Alright, I’m going to bore you all to pieces and do a little boasting. I am the only living master of three valued propositional logic. You will not find what I can teach you about it you in any textbook. (Among other reasons, because I haven’t yet written the textbook, and don’t intend to until I can find some way of getting paid for it. It’s not that much fun.) That’s not because it’s a hard subject. In fact, it’s quite easy, once you know how. It’s only unknown because no one will pay any
redacted attention. Like Colombus is said to have claimed about reaching the New World, it’s quite easy once you know it can be done. Being the first was the hard part. Pay attention and I’ll reveal all the secrets, including the tortuous paths of discovery, missteps and false trails. Free of charge, even, for now. It’s of the benefits of following this here blog here. It’s my thing, and like Woo Young-woo’s whales (Extraordinary Attorney Woo, currently showing on Netflix), I’m going to keep talking about it until somebody shows an interest, and then talk about it some more.
So, a little bit of background. Back in the early 1980s when I came home from my LDS mission to Bolivia, I had intended to go back to school at BYU to continue my studies in Chemical Engineering. Due to a unfortunate combination of factors, I wasn’t able to get back in. However, I was living in Provo and withing walking distance of the Harold B. Lee Library. And, since there was no one to tell me no, I spent a large portion of my days in the stacks down on the 2nd level in the mathematics section, reading up on the foundations of mathematics including Logic, set theory, and mathematical structure. gathering a smattering of understanding of the history, controversies, and unsolved problems. I’ll come back to some of those later. A lot of it was over my head and I didn’t do much with the exercises in the textbooks, but I thought about the concepts. Basic propositional logic, boolean algebra I understood, since my sophomore high school geometry had included it in in the section on logic and mathematical proofs, and so did basic computer science, which I also studied on my own without benefit of teacher.
Since I didn’t have a teacher, I developed a lot of what you might call unorthodox theories about the nature of logic. Contrary to any impression you might have gained from watching Star Trek or reading E.E. “Doc” Smith’s Skylark series (Both of which I had done, showing off my nerd credentials). I came appreciate that logic is useless in finding “absolute” truth. It is only useful for “relative” truth, that is, this statement is just as true as that one. In logical argumentation, proof, or deductive reasoning you must always start with something you assume to be true; or believe for other reasons. The reason you believe something can be quite arbitrary: It may be as simple as something you declare to be so. The fun is in examining the consequences of that declaration.
Also, it’s perfectly possible to reach true conclusions with faulty reasoning. Logically valid reasoning has another purpose, which I came to appreciate more fully somewhat later.
Also, mathematical discovery and logical deduction are two different things. Typically, mathematical discovery is more of creative, experimental process. The deductive part, where you test or prove that the ideas you have created or discovered are correct, is something else. As my High School Geometry teacher was fond of saying ” ‘It’s obvious’ is not a proof”.
I picked up a couple of other notions along the way. One of these was modal logic, which is the logic of possibility and necessity, and comes back into the story later.
Stay tuned for the next episode, in which I made an exciting original discovery, only to find that that someone else had beaten me to it long before.