Friday, April 28, 2023

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.

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.

Tuesday, March 14, 2023

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

Friday, January 27, 2023

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


The following note on engrams was inserted Jan. 27, 2023.
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.
                             A
                           // \   
                          B    C

AB > AC. We also have (CB --> A) > (BC --> A). That is the engram order CB triggers engram A more readily than does order BC.

It's possible of course to assign numerical values to links. If we make 1 the strongest possible value and 0 the lowest, we may approximate intermediary values using the real number continuum or we may assign some lowest possible finite value to an engram link. It's conceivable that in some sets, the engrams are "coherent" in such a manner that their values can be simply added while in other cases they behave as if under destructive interference, with the set value going to 0. In most cases, we would have sets of mixed value -- the engram links are "out of phase" and yield an imperfect memory, blurred in places and lacking certain links that would be regarded as important (components of the memory set are lacking).

Both fatigue and competing mental activity can affect the cohesion of memory sets.

How does this model fit with machine learning? Machine learning essentially requires that success be rewarded, which means reliable attainment of sets of numbers. The machine is programed to filter results thru negative feedback control. In the case of human memory, the system behaves analogously. The primary engrams may not be specifically of memories. They might be the instincts, the axioms of human cognition. (The archetypes of Jung we see not as axioms, but as cultural artifacts that arise in the manner of parallel evolution of species.)

Tuesday, January 24, 2023

Freud on telepathy

First published Oct. 10, 2013.
An amended copy published on Substack Jan. 18, 2023.
The version below has been further amended, tho not extensively.


Following Kant, I have taken lately to using the terms "noumena" and "noumenal world" to describe the reality behind the phenomenal world of appearances.

If one concedes a noumenal world, does not that open a Pandora's box of delusional thinking from untutored enthusiasts? Unfortunately, that is the case. In fact this is why Ernest Jones, Freud's collaborator, reportedly urged Freud to tone down discussion of phenomena known under the heading of telepathy. Freud however revealed his thoughts in an article, Dreams and Telepathy, that appeared in Imago, a journal for Freudian ideas in society and culture, in 1922 and in New Introductory Lectures on Psycho-analysis (Chapter 2, Dreams and the Occult, Lecture XXX) that was published in 1933.

In the Introductory Lectures, Freud points out that if one were to say the earth's core contains carbonic acid, that idea would be viewed with suspicion, but as not altogether inconceivable. However, if one claimed the core is composed of jam, we have a right to dismiss the claim out of hand, jam coming from human actions on fruit. So, though one is entitled to reject some claims prior to examination, Freud is concerned that claims about occult phenomena may sometimes be rejected too quickly. He recalled the negative reaction that greeted his ideas about unconscious influences and sexual impulses.

In this light, Freud cites the scientific derision that greeted those who claimed that certain rocks found on the ground had fallen from the sky or that shells found on mountains implied that that terrain had once been seabed.

Using the term "occult" in the sense of unseen influences without suggesting a spirit domain, Freud sees much of occultist literature as representing a reflection of the anti-rationalism found among humans. Even scientists, after the conference is over, enjoy poking fun at their own activities; serious men enjoying a joke (and, as Freud observed, jokes reflect a need of the unconscious for irrationality, relief from "control"). So Freud is saying that occultist literature often expresses the strong anti-rationalist impulses common to all humans. We like to suspend the cold laws of nature, the machine-side of existence.

He grants that it may be "hard to avoid suspicion that the interest in occultism is a religious" ploy to overturn hard science, whereby the occultists are secretly trying to aid religion, but he argues, "at some point, we must overcome our disinclinations."

A problem is that "we are told that in fact our unbelieving -- that is to say, critical -- attitude may prevent the expected phenomena from happening." Freud is talking here about seances and mediums, most of whom he sees as charlatans. However, as pointed out in my paper, Toward a Signal Model of Perception, the reality construction process described there could very well be limited by negative belief.

Toward a signal model of perception
http://paulpages.blogspot.com/2013/03/toward-signal-model-of-perception.html

At any rate, Freud sees a "real core of yet unrecognized facts in occultism around which cheating and phantasies have spun a veil which is hard to pierce."

In the particular case of telepathy, most reported instances can be dismissed, he says. But a few remain that are hard to wave away. Freud insists he remains neutral on the subject, but it is clear that he is quite persuaded of something odd going on.

He asserts that in a telepathic dream the telepathic element plays the same role as any other residue (dream "trigger") of the day.

Freud gives an example of a man who dreamed his wife had twins; not long after, his daughter, who was some distance away, gave birth to twins (this was in the era before technology might have tipped him off). Freud weighs in with a psychoanalytic explanation, but nevertheless concedes what appears to be a telepathic element, which even so may have a natural explanation.

Freud's discussion of another situation -- his patient P's thought transference with respect to "Dr. Forsyth" -- would be dismissed by many probabilists on the random coincidence idea as discussed in Toward. However, it is often the case that those who have such experiences as described by Freud regard them as meaningful. There is a "shock of recognition" or a "strumming of an inner cord" that in my estimate may sometimes equate to a realization that we are seeing some effect of a noumenal world. Jung gave the name synchronicity to effects of the noumenal world; others describe such effects as the work of the realm of spirits. I could defend the idea of spirit as that part of the personality that inhabits the noumenal world, analogous to a software program inhabiting a mainframe computer. If the software program were conscious, it would not directly relate to the mainframe.

"One is led to the suspicion," maintains Freud, that telepathy is "the original, archaic method of communication between individuals and in the course of phylogenetic evolution it has been replaced with the better method of giving information via signals which are picked up by the sense organs."

Freud relates a report of Dorothy Burlingham, a psychoanalyst and "trustworthy witness." (She and colleague Anna Freud did pioneering work in child psychology.)

A mother and child were in analysis together. One day she spoke during analysis of a gold coin that had played a particular part in one of her childhood experiences. On returning home, her boy, who was about 10, came to her room and gave her a gold coin which he asked her to keep for him. Astonished, she asked him where he had got it. It turned out that it had been given him as a birthday present a few months previously, but there was no obvious reason why he had chosen that time to bring her the coin.

Freud sees this report as potential evidence of telepathy. One might also suspect it as an instance of "synchronicity" or the reality construction process described in Toward.

At any rate, a few weeks later the woman, on her analyst's instructions, sat down to write an account of the gold coin incident. Just then her child approached her and asked for his coin back, as he wanted to show it during his analysis session.

Freud argues that there is no need for science to fear telepathy (though his collaborator, Ernest Jones, certainly seems to have feared the ridicule the subject might bring); he is even open-minded about other paranormal phenomena. His suspicion that such phenomena are occurring via some unknown pathway never convinced him to renounce his atheism.

At the end of his earlier paper, Dreams and Telepathy, Freud wrote, "Have I given you the impression that I am secretly inclined to support the reality of telepathy in the occult sense? If so. I should very much regret that it is so difficult to avoid giving such an impression. In reality, however, I was anxious to be strictly impartial. I have every reason to be so, for I have no opinion; I know nothing about it."

Clearly his opinion had evolved over the years. Yet when he denied "occult" phenomena, he meant to deny the spirit domain, the mystical. The trouble is that since he knew nothing about the physics of telepathy, he could not help but seem sympathetic to the mystics.

From our perspective, we argue that reports of "paranormal" communication and other such phenomena tip us off to an interaction with a noumenal world that is the reality behind appearances -- appearances being phenomena generally accepted as ordinary, whether or not unusual.

Freud, of course, was no mathematician and could only give what seemed to him a reasonable assessment of what was going on. J.M. Keynes's view was similar to Freud's. He was willing to accept the possibility of telepathy but rejected the "logical limbo" of explaining that and other "psychic phenomena" with other-worldly spirits.

Many scientists, of course, are implacably opposed to the possibility of telepathy in any form, and there has been considerable controversy over the validity of statistical studies for and against such an effect.

On the other hand, Nobelist Brian Josephson has taken on the "scientific system" and upheld the existence of telepathy, seeing it as a consequence of quantum effects.

Josephson's page of psychic phenomena links
http://www.tcm.phy.cam.ac.uk/~bdj10/psi.html

Monday, January 23, 2023

Footnote JH.36

Footnote JH.36: A useful discussion of this contentious issue is found in The Classical Mind by W.T. Jones (2d ed. of Vol. I of A History of Western Philosophy, Harcourt Brace Jovanovich 1970).

Thursday, January 19, 2023

Toward footnote Xz.151

Added Jan. 19, 2023
Footnote Xz.151.

Freud in The Interpretation of Dreams (1914 translation by A.A. Brill) highlights the idea that the difference between waking reality and dream reality stems from "tests" applied by the awake-state's reality perceiver.

In fact, when such tests fail, the perceiver is deemed to be hallucinating and-or suffering from delusive notions. (Still, one must concede that it can occur that the "ailing" person perceives that our reality is faulty, being based on flawed tests -- as with the assumption that "our government officials would never collude to tell us a monstrous lie.")
It is a question now of attempting to explain the credulity of the mind in reference to the dream hallucinations, which can only appear after the suspension of a certain arbitrary activity. Strümpell asserts that the mind behaves in this respect correctly, and in conformity with its mechanism. The dream elements are by no means mere presentations, but true and real experiences of the mind, similar to those that appear in the waking state as a result of the senses (p. 34). Whereas in the waking state the mind represents and thinks in word pictures and language, in the dream it represents and thinks in real tangible pictures (p. 35). Besides, the dream manifests a consciousness of space by transferring the sensations and pictures, just as in the waking state, into an outer space (p. 36). It must therefore be admitted that the mind in the dream is in the same relation to its pictures and perceptions as in the waking state (p. 43). If, however, it is thereby led astray, this is due to the fact that it lacks in sleep the criticism which alone can distinguish between the sensory perceptions emanating from within or from without. It cannot subject its pictures to the tests which alone can prove their objective reality. It furthermore neglects to differentiate between pictures that are arbitrarily interchanged and others where there is no free choice. It errs because it cannot apply to its content the law of causality (p. 58). In brief, its alienation from the outer world contains also the reason for its belief in the subjective dream world.
But how important are such tests?
Delbœuf reaches the same conclusion through a somewhat different line of argument. We give to the dream pictures the credence of reality because in sleep we have no other impressions to compare them with, because we are cut off from the outer world. But it is not perhaps because we are unable to make tests in our sleep, that we believe in the truth of our hallucinations. The dream may delude us with 43all these tests, it may make us believe that we may touch the rose that we see in the dream, and still we only dream. According to Delbœuf there is no valid criterion to show whether something is a dream or a conscious reality, except—and that only in practical generality—the fact of awakening. “I declare delusional everything that is experienced between the period of falling asleep and awakening, if I notice on awakening that I lie in my bed undressed” (p. 84). “I have considered the dream pictures real during sleep in consequence of the mental habit, which cannot be put to sleep, of perceiving an outer world with which I can contrast my ego.”
The criterion for awake-state reality seems to be heightened alertness and cohesive sense of self. When self-cohesion is weak, the person is often perceived as "troubled" or perhaps "dreamy" and possibly in need of psychiatric attention.

What lies at the root of the awake sense of self? An old notion is that in a timeless noumenal realm a being exists, which is denominated as "the soul." Even if true, we would have here only a glimmering of the problems associated with reality construction.

Your example: [(p-->q) + (q --> p)] [~(p-->q) v (~q --> p]).~[q p] Dot means "and." The above can be r...