Alfred Korzybski (1879 – 1950), the developer of general semantics, was vocal about philosophy not having followed suit when physics, theology, psychology, biology, mathematics and so many others were advancing to a new level in the twentieth century. These disciplines could somehow systematize and transcend their foundations and remain scientific but philosophy couldn't.
The aim of this wiki is to introduce an analytically defined theory that combines the major branches of metaphysics – ontology, epistemology and ethics – into a coherent whole that has applications within the field of computer science, Jungian psychology and even some forms of mysticism. The theory is a modified version of the Metaphysics of Quality called the Analytic Metaphysics of Quality or AMOQ. The AMOQ is a general theory of emergence.
The Canonic Metaphysics of Quality was introduced by Robert Pirsig in Zen and the Art of Motorcycle Maintenance (1974) and Lila (1991). In this wiki we approach Pirsig's theory by examining its structure. In other words, our approach will be the opposite of how Robert Pirsig would probably choose to deliver a holistic philosophical experience. Pirsig would first involve us with metaphysical questions and then answer them in captivating ways that happen to be structurally detailed. I, on the other hand, do not expect to reach out to all kinds of people with my theoretical research. I believe that my work is comparable to what number theory was in the beginning of the 20th century: despite no foreseeable practical application the topic was worthy of research because a decent methodology has been established. The top secret military encyption algorithms based on number theory would come later. I expect my work to be relevant for artificial intelligence.
A screenshot of Four Mountains artificial intelligence (v. 154) based on the Analytic Metaphysics of Quality
Pirsig's Metaphysics of Quality is not exactly a metaphysical theory because that would imply it is a single theory. It would more appropriately be described as two separate theories, each one presented in a different book. It is my understanding that confused attempts to combine these two theories split the Metaphysics of Quality online community into two parties that could not agree on how exactly should they be combined. This happened even despite the fact that one such attempt appears to have been made by Pirsig himself. The result of this split is that MoQ-Discuss, moderated by Horse on www.moq.org, is dedicated to preserving Pirsig's work, with focus on everything Pirsig got right. Lila Squad, moderated by Mary on www.lilasquad.com, focuses generally on the Metaphysics of Quality. The book Lila's Child (non-free, 2003), compiled by Dan Glover, features discussion within the community before Bodvar Skutvik combined the two variants of the Metaphysics of Quality in a way which conflicted that of Pirsig. Some Pirsig's assertions might be deemed inconsistent. Nevertheless, after that Bo's participation was no longer found desirable by Horse and some other MoQ-Discuss actives. Bo and some others left and founded Lila Squad. Pirsig reacted to Skutvik's metaphysical contribution in a 2003 letter to Paul Turner by stating that he does not understand it.
How to Begin
The following articles have been designed so that you can read all of the essential information simply by always clicking the first link in the "See also" links. No need for you to worry about navigation that way. In order to begin studying the AMOQ right from the beginning go here:
If you want to know more about how to apply the AMOQ continue from here:
- Academic Philosophy
- Psychology (There's a separate article dedicated to Socionics and a disorganized collection of notes from my Socionics research.)
- Alternative Candidates for the Standard Model of Metaphysics
- Computer Science
- Correspondence Tables
Metaphysical research such as this was considered important in the beginning of the 20th century, when academic researchers were trying to establish the limits of metaphysical knowledge. When Moritz Schlick (1882 – 1936) gave up that pursuit he was murdered. He was the chairman of the infamous Vienna circle and his murder was praised by Austrian fascists. The murderer told Schlick's anti-metaphysical attitude disturbed his moral consideration. The Second World War began soon after.
It is most unfortunate to associate such a peaceful pursuit as metaphysics to war. But that association is caused by how metaphysics provides similar trust and confidence for people as religion or even family relationships, although I'm not claiming these are interchangeable.
In a modern world in which technology frequently transcends many aspects of everyday life people will need to also update their metaphysical views every now and then. However, metaphysics can be just as complicated as computer technology. Therefore it may be difficult to convey the importance of metaphysics to people without associating it to something threatening. However, I wish to do as little of that as possible without risking that metaphysics appears irrelevant and detached.
I should mention the following anecdote about Frege, Gödel and Russell.
- Frege tried to make a certain kind of theory.
- Russell pointed out that there's a mistake in that theory.
- Finally, Gödel proved that no such theory could have been made.
Even the printing of Frege’s book wasn’t complete before Russell pointed out the aforementioned a mistake in it. The mistake was that that the system of mathematics presented in the book – that of arithmetic – was inconsistent. This means that for every provable statement it is also possible to prove the negation of that statement. For example, it would be possible to prove that two equals two, but it would also be possible to prove that two doesn’t equal two. That’s not the kind of a mathematical system a scientists would usually want to use or have anything to do with.
As a continuation of Frege’s efforts, David Hilbert (1862 – 1943) embarked on a ambitious quest to complete the whole body of mathematics in a manner that would have encapsulated the notion of mathematical theoremhood in a way that is called complete and consistent. The former means that every closed sentence of any language of a theory could be either proven or disproven, i.e. it would either be a theorem or its negation would be a theorem. Consistency of a theory, on the other hand, means that for any sentence of the language of the theorem (closed or open), it is not possible to prove both the sentence and its negation. In 1900, he presented as one of the so-called Hilbert’s problems (the 2nd one) a problem of showing the consistency of arithmetic.
The devastating shock came in 1931 when Kurt Gödel (1906 – 1978) proved that there cannot be a complete system of recursive arithmetic that is at least as ”powerful” as Russell’s and Whitehead’s (1861 – 1947) magnum opus Pricipia Mathematica, which formed a recursive type theory that tried to correct the mistake of Frege’s Grundlagen and extend it. By ”powerfulness” we mean what kind of statements that formal system can express. Weaker systems can express a lesser variety of statements than more powerful system. Also, the first-order recursive Peano arithmetic fell victim to this problem. (The second-order one, the original, did not, but it was not recursive.)
We must briefly explain why recursiveness is so important to any theory of mathematics. If a system is recursive, we can prove any of its theorems mechanically, for instance with a computer. We can also list them in some order mechanically. But for non-recursive systems most of its theorems are far more difficult to prove. Of course, every recursively proven theorem of a non-recursive theory is a theorem, but there are infinitely many non-recursive theorems to prove for which we must use other methods, often very ingenious. For instance, they may be model-theoretic in nature. They may employ non-standard proof-methods such as Hilbert’s ω-rule, etc.
This kind of power comes at a cost. The cost is incompleteness. Any system that has certain trivial mathematical features that are even taught in elementary school are incomplete. For example, if the system of arithmetic allows multiplication with variables, it is very likely to be incomplete. Considering only elementary arithmetics, only functions of constants can be the basic operations of a system that is complete and consistent.
First-order recursive Peano axioms are a powerful system. Lambda calculus, if I’ve understood correctly (remember that I’m an amateur) is even more powerful.
Gödel's proof was so shattering because most of physics relied on Peano axioms and other such complicated mathematics, even complex numbers. At that time, the general consensus among scientists was that physics is the science and that reality is ultimately physical. Of course there were also differing views, but the ultimacy of physics was supported by the fact that life seemed to emerge from cellular-level chemical reactions, society seemed to emerge from life and intellect seemed to emerge from sociality or culture. Because of this, it was a huge shock to find out that the mathematics, on which physics is based, is incomplete.
There would've been alternatives. These alternatives aren't very good at modeling physics but they facilitate basic arithmetic operations such as summation. When combined with other mathematical constructs, such as the Cartesian coordinate system, they do allow for rather complicated systems. However, in the early 20th century nobody would've been knowledgeable enough to use them that way.
The most notable complete, consistent and decidable system of arithmetic was introduced by Mojżesz Presburger [1904 – 1943? (the latter year is not sure because he died in the Holocaust)] in 1929. It is particularly interesting, because all the aforementioned properties can be proven using quantifier elimination, which is close to Hilbert’s finitistic methods. Hilbert was determined to use exclusively these methods to prove all the foundations of mathematics before Gödel crushed this dream. (Presburger’s theory included a first-order version of the induction axiom schema, which is inherently infinite. Thus the arithmetic could not be proven with finitistic methods, by definition.)
Rather recently, Dan Willard introduced a series of systems of arithmetic that are slightly more powerful and also ”provable” and even ”self-provable” as consistent. However, they are completely inferior to Presburger’s, since they only ”prove” their consistency relative to some other, more powerful system such as the first-order recursive Peano arithmetic and just ”self-prove their consistency” simply by adding this consistency as an axiom! They are also neither complete nor decidable.
All of these simple arithmetics are too simple for modern physics. But they are not too simple for metaphysics. The only reason the haven't been used for anything obviously important is, as far as I can tell, that nobody has developed a theory in which these arithmetics would be particularly suitable. The AMOQ, however, is such a theory. Had Eastern or Buddhist philosophy been popular in the West before the wars, perhaps Schlick could've developed the AMOQ.
Mathematically, the AMOQ is a theory that can be mostly or essentially expressed in very simple arithmetic. It relies on vector summation. No other vector operations are defined so far. Hence, as a metaphysical theory, the AMOQ is inherently mathematical, but also consistent, complete and decidable. Decidability means that for every statement of AMOQ there is an algorithm that proves or falsifies the statement. There is no room for uncertainty in the mathematical structure of AMOQ. There is only uncertainty regarding how to interpret language in terms of the AMOQ. It's a win-win situation. The mathematicians, who rely on deduction, get their "Holy Grail" while the humanists get to fine tune as many subtle nuances as they care.
These articles pertain to readers who are generally interested of philosophy. Demonstrations are articles that are technically too elaborate to fit in the wiki.
- Demonstration 1: On the Origin of Metaphysical Differences of Opinion
- Performative Evaluation in Associative Epistemology