Graham Priest - 6. Paradoxes

[@LaTortuePGM]

it's funny how hegel's solution to the paradox of the arrow looks very much like vector fields, only half or a whole century before it was conceptualised.

[@drewduncan5774]

Philosophy so deep you'll forget the word "purple".

[@chrisg3030]

Graham considers the indicative version of the Liar paradox. In grammar an indicative sentence is one used to make a statement like "It's raining" or "They went that a-way" and can be either true or false. Conventional grammar recognizes at least two other kinds of sentence, imperative for commands and interrogative for questions. The liar paradox for a command is "Don't obey this command". If you obey it then you don't , and if you don't then you do. Or you both obey it and you don't. The interrogative form is "What's the incorrect answer to this question?" If answered correctly then it's answered incorrectly, and vice versa. Or any answer is both correct and incorrect. Fun.

[@patrickwithee7625]

The interrogative form of the Liar Sentence isn’t really paradoxical. There may not be a unique incorrect answer to the question, as there is no present King of Tokyo.

[@NashRespect]

​@@patrickwithee7625 So you think the incorrect answer to the question "what is the incorrect answer ...?" Is "that this question has an answer"?

[@patrickwithee7625]

@@NashRespect it’s more like “it’s incorrect that the seeming question at hand is actually a question.”

[@NashRespect]

@@patrickwithee7625 Yeah, I suppose your point is that the only possible way to avoid a paradox is to deny the question's questionhood. That said, I'm hard-pressed to buy that "What is the incorrect answer to this question?" isn't a question, rather than just being a liar paradox. It feels contrived for the sake of avoiding a paradox to deny that it Isn't Even A Question.

[@DoggARithm]

The solution to the barber's paradox comes from dynamically typed programming languages like Python. In dynamic languages, there is a set of scopes in which the same exact variable name can be assigned to different objects, depending on the scope. All the town barber has to do is have an ontologically sufficient case of multiple personality disorder. Suppose shaving theirself triggers an episode, and he "becomes another person" Then it can be said the barber DOES in fact shave the beards of every man in town, who does not shave their own beard. □

[@williamhiggins6321]

Zeno's Paradox of the arrow in motion is based on the metaphysical axiom of mathematics that space is the sum of all points is Reality not simply a mathematical projection. In short, an arrow must traverse an infinity of points in a finite amount of time, which is a contradiction and motion is an illusion, an appearance in the face of the Reality that points in space are The Reality of space and time. The reduction of space to the set of all points is the basis of Russell's continuum theory, and mathematics is an anthropomorphic projection, because obviously the arrow traverses an infinity of points, and mathematics is a reality not The Reality. These patterns of human discovery solidify the concept that order is created not discovered, even though it is a fad to think science and mathematics have something to do with a metaphysical Reality. All paradoxes of pure reason are a construct of reflective thought and arise from the assumption that reason and order in space, time, and the world as we live it are reducible to the ontological primitiveness of reflective thought, when, in fact, we also understand that the logic of space, time and the world as we live it is a product of pre-reflective dialectics of the body. Pre-reflective dialectics signify phenomena at the level of space, time and the world as we live them and are ontologically prior to objective and reflective thought.

[@ElectricQualia]

William Higgins look into the CTMU, it solves all these paradoxes by identifying reality as a self resolving paradox. Paradox is where information comes from and the source of creativity and multiplicity while the self resolving part enforces a logical glue on that so as to be inter subjectively intelligible. The implications of this are monumental. It implies that a theological interpretation to reality amongst other things.

[@MTd2]

Zeno's paradox is not solved but it is avoided with the concept of limit. These paradoxes happen because you don't have a good enough definition to deal with the problems they try to solve. Generally, you have to add more information. It is the type of thing where the principle of parsimony asks you to add more information. If you cannot add more information, this is because you don't have access to any type of non empirical data. Note that the cases where it can be solved rely on appealing to the real world.

[@MTd2]

@Oners82 Besides "it is solved by limits", the rest of your post isn't helpful.

[@ruvstof]

@Oners82 Somewhat like dialetheism?

[@davidqin7033]

"In short, an arrow must traverse an infinity of points in a finite amount of time, which is a contradiction and motion is an illusion" You can get rid of the contradiction by infinitely dividing a finite amount of time. Simple !

[@zubrz]

Sorites paradox reminded me of percolation and percolation threshold - you have some parameter, which you add a bit by bit, and you have 2 states, and somehow you can transit from one to the other; so there's no paradox in some sense, if we accept percolation theory as an explanation

[@scottblair8261]

How does dialetheism interact with fuzzy logic? Sorites especially seems to lend itself more natural to fuzzy logic rather than paraconsistant logic.

[@LaTortuePGM]

i'd argue they serve a different purpose. fuzzy logic helps bring a sense of nuance to how much something is X or Y, which is notably useful within machine learning although it usually has a different name... probabilities. (lol.) however, dialetheism helps stay in a more basic true/false setting, as well as to put contradictions in perspective ; some contradictions are so minor they don't need resolving, or resolve once we precise far enough in some way or another, the cumulation of the true/false/both/neither values in each helping build that very sense of nuance fuzzy logic bases itself over. dialetheism helps formalize fuzzy logic, just like the usually deterministic field of measure theory helps formalize probabilites, both of which resolve their own logic-like paradoxes, like how open segments have nonzero length, but are composed of infinitely, uncountably many points of zero length, a bit like- oh look, it's sorites again !

[@mrtrench6784]

It seems to me that all apart from the liar's paradox result from trying to impose discrete categories onto continuous data. I was expecting quantum physics to be mentioned wrt dialetheism.

[@noobslayeru]

Would Sorites’ paradox be able to be solved with fuzzy logic?

[@ChungPong2000]

this is not good, not good solutions,