So being a Christian who is interested in mathematics and the more theoretical aspects of science, I've come across the proof that there is no algorithm that solves the halting problem for every algorithm.
I'm wondering how this result intersects with the notion of an entity/object that possesses something like omniscience. So in theory, God knows everything that can be known (for example, He can't know a fact x such that knowing x entails a contradiction). Essentially He acts as a flawlessly accurate oracle.
So, given some arbitrary algorithm A, God looks at A and knows whether it halts. God then tabulates this in a countably infinite mental list. God therefore has a list of all algorithms, and a corresponding accurate list of whether or not the given algorithm halts. You can then construct an algorithm that takes as input a given algorithm, looks it up in God's list, and returns whether that algorithm halts. This violates the previously established result that no such algorithm can exist.
So, it seems, either there exists an algorithm A such that it can't be known whether A halts, or God can't possibly possess omniscience.
Can anyone more knowledgeable than myself give me either some pushback or maybe point me in the direction of a source that discusses oracles vis-a-vis the halting problem?
I'm wondering how this result intersects with the notion of an entity/object that possesses something like omniscience. So in theory, God knows everything that can be known (for example, He can't know a fact x such that knowing x entails a contradiction). Essentially He acts as a flawlessly accurate oracle.
So, given some arbitrary algorithm A, God looks at A and knows whether it halts. God then tabulates this in a countably infinite mental list. God therefore has a list of all algorithms, and a corresponding accurate list of whether or not the given algorithm halts. You can then construct an algorithm that takes as input a given algorithm, looks it up in God's list, and returns whether that algorithm halts. This violates the previously established result that no such algorithm can exist.
So, it seems, either there exists an algorithm A such that it can't be known whether A halts, or God can't possibly possess omniscience.
Can anyone more knowledgeable than myself give me either some pushback or maybe point me in the direction of a source that discusses oracles vis-a-vis the halting problem?
“The truth of our faith becomes a matter of ridicule among the infidels if any Catholic, not gifted with the necessary scientific learning, presents as dogma what scientific scrutiny shows to be false.”
