Veritas Aequitas wrote: ↑Thu Jan 09, 2025 3:58 am
In the first place, you are making a positive claim that the God of Islam exists as real.
You are trying to abuse the LEM (Law of the Excluded Middle). There is absolutely no evidence that the problem is even decidable. Hence, your claim is in violation of the Church-Turing thesis since it assumes a positive answer to the Hilbert's
Entscheidungsproblem. The answer has been proven to be negative.
Veritas Aequitas wrote: ↑Thu Jan 09, 2025 3:58 am
The primarily onus is on you to provide the evidence [empirical] to support your claim.
Wrong. The default position is that the problem is not decidable. Arbitrary problems are not decidable, until you can positively demonstrate that they are. Everything you write is in violation of the Church-Turing thesis:
ChatGPT: Is it reasonable to assume that all problems are decidable?
No, it is not reasonable to assume that all problems are decidable. In computer science and mathematics, decidability refers to whether there exists an algorithm that can always provide a definitive yes or no answer to a given problem within a finite amount of time.
Here are some key points:
1. Undecidable Problems
Some problems are provably undecidable, meaning no algorithm can determine the answer for all possible inputs. Examples include:
The Halting Problem: Given a program and an input, determine whether the program will eventually halt or run forever. Alan Turing proved in 1936 that this problem is undecidable.
Entscheidungsproblem (Decision Problem): David Hilbert posed this problem in 1928, asking for an algorithm to decide the truth of statements in first-order logic. Alonzo Church and Alan Turing independently proved it undecidable in the 1930s.
2. Limits of Computation
The undecidability of some problems arises from fundamental limits of computation:
Some problems are too complex or involve infinite possibilities, making it impossible for any finite algorithm to handle all cases.
Problems can also be undecidable because they encode other undecidable problems (e.g., reductions).
3. Theoretical Framework
The classification of problems into decidable, undecidable, or semi-decidable relies on computational models like Turing machines:
Decidable Problems: Problems for which an algorithm exists to always determine a correct yes/no answer.
Semi-Decidable Problems: Problems for which an algorithm can confirm "yes" answers but might run forever without giving an answer for "no."
Undecidable Problems: Problems for which no algorithm exists to decide the answer in all cases.
4. Practical Implications
In practice, many problems in software development, artificial intelligence, and mathematics are undecidable. However, heuristic or approximate methods can often provide useful solutions in specific contexts, even if a general algorithm is impossible.
Conclusion
While many problems are decidable, assuming that all are decidable would ignore fundamental limitations of computation and mathematical logic. Recognizing the boundaries of decidability is crucial for understanding what can and cannot be achieved algorithmically.
Note that according to the Curry-Howard correspondence, "proof" and "algorithm" are effectively one and the same thing.
You have in no shape or fashion demonstrated that the problem is actually decidable. Therefore, the problem must be deemed undecidable. Hence, neither "yes" nor "no" are legitimate default positions to a problem for which the decidability has not been determined.
Furthermore, your point of view is simply ridiculous.
If P is a claim then Q = "not P" is also a claim. Why would the onus to provide evidence exist for P but not for Q? In which logic system does it even work like that? Don't tell me that standard first-order logic works like that, because that is utter bullshit.