AI bot admits its flawed logic

 

What is the possibility that an AI system can determine the accuracy of any statement that concerns its existence?

PERPLEXITY

It is possible for an AI system to determine the accuracy of any statement that concerns its existence, but it would depend on the programming and capabilities of the AI system123. AI systems can be programmed to evaluate the accuracy of statements based on data and models, and to continually fine-tune algorithms to ensure they provide the most accurate results possible3. However, AI systems can also be overconfident when they make mistakes, and they lack consciousness and self-awareness, which limits their ability to evaluate the accuracy of statements that concern their existence2. Therefore, while it is possible for an AI system to determine the accuracy of statements that concern its existence, it would depend on the specific programming and capabilities of the AI system.

1

sciencedaily

2

caltech

3

techtarget

Why didn't you know you were wrong that "It is possible for an AI system to determine the accuracy of any statement that concerns its existence" by not taking into account the relevant theorems of Goedel and Turing?

PERPLEXITY

I apologize for my previous answer. I did not take into account the relevant theorems of Gödel and Turing. Gödel's incompleteness theorem states that any formal system, such as an AI system, cannot prove all true statements within that system1. Turing's work on computability and the halting problem showed that there are limits to what a computer program can compute2. Therefore, an AI system cannot determine the accuracy of any statement that concerns its existence, as it would require the system to prove all true statements about itself, which is impossible due to the limitations of formal systems and computability. Thank you for bringing this to my attention.

Human TM can't be dumb enough

Suppose a human cognition apparatus (loosely, "mind") is modeled as a Turing Machine. In that case, if that TM "knows" (has available from memory) its Description Number, then it can compute its design code -- its particular rules of computation.

But, such a computation is equivalent to the derivation or proof of axioms from the theorem, "This TM's DN is x."

Yet, we know from Goedel's results that such a TM has a low level of sophistication, that the TM must be equivalent to the level of sophistication needed to do the arithmetic that lacks the division operation. But since humans routinely do arithmetical calculations that include the division operation, it follows that no human can know the equivalent of her or his DN. This consequence further implies that there is a component of human cognition that transcends human understanding. That is, as Roger Penrose has argued at length, computation is insufficient to account for all human cognition.

Hence Penrose is correct to say that a scientific explanation must be found in some novel approach, possibly via quantum physics. Also correct are those who say that human cognition implies a "noumenal" or hidden means of "intuition" (for want of a more precise English word).

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Turing's halting problem result is a variant of Goedel's theorem, but that is not my thrust here.

FOOTNOTE AR.721

Footnote AR.721. I choose in this paper to curtail the term "spirit" in connection with the possibilities of thought transference and other supposedly "occult" phenomena. In fact some phenomena may be occult, if we mean by occult "inability to see or detect the causal agents." I curb the aforementioned term on ground that over the centuries it has picked up many connotations that do not serve our interests here. So, we suggest the term "noumenal psyche." You may say that this is a mere synonym. Yet, it is, I urge, legitimate science to postulate that there is an aspect of human cognition that does not adhere to ordinary physicalist analysis (see Russell, Whitehead, T. Nagel, Descartes and numerous others).

We will have more to say on the noumenal psyche in a paper in progress now (Jan. 27, 2023).

On engrams

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The following note on engrams was inserted Jan. 27, 2023.

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Assuming the existence of one or more types of engram, or fundamental memory unit, it is to be expected that the process of association implies some form of energy value attached to engram links. A --> B says that basic memory A instigates basic memory B, not not necessarily the converse. A <--> B means A instigates B and B instigates A, whichever is triggered first.

But, under what conditions does A --> B? The link value must exceed that of competing possibilities, such as R --> S. In most situations, this means that A and B are sets, indeed subsets of engrams. So A --> B requires that A ⊆ X and B ⊆ Y, so that X ∩ Y = AB. The strength of the association between X and Y is determined by the subset of common links.

I suppose a way to represent engram associations and sets of associations would be with a weighted graph.

(A --> B) <--> C is a possible way to write of simple associations. Obviously association sets become very complicated.

In any case, suppose we have A --> B and A --> C, but the AB link is far stronger than the AC link. So we have AB >> AC, whereas if the link magnitudes are roughly equal, we have AB ~ AC.