Bruno, I have found myself in this lifetime to be a staunch OP-ponent and challenger to Godel's incompleteness theorems.
In the way that they are structured - with the premises Godel preset, of initial boundaries for what he was about to design by 'proof' - his theorems are both sufficiently closed and constituently -accurate- in their conclusion and notions. _But_, what I find disturbing about them is that they are RELIANT on a more formative -presumption-, which presumption enables an analyst to draw quite a -contradiction aspect- to what Godel announced. A self-discontinuity _within_ his theorems, as it were. Clearly, this: He tacitly identifies any information resident -outside- any current/known, as -eventually accessible, connectible, relatable-, even if it means restructuring known-information in regard to alternative/new criteria and standards definitions, descriptions, statements. It is through this process of "add then rerevaluate" that new paradigms are achieved. But, it is dependent on the compatibility of the whole scope of all the information -then- present; and the eventual capacity to coordinate statements with all content addressable by statements. So, his thesis that at any given moment in time, not all information is present or gathered, and that this makes for limited statement making, where some evaluation statements in the data-set may instead be reliant on future/other yet-to-be-included information .. is a worthy logical notion. A closed system may not completely evaluate itself -- some evaluations are indeterminant. But, think for a moment about what that presumption of eventual includability dictates: That we -can- (right now) state something specific and projective about the qualia and nature of knowledge and information -- currently -beyond- the bounds of actual experience and encounter and access. It also aserts: information 'unknown' is compatible with and eventually relatable with information 'known'. The first foundation of Godel's '"I can't decide about that" Theorems' is the moot statement: 'I -can- decide about -everything- and here's why'; --which is a contradiction of logic. The "limited" set can make true-false statement about the totality of existence (internal and external to known-ness), but it cannot guarantee it's own true-false statements without added 'external' information made internal. Therefore, the logic of future science and knowledge, I assert, is -incorrectly- contrained and defined by this - by Godel and his Incompleteness Theorems. Rather, the logic of future science and knowledge is premised in Information and Performance Holism. The unitary interactional and information accessible quality of Existence. Which fundamental notion is what Godel ignores and rejects and tries to discredit. Where, we CAN in fact make VALID STATEMENTS -about that which- the incompleteness theorems 'conclude': we should not be able to say -anything- at all. You can absolutely place me in the community of thinkers who do not "swallow the incompleteness phenomena". Because my statements/logic are not incorrect and they do identify flaw/weakness/incorrectness in Godel. He used not a tautology but a strange negative tautology. If A then not-A ; if not-A, then never(A) as long as not-A exists; and since not-A always exists then A is not accessible to evaluate not-A; but not-A can assert A and assess A. All Godel did was give a validation for information hiding and manipulation -- something useful to politicians and economic manipulators and spiritual advocates. He didn't do science or logic or math any favors. Or the future for that matter. James N Rose Bruno Marchal wrote: > > Le 01-juil.-06, à 19:59, James N Rose a écrit : > > > > > Math and reductive science ignore and dis-consider collateral > > co-extancy. > > The comp assumption leads to the less reductive possible account of the > person and person POVs. > For example, comp does not guaranties *any* survival, but it guaranties > that no such survival-guaranties are possible. It guaranties > eventually that personal identity can only be a matter of ... > *personal* matter. > > Perhaps are you confusing math before and after > Post-Turing-Church-Godel-Lob ... > > ... or you refer to those mathematicians who have not yet swallow the > incompleteness phenomena... > > Actually I believe that the incompleteness theorem (especially with > comp or weaker) makes it impossible for science, or better, for the > scientific attitude, to be reductive. With comp the diagonalization > tale is before all a lesson of modesty. > > Despite this, Goel's incompleteness theorem is a constructive theorem, > and it leads to the discovery that "machine ignorance" is wonderfully > structured, rich, productive ... > And UDA justifies why the laws of physics comes from there, in a > testable way. > > To assume our finiteness, what comp really is about, enlarges the range > of our possible infinite realms. With comp only the gods can miss the > unconceivable freedom. Somehow. > > Bruno > http://iridia.ulb.ac.be/~marchal/ > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to email@example.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---