Godel's incompleteness states that mathematical solutions do not exist for everything, and AI does not provide mathematical models for everything because it is heuristic and still incomplete without quantum computing. In this context, Turing's completeness event horizon is still true.

Thanks Professor Vivek Kumar Sharma,

I'll respond more fully in a few days but in short there is a higher order of reasoning that I need to try and frame for you. I'm dealing with an #InfoRec thing atm so can't respond immediately. Also thankyou for acknowledging the possibility of #TuringCompleteEventHorizon - I've got more to add here when the time is right.

Chat soon!

ap

Most Welcome ! Professor Andrew Prendergast

We are waiting for further discussion and as per the Godel and Indian Philosophy, The reasoning is not explainable for everything(Quantum Mechanics).

Thanks Very much

Dear Professor Vivek Kumar Sharma ,

I have given this a bit of thought and what you need to consider is the possibility that Bayesian reasoning is a higher order of reasoning that:

• subsumes Propositional Logic (as I demonstrate in the preprint excerpt mentioned above),
• subsumes Predicate Logic,
• subsumes Set Logic and
• can implement Fuzzy & Fuzzy Set Logic successfully without any problems,

and when one moves a calculus or system into the Bayesian Calculus, typically it fixes many edge cases and one also acquires the additional fidelity, expressiveness and parsimony of the Bayesian Calculus.

For example, Bayesian Shapley is much better than classical Shapley as it fixes some annoying quirks and can do a little more.

This is why I say that resolving Gödel's incompleness-es is a possibility with the higher order reasoning capabilities of the Bayesian Calculus, particularly if the Bayesian Calculus is the single normative system into which all others can be represented/subsumed. I could be wrong, but it's something worth considering.

Also you will find my Probabilistic Logic calculus isn't heuristic - it is closed form and complete. It's a bit different to the LLM stuff the tech bros are pursuing. Just the asymptotic complexity of my thesis is quite an extraordinary thing to study, making it impractical for practical application without adding some sort of heuristics or estimation to reduce down the size of the networks produced. To that end, I do wonder and posit that the LLM systems are actually modelling my closed form functions.

For a system to be properly subsumed or represented in the Bayesian Calculus, it needs to be reduced down to it's most elemental components, each component needs to be passed through the Bayesian Network Chain Rule and re-produced on the other side probabilistically, then all the component parts can then be re-assembled into a Bayesian representation of the system in question.

This is what I have done with Logic; but one could just as easily apply the same methodology to Fourier Domain or to General Relativity, and acquire the additional power of Bayesian Reasoning after doing so. It is time consuming and I have over-simplified it here, but that is basically how things go in Bayesian land.

For what I did with logic, it is much like trying to thread Aristotle through the eye of a needle and on the other side we get the additional fidelity, expressiveness and parsimony of Bayesian-ism added to his thesis.

If this interests you, I'm more than happy to do a Google Meet session or two where I explain & demonstrate Probabilistic Logic to you as a Bayesian network and show you it in operation. I am more than happy to show you some basics of using Bayesian inference tools as well to bring you up to speed and so you can form your own opinion, if you like.

Please reach out to me by email if the above interests you at [email protected]. I also hope the above explanation was sufficiently clear, please let me know if any aspect of it is not.

I look forward to your response.

Best Regards,

AP on CompSciFutures