>>16696390>according to Sobel, I wonder what his counter defense to Koons was.Most criticism of Gödel's proof is aimed at its axioms: as with any proof in any logical system, if the axioms the proof depends on are doubted, then the conclusions can be doubted. It is particularly applicable to Gödel's proof – because it rests on five axioms, some of which are considered questionable. A proof does not necessitate that the conclusion be correct, but rather that by accepting the axioms, the conclusion follows logically.
The first layer of criticism is simply that there are no arguments presented that give reasons why the axioms are true. A second layer is that these particular axioms lead to unwelcome conclusions. This line of thought was argued by Sobel, showing that if the axioms are accepted, they lead to a "modal collapse" where every statement that is true is necessarily true, i.e. the sets of necessary, of contingent, and of possible truths all coincide (provided there are accessible worlds at all). According to Koons,Sobel suggested in a 2005 that Gödel might have welcomed modal collapse.
Sobel's proof of modal collapse has been questioned by Koons, but a counter-defence has been given.
Criticisms also focus on the question of whether these axioms must be rejected to avoid odd conclusions. The broader criticism is that even if the axioms cannot be shown to be false, that does not mean that they are true. Hilbert's famous remark about interchangeability of the primitives' names applies to those in Gödel's ontological axioms ("positive", "god-like", "essence") as well as to those in Hilbert's geometry axioms ("point", "line", "plane"). According to André Fuhrmann (2005) it remains to show that the dazzling notion prescribed by traditions and often believed to be essentially mysterious satisfies Gödel's axioms. This is not a mathematical, but a theological task. It is this task which decides which religion's god has been proven to exist.
