Liar's paradoxes show us that certain assumptions we make lead to illogical conclusions. That's incredibly important, because what if you are making those assumptions in arguments that are not liar's paradoxes? — Philosophim
So if the sentence is false, its true, and if its true, its false. We definitely have a contradiction. — Philosophim
We realize we've said nonsense by being too implicit. That's the lesson we can glean. Just because we can say or posit an idea in language, doesn't mean it makes sense. You've previously posted the question, "What is metaphysics?" Many times people use metaphysics to disguise liars paradoxes. Terms that are ambiguous are great ways to hide nonsense terms and conclusions within them. If you can pick them out, you can ask for clarification. — Philosophim
Solving the liar's paradox can give us a tool to solve other nonsense points while keeping within the spirit of the discussion. — Philosophim
Liar's paradoxes are a great teaching tool about the ambiguity of language, but also about seeing through the intentionality of a person's argument. — Philosophim
I don't think this analogy applies. Seems like with the Russel paradox, we start with what appear to be consistent rules and get contradictory results. — T Clark
what if you are making those assumptions in arguments that are not liar's paradoxes — Philosophim
The liar's paradox only shows up when we are talking about sentences that we would never use in normal speech — T Clark
Is this the issue, that mathematicians and logicians don't believe math was invented by humans? That they think it is intrinsic to the world? — T Clark
I don't get it. — T Clark
There are certainly people who believe that the Russell paradox says something profound about math and logic. — T Clark
You are right: there is only a danger if this paradox within set theory has an effect within the practical mathematics (which I suggested would necessarily always be detectable, but maybe not trivially apparent). I don't have an example to hand, although they might be found in e.g. differential geometry (foundation for General Relativity) or, where this all came to light, in computability theory (foundation for, well, computers). — the affirmation of strife
math paradoxes we're talking about are trivial — T Clark
It has magnitude and direction? Cool, so what's a direction? — the affirmation of strife
So, my impression is that most self-reference is useless. — T Clark
As to the usefulness of self-reference, it was pointed out that it is pivotal to iteration. Any iterative procedure by definition calls itself. Now that's indispensable in coding, but it also leads to many a curiosity. So for example, this beast: — Banno
Douglas Hofstadter made use of iteration in his discussion of consciousness, a notion that has not dissipated over the years. Chaos theory in general relies on iteration. — Banno
Self-referentiality points to our tendency to conflate the thing with our thoughts about said thing. — baker
Also, more generally, it points to the possibility of saying one thing and meaning two things. — baker
Confusing "the moon" with the moon doesn't strike me as a self-reference issue. — T Clark
Also, more generally, it points to the possibility of saying one thing and meaning two things.
— baker
I don't understand what you mean.
BTW perturbative quantum field theory was recently put on pretty firm mathematical footing (see Perturbative Algebraic Quantum Field Theory by Kasia Rejzner). This uses Greens functions which are calculated recursively (i.e. G = f[G]). — Kenosha Kid
I saw a nice self-referencing puzzle the other day.
Question: If you pick an answer at random, what are the chances that the percentage written in the pick is equal to the chance of picking that percentage?
There were four answers given from which you could pick at random. One said 50%. One said 25%. One said 60%. And another one said 25%. Altogether there were four answers from which a random choice would be made. — god must be atheist
Are all iterative processes self-referential? Maybe someone else brought this up previously. Is that the same kind of self-reference we're talking about? — T Clark
All recursive ones processes are, and calculation of the Greens function is recursive. But no, not all iterative ones. — Kenosha Kid
can find non-trivial self-referential paradoxes, such that they could arise from seemingly well-founded frameworks. I'm no longer sure that it is even possible, — the affirmation of strife
# Iterative iterative_factorial( x ): x_factorial = 1 while x > 1: x_factorial *= x x -= 1 return x_factorial # Recursive recursive_factorial( x ): return 1 if x == 0 else (x * recursive_factorial(x-1))
# This function prints the path to the exit, if there is one. navigate( maze, path_taken ): current_position = get_position(maze, path_taken) past_positions = [get_position(maze, path_taken[:n]) for n in len(path_taken)] if current_position not in past_positions: if AT_EXIT: print( path_taken ) exit_program() else: if CAN_GO_STRAIGHT: navigate(maze, path_taken + [ STRAIGHT ]) if CAN_GO_LEFT: navigate(maze, path_taken + [ LEFT ]) if CAN_GO_RIGHT: navigate(maze, path_taken + [ RIGHT ])
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