Help, I've fallen in a rat hole!

With a double Americano and a philosophy podcast, I have had an introduction to paraconsistent logic. That, unfortunately, is exactly what it sounds like, either of the dictionary meanings "near" or "contrary" working just fine.

There was a discussion of logics, meaning multiple different schemas for understaning things logically, an implication that living within "one true logic" was a small minded way of living in a gated community where nasty complicated ideas were just carefully excluded so they wouldn't have to be faced.  An analogy, poorly executed IMO, to various geometries (each individually consistent with it's axioms, I say) and various physics was made (Re: various physics, I feel there's just one, although there exist heirarchical layers of approximations, useful in greater degree as restrictions such as "for  v << c" apply.) Poorly executed because the same limitations were not acknowledged in logic. Wikipedia does describe paraconsistent logics as a weaker subset rather than something entirely different, an idea that appeals to me.

Are these guys nuts, or am I?  I know that I have a weakness, feel the seductive pull of the crazy, and I want to dive into these roiled waters & see where the waterfall goes. I know it's cool to be consistent  and everything, so I'm embarrassed to like these word games. Often, I've felt they were nothing more, but today in the early dark, I'm not so sure...  Hence the cry for help.

Kantor's work on infinity was cited in support of the need for paraconsistent logic, and the canonical example, the Lie Paradox, (the statement inside these parens is a lie) was ponderously explaned, like it was a computer program being iterated* and then cutely expanded into something different as follows: "this statement is either False, or Neither-true-nor-false." That's the "revenge paradox" cute not just for the name but because it is at least consistent to say that the statement is neither. I feel that the statement is just a wrapper within which the nut of the problem is hidden: is "neither T nor F" maybe nonsense?  I think maybe so, in statements of fact.

*I like "iterated" here. That has saved me from the rabbit hole in the past, and may yet let me jumar my way out of it this time, too.  In computer programming, we have very clear true (1) and false (0). Data and control systems make great use of self referential mathematics: that's the idea of feedback, signals (or ideas) looping around and affecting themselves. Coerced inexorably into what I call "reality" so they can be useful and implemented on rational things like computers, the programs simply throw an error if you try to code up a Lie Paradox, and I understand self referential math to involve either (a) a distinction in time, meaning the discrete interval prior to this one, the one after, and so forth (parenthetically the formal discrete time mathematics of  F(z)) or (b) a derivative, meaning no instantaneous change but instead a rate, i.e. the Laplace transform.  Those are a couple of pretty robust branches of math, which which I'm acquainted, and in which simultaneity of trud & false is just disallowed.  The philosophers would say I've restricted my domain the the consistent one where things make sense for my pea brain. The podcast calls Wittgenstein's "inadequate diet of examples" humorously to bear, & it's certianly true: maybe I've just been living on a flat earth model so long that I intuitively grant premises that should be picked at more carefully.


  1. I'm gonna re-read Infinity & More in the wake of this.

  2. Miles says it's all just word games.

    The feedback on the site meanwhile focuses on the absence of any meaningful subject in the sentence to be the object of a true or false.

    I think this is a powerful point, bucause with any meaningful subject, the paradox vanishes.

    As to the barber who "shaves everyone who does not shave himself," I say it's just false.

  3. Listening now -- my notes as I listen:

    --re: 'explosion' -- seems like Bayes deals with that just fine. I.e. 'for the hypothesis that the moon is made of green cheese, I am a frog' is true only 0.001% of the time.

    --the main philosopher guy keeps changing the subject -- I found it frustrating.

    --he calls Bohr's theory 'Dialetheism' -- very confused there. he then says that 'Bohr's theorem was never meant to be taken as fact...but NONETHELESS [it's an example of paraconsistent logic]' huh???

    --There was a recent physics colloquium about Bohr -- and the philosopher guy has it backwards. Bohr already knew about the spectrum of hydrogen and developed a theory around that and the new quantum mechanics -- it was never meant to be a theory of 'why' just a theory of 'here's the pattern'...

    --'plurality of physics' -- I call 100% bullshit on that one.

    --I agree with almost everything the girl says in that podcast

    Okay, so overall, I'm not sure Graham Priest said too much in that whole interview. My dander gets up whenever anyone says 'well Obviously, xxx follows' -- he seems to do that really way too often and it's not obvious to me.

    Anyway, yeah, the guy didn't seem to say much. His paradoxes are really just nonsense, like the girl pointed out. Actually I think she was about to bury the guy but the other host wouldn't let her -- I found that annoying. The guy host seemed like a fan-boy.

    Overall, I don't think any of it was that important. Any of those paradoxes can be gotten away from by saying "oh it's just semantics" or equivalently "well, yeah, but that's just 'cause what you said it nonsense" or by Bayes, as above.

    Sorry, a bit scattered, but I generally agree with your post.

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  5. I have to say this has gotten somewhat worse for me.
    What was offered in that podcast? Two things, I think:

    1) There's utility in paraconsistent logic, wherein contradictions can be contained instead of creating "explosion." Explosion is "ex contradictione quodlibet," or ECQ for short, meaning, "from contradiction, everything follows," which is why contradiction is bad! Very cool point.

    2) As an example of the utility, the offer a third alternative to boring boolean T or F, namely "neither true nor false" which supposedly answers the Lie Paradox. It's called the Revenge of the Liar, and is,

    "This is either F or neither."

    Item 2 uses self-referential language, and I think that's valid. A pretty good analogy to recursion seems to pertain. That recursion is a legitimate technique seems to deflate the otherwise very satisfying counterarguments from the web site: they decried the lack of a distinct subject for the lie paradox to operate on. If my analogy's any good, those critiques are wrongfully disapproving of recursion.

    I said earlier I didn't like "neither" as a choice in the logical equation and I'll stick with that. It's true that you can imagine your computer brain trying to run the recursive algorithm successfully to completion when the code reads:
    X = (F or Neither) The fact that allows you to return from an otherwise infinite loop is evaluating X=(F or N) as True, if N pertains. If N stood for 9, that would work. In the case of x=9, it'd be true, but that's because we only have two exclusive choices, T or F we have to deal with. When N means Neither true nor false we have three choices. Our symbolic processor has failed because (F or N) is true if X=N, and that is neither F nor N, and so does not stop the recursion.

    My earlier point about iteration is a little clearer to me now too. What we're trying to do is run an infinite series to convergence. We put a logical test case in the sentence and then "run it" for a few iterations to see if the answer remains stable. Then we get satisfied. The series doesn't terminate though, the recursion runs out of stack space, but that doesn't bother us as long as we can see the light at the end of the tunnel and imagine the series converges. But that series can oscillate in time, eg: 1/(z+.2) (That's notation for a convergent oscillation in my lingo. Sorry, but this is mostly for myself so I excuse myself!) There's no problem with that. Consider "the sun is up." That's not true or false, if you remember that it depends on time! There was an implicit assumption of singular time "right now" that presumes too much.

  6. crap even more brain twisters. Basically starting with N, X=(F or N) still diverges to T-F-T-F-T...