@Zoldy Quines are cool, I didn't know about their application in satellites!

Another thing I remembered is that the self-referential paradox known as the Berry Paradox is used to prove that the Kolmogorov complexity of an algorithm is not computable. This could be considered "practical" in the sense that we can be sure that trying to calculate the minimum required "complexity" of a computer program is a waste of effort (although there may be other ways to estimate it). Though again, this is all very much in the field of computer science and mathematics rather than philosphy per se, although simplicity plays a (large?) role in the philosophy of science.

There are certainly people who believe that the Russell paradox says something profound about math and logic. — Clarky

Reading some Penrose lately. I think I see now where this is coming from, it has to do with the idea that some mathematicians have of mathematical "entities" inhabiting a sort of world of ideal forms (see e.g. Plato). That is probably a topic for another thread, but I would agree that paradoxes (incl. self-referential) can say something about the limitations of mathematics, even if it is just regarded as a language.

Alas, I'm not able to bring any surprising yet practical paradoxes this time, just a little more rambling...

You get the feeling that you’ve stumbled on something profound and important. — Clarky

:snicker: ...and it's neither!

but it’s clear it’s neither profound nor important. — Clarky

:grin:

You read my mind!

Self-reference in re the liar sentence, as you would've already noticed, is in the third person ("this"). Second, it involves negation of some kind that contradicts a property that's necessary to selfhood, assuming such a word exists and is imbued with the meaning that I have in mind.

Caesar used to refer to himself in the third person which is in a way quite noble of him - he alludes to the position that he holds (Emperor) instead of himself (Julius). Which leader can do that? :snicker:

I wonder what implications this has on the so-called hard problem of consciousness which is premised on the alleged restriction on consciousness to the first person mode?

@Wayfarer $\uparrow$

I seem to have missed this thread when it ran seven months ago. Kenosha Kid gave some good answers to questions about recursive vs iterative. I usually think of iterative as involving the same function in a loop, like fractals, but I suppose the following, which I have explored extensively, might be considered iterative. Maybe not. It makes no difference what it is called, although I refer to it as infinite compositions.


${{g}_{n}}(z)=z+{{\rho }_{n}}{{\varphi }_{n}}(z)$

${{G}_{1}}(z)={{g}_{1}}(z),\text{ }{{G}_{n+1}}(z)={{g}_{n+1}}({{G}_{n}}(z))$,
$n\to \infty$

Agent Smith doesn't exist. — Agent Smith

It's basically a catch-22 situation: For x such that Px, Px $\to$ ~x.

The liar sentence uses true/false, false to be precise, as a predicate. Is truth value a valid predicate? If no, how did Gödel break math with his incompleteness theorems?

:chin: