
This Post Is Meaningless – The Liar Paradox - mr_tyzic
https://billwadge.wordpress.com/2017/05/10/this-post-is-meaningless-the-liar-paradox/
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CodeMage
For a post that claims that you can explain the Liar Paradox "without getting
too technical", it got way too technical really fast.

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bluetwo
Agree.

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colorint
The problem is much simpler: logical systems are undecidable, and the Liar's
Paradox is the logic analogue of infinite loops. But this does require you
understand logic as a process (something people do) rather than having weird
dualistic notions about natural laws of logic.

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kazinator
"This sentence is true" is also ungrounded.

It's consistent; but the problem is that it's that way whether we assume it to
be true or false, oops.

For some reason, "this sentence is true" isn't famous, like its cousing, the
Liar Paradox, even though it has something significant to add.

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kyleschiller
The Liar Paradox is famous because it seems to break the foundational tenant
of classical that all statements are either true or false.

Your example is also interesting, but doesn't really break things in the same
way.

I don't necessarily agree with this, I think there are plenty of important
things to consider with both, but that's why one became famous without the
other.

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kazinator
It does break things in the same way, because the tenet is that all statements
are either true _exclusive or_ false.

If we can follow sound reasoning such that some statement can be either true
or false, based on the exact steps we take, that is exactly the same problem:
a contradiction somewhere.

"This sentence is true" doesn't contradict itself, but two different ways of
evaluating it contradict each other.

Researcher A assumes the sentence is true and comes to the conclusion that it
is.

Researcher B assumes that it is false, substitutes in the value and also
concludes that it is correct.

Neither has found a contradiction in isolation, but A and B's findings
contradict each other.

In terms of electronics-based intuition, "this sentence is false" is like an
unstable circuit: e.g. an inverter feeding its own output to its output. This
might result in oscillation. "This sentence is true" is like bistable
feedback: it gives us a flip-flop which "latches" whichever value we inject.

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AnimalMuppet
At a minimum, you can say of statements that are self-contradictory that they
are self-refuting. Whatever paradoxical class you wish to put them in, they at
least are not true.

By the way, the Liar Paradox is not just an academic curiosity. You run into
it in pop philosophy a lot. "There are no absolute truths" is self-
contradictory in the same way the Liar Paradox is. So is "Science is the only
way we can really know what's true".

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heinrich5991
"There are no absolute truths." can simply be false: There are some (doesn't
need to be that particular sentence that is absolutely true).

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AnimalMuppet
Sure, it can be simply false. It can't be simply true, though.

[Edit: Ah, I see. You're saying that it can be simply false _without self-
refutation entering the picture at all_. Yes, it can.]

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nthcolumn
Are there any uses or applications for Gödel's theorems (other than their mere
implications)?

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atqtion
_> Are there any uses or applications for Gödel's theorems (other than their
mere implications)? _

Theorems _are_ implications, so I'm not quite sure what you mean.

There are _practical applications_ of Gödel's theorems, if that's what you
mean.

His incompleteness theorems are useful for determining when to give up on a
certain class of approaches toward a problem. I think this is what you meant
by "implication", but the importance of this knowledge is difficult to over-
state.

His completeness theorems form the groundwork for first-order theorem proving,
which has plenty of practical applications.

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vorotato
"This post is meaningless", sounds about right...

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martin1975
suddenly I get reminded that colorless green ideas sleep furiously

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kazinator
Something can be colorless, yet green metaphorically (immature, new,
inexperienced). Ideas can certainly be green in this sense, and lacking
physical form they are colorless.

Something can sleep metaphorically if it is not being put to use.

Sleep can be furious; I've seen it. Just perhaps not the kind of sleep that is
slept by ideas that have fallen by the wayside.

That may be the irresolvable crux of the problem with that sentence: finding a
semantics for "sleep" which is compatible with some interpretation of
"furiously", where the sleeping subject can be "ideas".

Perhaps the modern grammatical transitive sense of "to sleep" can rescue it.
These days we can "sleep a device" meaning "to put it to sleep". "Bob
furiously slept his tablet computer, turned out the lights and himself went to
sleep".

Maybe some ideas furiously sleep us.

This entire comment sleeps furiously nearly every reader.

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martin1975
Noam would be proud

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sharemywin
This statement is both true and false as the same time.

[https://en.wikipedia.org/wiki/Uncertainty_principle](https://en.wikipedia.org/wiki/Uncertainty_principle)

