Re: [PEN-L] More Godel
Les Schaffer wrote:
> in relation to a question raised on marxmail regarding any relationship
> between Godel's and Heisenberg's work: next to Goldstein's book at the
> Border's Bookstore math section stood an interesting work by Palle
> Yourgrau (philosopher at Brandeis) entitled "A World Without Time: The
> Forgotten Legacy Of Godel And Einstein".
>
**IMHO**, based on my struggles with another book ("godel meets
einstein") of his books, yourgrau is a tough read of questionable
value... but that may just be my own limitation.
--ravi
Re: [PEN-L] More Godel
michael perelman wrote: Mirowski says that Godel's proof rattled both Turing & Van Neuman, making them turn from formalizing to matters such as game theory & computers. i grabbed a copy of Goldstein's book this morning in the bookstore and gave it a fast read (good on history and philosophical context for the work, weak on appreciation of what Godel produced, IMHO: too much loose philosophical interpretation). turns out von Neumann was at the conference where Godel presented his results, and caught its significance immediately, particularly in after-lecture discussions with Godel. He returned to Princeton and really pushed the ideas in lectures and discussions. he wrote Godel shortly thereafter with an extension to Godel's theorem which the latter hadnt presented in the conference but in fact had already worked out. Godel was evidently pleased that a "giant" like von neumann got the message, a result that Goldstein says was absent in the case of Wittgenstein's misunderstandings of Godels proofs. Likewise Turing picked up the ball in the mid-30's and ran rather far with it in computational matters, as ravi points out in a later post. This thread continues to the present day, to the point where a commited amateur can now browse the web for work of Gregory Chaitin and actually download programs which concretely illustrate the results (Chaitin as i recall provides a slightly modified LISP suitable for running his code). in relation to a question raised on marxmail regarding any relationship between Godel's and Heisenberg's work: next to Goldstein's book at the Border's Bookstore math section stood an interesting work by Palle Yourgrau (philosopher at Brandeis) entitled "A World Without Time: The Forgotten Legacy Of Godel And Einstein". midway into the book Yourgrau relates an incident involving John Wheeler, a Princeton physicist, and the two co-authors of his (ahem) massive treatise on general relativity (Gravitation). Wheeler et al one afternoon decided to pay Godel a visit across campus, and they asked him directly if there was any relationship between the incompleteness theorems and the uncertainty principle. Godel's answer was apparently fairly brief with a "NO" for the upshot. Yourgrau goes on to speculate on why Godel would have felt this way, and discusses how Godel abhorred the positivist-like approach of the Copenhagen school whereas Godel would have seen himself -- an unabashed Platonist and believer in the reality of mathematical ideas -- and his theorems as in part exposing the barrenness of a formalism which would also deny physical reality to electrons et al. Both Goldstein and Yourgrau discuss extensively the Vienna school, and i am hoping Jim Farmelant kicks in here with some further insights. [Jim: i'll get to Dumain's questions hopefully tmw] les schaffer
Re: [PEN-L] More Godel
Charles Brown wrote: > > CB: As Carlos on Marxmail suggested might be pertinent to this: > > "The question whether objective truth can be attributed to human thinking is > not a question of theory but is a practical question. Man must prove the > truth, i.e., the reality and power, the this-sidedness [Diesseitigkeit] of > his thinking, in practice. The dispute over the reality or non-reality of > thinking which is isolated from practice is a purely scholastic question." > 2nd Thesis on Feuerbach > > > Carlos said over there on Marxmail: > >>"... Godel, in this paper which established his two great theorems by >>methods which are constructive in a precise sense, on the one hand >>showed the essential limitations imposed upon constructivist formal >>systems (which include all systems basing a calculus for arithmetic upon >>"mathematical induction"), and on the other hand displayed the power of >>constructivist methods for establishing metamathematical truths." > > Carlos: Behind the jargon, isn't this Thesis II? > its amusing to note that i find the first quote (2nd thesis on feuerbach) impenetrable jargon, while the second (on godel's result) is precise and clear to me. it all depends on your indoctrination, i guess ;-). --ravi
Re: [PEN-L] More Godel
michael perelman wrote: > Mirowski says that Godel's proof rattled both Turing & Van Neuman, > making them turn from formalizing to matters such as game theory & > computers. > probably true, but IIRC turing published his halting problem result after 'undecidability propositions of principia mathematica ...'... i'll have to look it up. one could say thats computational theory, but since turing's model of computation turns out to be the best available (turing himself, IIRC having shown the equivalence of the lambda calculus, etc), and some clear notion of computation being of use in demonstrating decidability ... blah, blah ... in fact, in computer science curriculum godel's theorem is often introduced by way of turing machines. as an interesting side-note: a series of further interesting results were established post godel. i point you, for fun, to paul cohen's undecidability proof of the continuum hypothesis in ZFC, and some of his other results in the space. --ravi
[PEN-L] More Godel
Michael Perelman: Mirowski says that Godel's proof rattled both Turing & Van Neuman, making them turn from formalizing to matters such as game theory & computers. -clip- CB: As Carlos on Marxmail suggested might be pertinent to this: "The question whether objective truth can be attributed to human thinking is not a question of theory but is a practical question. Man must prove the truth, i.e., the reality and power, the this-sidedness [Diesseitigkeit] of his thinking, in practice. The dispute over the reality or non-reality of thinking which is isolated from practice is a purely scholastic question." 2nd Thesis on Feuerbach Carlos said over there on Marxmail: > > "... Godel, in this paper which established his two great theorems by > methods which are constructive in a precise sense, on the one hand > showed the essential limitations imposed upon constructivist formal > systems (which include all systems basing a calculus for arithmetic upon > "mathematical induction"), and on the other hand displayed the power of > constructivist methods for establishing metamathematical truths." Carlos: Behind the jargon, isn't this Thesis II?
[PEN-L] More Godel
Mirowski says that Godel's proof rattled both Turing & Van Neuman, making them turn from formalizing to matters such as game theory & computers. Mirowski, Philip. 1991. "When Games Grow Deadly Serious: The Military Influence on the Evolution of Game Theory." Craufurd D. Goodwin, ed. Economics and National Security: A History of their Interaction (Durham: Duke University Press): pp. 227-55. -- Michael Perelman Economics Department California State University michael at ecst.csuchico.edu Chico, CA 95929 530-898-5321 fax 530-898-5901
