Decidability, provability, computability and predictability are all instances of *algorithmic determinism*. The crux with the latter is that it a-priori assumes for every mathematically well-posed question that either an answer exists or a proof that the question has no answer or a proof that there is no proof etc. But all of the just listed assumptions are by no means guaranteed to be constructible or to be at all mathematically existent for each and every case. Moreover, since algorithmic determinism is equivalent with the process of deductive reasoning, consequently deciding, proving, computing and predicting arrive at their natural limit when the deductive method arrives at its natural limit. Furthermore the method of deduction is often limited in its reliability by the unprovability of its starting premises. Much worse, for many unprovable false starting premises – for example about some unknown physical circumstances – the resulting conclusions cannot be proven to be false by any algorithmic procedure or physical experiment. Nonetheless, algorithmic determinism rigidly suggests that everything in nature has to be considered as being completely formalizable, despite the fact that this claim already fails when it comes to predict single quantum events. By revisiting Gödel's incompleteness results we argue that the above mentioned failure has its roots in the incompleteness of physicalism, because if physical reality would exclusively only behave due to algorithmic determinism, the latter would determine itself to be forever non-detectable. We further argue that this non-detectability is an instance of Gödel-undecidability, because just as with the latter it demonstrates that only something *outside the system* can distinguish causal-algorithmic incompleteness from causal-algorithmic inconsistency: the latter would render Quantum Theory impossible to at all being predictive whereas the former is merely incomplete due to a filtering-process from outside space-time.
Stefan Weckbach