Thought Systems As Inputs For Turing Machines‐Our Tool For Framing Metaphors Of Intersubjective Truths - jalToorey/IdealMoney GitHub Wiki

Thought Systems As Inputs For Turing Machines: Our Tool For Framing Metaphors Of Intersubjective Truths or Complex Traditions Related to Interpersonal Behavior

In our last essay we outlined a tool for traversing intersubjective truths or complex traditions related to interpersonal behavior. Borrowing the concept from Nick Szabo we call it Szabonian deconstruction.

It is Szabonian in that:

there is the consideration of metaphors and games as useful frameworks for observation

there is the consideration of the depth of complexity of an object in relation to another

there can be horizontal (transient) or vertical (traditional) distance in this regard

the intent is to reduce complexity through choice of framing

shallow complexity is likely unreliable in contrast to deeply evolved complexity

Representing Civilizations as Turing Machines That Compute to Evaluate Religious Truths

We want to think of systems of thought as inputs for a turing machine.

In An Introduction to Algorithmic Information Theory Szabo gives us a formalized framework with which we can view systems of thought as turing machines:

The description method that meets these criteria is the Kolmogorov complexity: the size of the shortest program (in bits) that without additional data, computes the string and terminates. Formally:

K(x) = min|p|:U(p)=x where U is a universal Turing machine.

Civilizations are in this sense seen like a natural simulation that allows us to look back and understand actual nature by observing what Szabo hints at:

i) whether or when it flourished or faded, ii) whether and when it was more or less prosperous, iii) and of it’s knowledge and command of nature:

On Teasing Out Hermeneutic Truths In a Useful Fashion

ChatGTP on Gödel's Incompleteness Theorems:

Kurt Gödel, an Austrian logician, mathematician, and philosopher, published two incompleteness theorems in 1931 that have profound implications for the field of mathematics, logic, and beyond:

First Incompleteness Theorem: Gödel's first theorem states that in any consistent formal system that is capable of expressing basic arithmetic, there are propositions (statements) that cannot be proven or disproven within the system. This means that the system is "incomplete" because there are true statements about natural numbers that the system cannot prove to be true.

Second Incompleteness Theorem: The second theorem builds on the first by showing that no consistent system can prove its own consistency. In other words, assuming the system is capable of doing a certain amount of arithmetic, if the system can prove its own consistency, it would actually be inconsistent.

If we are to consider cultures as systems of thought as inputs to turing machines we can understand the difference between Godels theorems and actual nature. Here we use a Szabonian tool from our last essay:

A good rule of thumb for rational interpretation of theological justification: map the objective fact of cultural evolution to the intersubjective truth of God.

Moveover, consider Gödel's statement-that in any consistent system capable of expressing basic arithmetic, there are propositions that cannot be proven or disproven within the system-with respect to another Szabonian tool from our Deconstruction tool set:

In other words, treat God or the gods as a metaphor for our modern insights into cultural evolution

If we mean to consider propositions that cannot be proven within a system then we dare say a culture would naturally tend to ‘cover up’ these unprovable truths (who would deny this as human nature!?).

If we are thinking from Szabo’s intention we can see that this would imply adding an axiom to the thought system, or an additional narrative to the religion, that explains or asserts the unprovable truth to be truth.

Holy truths then, are clues as such. They are byproducts of other axioms. If we are thinking from terms of the observation of a culture they would exist after the culture was exposed to phenomenon not explainable, and not previously explained within the system.

This is the type of framework that Szabo shows us is useful.

On the Axiom of Self-Consistency In the Face of Natural Inconsistency In a System of Belief

Consider then with this framework the effects of Gödel's second theorem that no consistent system can prove its own consistency.

And yet in the face of inconsistency don’t we expect a cultural or a thought system, one that is highly evolved to be survivable, to at least attempt to survive, and if by nothing else by adding an axiom of self-consistency?

“Ah but you have broken Gödel's truth”, you might say.

But we haven’t broken it.

Rather, the unsuspecting civilization has unknowingly adopted an axiom that is intrinsically false. The civilization, that in the face of some certain phenomenon, that caused them to face the truth of their system's inconsistency adopted somehow an axiom that simply re-asserts the system's consistency.

We shouldn’t forget then, that just because we later prove something to be false, that we didn’t repeatedly in our past use it as if it was true.

This is a tool that we further derive from Szabo’s explanation of how to look through this type of complexity.

On the Problem of Asserting Unprovable Truths As Truth Or Rather Provably False Beliefs As True

We can see the problem then for the unsuspecting civilization that has unknowingly adopted an axiom that is intrinsically false.

They hold themselves to the behest of any exogenous natural force that means to test the inconsistency of their system.

And they are thus unable to use reason to lift themselves beyond their limitation.