taoist
New member
Yes.Originally posted by Bob Enyart
Taoist wrote: "In 1931, delivering a body blow to mathematics, Kurt Godel showed once and for all that given any axiomatic system of thought, it is possible to create undecidable propositions."
Taoist, but was Godel's argument true? -Bob
Note that only decidable propositions can be said to be true or false. GIC is a decideable proposition, as evidenced by the fact that it has been proved within the realm of axiomatic proving systems.
This is a question of definition. A minor variation of your opening query yields a different answer. To wit, "Do truths exist?" The answer to this question is instead yes.
Truth, on the other hand, would reflect the collection of all true propositions, a collection whose complement would then be those things which are false. Such a collection does not exist, as it would require that all propositions are decidable, in contradiction to GIC.
This is especially appropriate to the question at hand, as the class of undecidable propositions is intimately related with those propositions which are recursively defined. Each time I have mapped out the question, Does God exist?, axiomatically assigning powers and properties to god, I have netted a recursive construction. An uncreated creator. An omnipotent omniscient. To show these propositions undecidable, it is necessary to reduce them to some form of Epimenides Paradox.
Fundamentally, I feel that the existence of a supernatural being may well be unprovable using evidence exclusively from the natural sciences. And no, I'm not sure if that question is decidable either.
Excuse the delay in my response, but I had been otherwise occupied.