Gödel’s Argument, Formally

Abstract

AbstractThe last Chapter ended with an informal presentation of Gödel’s argument. This one is devoted to a formalized version. I’ll also consider some objections and modifications. There are two kinds of objections. One amounts to saying that Godel committed the same fallacy Descartes did: assuming something equivalent to God’s existence. Nonetheless, again as in the Descartes case, much of the argument is of interest even if it falls short of establishing the desired conclusion. The second kind of objection is that Gödel’s axioms are too strong, and lead to a collapse of the modal system involved. Various extensions and modifications of Gödel’s axioms have been proposed, to avoid this modal collapse. I’ll discuss these, and propose a modification of my own. Now down to details, with the proof of God’s possible existence coming first. I will not try to match the numbering of the informal axioms in the last chapter, but I will refer to them when appropriate.KeywordsPositive PropertyLeft BranchConstant SymbolModal CollapseOntological ArgumentThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.