Pinocchio Paradox

Off Topic
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[quote]Bill Roberts wrote:
Well, more briefly:

Many are ASSUMING that there is something impossible about a statement being neither simply true nor false, and then coming to conclusions based on that assumption. Without being aware that a “problem” exists only if making that assumption, which they cannot prove is correct.

It is like freaking out about someone – for example – making better gains by using lighter weight than he had previously, on an assumption that this is impossible, and as a result coming up with contorted explanations such as accusations of steroid use, etc.

Instead, evaluate the assumptions.

On statements being neither simply true nor false, here’s a totally different sort of example:

“If the moon were made of green cheese, and there were giant space rats, they would be able to eat the entire moon in a space of 1000 years.”

Is that statement true, or false?

Yes, most statements can be divided into true or false, but there are situations where this is more likely not to be so. Particularly, statements about non-factual conditions – e.g. a puppet whose nose “always grows” when making an untrue statement – or self-referential statements are particularly able to be neither simply true nor false.[/quote]

I think you’re simplifying it to an unnecessary point as well. This is a mattter of lying versus not lying, ratther than truth and untruth because Pinocchio is aware of his situation. He has a priori knowledge of the possibilities, just not the definite conclusion.

It seems to me there is intent to lie in his statement. I don’t see a lack of knowledge, self awareness or intent.

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But it seems to me you’re working to avoid, or at least succeeding in avoiding, the intent of the person presenting the thing.

He wouldn’t be calling it an “epic paradox” if the intended issue were one escaped by arguments based on intent, incorrect knowledge, particular nose-growing properties, etc as supposedly being a resolution. Those are trivial.

I believe that to understand it as it was intended, this needs to be read as being the situation where Pinocchio’s nose will grow for any untrue statement, and not in response to any true statement.

Because the “epic paradox” referred to is presumably the Liar’s Paradox, which is probably best expressed as “This statement is only false,” though more classically as “All Cretans are liars: I am a Cretan.”

(The latter being a formulation, however, that also allows lawyerly escapes.)

The author makes clear in his further small-print explanation that this is the paradox he is trying to present.

Lawyering up these things, or playing word games, just is evading the point.

The cartoon would have been more clearly presented as Pinocchio simply saying “This statement is only false,” but it wouldn’t have been as catchy or as cute, or original.

But yes, the author should have anticipated attempted workarounds such as have been tried, that escape the fundamental matter.

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I’m hoping beavers and termites infest this thread.

lol

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[quote]Bill Roberts wrote:
It would seem to me that that would be playing lawyer with the wording in an attempt to change the statement into something clearly different than what was intended by the author of the paradox.

The intended meaning was, “My nose will grow as a result of my making this statement,” under an understood stiuation where his nose never grows as a consequence of telling the truth, but always grows as a consequence of making an untrue statement.

(Typically we understand Pinocchio’s situation as nose growth being a result of lying, but for the purposes of the paradox, the necessary situation is one of telling an untrue statement.)

Yes, one can convert the statement and situation to one different than intended. But that escapes thinking about the real point.[/quote]

No it doesn’t.

My solution speaks to the exact and literal nature of the paradox.

Is now when you say it, or is it at another point which you believe it should be?

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If you want to limit yourself to that, which rather clearly is not what the presenter intended, and isn’t (so far as I can tell) a matter of any general significance, then of course that’s completely your prerogative.

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SkyzykS, since you don’t prefer to interpret the original post as being the Liar’s Paradox, but instead as being a trick question about the word “now,” then would you be interested in considering that as a followup matter?

Specific statement to evaluate:

This statement has no truth to it.

What say you?

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My theory is that the magic little fairy that cursed him knows when he’s being a smart-ass…thus his nose will not grow.

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my theory is that pinocchio is a queer.

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I think of his nose actually grows it is a paradox…
BUT if it doesn’t then he’s statement is a contradiction…

or is it vice-versa??

Somethings just can’t happen or be defined??
n/0 = â??

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380×504 189 KB

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You guys are so high right now

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Pinocchio’s nose only ever grows as a result of him lying to cover up something he has already done, or through elevated stress levels caused by the risk of him being exposed as a liar (basically a built-in lie detector): hooter hypertrophy only results from an intentional lie (which implies his foreknowledge that his statement will qualify as a lie. An intentional lie here is impossible because he can’t predict the outcome). So, in order for his nose to extend he would have to have lied about something other than simply saying his nose is about to grow. He doesn’t, so it won’t.

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[quote]Bill Roberts wrote:
SkyzykS, since you don’t prefer to interpret the original post as being the Liar’s Paradox, but instead as being a trick question about the word “now,” then would you be interested in considering that as a followup matter?

Specific statement to evaluate:

This statement has no truth to it.

What say you?[/quote]

I would say that is a true paradox, because if it is true then it is false, but if it is false then it is true.

I would also say that the pinocchio paradox is not a true paradox, rather a clever question.

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The statement below is untrue

The statement above is true

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[quote]SkyzykS wrote:

[quote]Bill Roberts wrote:
SkyzykS, since you don’t prefer to interpret the original post as being the Liar’s Paradox, but instead as being a trick question about the word “now,” then would you be interested in considering that as a followup matter?

Specific statement to evaluate:

This statement has no truth to it.

What say you?[/quote]

I would say that is a true paradox, because if it is true then it is false, but if it is false then it is true.

I would also say that the pinocchio paradox is not a true paradox, rather a clever question.
[/quote]

Fair enough! :slight_smile: