'sleight of hand'! Admittedly there is an air of the conjuring trick about the argument, but it is perfectly legitimate, and it only gains in strength the more minutely it is examined. We have found a computation Ck(k) that we know does not stop; yet the given computational procedure A is not powerful enough to ascertain that facet. This is the Godel(-Turing) theorem in the form that I require. It applies to any computational procedure A whatever for ascertaining that computations do not stop, so long as we know it to be sound. We deduce that no knowably sound set of computational rules (such as A) can ever suffice for ascertaining that computations do not stop, since there are some non-stopping computations (such as Ck(k)) that must elude these rules. Moreover, since from the knowledge of A and of its soundness, we can actually construct a computation Ck(k) that we can see does not ever stop, we deduce that A cannot be a formalization of the procedures available to mathematicians for ascertaining that computations do not stop, no matter what A is. Hence: (G) Human mathematicians are not using a knowably sound algorithm in order to ascertain mathematical truth. It seems to me that this conclusion is inescapable. However, many people have tried to argue against it-bringing in objections like those summarized in the queries Q1-Q20 of 2.6 and 2.10 below-and certainly many would argue against the stronger deduction that there must be something fundamentally non-computational in our thought processes. The reader may indeed wonder what on earth mathematical reasoning like this, concerning the abstract nature of computations, can have to say about the workings of the human mind. What, after all, does any of this have to do with the issue of conscious awareness? The answer is that the argument indeed says something very significant about the mental quality of understanding-in relation to the general issue of computation-and, as was argued in 1.12, the quality of understanding is something dependent upon conscious awareness. It is true that, for the most part, the foregoing reasoning has been presented as just a piece of mathematics, but there is the essential point that the algorithm A enters the argument at two quite different levels. At the one level, it is being treated as just some algorithm that has certain properties, but at the other, we attempt to regard A as being actually 'the algorithm that we ourselves use' in coming to believe that a computation will not stop. The argument is not simply about computations. It is also about how we use our conscious understanding in order to infer the validity of some mathematical claim-here the non-stopping character of Ck(k). It is the interplay between the two different levels at which the algorithm A is being considered-as a putative instance of conscious activity and as a computation itself-that allows us to arrive at a conclusion expressing a fundamental conflict between such conscious activity and mere computation.

This experiment succeeds as hoped and promises to metaphysics, in its first part, which deals with those *a priori* concepts to which the corresponding objects may be given in experience, the secure course of a science. For by thus changing our point of view, the possibility of *a priori* knowledge can well be explained, and, what is still more, the laws which *a priori* lie at the foundation of nature, as the sum total of the objects of experience, may be supplied with satisfactory proofs, neither of which was possible within the procedure hitherto adopted. But there arises from this deduction of our faculty of knowing *a priori*, as given in the first part of metaphysics, a somewhat startling result, apparently most detrimental to that purpose of metaphysics which has to be treated in its second part, namely the impossibly of using this faculty to transcend the limits of possible experience, which is precisely the most essential concern of the science of metaphysics. But here we have exactly the experiment which, by disproving the opposite, establishes the truth of the first estimate of our *a priori* rational knowledge, namely, that it is directed only at appearances and must leave the thing in itself as real for itself but unknown to us. For that which necessarily impels us to to go beyond the limits of experience and of all appearances is the *unconditioned*, which reason rightfully and necessarily demands, aside from everything conditioned, in all things in themselves, so that the series of conditions be completed. If, then, we find that, under the supposition that our empirical knowledge conforms to objects as things in themselves, the unconditioned *cannot be thought without contradiction*, while under the supposition that our representation of things as they are given to us does not conform to them as things in themselves, but, on the contrary, that these objects as appearance conform to our mode of representation, then *the contradiction vanishes*; and if we find, therefore, that the unconditioned cannot be encountered in things insofar as we are acquainted with them (insofar as they are given to us), but only in things insofar as we are not acquainted with them, that is, insofar as they are things in themselves; then it becomes apparent that what we at first assumed only for the sake of experiment is well founded. However, with speculative reason unable to make progress in the field of the supersensible, it is still open to us to investigate whether in reason's practical knowledge data may not be found which would enable us to determine that transcendent rational concept of the unconditioned, so as to allow us, in accordance with the wish of metaphysics, to get beyond the limits of all possible experience with our *a priori* knowledge, which is possible in practical matters only. Within such a procedure, speculative reason has always at least created a space for such an expansion, even if it has to leave it empty; none the less we are at liberty, indeed we are summoned, to fill it, if we are able to do so, with practical *data* of reason." ―from_Critique of Pure Reason_. Preface to the Second Edition. Translated, edited, and with an Introduction by Marcus Weigelt, based on the translation by Max Müller, pp. 19-21