Discomfiting aspects of Pirsig's new philosophy, i.e., concepts
which still are personally problematic for Doug Renselle:
Those are big issues which bother us. We think there may be others, nonapparent just now (hand-written notes stashed in deep piles J). Please share any issues you may perceive, and if you want them published here, provide authorization and state whether you want attribution.
Here is another issue which arose during Doug's time with The Lila Squad, which Doug just recently addressed (20Jan2000):
September 14, 1997 - Doug Renselle Need to resolve the following:
Problematic: Is proof by contradiction proof? Are all proofs incomplete in a Gödelian sense? (related to our completeness issue above)
Pirsig claims MoQ complete. (Does he mean classically or quantumly? If he had been able to use our English Language Remediation we would know, wouldn't we? I.e., he would have used 'complete' for classical contexts, and he w¤uld have used c¤mplete f¤r quantum comtexts. Doug - 1Jun2001) We do not [Doug did not at that time: over two years ago.] believe that is possible - again in a Gödelian sense. Pirsig contradicts himself:
"Then one doesn't seek the absolute truth. One seeks instead the highest quality intellectual explanation of things with the knowledge that if the past is any guide to the future this explanation must be taken provisionally; as useful until something better comes along." Page 100, Lila, Bantam hardbound 1st edition, 1991.
"Phædrus had once called metaphysics 'the high country of the mind'-an analogy to the 'high country' of mountain climbing. It takes a lot of effort to get there and more effort when you arrive, but unless you can make the journey you are confined to one valley of thought all your life. This high country passage through the MoQ allowed entry to another valley of thought in which the facts of life get a much richer interpretation. The valley spreads out into a huge fertile plain of understanding.
"In this plain of understanding static patterns of value are divided into four systems: inorganic patterns, biological patterns, social patterns and intellectual patterns. They are exhaustive. That's all there are. If you construct an encyclopedia of four topics-Inorganic, Biological, Social, and Intellectual-nothing is left out. No 'thing' that is. Only Dynamic Quality, which cannot be described in any encyclopedia, is absent" Opening of chapter 12 - page 149, Lila, Bantam hardbound 1st edition, 1991.
In our opinion, on first blush, Pirsig first says everything is provisional, not absolute. Then he says MoQ is (dialectically) complete. We know, according to Gödel's Incompleteness theorems that 'All consistent axiomatic formulations include undecidable propositions.' Therefore, at a first [SOMitic] blush, MoQ is incomplete. A SOMite, in naïve judgment absent any quantum context, might conclude Pirsig would have been better to state that it is the best metaphysics of the reality of quality that he has been able to develop.
Doug's answer, over two years later, on January 20, 2000:
As do all mathematicians, Gödel assumes a global context (or equivalently that mathematics is 'free' of context). Thus he states both his Incompleteness theorems with an ellipsis. Let's use Hofstadter's word dual of Incompleteness theorem one to exemplify, "All consistent axiomatic formulations in number theory include undecidable propositions " Note, Hofstadter did not show our ellipsis! He used a period. We think an ellipsis should be added something like this, " in an unlimited context, or in some conventional context."
If Gödel assumed a SOM philosophy and context, then his theorems are innately incomplete. However, we choose to think Gödel's Incompleteness theorems are a quanton: A quanton of both completeness and consistency. We express Gödel's quanton like this: quanton(complete,consistent). As a result we can see that Gödel is telling us all innate analogues (finite intellect-developed analogues) are an uncertainty relationship of completeness and consistency.
We need to compare Gödelian Incompleteness with Pirsigean Completeness.
When Gödel speaks of propositional Incompleteness he is considering sentient capability to assess absolute SOM decidable truth. He is saying something like this:
SOM absolute truth completeness: States all truths.
SOM absolute truth consistency: Always states truth.
When Pirsig speaks of philosophical completeness he is speaking of nature's intrinsic capability to impose absolute change. He is saying something like this:
MoQ absolute Quality completeness: Changes all.
MoQ absolute Quality consistency: Always changes.
Note how Pirsig adds his own unlimited ellipsis. He calls it DQ! MoQ's reality defined philosophically as both DQ and SQ is innately complete! SQ is tentative, known, innate analogues. DQ is all possibilities and all unknown. DQ is Pirsig's ellipsis! By comparison, SOM leaves DQ out, and worse, it leaves out SQ's subjective patterns of value. Worse, SOM insists SQ's subjective patterns of value do not exist!
Left to discuss are answers to our original questions above about proof in SOM's Church of Reason, "Is proof by contradiction proof? Are all proofs incomplete in a Gödelian sense?" Simple answer to question one is, "In general, no!" Simple answer to question two is, "Yes! All proofs are SQ. All SQ is innately incomplete (by MoQ axiom, SQ commingles DQ, but SQ cannot subsume DQ)!" To stretch a bit further, all that we know is SQ, thus all we know is innately incomplete! And to make matters a tad more difficult, all we know changes faster or slower (over a 'Planck unit time' to 'infinite flux-period (zero flux)' scale) to something new.
We have answered this issue in multiple ways and venues here in Quantonics. Essentially, a correct answer is, "SOM logic is innately incapable of assessing absolute truth in any sense of establishing proof. SOM logic is bivalent (both discrete TRUE/FALSE and continuous FUZZY)." Contradiction depends upon SOM propositional logic which depends upon non-included-middle Aristotelian syllogisms which do not model reality (reality's middle is included). Finally, using Gödel's theorems, we can conclude that no SOM analogue of reality can be absolute! Please examine other works here in Quantonics regarding MoQ compared to SOM, and even more: MoQ compared to both SOM and Cultural Relativism, CR.
Also see our more recent Quantonics English Language Remediation (QELR) of Proof.
Thanks for reading,