On Marxmail, there was also the following post on this thread. In it, Carlos suggests Goedel's work as an expression of Leninist epistemology in mathematics. So, perhaps "incompleteness" is an expression of Engels and Lenin's dialectic of absolute and relative truth, and their metaphor of the mathematical asymptotic curve; relative truth as a curve progesses toward the "line" that it absolute truth but never reaches it, is _incomplete_. As finite beings our knowledge of the infinite universe is always incomplete. Materialist mathematics should reflect that.
Charles ----- Original Message ----- From: "Les Schaffer" <schaffer at optonline.net> > > "... 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." Behind the jargon, isn't this Thesis II? > > In some fundamental sense human (mathematical) activity > cannot be reduced to formalism alone, such formal systems are incomplete. So we can say that Godel et al, do for Enlighment mathematics and logic what Marx et al did to philosophy? > > The military-industrial complex aside, far from undermining the > foundations of mathematics, Godel succeeding in opening a whole new > avenue of investigation. via the work of Tarski, Barkeley Rosser (father > of marxmail alumni J Barkeley Rosser), Church/Turing, and Gregory > Chaitin, we now have deep connections between mathematics, computational > systems, and, more recently, physics. My main criticism of Academic marxism, in particular in the USA and the Americas, but even in Europe, is that they have let the pomos claim all of those developments as their own, as a matter of fact going ahead and violently trying to question every little word of every brilliant scientist and mathematician simply because wither the pomos captured them as their own, or because they themselves went to the side of the pomos. While I am not an academic, nor have more than pedestrian knowledge of many things, I do feel we need to connect with a lot of the 20th century scientific developments, something that was apparently lost outside of the States that were marxist experiments. Cybernetics and digital fault protection as the mathematical realization of Leninism, if you will. Interestingly, pomos do such no errors, and try to turn even a solid socialist Einstein into a support of Liberalism, the eternal. I am very interested in learning about current and old debates around all those questions. Pomos love to connect, say, thermodynamics and linguistics, and I see nothing anti-marxist in that process, and moreso, I see it as a political capitulation on the part of the academic marxists that they have preffered to differenciate rather than co-opt the pomo discourse, which is in very Godelian terms actuall very much more "mo" than "po". Did this rant make sense? sks ps BTW my organization has several scientists, including a spokesperson who is an MIT alumni in astro-physics (besides a siesmologist, several chemists, a pure math guy, and quite a few science teachers, including the Union president), so this is post-meeting beer conversation topic that is frequently touched. I just haven't seen it addressed from a progressive/marxist stand point in anyway that is not defeatists or negative, but doubt this is the case... so share please! Jim Farmelant farmelantj On Wed, 16 Mar 2005 15:37:26 -0500 (GMT-05:00) Ralph Dumain <rdumain at igc.org <http://lists.econ.utah.edu/mailman/listinfo/marxism-thaxis> > writes: > I don't quite understand the remark about the mixing od semnatic and > syntactic arguments by Godel. Also, what is the relation to > physics? I am not too sure about the mixing of semantic and syntactic arguments by Gödel. Apparently, there is some controversy in regards to how he should be interpreted concerning those issues. as suggested in the discussions that I found on a list devoted to C.S. Peirce. http://members.door.net/arisbe/menu/people/peirce-l/1324.htm http://members.door.net/arisbe/menu/people/peirce-l/1327.htm I think the standard interpretations assume truth to be a semantic notion whereas consistency is taken to be a syntactic property of formal systems. Gödel's Incompletness Theorems bring the two concepts together. I am not quite sure as to what Les was referring to in terms of the relations between Gödel's Incompleteness Theorems and physics. I know that Stephen Hawking for instance does think that Gödel's work does have implications for physical theory. In his lecture, "Gödel and the end of physics," (http://www.damtp.cam.ac.uk/strtst/dirac/hawking/), he contends that physical theory, like Arithmetic, may be incomplete in Gödel's sense because for one thing, our physical theories are formulated in terms of the very mathematics that Gödel had proven to be incomplete. Therefore, there will be physical problems that cannot be predicted on the basis of our physical theories. Furthermore, Hawking contends that : "Although this is incompleteness of sort, it is not the kind of unpredictability I mean.gIven a specific number of blocks, one can determine with a finite number of trials, whether they can be divided into two primes. But I think that quantum theory and gravity together, introduces a new element into the discussion, that wasn't present with classical Newtonian theory. In the standard positivist approach to the philosophy of science, physical theories live rent free in a Platonic heaven of ideal mathematical models. That is, a model can be arbitrarily detailed, and can contain an arbitrary amount of information, without affecting the universes they describe. But we are not angels, who view the universe from the outside. Instead, we and our models, are both part of the universe we are describing. Thus a physical theory, is self referencing, like in Goedels theorem. One might therefore expect it to be either inconsistent, or imcomplete. The theories we have so far, are both inconsistent, and incomplete." Hawking's lecture represents a reversal of his previously longheld position that a final physical theory is possible (and that we were close to attaining it). Now, Hawking holds that such a thing may never be possible. Hawking's new position is not unlike the one that David Bohm took in writings such as*Causality and Change in Modern Physics* (London, 1957) in which he presented a philosophy of nature in support of his hidden-variable interpretation of QM, that was broadly consonant with Friedrich Engels' philosophy of nature as presented in *Anti-Durhing* and *The Dialectics of Nature*. (Bohm was a Marxist at the time that he wrote that book). _______________________________________________ Marxism-Thaxis mailing list Marxism-Thaxis@lists.econ.utah.edu To change your options or unsubscribe go to: http://lists.econ.utah.edu/mailman/listinfo/marxism-thaxis
