Graham Priest - 6. Paradoxes

LOGIC: A SHORT INTRODUCTION - Lecture 6
Graham Priest, CUNY Graduate Center (NY), University of Melbourne

[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.

[drewduncan]

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

[chrisg]

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.

[williamhiggins]

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.

[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

[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. □

[scottblair]

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

[mrtrench]

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?