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The learned professors

A throwaway line I posted as a comment on Sarah Hoyt’s blog “The learned professors of formal logic are so far up the wrong trees they can’t even see the ground” interested a reader.
If you don’t understand the technical jargon, ask.
I had been working on three valued logic (a logic incorporating values for “True”, “False”, and “Maybe”) on and off since the early 1980s, and I couldn’t figure out why it didn’t work. When I consulted Ackerman’s work on “Three Valued Logic”, I found that some work had already been done, but none of the systems presented were wholly satisfactory and set it aside for a few years. Later, when I took a course on formal logic, I came back to it. I got as far as recreating modal functions for “definitely true” and “Possibly true”, and was able to recreate some of the classical laws of modality; for instance: “Not possible” equals “certainly not’, “not necessarily” equals “possibly not” I returned to the reference and I was disappointed to learn that everything I had done so far had been anticipated by the Polish logician Jan Lukasiewicz in the 1920s. I started looking up the work of C.I, Lewis, who is noted for his work in modal logic using an axiomatic approach. Lewis and Langford discussed the work of Lukasiewize and noted that it had a severe deficiency, in that the standard methods of modus ponens and transitive conditionals were not valid, which crippled its usefuless as a system of logic. On the other hand, the Lewis systems have the major disadvantage of not being able to be expressed using truth tables. I wondered technically why the two systems were incompatible, and set myself to the task of figuring it out. I searched more deeply in the literature of both multivalued logic and modal logic, looking for interconnections, but beyond a proof that the more useful Lewis systems could not be reduced to a finite number of values and a demonstrated inadequacy of the Lukasiewicz logic in providing standard methods of logical proof, the subject was scarcely mentioned. I also explored the axioms of intuitionism; this has a similarity to the Lewis Systems in that it is developed axiomatically and cannot be reduced to a finite number of truth values, but there was no unified approach. There was a throwaway line that “despite a promising beginning, the connections of three valued logic and modal logic didn’t work”. I wanted to know _why_ it didn’t work.
In the early 1990s I found a clue. I was looking again through a discussion of multi-valued logics, using updated works from Malinowski, and Bolc and Borowitz, and noticed that of the three valued logics which discussed logical equivalence, their equivalences were generally not equivalence relations; that it, they were not reflexive, symmetric, and transitive, which were the criteria laid down for equivalence relations in studies of finite math and the foundations of mathematical structure. I thought “why not add one to Lukasiewicz logic”. These results were much more satisfactory, and I could establish several of the axioms of the Lewis System S5 as valid three valued tautologies. But not all of them. Next, I noticed that I could express the table for my equivalency by applying the “definitely” operator to the Lukasiewiz biconditional. Then I thought “What’s good for the biconditional must be good for the conditional as well. I tried this, and in a dazzling, blinding flash of hindsight, I realized “of course it must be so”.
The Lukasiewicz conditional as defined allows conditionals to have the third logical value. In order to have valid reasoning, you need logical laws that do not introduce error. Modus ponens and the transitive law of the conditional when applied to the unmodified Ludasiewiz conditional allow false conclusions to be reached from true premise, and the truth tables show how. As a remedy, it is necessary and sufficient to modify these methods to require “strict” or “Definite” conditionals and forbid doubtful ones. This is reinforced by noticing that the “Strict” version of the Lukasiewicz conditional is an ordering relation; reflexive, antisymmetric, and transitive, which assures “if p then q” is definitely true, then q is not less true than p”. The common material conditional is such an ordering relation and assures this for classical two valued logic, which is why it works; most of the analogues proposed in three valued logics do not, which is why they don’t.
This is not quite the same as the strict conditional proposed by Lewis. Lewis held strictly to the law of the excluded middle, and incorporated it into his logical systems; Lukasiewicz denied it as a general law. In my view, this introduces a subtle inconsistency which breaks Lewis’ systems and makes them non-truth-functional.
I tried publishing these results about 2000; my paper was rejected by the one journal I attempted, in part in the grounds that they symbolism did not exceed the high school level. Excuse me? The ideas are simple enough for high school students to understand; they don’t need elaborate symbolism. I tried rewriting them and submitting them to selected experts individually, and met with profound lack of interest. Although the ideas behind multi-valued logic, modal logic, intuitionism, and fuzzy logic are closely related, in my observation the formal systems used to express them have become their own distinct and rather ossified bodies of research. Hence my comments about learned professors of logic. It’s intellectually painful to see how close the founders of these various fields came to a simple, robust theory that spans several such branches, without quite getting it right.


While I was at LTUE, I had occasion to give my son some advice about being proactive, not just waiting for things to happen. Later, I thought about it and decided that it’s a piece of advice I need to take myself. This is especially true with regard to my social life. Most of my life I have been much too passive about waiting for people to approach me, and disappointed when they did not. It’s about way past time for me to be more active about meeting people.

I also had occasion to ponder the difference between me and the hero I’m writing about in the book I’m working on. One of the reasons he is a hero is because he has habits of taking care of the little things, the daily chores, the small tasks. He doesn’t procrastinate his maintenance. Me…hah. That’s something I need to work on. It’s harder when you have to train yourself as an adult than it is to establish good habits when you’re young.

on Monday, there was a post on According to Hoyt, Nah King, Nah Queen that I spend most of the day composing and monitoring comments. I do that, sometimes, if the post and content are interesting; This is a fairly congenial bunch of commenters, and I agree with and like many of them.
Tuesday, I spent some time at , which was talking about book covers, and got a chapter written so I can take it to my writer’s group tomorrow night.
Today, I did some work on my Knowledge Base. I’m back to working in early prehistory, trying to expand and extend things useful to it.


Now that I am at home and can type faster than the not-so-smart phone I bought on this trip will let me do, I can give a better report. The day before, I took my older son out to lunch, and wound up giving him some Dadly advice, that he needed to chose his own direction, decide what he wants most in life, and do what it takes to get there. Afterwards I thought I need to take my own advice, when it comes to social interaction.
The night before LTUE started, I thought to check out the hotel and get familiar with the place and parking arrangements, and ran into David Farland. Last November, I attended one of his workshops. He remembered at least my face and asked how my writing was going. I was pleased to be able to report progress.
On Thursday, one of the panels that stood out to me had the title “How to Feed an Army”, with panelists Jonathan LaForce, Kal Spriggs, Brad Torgersen, and Paul H. Smith. These are all military or former military, and they talked about logistics and supply. Water, rations, gasoline and parts, medical supplies, casualties, presenting supply information so it is most useful to busy commanders, thieves, information management, and related. Since the main character in my story is conscripted into the king’s army, this was highly valuable. This was one of the blocks in my story. I wasn’t sure what he would be doing there. Now, I have a better idea and I can proceed. Kal Spriggs is the author of several works; I’ve read his “Children of Valor” series, starting with Valor’s child Valor’s Child, and liked it. I’ve only read one of Brad Torgersen’s works, The Chaplain’s War, but I liked that one, too.
I attended a “Kaffeklatsch” with Sarah Hoyt. I’ve become a fairly regular commenter on her blog, and wanted a chance to meet her. I did and introduced myself as one of her “Huns”, but she was busy and had other friends. I didn’t want to be too much of an obnoxious pest by hanging and following her around. Perhaps another time.

Friday, besides the keynote address by Jo Walton, and a panel on “Hidden disabilities”, I wound up attending surprisingly few. Most of the ones I wanted to attend were full by the time I got there, so I wound up wandering the halls. I did have a nice conversation with Jo Walton, whose work I haven’t read, although the name is familiar to me, and she kindly recommended a couple of her works. “Effective Networking for Authors and Artists” was highly useful, and I will be changing my approach my blogging and Facebook activity based on their advice. I had a chance to speak with panelist Donna Milakovic afterwards, and she was very friendly and encouraging.

Saturday, I attended a 2-hour session on medieval weapons and armor, by C. David Belt. Since had invited those attending his session to ask him about the subject, and he was fairly mobbed, I skipped the crown and went to attend the talk by Todd McAffrey, but afterward I buttonholed him in the hallway when a panel I wanted to attend was full, and he gave me some highly useful worldbuilding advice on my hero’s probable weapons, armor, and gear. The next panel I got into was on “Writing Children”, with Sarah Hoyt among others, and another one was “From Peasant to Noble: Social Mobility in Feudal Societies”. That clarified some of the rather vague notions I had about the “Now what?” after my hero kills the dragon.

I was hoping to meet Marion G. Harmon, author of the Wearing the Cape series, which I have greatly enjoyed. I did spot him and tell him I had read and enjoyed his work. He was unnecessarily apologetic about the delay in writing the next book in his series, and appeared preoccupied about something, so after telling him his series is one of my re-reads, I left him alone.

There was more, but, hey, why try to tell all? It was one of the more productive and enjoyable events I’ve ever been to. Next time I go to one of these things, I’ll be better prepared.


Still at LTUE. I got a few tips about networking, a few tips about my novel, attended some interesting panels,and had a good time. It was suggested that for networking purposes, I need to attend as many face-to-face events related to writing (and my other working interests) as possible, and become active on social media such as Twitter & Facebook. I think I need to get home & assimilate first.


Mostly just a test of my smart phone and ability to do mobile blogging. I met a few authors, got a few hints on scenes to work on for “Dragonkiller”, made a couple of contacts for possible future editorial and artistic work, and had a few other nice conversations.


Yes, this blog is perishing of loneliness. Partly due lack of attention from me, partly due to lack of visitors (other than spammers). Comments would be highly welcome.

I will be attending the “Life, the Universe, and Everything” symposium in Provo, Utah. There are a few authors and their fans that I’m especially hoping to meet. Since most of my writing so far has been is nonfiction and goes into the Knowledge Base, I expect I will talk about the project there.

I’m also working on some fiction stories:
One of those is a fantasy; I’m only a few thousand words in. The working title for is “Dragonkiller”.
I’m also planning what I call a historical fantasy series. I haven’t actually begun writing it yet, but I have concept I like. The working title is “Magister”.

For “research” purposes, I’ve been building a e-library of GURPS supplements. I’m expecting to use this to help me build secondary characters and situations. I’ll have to see how this goes.


I’m still working toward my primary targets of current events and US history, but this week has been slow going. It feels as if I am having to clear a whole bunch of underbrush to get to them. For instance, 2017 isn’t quite connected to enough cities to distinguish regions of the United States, but it’s close. There are several other topics that are “close” to a target but aren’t quite there yet.


Quite a few of my pages have long lists of links to be connected; nations, cities, and biographies are some examples. For most of these, I nibble through the list, one or two links a day or a week, and eventually I get through them. However, every so often when a list is nearly done, it feels good to put my head down, bull through the rest of the list, and get it done. Then I can briefly savor a feeling of accomplishment before moving on to the next task.
The 20th century is being connected to biographies. Aurgh! I am really going to have to work on adding more people to the list.

This last week I have finished connecting peoples of the world to biographies. This lays the groundwork for connecting biographies to particular peoples, such as Western civilization and Asiatic peoples. I already know that this list of historical figures is horribly biased towards Western Civilization, but I need to pin that down.

Western Civilization is finally connected to the long list of other nations and cities, as far as I dare push them; some 65 nations and 36 cities. The extent of what I call Western Civilization is mostly defined by these lists. This is a significant milestone. Now, I can concentrate on the relations to other peoples and the structure of Western civilization, as well as component peoples.

Asiatic peoples are less well defined, although this push to work through the list means that I have also finally finished the connection to nations (55 of them) and I can now connect to more cities. This is also a significant milestone. I have 39 cities so far and over 40 to review.

Been away

I’m running late. Last Thursday drove up to Provo, Utah, and I went to a writing workshop in Provo, on Friday and Saturday. I stayed over Sunday to visit family, and drove back down on Monday. I haven’t done much on the Knowledge Base, and it may take a few days to catch up.


I keep trying different approaches to organizing how I work on the SKB. What I’ve decided to do is focus on a variety of specific targets and do what I can to develop them. For the historical target, I’m trying to get caught up to current events in October 2017.
For Sociology, I am leading with the Western United States. For Institutions, I am looking at Mormonism, and the United Nations.
Because of the way subjects are interconnected, many times work on one of these involves work on the others as well. For instance, as I work on 2017 in general, I am connecting to increasingly smaller nations. As I work on the Western United States, which is not yet well connected to the late 20th century, the effort to improve the late 20th century is giving more detail of Europe, and points to a need to further investigate the UN and the European Union.