Incompleteness, constructivism and truth
DOI:
https://doi.org/10.12775/LLP.1998.004Abstract
Although Gödel proved the first incompleteness theorem by intuitionistically respectable means, Gödel’s formula, true although undecidable, seems to offer a counter-example to the general constructivist or anti-realist claim that truth may not transcend recognizability in principle. It is argued here that our understanding of the formula consists in a knowledge of its truth-conditions, that it is true in a minimal sense (in virtue of a reduction ad absurdum) and, finally, that it is recognized as such given the consistency and !-consistency of P. The philosophical lesson to be drawn from Gödel’s proof is that our capacities for justification in favour of minimal truth exceed what is strictly speaking formally provable in P by means of an algorithm.References
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