Pause only for a moment to contemplate Ashtamangala, or the Eight Auspicious Symbols of Buddhism:
Further Reading:
https://en.wikipedia.org/wiki/Ashtamangala
http://www.buddhanet.net/e-learning/history/b8symbol.htm
https://www.nwrafting.com/international/whitewater-rafters-guide-8-auspicious-symbols-buddhism
[*12.14]
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Gene Wolfe’s “Book of the New Sun” tetralogy is said to be rife with alchemical symbolism. I have not read it yet, although it has been on my to-read stack for years. Nonetheless, here is a diagram for you, partly because it’s an easy post, but also for me, so that I can add interesting links as I might find them.
Of course, there are a few other tetralogies that exist, although they are not as common as trilogies. One already mentioned on this blog is the Aeygpt Tetralogy by John Crowley.
Further Reading:
https://en.wikipedia.org/wiki/The_Book_of_the_New_Sun
https://en.wikipedia.org/wiki/Tetralogy
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Logic is not as absolute as we would like it to be. For example, linear logic breaks down normal logic into a realm of substructurality. There seems to be several ways to consider expanding classical two-valued logic to four values.
Let this post be a placeholder for considering expansion of classical two-valued logic to four values. For example, one might have:
Further Reading:
https://en.wikipedia.org/wiki/Four-valued_logic
J. Michael Dunn / Two, Three, Four, Infinity: The Path to the Four-Valued Logic and Beyond
https://link.springer.com/chapter/10.1007/978-3-030-31136-0_6
Katalin Bimbo & J. Michael Dunn / Four-valued Logic
https://projecteuclid.org/euclid.ndjfl/1063372199
J. Ulisses Ferreira / A Four-Valued Logic
https://doi.org/10.5121%2Fcsit.2017.71206
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The first three of Arthur Schopenhauer’s Four Laws of Thought are pretty much the same as the classical three laws of thought. Schopenhauer added a fourth law that was basically for his Principle of Sufficient Reason.
These Four Laws are often given in two flavors: the first, in fairly concrete terms of subjects and predicates, and the second, more glib in terms of existence and being and such (isness).
The phrase ‘it can be found’ sounds like a constructive method rather than a mere existence proof, but the common theological technique that combines both by saying “everything happens for a reason” avers the reason to an ineffable deity. (I bet Schopenhauer would have disliked this view because from what I understand he was an atheist.)
Moving on, I would like to represent these four laws in even more concrete terms of logical expressions. In the following attempt, let a, b be subjects (or objects), and P, Q be predicates (or qualities):
When detailed in this way, these four laws don’t seem very complete, or don’t quite form a unity, as implication and equivalence are each in only one of them. Even though it doesn’t help that criticism, perhaps one can succinctly say:
In addition, I quite liked this Goodread review which aligns Aristotle’s Four Causes with Schopenhauer’s Fourfold Root. So then:
Further Reading:
https://en.wikipedia.org/wiki/Law_of_thought
https://en.wikipedia.org/wiki/Law_of_identity
https://en.wikipedia.org/wiki/Law_of_excluded_middle
https://en.wikipedia.org/wiki/Law_of_noncontradiction
https://en.wikipedia.org/wiki/Principle_of_sufficient_reason
https://plato.stanford.edu/entries/sufficient-reason/
https://plato.stanford.edu/entries/schopenhauer/
https://en.wikipedia.org/wiki/Quantifier_(logic)
https://en.wikipedia.org/wiki/Universal_quantification
https://en.wikipedia.org/wiki/Existential_quantification
https://www.goodreads.com/review/show/1328220242
Schopenhauer’s Fourfold Root of the Principle of Sufficient Reason
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Notes:
At some point, I need to understand the difference between the law of the excluded middle and the principle of bivalence.
https://en.wikipedia.org/wiki/Principle_of_bivalence
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Jung’s diagram of his alchemical tetrameria is supposed to represent the evolving self, and suggests movement, succession, and change and yet stillness, consistency, and renewal. His own diagram is quite different from mine, but I do think that mine has some merit.
What are those elements A, B, C, D, and a, b, c, d, and the subscripts 1, 2, 3, 4, indicating the modification of them? I’m not quite sure that it matters, except that for the relationships between the two, and the relationships between the four squares, and the relationships between the four parts of the four squares.
In Jung’s diagram, A equals a cycle of a, b, c, and d, and likewise B a cycle of a1, b1, c1, and d1, etc., and so we can instead say A is a cycle of Aa, Ab, Ac, and Ad, and likewise B is a cycle of Ba, Bb, Bc, and Bd, etc. In that sense my diagram denotes much the same as Jung’s.
Nevertheless, I’m going to have to cycle through some more thoughts about why one should spend too much time contemplating this diagram.
Further Reading:
https://elements.spiritalchemy.com/t3-Ch3.html
http://finitegeometry.org/sc/ph/imago.html
http://www.log24.com/philo/Jung/Aion14.html
Murray Stein / Jung’s Map of the Soul: an introduction
Leslie Stein / Becoming Whole: Jung’s equation for realizing God
Carl Jung / Aion
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This blog obviously needs more cute animals, right? So to symbolize the Growth-Share matrix of product marketing I give you the diagram above.
Please refer to the article below for more explanation.
Further Reading:
https://en.wikipedia.org/wiki/Growth%E2%80%93share_matrix
[*11.194]
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Like it or not, we are all betting individuals. But what interactions are there between the perceived and actual probabilities of things happening and the choices made for or against them? The likelihood of their occurrence, coupled with the size of the gains or losses from anticipating and acting on them, show that people are not entirely the rational agents that we think they are.
Instead of armchair introspection, careful experimental methods were used to give us these (not so) unexpected results. What is demonstrated is that deciding individuals make asymmetric choices based on their poor understanding of relative likelihoods. All sorts of biases and poor thinking on our part contribute to non-rational evaluations of how we end up choosing between alternatives.
The findings are that the near certainty of events happening is undervalued in our estimation, and the merely possible is overvalued. So those things very likely to occur have a diminished weight in our minds, and those things unlikely but possible have an increased weight. These are called the certainty effect and the possibility effect, respectively.
This asymmetry in valuation leads fearful individuals to accept early settlements and buy too much insurance, or hopeful individuals to buy lottery tickets and play the casino more often then they should if choosing optimally. What factors contribute to this behavior? Emotions, beliefs, and biases, probably all play a role in these perceived payoffs between dread and excitement.
In some “Dirty Harry” movie, the lead character essentially asks “do you feel lucky, punk?”, to goad another into taking a risk. In the movie “War Games”, the supercomputer more or less temptingly asks, “would you like to play a game?”, to encourage the playing of unwinnable matches. Watch out for those that know how to play the odds of hope and fear to manipulate our prospects and decisions.
Further Reading:
https://theoryofself.com/the-four-fold-pattern-decisions-under-risk-e4e634eefc61
https://en.wikipedia.org/wiki/Prospect_theory
Daniel Kahneman / Thinking Fast and Slow
[*11.180]
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Let us calculate!
— Gottfried Leibnitz
I admit it, I’m rather a Utopian.
Perhaps I’ve been thinking all this time that it should be possible to find a reduced set of words, symbols, or even concepts that could serve as a basic core of human expression and being, some kind of fundamental proto-language that might cut across all cultures and yet connect all individuals. Something to undo the “Tower of Babel” and be able to heal all misunderstandings, resolve all disagreements, and find everyone’s common ground. I see now I have fallen down the “perfect language” rabbit-hole.
Of course, along with our imperfect languages we also have to deal with our imperfect thoughts and our imperfect feelings. Not only do we want to hide what we’re really thinking and feeling from others, we want to hide it from ourselves. Is it because we don’t want others to know the weakness and darkness within us, or we don’t want to face those parts of our own identities? Perhaps that is the main problem with language, the ease with which we can lie to both ourselves and others, and our eagerness to accept these lies.
Psychology is supposed to help us understand ourselves better. But before that, there were the Tarot decks, Ouija boards, and the I Chings that were supposed to illuminate our thoughts and actions, and help us perceive, however dimly, a little clearer into the past and future. I’m sure I’m not alone in thinking that such devices merely bring concepts to the forefront of the conscious mind and allow one to engage in creative and playful thinking. Maybe they tie into the “unconscious”, whatever that really means, and if not, then what is the source of their utility?
In the same vein, there are other instruments purported to aid in the effort to know thyself, such as Astrology and Myers-Briggs. Astrology has also been used for divination and that is its popular and sad ubiquity, that is “your daily horoscope”. Myers-Briggs is popular in the business world to help the managers manage and to resolve conflicts, and takes itself more seriously. In my foolishness, even though I didn’t believe that there was a perfect language lost in antiquity, perhaps I thought I could invent one anew like Ramon Llull or Gottfried Leibnitz!
Does language reveal reality or does it mask it? Can it blend and synthesize different realities or can it shape and create the very reality we inhabit? I’ve been mulling over the idea of what the next combogenetic alphakit might be, after chemical-molecular, biological-genetic, and symbolic-linguistic. Could it be something hyper-linguistic or hyper-cognitive, to serve as a perfect language, melding syntax, semantics, pragmatics? Or could it be something completely different, a blending of mathematics and philosophy?
Or even a new type of computer science? Such studies are still in their infacy, so one hopes for future breakthroughs and grand theories of logical systems and (e)valuations. Could a machine that creates reality from mere thought be the perfect language we seek, one that performatively produces no ambiguity by changing the abstract into the concrete, the inner into the outer? The Krell machine in the movie Forbidden Planet was one such hypothetical device, and showed the folly of a scheme that granted god-like powers to mere mortals.
Possibly better is a system that starts from grounding axioms that are so simple and fundamental that all must agree with their basis, utilizes logics that are so straightforward and rational that all must agree with their validity, demonstrates proofs that are so rigorous that all must agree with their worth, all enabled by overarching schemas that allow the truth of all things to vigorously and irrefutably shine. Even then, humankind might be too weak to suffer the onslaught against its fragile and flawed cogitations.
But O, what a wonderful world it might be.
Further Reading:
Umberto Eco / The Search for the Perfect Language
https://en.wikipedia.org/wiki/Hedgehog%27s_dilemma
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The Prisoner’s Dilemma is a simple game designed to show how the success or failure of cooperation between individuals can be contingent on various factors, primarily some sort of reward. Shown above is a representative payoff matrix between two players; each square shows the two choices and the two winnings for each. Each player cooperates (A or B) or cheats (A’ or B’) with the other player, so for example if A and B’ obtains (A cooperates but B cheats) then A loses 1 and B wins 3.
Each player knows all the values of the payoff matrix so it is said they have perfect information, except they don’t know what their opponent will do. If they are rational and believe their opponent to be as well, the wisest thing to do is for both to cooperate to maximize their winnings, knowing that their opponent knows that they could also cheat. If the game is played only once, however, that is clearly not the case.
If the game is iterated, things change. If each player remembers what their opponent did previously, and it is considered to be informative for what they might do next, then the player could use it to condition their decision to cooperate or cheat. Different algorithms or personalities can be considered for the players, with more or less thinking about what to do and more or less willingness to cooperate, and it is interesting to try different strategies, all the while seeing what adjustments of the payoff matrix might do to the results.
This Evolution of Trust site is a very nice lesson in some of the complications that can result for such algorithms and adjustments. On the whole, this site indicates that rationality and consideration for others can thrive, if conditions are right. In the traditional Prisoner’s Dilemma, the reward values in the payoff matrix are usually considered to be jail sentence time (so less is better), or for the site mentioned above where I’ve taken the representative matrix, monetary value (so more is better).
One thing of note in these examples is that each player doesn’t distinguish their opponent by anything other than their posteriori plays, because these players are supposed to be all part of the same group or society. But what if there is an a priori distinction that conditions their decision? So, if your opponent is a known Y, and you are a X, then you might want to raise your social credit with your other Xs by punishing a Y, even if it punishes you or even other Xs in the long run.
For example if you are a member of gang X, you wouldn’t want to cheat against another X. But cheating against a member of gang Y might raise your in-group social capital and be as important as the value of the reward. Or you might want to punish your opponent in group Y by not granting them any benefits even at the cost of your own benefit. Such distinctions are not usually part and parcel of the Prisoner’s Dilemma game, but they would add an interesting and realistic dimension to the game.
And thus lend insight into the woes of our modern political scene and culturally diverse society.
Further Reading:
https://en.wikipedia.org/wiki/Prisoner%27s_dilemma
https://en.wikipedia.org/wiki/The_Sneetches_and_Other_Stories
https://en.wikipedia.org/wiki/Devolution_(biology)
[*11.24, *11.172]
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Just the facts, ma’am.
— Detective Joe Friday
The Tractatus has seven propositions, most with sub-propositions and sub-sub-propositions, etc. 
I have added the eighth, which is the actual silence of all one cannot speak of. Quite a large section, for all its emptiness.
I also thought it would be nice to have an internet version where you could click and expand down through the sub-sentences. There are already many such versions available for your enjoyment.
I can’t decide whether I like the English or the German version better, so here are both.
Further Reading:
https://en.wikipedia.org/wiki/Tractatus_Logico-Philosophicus
http://www.bazzocchi.com/wittgenstein/tractatus/eng/index.htm
http://www.kfs.org/jonathan/witt/ten.html
https://pbellon.github.io/tractatus-tree/#/
http://daxoliver.com/tractatus/
http://people.umass.edu/klement/tlp/
[*11.170]
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