On Oct 27, 3:23 pm, CrossBow <[EMAIL PROTECTED]> wrote: > so is that a perfect example of what I just said...Logic is only limited by > human use of it? did I have to say "misuse'? did I have to say flawed use > of it to make it clearer? You know, my emails have the potential of being > too long if I cover my butt on every angle...
I didn't bother to read the following link but I am familiar with the work of Kurt Godel who formaly proved that there were limits to formal systems. http://plus.maths.org/issue39/features/dawson/ Gödel and the limits of logic by John W Dawson Jr. The man in the photograph on the right looks formal, reserved and somewhat undernourished. His face and his writings are unfamiliar to most, except for a few philosophers and mathematical logicians. He was Kurt Gödel, celebrated for his incompleteness theorems, the implications of which are far-reaching for the foundations of mathematics and computer science. The story of his life and work is that of a persistent quest for rationality in all things, pursued against a background of recurrent mental instability. Gödel proved that the mathematical methods in place since the time of Euclid (around 300 BC) were inadequate for discovering all that is true about the natural numbers. His discovery undercut the foundations on which mathematics had been built up to the 20th century, stimulated thinkers to seek alternatives and generated a lively philosophical debate about the nature of truth. Gödel's innovative techniques, which could readily be applied to algorithms for computations, also laid the foundation for modern computer science. Mr Why Born on April 28, 1906, in Brno, Moravia, Gödel was the second of two children of Rudolf and Marianne Gödel, expatriate Germans whose families were associated with the city's textile industry. Gödel and his brother were both sent to private German language schools, where they did very well in their studies. Indeed, only once during his primary and secondary school career did young Kurt ever receive less than the highest mark in any subject (mathematics!). Yet he gave no early intimation of genius. He was a highly inquisitive child, so much so that he was nicknamed der Herr Warum ("Mr. Why"). But he was also introverted, sensitive and somewhat sickly. At about the age of eight he contracted rheumatic fever, and although it seems not to have caused lasting physical damage, it kept him out of school for some time and may have fostered the exaggerated concern for his health and diet that was to become increasingly prominent over the years. The reticent genius In 1924 Gödel left his homeland to enrol at the University of Vienna. At the time of his enrolment Gödel intended to seek a degree in physics. But after a short while, impressed by the lectures of professors Philipp Furtwängler and Hans Hahn, he switched to mathematics. His remarkable talents soon attracted attention — so much so that just two years after his matriculation he was invited to attend sessions of a discussion group that Hahn and philosopher Moritz Schlick had founded two years earlier. The group, which was later to become famous as the Vienna Circle, was inspired by the writings of Ernst Mach, a champion of rationalism who believed that all things could be explained by logic and empirical observation, without recourse to metaphysics. The Circle brought Gödel into contact with scholars such as philosopher of science Rudolf Carnap and mathematician Karl Menger and helped to acquaint him with the literature of mathematical logic and philosophy. In particular, the Circle was immersed in the writings of Ludwig Wittgenstein, whose concern about the extent to which language can speak about language may have prompted Gödel to probe analogous questions about mathematics. Gödel did not, however, share the positivistic philosophical outlook of the Circle, which extended Mach's ideas. Instead he was a Platonist: he believed that in addition to objects, there exists a world of concepts to which humans have access by intuition. For Plato, who lived around 400 BC, concepts such as truth were not products of the human mind which can change according to the thinker's point of view, as some philosophers believe, but existed independently of the human observer. Thus, a statement could have a definite "truth value" — be true or not — whether or not it had been proved or could be empirically confirmed or refuted by humans. Gödel subscribed to this philosophy, and, in his own view, this was an aid to his remarkable mathematical insights. Although Gödel was an attentive observer and clearly brilliant, he rarely contributed to the Circle's discussions, unless they were about mathematics. Shy and reclusive, he had few close friends. (He did, however, like the company of women and was apparently quite attractive to them.) After 1928 he seldom attended the group's meetings but became active instead in a mathematical colloquium organised by Menger. Moment of impact During this period, Gödel suddenly acquired international stature in mathematical logic. Two papers in particular thrust him into prominence. One was his doctoral dissertation, submitted to the University of Vienna in 1929 and published the next year. The other was his treatise On Formally Undecidable Propositions of Principia Mathematica and Related Systems, published in German in 1931 and submitted as his Habilitationsschrift (qualifying dissertation for entrance into the teaching profession) in 1932. The dissertation, entitled The Completeness of the Axioms of the First- Order Functional Calculus, solved an open problem that David Hilbert and Wilhelm Ackermann had posed in their 1928 textbook Grundzüge der theoretischen Logik (Foundations of Theoretical Logic). The problem concerned formalised mathematical systems and the accepted rules for logical reasoning, which were stated in the book. A formalised mathematical system is described by a set of axioms. These are pre-determined truths that define the objects in the system and are never called into question. The ancient mathematician Euclid, for example, based his theory of plane geometry on five axioms. The statements "any two points can be joined by a straight line segment" (fig 1), and "any straight line segment can be extended indefinitely" (fig 2), are two of these axioms For the rest of the article go to the link. http://plus.maths.org/issue39/features/dawson/ On Oct 27, 3:23 pm, CrossBow <[EMAIL PROTECTED]> wrote: > so is that a perfect example of what I just said...Logic is only limited by > human use of it? did I have to say "misuse'? did I have to say flawed use > of it to make it clearer? You know, my emails have the potential of being > too long if I cover my butt on every angle... > > yes, I am a crotchblow and a very fine one at that. > > > > On Mon, Oct 27, 2008 at 3:09 PM, stem cell <[EMAIL PROTECTED]> wrote: > > > Crotchblow said >>> Logic is not limited in scope, only the "human" > > use of it is. <<< > > > Does this make sense in this regard? > > > 1. All birds are mammals. (premise) > > 2. A platypus is a bird. (premise) > > 3. Therefore, the platypus is a mammal. (conclusion) > > > "This is a valid deductive argument, even though the premises are both > > false. But because those premises are not true, the argument is not > > sound. It is interesting to note that the conclusion is true — this > > demonstrates that an argument with false premises can nevertheless > > produce a true conclusion." > > > Critiquing Arguments > > How To Tell When Arguments Are Valid And/Or Sound > > By Austin Cline, About.com > > > Rick S said >>>For example, Carl Jung talked about a "collective > > unconsious". And there's intuition, like when twins separated by > > some > > distance know the other is hurt. Logic is great but it is not the > > only tool in the toolbox. >>> > > > The link was about "truth", correct? I'm not trying to be a smart > > arse. If I am wrong about this assertion then I will go back and read > > the article link again. I have quoted this saying in the past and > > will do so again. "True for you or true for all? If true for all > > then you must give us some kind of objective standard to go by." > > > stemcell > > > On Oct 27, 10:14 am, "C B" <[EMAIL PROTECTED]> wrote: > > > Logic is not limited in scope, only the "human" use of it is. Logic is > > not > > > an isolated system because the brain is not structured that way. Crays or > > > thier ilk could be the only true isolated-logic producers we have. Our > > fat > > > little pinkish grey brain cells can make up some pretty interesting stuff > > > like "faith" - you can get lost squirming in metaphysics, which, in my > > > opinion, does not take an intuitive thinker, but one that is willing to > > be > > > led from logic toward delusion. Okay, stake me in the heart, for that > > one, > > > but I can't go there and believe me I have tried numerous times. > > > > Would you agree that Humans only have one perspective for each brain that > > > can only be glimpsed by another brain and much of what we think is a > > > delusion to someone else (that is not to be construed as disparaging to > > > anyone else)? Logic may be our only bridge.... > > > > On Mon, Oct 27, 2008 at 9:23 AM, stem cell <[EMAIL PROTECTED]> > > wrote: > > > > > >>>Rick S said, "My aim is not to disparage logic, > > > > only to point out that it is limited in scope." > > > > > Can you provide an example of another type of verification system that > > > > works better than logic? Do you know of any system that is not > > > > "limited" or at least not as "limited" and what is that system? > > > > > The only ones I can come up with are psychic abilities and > > > > FAITH. :-) Not sure "FAITH" is a "system" but go with me here. :-) > > > > > >>>Taylor said, "Most people who go to great lengths to point out > > limits of > > > > science > > > > (real or imagined) are usually doing so in order to remove obstacles > > > > to your believing in their brand of woo." > > > > > Dr. Wayne Dyer, perhaps? Charles Gillihan? Michael Behe? Oooh > > > > oooh! Wait...Steven C. Myer of the Discovery Institute. > > > > > >>>Taylor said, " I see nothing on the site about who "Dr. Terry > > Halwes" is > > > > or what his > > > > credentials are. That normally means a medical doctor or dentist, at > > > > best, but more likely a Ph.D. in theology or some other pseudo > > > > science. In other words, not a scientist." > > > > > What about a phone psychic? Wait...did I just say that or think it? > > > > > stemcell > > > > > On Oct 26, 11:53 pm, Rick S <[EMAIL PROTECTED]> wrote: > > > > > Hi all, > > > > > In researching an idea for an essay I had about the limits of > > > > > logic, I came across a very interesting essay by a scientist, to > > which > > > > > I will provide a link. By the way, I also picked up some very > > > > > interesting quotes about logic. My aim is not to disparage logic, > > > > > only to point out that it is limited in scope. First the quotes: > > > > > > "What is laid down, ordered, factual is never enough to embrace the > > > > > whole truth: life always spills over the rim of every cup." > > > > > - Boris Pasternak > > > > > > "Pure logic is the ruin of the spirit." > > > > > - Antoine de Saint-Exupery > > > > > > "A mind all logic is like a knife all blade. It makes the hand bleed > > > > > that uses it." > > > > > - Rabindranath Tagore > > > > > > The wrong view of science betrays itself in the craving to be right; > > > > > for it is not his possession of knowledge, of irrefutable truth, that > > > > > makes the man of science, but his persistent and recklessly critical > > > > > quest for truth. > > > > > Sir Karl Popper > > > > > The Logic of Scientific Discovery > > > > > > Here's the link: http://dharma-haven.org/science/terrible-truth.htm > > . > > > > > > Rick S- Hide quoted text - > > > > - Show quoted text -- Hide quoted text - > > - Show quoted text - --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Memphis Freethought Alliance" group. 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