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.
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.
