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model proof
model proof
From the Dictionary of Theories
© 2002 by Visible Ink Press
model theory (20th century) Mathematics
The branch of logic which studies the semantic (rather than the syntactic) properties of formal theories. In particular, it is concerned with the concepts of truth, satisfaction, and validity, rather than the intrinsic property of formal deduction. Compare with Proof Theory.
Encyclopedic Dictionary of Mathematics (MIT Press, 1987)
From the Dictionary of Theories (Visible Ink Press, 2002)
proof theory (20th century) Mathematics
The branch of logic which studies the syntactic (rather than the semantic) properties of formal theories. In particular, it is concerned with formal deductions rather than the concepts of truth, satisfaction, and validity. Compare with Model Theory.
Encyclopedic Dictionary of Mathematics (MIT Press, 1987)
From the Dictionary of Theories (Visible Ink Press, 2002)
It's all about context
It's a lonely world
The Con Text
[Excerpts from an article by Sharon Begley on new evidence that people tend to hang on to information (in their memories) that supports their world view even when they know on some level that this information or memory is false.]
1. FUNNY THING, memory.
2. ... further evidence that what we remember depends on what we believe.
3. "People build mental models," explains Stephan Lewandowsky, a psychology professor at the University of Western Australia, Crawley, who led the study that will be published in Psychological Science. "By the time they receive a (news story) retraction, the original misinformation has already become an integral part of that mental model, or world view, and disregarding it would leave the world view a shambles." Therefore, he and his colleagues conclude in their paper, "People continue to rely on misinformation even if they demonstrably remember and understand a subsequent retraction."
4. If the report had been retracted, surely people would no longer regard it as true, would they? Here is where memory parts ways with reason.
5. That comes as no surprise to memory researchers. Time and again, lab studies show that people have an astonishing propensity to recall things that never happened.
6. They held fast to what they had originally heard "because it fits with their mental model," which people seek to retain "whatever it takes."
7. The news media would do well to keep in mind that once we report something, some people will always believe it even if we try to stuff the genie back in the bottle.
8. The findings also offer Machiavellian possibilities for politicians. They can make a false claim that helps their cause, contritely retract it—and rest assured that some people will nevertheless keep thinking of it as true.
9. Conclusion: "People largely believe what they want to believe." This trite observation is nevertheless made newly distubing with every new evidence of it that has the power to remind us of just how powerful this tendency really is in all of us. And for those who may want to believe in this story, why not see just how far down the rabbit hole this story really goes?
Down the Rabbit Hole: I want to believe: I want to be: I want: I
This is the story of "I want to believe. I want to be. I want. I."
And the storyline goes like this: "I want to believe so and so. I want to believe such and such. I want to be so and so. I want to be such and such. I want to believe... I want to be... I want... I..."
10. Epiphany: I want to believe = I want to be = I want = I.
(People largely believe what they want to believe: themselves. That's who / what they're chasing. Everything else is just a sideshow along for the ride. So what do I want? I want you... to believe in me... and buy me T-shirt.)
Just How Far Down The Rabbit Hole Does The Theory Go? "The Only Thing More Important Than Being Rich Is Being Famous." "Attention! Attention!" Every man is a salesman. Selling himself and the world on the idea of his own importance and worth and the very idea of his being... being important enough to be worth attention, his and yours. Every salesman is a showman. Showing himself and others what to pay attention to. Showing himself and others what he is selling: his sense of truth, his sense of importance, his sense of pleasure. Attention is the essential truth of every man's reality. It is his highest pleasure and sense of importance. It is his highest reality. But this highly desirable reality is often only born out of pain, great pain. The man who pays attention is alive to this powerful sense of reality. The man who receives attention is alive to this powerful sense of reality. The only hope for a man who does not pay attention to himself or others or anything else... is to receive attention... from somewhere. For the man who neither pays nor receives attention is without all hope. Attention is the foundation of every faith. It is the essence of every belief. The man who pays attention and the man who receives attention are both powered by faith, by belief. For the act of attention itself is the de facto admission that something, someone, is believed (on faith alone) to be important enough to warrant attention. Even the man who pays attention only to disprove, destroy and disbelieve the importance of something or someone believes it is important to do so. Attention is the foundation of every faith and counterfaith. It is the essence of every belief and counterbelief. The only true unbeliever, the only true antifaith... —the only true absence of faith— is the absence of attention. Ø Dr. Painpang, from his book Chinese Democracy, "There Is No Business Except Show Business: Game Theory and the Bid for Attention & Money." |
(The incompleteness of all theories of completeness
... and other stories.)
From "Our Special Universe"
By Charles H. Townes
"The mathematician Gödel noted that to prove something we must start with a set of postulates, but then demonstrated that we can never prove the set of postulates are even self-consistent unless we make a new overarching set of postulates which themselves cannot be proven self-consistent. So, in science, too, we need faith—or what we normally call postulates. An extreme and somewhat amusing statement of our lack of firm proof was that of Bishop Berkeley, for whom my town of Berkeley, Calif., was named. He noted that we cannot absolutely prove that the people and things we think we see are really there—we may not be seeing them at all but only have such things in our imagination. The bishop was perhaps correct, but nevertheless we all believe those people and things we see are real."
By Charles H. Townes, Wall Street Journal, Friday, March 11, 2005.
[Mr. Townes is a 1964 Nobel laureate in physics and inventor of the laser. On Wednesday, he was awarded the 2005 Templeton prize for his study of the relation between science and religion.]
1. postulate (vb) : to assume as true
2. postulate (n) : a proposition taken for granted as true, especially as a basis for a chain of reasoning
Gödel's completeness theorem (1930) Mathematics
Named after the Czech-born American mathematician Kurt Gödel (1906-78) who gave its first demonstration, this is the result in logic whereby a propositional theory is consistent if and only if it has a model.
When expressed in terms of logical arguments, it is the theorem that an argument is valid (that is, the conclusion is true whenever all the premises are true) if and only if the argument has a formal proof (that is, the conclusion follows from the premises by applying certain rules of inference).
J E Rubin, Mathematical Logic: Applications and Theory (Saunders, 1990)
From the Dictionary of Theories (© 2002 by Visible Ink Press)
Gödel's incompleteness theorem (1931) Mathematics
Named after the Czech-born American mathematician Kurt Gödel (1906-78) who gave its first demonstration, this is the result in logic whereby if a system which formalizes the theory of the natural numbers is consistent, then this system contains a logical formula such that neither the formula nor its negation can be proved within the system. Thus one can never hope to capture truth entirely within the formal system.
Encyclopedic Dictionary of Mathematics (MIT Press, 1987)
From the Dictionary of Theories (Visible Ink Press, 2002)
"dear theo"
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