Lambda the Ultimate

New URL for Introducing and Modelling Polycontextural Logics

Other book: "Morphogrammatik: Eine Einführung in die Theorie der logischen Form" by Thomas Mahler. Chapter 10 ("Modellierung der Proemialrelation") is occupied with Lambda - Theory.

Yeah, it has a definite Transgressing the Boundaries vibe. Then again, it's just as possible that it's brilliant stuff that I'm just not clever enough to comprehend.

I can sort of see what he's trying to do (that is, I recognise some common Derridean themes in the apologetics he puts forward for the endeavour - writing "under erasure", "dissemination" and so on), but I think it's just too half-baked to come off. The ratio of wishes to horses is just too unbalanced - I was hoping for far greater argumentative horsepower.

The comparison with GEB is useful actually, because I think this comes off very badly in that comparison. Even where I struggled with the mathematics in GEB, I could see how one thing followed from another: the maze-like structure of the argument would be lost on the reader if it were simply too difficult to follow (or if whole chains of connecting passages were simply missing or occluded). GEB can be cute at times, but it has a clear (if convoluted) internal logic, contains some pretty decent explanations of some pretty solid math, and never abuses the speculative licence it sometimes gives itself. I can't say the same here at all.

G. E. B. Kivistik, the professional blatherer from Stephenson's Cryptonomicon?

I think Kivistik would find a lot to like about this...

why it was hosted on the loveparade site in the first place. Funny place for it, if you ask me.

The background to this piece is interesting, though not much less befuddling. I've googled around a bit for information on Gotthard Guenther, and turned up a small amount of somewhat enigmatic matter, much of it in German. Evaluation of his ideas (or the summaries presented by Kaehr and others) is simply beyond my competance, but even the parts I think I do understand are puzzling.

I'm puzzled by Kaehr's assertion that, for instance, self-modifying code (or code modified by other code, which it itself modifies) somehow defeats "classical" logic. It's somewhat circular, for sure, but you don't need to build a special sort of computer to do it. Implicit in some of what Kaehr seems to be saying is the notion that new and special kinds of computation are required to perform the new and special kinds of logical operations Guenther invented. At the same time, there's a purported implementation of a "proemial" combinator in standard ML! It's all very strange...

I've googled around a bit for information on Gotthard Guenther

I was actually surprised by how close his speech gets to Chinese Room without mentioning it.

The general concept of system (III) dates as far back as Plato´s dialogue "Theaethetus". In order to demonstrate that consciousness demands an integrating unit, Plato uses the example of the Trojan horse. Inside this horse were seated many Greek heroes, like Ulysses, Diomedes; and others. But although there were brain functions going on "inside" the horse, this wooden monster did not derive any consciousness from them. Accordingly, young Theaethetus is told: "It would be a singular thing, my lad, if each of us was, as it were, a wooden horse, and within us were seated many separate senses, since manifestly these senses unite into one nature, call it soul or what you will; and it is with this central form through the organs of sense that we perceive sensible objects."

Yes, you can see the similarities.

It occurs to me we haven't had a proper discussion/debate/argument/flamewar on LtU about AI, at least not while I've been reading. There was surely a time when it would have been hard to discuss programming languages (Lisp, Prolog) without being drawn into some such discussion periodically. I don't believe the issues people used to argue about have been decisively resolved; it may just be that everyone knows better than to get caught in that tarpit nowadays. Or have our horizons really narrowed?

One of the things that makes reading Guenther a strange experience is the assumptions he has that a) such things are worth discussing, and b) it's perfectly legitimate to bring Kant, Hegel, Husserl and Merleau-Ponty into the argument. I get the feeling that to do so here now would be like mentioning Freud at a convention of psychiatric professionals...

I guess you are right. For one thing, we try to stay focused on programming languages. More importantly, I think the current thinking regarding AI is that the interesting issues aren't really related to the choice of programming language.

In a nutshell, when symbol manipulation was a novel idea, so called "symbolic languages" were all the rage for AI. These days most languages support basic symbolic processing, but regardless of this, most AI research isn't about basic symbol manipulation anymore.

It may be damaged. But then, I cringe at the mention of Derrida & Co. Except for some of his ideas in linguistics, I don't believe a word he wrote.