h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

The formulation of this paradox that I saw took on two parts;

1> The following statement is true

2> The preceeding statement is false

I think Hofstaedter (or maybe Godel) referred to this as a 'strange loop' and I seem to recall it being inferred that such riddles might have fuzzy-logic applications for the development of AI. Probably only a true AI could try to run such a problem without crashing.

Interestingly enough, Zen Buddhists have been playing with these puzzles for a long time. They call them koans. One famous koan: What is the sound of one hand clapping? Koans are riddles with no solution. By meditating on a koan, and sometimes with the help of a whack upside the head, a Zen student may have a moment of enlightened insight.

One other problem that has been noted by others to have relative applicability with Godel's theorem and with Zen koans is Werner Heisenberg's uncertainty principle, which states that one cannot know the position and trajectory of a sub-atomic particle simultaneously, and that subsequently, a sub-atomic particle cannot be said meaningfully to have both properties simultaneously. The reason for this is pretty simple; in order to observe, say, an electron, one has to ping it with a photon, which tends to send it flying off randomly like a pool ball. By the time the information is read out, it is no longer even remotely accurate. Anyways, one can think of the properties of a quantum particle as being similar to the two statements defined above; if both are taken together, then they negate each other's value.

Oh, yeah. Fractal mathematics as well. Take the Mandelbrot equation. (z=z^2+c) One side of the equation feeds the other side of it, but modifies it such that the result varies. Iterative repititions of the equation generates a fractional reality which contains infinite variant subsets of itself.

I think my article on 'Critical Rationalism' may have some bearing on this discussion (http://www.h2g2.com/A262739.) To understand the sort of quandaries that come at us out of the Liar's paradox, one needs to sit back and consider the framework in which the paradox takes shape, ie a linguistic model. Linguistics is much more than simply a means of communcation; it shapes the paradigm of our consciousness, and is in some sense (ha) a sensory organ. What the liar's paradox is identifying is the limitation inherent in the bivalent logical system developed by the Greeks around 600 BC or so.

The model is pretty easy to breakdown, actually. What is called into question is the relative meaning of 'truth' and 'falsehood' as absolute values apart from contextual definition. This idea of an absolute external realm with geometric ontological properties probably originated with the greeks, and has since been absorbed linguistically into Western civilization until it has become a part of our unquestioned paradigm. But viewed from a standpoint of critical rationalism, such an idea loses its status as a fundamental tenet or assumption, and becomes merely a useful way of sorting information that nevertheless has inherent limitations.

The less formal formulations (ha) introduce some other interesting assumptions in the structure of their linguistic modelling efforts. For example, the statement 'I am lying' not only infers a tenet of absolute 'truth' but also infers the objective reality of the ego-driven 'I'. Descartes made this mistake. One might point out that 'I' or 'you' or whoever is uttering such a statement is functionally an illusion generated by your brain in an effort to map out its collection and storage of experience. Are you a process? If one snips the bridge connecting the halves of your brain, are you then a 'we'? Again, a model with some usefulness and applicability can be seen to have limitations as the object of a definitive declaration (if such a think can even meaningfully be sought after).

I hope this helps.

The computer scientist's solution...

statement 1 has no meaning until the meaning of statement 2 has been decided. Until you have parsed/understood the second statement, it is meaningless. But Statement 2 has no meaning until statement 1 has been parsed. Therefore both statements are meaningless...

I'm curious as to the applicability of such statements to fuzzy logic, though - unless it is the move away from bivalent logic that is useful, rather than the riddles themselves?

Gooday Twophlag Gargleblap,

For the most part your posting is beyond my capacity to comprehend, although I am trying. But I have drawn the inference that you think Descartes got something fundamentally wrong with his 'I think therefore I am' (perhaps it lost something in the translation!). My interest is aroused because our recent studies have dwelled upon this much quoted but often misunderstood statement. I would be really interested, and appreciative, if you could expand on your point of view. Also, in terms of 'what is truth', wasn't that effectively dealt with by Sophocles in 'Oedipus Rex'?

Walter.

Walter, how's it going, eh?

Descartes - I think what I was getting at here is that there are implicit assumptions built into our efforts to build linguistic models of experience, or of anything in general. Those assumptions have to be examined closely. Language, after all, is simply a series of symbols added to, subtracted from, and modifying one another. But the symbols themselves can be broken down, and really should be, before being accepted as useful or meaningful.

I think the concept of I, me, selfhood, or whatever, is obviously extremely meaningful to most people. But I question whether that meaning extends into statements such as Descartes seems to have been trying to formulate.

For example, "I" can postulate that "I" "exist". But what "am" "I"? A biochemical process, an epiphenomenal byproduct of neural activity, maybe just a hairless monkey with some sort of mental disorder called sentience? All of these models probably have some applicability, somwhere. Does the property of "me-ness" extend beyond my brain, beyond my body, or beyond either end of my life-span? Did the brain that is currently producing this words just concoct the notion of "me" in order to provide a context in which to interpret the various experiences it is recording?

My point is not that Descartes is "wrong" per se, but simply that he is assuming quite a lot with the statement "I think therefore I am". It is a nearly meaningless statement in my mind (sorry, in "my" "mind" ;-P )and I think it is rather similar to the aforementioned liar's paradox Interestingly enough for this discussion, the same idea framed in the context of a different language, Latin, comes out as 'cogito ergo sum' which seems to put a slightly different spin on the issue. Goes to demonstrate that really deep philosophy is almost inseperable from semantic precision past a certain point.

"also, in terms of 'what is truth', wasn't that effectively dealt with by Sophocles in 'Oedipus Rex'?"

All I can say to this is "gee, is that true?"

Pardon me, I think I have to go get trampled at that zebra crossing up ahead.

Lucinda;

I am not a computer scientist or an AI specialist, but I would conjecture that yes, the move away from or beyond bivalent logic is what is or was recognized as important in the "strange loop" phenomenon.

Whitehead conjectured that when linguistic or mathematical models reached their limits, they could be encompassed by 'meta-models' which could provide a context for understanding why those limitations are in place. Of course, the meta-models would have limitations as well, and this leads to an infinite array of meta-models of expanding complexity. Fractal logic, hrmm?

Understood - but you'd got the reference, so I was wondering what you'd read/seen/heard...

re: meta-models - interesting idea I heard about consciousness/self-awareness.

1st level - we build a model of the world and use it to make decisions.
-> I see a bear. I punch the bear.
2nd level - we build a model of what we are doing to the world and use it to make decisions.
-> I note that I am punching a bear. I panic.
3rd level - we build a model of how we are modelling the world and again use it.
-> I note that I am panicking. I take deep breaths to calm down.

The guy's idea was that humans have an infinite number of these models - each simpler than the last in some sort of geometric progression - so they all fit into finite space. In this case the meta-models of consciousness get simpler and simpler, and at the limit they're probably just "cog. ergo sum"...

Potentially same thing with models of lingusitics? *shrug*

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More likely to find it there than smashing large quantities of matter together and watching what comes out...