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May
2nd
Thu
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All opinions are not equal. Some are a very great deal more robust, sophisticated and well supported in logic and argument than others.
Douglas Adams, English writer and dramatist (1952-2001), The Salmon of Doubt: Hitchhiking the Galaxy One Last Time (2002)
May
25th
Fri
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Ludwig Wittgenstein On Certainty

#253 “At the core of all well-founded belief lies belief that is unfounded.”

#174. “I act with complete certainty. But this certainty is my own.”

#176. “Instead of “I know it” one may say in some cases “That’s how it is—rely upon it.” In some cases, however “I learned it years and years ago”; and sometimes: “I am sure it is so.”

#189. “At some point one has to pass from explanation to mere description.”

#191. “Well, if everything speaks for an hypothesis and nothing against it – is it then certainly true? One may designate it as such.—But does it certainly agree with reality, with the facts?—With this question you are already going round in a circle.”

#207. “Strange coincidence, that every man whose skull has been opened had a brain!
Ludwig Wittgenstein, Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language (1889-1951), On Certainty (Über Gewissheit), J. & J. Harper Editions, New York, 1969.  
Mar
2nd
Fri
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“The most beautiful and satisfying experiences open to humankind are not derived from the outside, but are bound up with the development of the individual’s own feeling, thinking and acting. The genuine artists, investigators and thinkers have always been persons of this kind. However inconspicuously the life of these individuals runs its course, none the less the fruits of their endeavors are the most valuable contributions which one generation can make to its successors. (…)

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.” “
Albert Einstein, German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics, Nobel Prize laureate (1879-1955), Professor Einstein Writes in Appreciation of a Fellow-Mathematician. To the Editor of The New York Times, Princeton University, May 1, 1935.
(Illustration: Albert Einstein sailing his boat on Saranac Lake (Courtesy: The Fantova Collection, Princeton University)
Nov
7th
Mon
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" "Two plus two is four" is not so clear, you know, and it is not always so. But "Form is emptiness, and emptiness is form" is very accurate." "
Shunryu Suzuki, a Sōtō Zen roshi (1904-1971), Emptiness is Form, July 03, 1969
Jun
27th
Mon
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If by eternity is understood not endless temporal duration but timelessness, then he lives eternally who lives in the present.
Ludwig Wittgenstein, Austrian philosopher, mathematician, logician, who held the professorship in philosophy at the University of Cambridge (1889-1951), Tractatus Logico-Philosophicus 5.4311, Cosimo, Inc., 2007, p. 106.
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Logic takes care of itself; all we have to do is to look and see how it does it.
Ludwig Wittgenstein, Austrian philosopher, mathematician, logician, who held the professorship in philosophy at the University of Cambridge (1889-1951) See also: Jorinde Voigt’s illustrations
May
28th
Sat
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Edward De Bono on lateral thinking

“With logic you start out with certain ingredients just as in playing chess you start out with given pieces. But what are those pieces? In most real life situations the pieces are not given, we just assume they are there. We assume certain perceptions, certain concepts and certain boundaries. Lateral thinking is concerned not with playing with the existing pieces but with seeking to change those very pieces. Lateral thinking is concerned with the perception part of thinking. This is where we organise the external world into the pieces we can then ”process”.” “
Edward de Bono, a physician, author, inventor, and consultant, Lateral Thinking & Parallel Thinking
Apr
30th
Sat
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Isaac Asimov on The Relativity of Wrong

"John, when people thought the Earth was flat, they were wrong. When people thought the Earth was spherical, they were wrong. But if you think that thinking the Earth is spherical is just as wrong as thinking the Earth is flat, then your view is wronger than both of them put together.

The basic trouble, you see, is that people think that “right” and “wrong” are absolute; that everything that isn’t perfectly and completely right is totally and equally wrong.

However, I don’t think that’s so. It seems to me that right and wrong are fuzzy concepts. (…)

First, let me dispose of Socrates because I am sick and tired of this pretense that knowing you know nothing is a mark of wisdom.

No one knows nothing. In a matter of days, babies learn to recognize their mothers.

Socrates would agree, of course, and explain that knowledge of trivia is not what he means. He means that in the great abstractions over which human beings debate, one should start without preconceived, unexamined notions, and that he alone knew this. (What an enormously arrogant claim!)

In his discussions of such matters as “What is justice?” or “What is virtue?” he took the attitude that he knew nothing and had to be instructed by others. (This is called “Socratic irony,” for Socrates knew very well that he knew a great deal more than the poor souls he was picking on.) By pretending ignorance, Socrates lured others into propounding their views on such abstractions. Socrates then, by a series of ignorant-sounding questions, forced the others into such a mélange of self-contradictions that they would finally break down and admit they didn’t know what they were talking about.

It is the mark of the marvelous toleration of the Athenians that they let this continue for decades and that it wasn’t till Socrates turned seventy that they broke down and forced him to drink poison.

Now where do we get the notion that “right” and “wrong” are absolutes? It seems to me that this arises in the early grades, when children who know very little are taught by teachers who know very little more.

Young children learn spelling and arithmetic, for instance, and here we tumble into apparent absolutes.

How do you spell “sugar?” Answer: s-u-g-a-r. That is right. Anything else is wrong.

How much is 2 + 2? The answer is 4. That is right. Anything else is wrong.

Having exact answers, and having absolute rights and wrongs, minimizes the necessity of thinking, and that pleases both students and teachers. For that reason, students and teachers alike prefer short-answer tests to essay tests; multiple-choice over blank short-answer tests; and true-false tests over multiple-choice.

But short-answer tests are, to my way of thinking, useless as a measure of the student’s understanding of a subject. They are merely a test of the efficiency of his ability to memorize.

You can see what I mean as soon as you admit that right and wrong are relative.

How do you spell “sugar?” Suppose Alice spells it p-q-z-z-f and Genevieve spells it s-h-u-g-e-r. Both are wrong, but is there any doubt that Alice is wronger than Genevieve? For that matter, I think it is possible to argue that Genevieve’s spelling is superior to the “right” one.

Or suppose you spell “sugar”: s-u-c-r-o-s-e, or C12H22O11. Strictly speaking, you are wrong each time, but you’re displaying a certain knowledge of the subject beyond conventional spelling.

Suppose then the test question was: how many different ways can you spell “sugar?” Justify each. (…)

Again, how much is 2 + 2? Suppose Joseph says: 2 + 2 = purple, while Maxwell says: 2 + 2 = 17. Both are wrong but isn’t it fair to say that Joseph is wronger than Maxwell?

Suppose you said: 2 + 2 = an integer. You’d be right, wouldn’t you? Or suppose you said: 2 + 2 = an even integer. You’d be righter. Or suppose you said: 2 + 2 = 3.999. Wouldn’t you be nearly right?

If the teacher wants 4 for an answer and won’t distinguish between the various wrongs, doesn’t that set an unnecessary limit to understanding?

Suppose the question is, how much is 9 + 5?, and you answer 2. Will you not be excoriated and held up to ridicule, and will you not be told that 9 + 5 = 14?

If you were then told that 9 hours had pass since midnight and it was therefore 9 o’clock, and were asked what time it would be in 5 more hours, and you answered 14 o’clock on the grounds that 9 + 5 = 14, would you not be excoriated again, and told that it would be 2 o’clock? Apparently, in that case, 9 + 5 = 2 after all. (…)

Here’s another example. The teacher asks: “Who is the fortieth President of the United States?” and Barbara says, “There isn’t any, teacher.”

"Wrong!" says the teacher, "Ronald Reagan is the fortieth President of the United States."

"Not at all," says Barbara, "I have here a list of all the men who have served as President of the United States under the Constitution, from George Washington to Ronald Reagan, and there are only thirty-nine of them, so there is no fortieth President."

"Ah," says the teacher, "but Grover Cleveland served two nonconsecutive terms, one from 1885 to 1889, and the second from 1893 to 1897. He counts as both the twenty-second and twenty-fourth President. That is why Ronald Reagan is the thirty-ninth person to serve as President of the United States, and is, at the same time, the fortieth President of the United States."

Isn’t that ridiculous? Why should a person be counted twice if his terms are nonconsecutive, and only once if he served two consecutive terms? Pure convention! Yet Barbara is marked wrong—just as wrong as if she had said that the fortieth President of the United States is Fidel Castro.

Therefore, when my friend the English Literature expert tells me that in every century scientists think they have worked out the Universe and are always wrong, what I want to know is how wrong are they? Are they always wrong to the same degree? (…)”

Isaac Asimov, American author and professor of biochemistry at Boston University (1920-1992), The Relativity of Wrong ☞ See also: The Relativity of Truth - a brief résumé
Apr
28th
Thu
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Isaac Asimov on Faith and Reason

“If you can’t go by reason, what can you go by? One answer is faith. But faith in what? I notice there’s no general agreement in the world. These matters of faith, they are not compelling. I have my faith, you have your faith, and there’s no way in which I can translate my faith to you or vice versa. At least, as far as reason is concerned, there’s a system of transfer, a system of rational argument following the laws of logic that a great many people agree on, so that in reason, there are what we call compelling arguments. If I locate certain kinds of evidence, even people who disagreed with me to begin with, find themselves compelled by the evidence to agree. But whenever we go beyond reason into faith, there’s no such thing as compelling evidence. Even if you have a revelation, how can you transfer that revelation to others? By what system?

Q: So you find your hope for the future in the mind.

Yes, I have to say, I can’t wait until everyone in the world is rational, or until just enough are rational to make a difference.” “
Isaac Asimov, American author and professor of biochemistry at Boston University, best known for his works of science fiction and for his popular science books (1920-1992), Bill Moyers interviewed author Isaac Asimov, World of Ideas, PBS, 1988. ☞ See also: Isaac Asimov predicted the Internet of today 20 years ago (1988)
Apr
26th
Tue
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When the answer cannot be put into words, neither can the question be put into words.

The riddle does not exist.
If a question can be framed at all, it is also possible to answer it.
(…)

For doubt can exist only where a question exist, a question only where an answer exist, and an answer only where something can be said.

We feel that even when all possible scientific questions have been asnwered, the problem of life remain completely untouched. Of course there are then no questions left, and this itself is the answer.

The solution of the problem of life is seen in the vanishing of the problem.
Ludwig Wittgenstein, Austrian philosopher who held the professorship in philosophy at the University of Cambridge (1939-1947), known for having inspired two of the century’s principal philosophical movements, logical positivism and ordinary language philosophy, Tractatus Logico-Philosophicus, (Tractatus 6.5), Cosimo, Inc., 2010,  p.107.
Mar
27th
Sun
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The Story of a Clever Young Man who dreamed of reducing the world to pure logic

“Let me tell you a little story.

There was once a young man who dreamed of reducing the world to pure logic. Because he was a very clever young man, he actually managed to do it. And when he’d finished his work, he stood back and admired it. It was beautiful. A world purged of imperfection and indeterminacy. Countless acres of gleaming ice stretching to the horizon.

So the clever young man looked around the world he had created, and decided to explore it. He took one step forward and fell flat on his back. You see, he had forgotten about friction. The ice was smooth and level and stainless, but you couldn’t walk there. So the clever young man sat down and wept bitter tears. But as he grew into a wise old man, he came to understand that roughness and ambiguity aren’t imperfections. They’re what make the world turn. He wanted to run and dance. And the words and things scattered upon this ground were all battered and tarnished and ambiguous, and the wise old man saw that that was the way things were.

But something in him was still homesick for the ice, where everything was radiant and absolute and relentless. Though he had come to like the idea of the rough ground, he couldn’t bring himself to live there. So now he was marooned between earth and ice, at home in neither.

And this was the cause of all his grief.” “
— the story told by J. M. Keynes (John Quentin) to Ludwig Wittgenstein in his death bed in a Derek Jarman's movie Wittgenstein, cited in Deniz Cem Önduygu, The Story of a Clever Young Man, Phylomeny
Feb
28th
Mon
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To develop craft, strategy, language, logic, and arithmetic the mind must range back and forth along the line of past, present, and future. The ability to fashion a tool with the right hand issues out of the left brain and depends heavily on the ability to memorize a series of steps in sequence. The dominant hand is a specialized limb that is an extension of the sequential left hemisphere.
Leonard Shlain, Art & Physics: Parallel Visions in Space, Time, and Light, New York: Harper Perennial, 1991. 2007 (tnx carvalhais)
Feb
25th
Fri
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The actual science of logic is conversant at present only with things either certain, impossible, or entirely doubtful, none of which (fortunately) we have to reason on. Therefore the true logic for this world is the calculus of Probabilities, which takes account of the magnitude of the probability which is, or ought to be, in a reasonable man’s mind.
Sep
24th
Fri
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Gilles Fauconnier & Mark Turner on the cause, effect and logic

“There is nothing more basic in human life than cause and effect. It has been a triumph of mathematics, science, and engineering to break up unified events into causal chains made up of much more elementary events, such that each is the effect of the previous one and the cause of the next. This kind of analysis gives us the feeling that we understand the complex event, having consciously reduced it to a set of basic events that are taken as self-evident. This type of explanation lends itself especially well to expression in form approaches because we can code the basic events and the causal relations symbolically, in such a way that manipulation of the formal objects correlates with the changes in the complex system they code.

For example, life and death are the biggest mysteries, and the moment of death is dramatic and punctual, but medical science breaks the event into complicated causal chains involving simply cellular and metabolic events based on heart rates, blood flow, oxygen delivery, neuronal activation, and so on. Similarly, a mathematical truth can seem striking and even mysterious, but the method of proof breaks the mystery down into a sequence of logical steps, each seemingly simply and obvious, and each leading to the subsequent step until the conclusion is reached. This was Aristotle’s insight, which also drives modern computers.” “
Gilles Fauconnier & Mark Turner, The Way We Think. Conceptual Blending & the Mind’s Hidden Complexities, Basic Books, a member of the Perseus Books Group, 2002, p.75.
May
17th
Mon
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Henri Poincaré on certainty and doubt in science

“To the superficial observer scientific truth is unassailable, the logic of science is infallible; and if scientific men sometimes make mistakes, it is because they have not understood the rules of the game. Mathematical truths are derived from a few self-evident propositions, by a chain of flawless reasonings; they are imposed not only on us, but on Nature itself. By them the Creator is fettered, as it were, and His choice is limited to a relatively small number of solutions. A few experiments, therefore, will be sufficient to enable us to determine what choice He has made. From each experiment a number of consequences will follow by a series of mathematical deductions, and in this way each of them will reveal to us a corner of the universe. This, to the minds of most people, and to students who are getting their first ideas of physics, is the origin of certainty in science. This is what they take to be the role of experiment and mathematics. And thus, too, it was understood a hundred years ago by many men of science who dreamed of constructing the world with the aid of the smallest possible amount of material borrowed from experiment.

But upon more mature reflection the position held by hypothesis was seen; it was recognised that it is as necessary to the experimenter as it is to the mathematician. And then the doubt arose if all these constructions are built on solid foundations. The conclusion was drawn that a breath would bring them to the ground. This sceptical attitude does not escape the charge of superficiality. To doubt everything or to believe everything are two equally convenient solutions; both dispense with the necessity of reflection.” “
Henri Poincaré in his Author’s Preface to Science and Hypothesis, translated from the French by William John Greenstreet, London; New York: The Walter Scott Publishing Co., Ltd., 1905, p. xxi, cited in Entersection