Is there a "loophole" in Goedel's interpretation of his formal reasoning and its consequences?

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dc.creatorAnand, Bhupinder Singh
dc.date2003-04-21
dc.date2003-05-17
dc.date.accessioned2026-07-07T04:57:09Z
dc.date.available2026-07-07T04:57:09Z
dc.descriptionWe formally define a "mathematical object" and "set". We then argue that expressions such as "(Ax)F(x)", and "(Ex)F(x)", in an interpretation M of a formal theory P, may be taken to mean "F(x) is true for all x in M", and "F(x) is true for some x in M", respectively, if, and only if, the predicate letter "F" is a mathematical object in P. In the absence of a proof, the expressions "(Ax)F(x)", and "(Ex)F(x)", can only be taken to mean that "F(x) is true for any given x in M", and "It is not true that F(x) is false for any given x in M", respectively, indicating that the predicate "F(x)" is well-defined, and effectively decidable individually, for any given value of x, but that there may be no uniform effective method (algorithm) for such decidability. We show how some paradoxical concepts of Quantum Mechanics can then be expressed in a constructive interpretation of standard Peano's Arithmetic.
dc.descriptionv2; revised para 5(xviii); introduced standardised ACI compliant notation for citations; 15 pages; an HTML version is available at http://alixcomsi.com/Is_there_a_loophole.htm
dc.identifierhttps://arxiv.org/abs/math/0304309
dc.identifierhttp://arxiv.org/abs/math/0304309
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/67172
dc.subjectGeneral Mathematics
dc.subject03B10
dc.titleIs there a "loophole" in Goedel's interpretation of his formal reasoning and its consequences?
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