The Old Liar Paradox

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The Old Liar Paradox

Post by Upton_O_Goode » Mon Dec 24, 2018 4:47 pm

You all know the paradox, I'm sure. I just came across a nice literary version of it, which I will paraphrase, as follows:

"If Pinocchio were to say, 'My nose is growing,' would he be telling the truth?" (Apparently, there's a drawing in a 1901 Italian edition of the story in which he says exactly that.)
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Re: The Old Liar Paradox

Post by scrmbldggs » Mon Dec 24, 2018 7:48 pm

:hmm: That's obviously this one. :pardon:
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Re: The Old Liar Paradox

Post by landrew » Mon Dec 24, 2018 8:05 pm

That one doesn't keep me awake at night. It's such a simple paradox.
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Re: The Old Liar Paradox

Post by bobbo_the_Pragmatist » Mon Dec 24, 2018 11:34 pm

Its not a paradox, but rather a false premise.

Mind the gap.
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Re: The Old Liar Paradox

Post by Scott Mayers » Wed Feb 13, 2019 10:36 am

Upton_O_Goode wrote:
Mon Dec 24, 2018 4:47 pm
You all know the paradox, I'm sure. I just came across a nice literary version of it, which I will paraphrase, as follows:

"If Pinocchio were to say, 'My nose is growing,' would he be telling the truth?" (Apparently, there's a drawing in a 1901 Italian edition of the story in which he says exactly that.)
Newton's First law asserts that inertial factors (constant states or states of non-accelerating change) remains constant unless an external force compels it to change. This law is (or can be) extendable to logic: For any variable assigned some constant, the variable remains with that assignment unless or until some 'external' factor changes that assignment.

The meaning assigned to a sentence can't assign its own meaning. So I may say something like, "This very sentence is not a sentence." Here, the variable may be thought of as the containing quotes that hold a variety of possible sentence I might want to put in it, such as

" "

Of the particular variety we can assign it the constant,

"This very sentence is not a sentence."

But the content has no meaning unless interpreted from without and so its meaning does not lie in the literal sentence being used to convey the message. Furthermore, you can't make this particular sentence act as the machine to cause another sentence to replace it let alone provide meaning to itself, such as,

"The last sentence here was incorrect."

You need an external factors to take the literal sentence that you interpret to have meaning outside of its context, interpret it and then replace it with another one you might treat as a conclusion in meaning by a different sentence. The sentence itself has no force nor power to alter anything. It needs to be interpreted from without.

Similarly, if someone asserts some claim that communicates some meaning, the one asserting it is not in power to verify the literal meaning of the words of the listener. They could have asserted what they claim in a foreign unknown language to the listener and so the act of speaking the claim has no power that compels the listener to draw a sincere judgement about the meaning the speaker intended.

A sentence has no power over its creation nor its alteration literally or in meaning and remains so unless something affects it from without.


Further digression on this:
We think of the liars paradox as a kind of 'feedback' mechanism such that it, in logical terms, "explodes". But to relate this to the real physical phenomena of feedback, if you set up a speaker with a mic and an amplifier in between, the actual feedback requires external energy to maintain the louder and louder feedback you hear once an initial 'seed' of sound is provided. Thus, the resulting affect (us hearing the feedback getting louder and louder that makes us respond to it) is a secondary factor external to the system. The overall energy of the system remains the same and the cause of it cannot go beyond what the supply of outside electricity permits. Usually, it will get to a point it will blow the speaker or reach a top limited volume then remain relatively constant. The sound as energy would match the input energy minus the heat of the circuit.

So even in real 'feedback' conditions, there is no paradox. Therefore, if one finds a discomfort to paradoxical sentences such as these, they have to realize that in reality, they are the ones providing the feedback to a larger cycle that is more than simply the sentence itself. It's an illusion that the sentence appears to have logical power to cause the confusion only. The feedback cycle is you reading the passive sentence, interpreting meaning from it, including the imposition of the sentence to have more power from some mystical place, re-reading or thinking about it, and re-interpreting it again. The cycle is fed not by the passive sentence you are interpreting as a 'seed' but to the energy you supply to attending to it. At some point it will either blow a mental circuit in you or reaches the limit to which you can handle it. The solution of the 'paradox' is to recognize THAT you are contributing to the force of its meaning by assigning it to your own dynamic input cyclically.
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Re: The Old Liar Paradox

Post by landrew » Wed Feb 13, 2019 10:12 pm

This gives me hope that Artificial Intelligence will never surpass the human mind. I think our ability to shrug or laugh at such paradoxes is a natural relief valve that would probably cause a machine intelligence to lock up.
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Re: The Old Liar Paradox

Post by Scott Mayers » Thu Feb 14, 2019 2:07 am

landrew wrote:
Wed Feb 13, 2019 10:12 pm
This gives me hope that Artificial Intelligence will never surpass the human mind. I think our ability to shrug or laugh at such paradoxes is a natural relief valve that would probably cause a machine intelligence to lock up.
The next evolution in A.I. that can actually productively work requires an architecture based on flexible components based similarly on biology. We've already succeeded the Genome project but the next and more important Protein project(s) [like those 'protein folding' projects as one part] will utilize microbiological logic if wanting to define technology that can be 'conscious'.

This would not require necessity for our purposes though. Consciousness is not an essential function for computing unless if we want it to have a 'motivation' function (...e-motion). On a neurological level, the neurons grow and shrink and/or die. This at present can only be mimicked by creating a network. But we HAVE this 'network' with the Internet. As such, our world IS becoming a large complex living being. We are but cells in this system. The Internet can and is evolving to act similarly to neural network logic and so this may still be a possible threat.

I hope I'm not busting any bubble. But I wouldn't fear change like this in a remote future for humanity as a whole. We evolved and it can be possible that some more advanced entity through our technology can foster the creation of a new species. Consciousness is only a function to motivate us to seek our environment for animals. If we evolved to be able to have a time when computers completely solve all our problems such that we can get anything we want or need, the human conscious state would no longer need to have a mechanism to motivate it to get things it can't get when it can for thinking it. We'd evolve to lack a need for consciousness and by then wouldn't be neither sad nor happy if our species was replaced.
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Re: The Old Liar Paradox

Post by landrew » Thu Feb 14, 2019 2:19 am

Scott Mayers wrote:
Thu Feb 14, 2019 2:07 am
landrew wrote:
Wed Feb 13, 2019 10:12 pm
This gives me hope that Artificial Intelligence will never surpass the human mind. I think our ability to shrug or laugh at such paradoxes is a natural relief valve that would probably cause a machine intelligence to lock up.
The next evolution in A.I. that can actually productively work requires an architecture based on flexible components based similarly on biology. We've already succeeded the Genome project but the next and more important Protein project(s) [like those 'protein folding' projects as one part] will utilize microbiological logic if wanting to define technology that can be 'conscious'.

This would not require necessity for our purposes though. Consciousness is not an essential function for computing unless if we want it to have a 'motivation' function (...e-motion). On a neurological level, the neurons grow and shrink and/or die. This at present can only be mimicked by creating a network. But we HAVE this 'network' with the Internet. As such, our world IS becoming a large complex living being. We are but cells in this system. The Internet can and is evolving to act similarly to neural network logic and so this may still be a possible threat.

I hope I'm not busting any bubble. But I wouldn't fear change like this in a remote future for humanity as a whole. We evolved and it can be possible that some more advanced entity through our technology can foster the creation of a new species. Consciousness is only a function to motivate us to seek our environment for animals. If we evolved to be able to have a time when computers completely solve all our problems such that we can get anything we want or need, the human conscious state would no longer need to have a mechanism to motivate it to get things it can't get when it can for thinking it. We'd evolve to lack a need for consciousness and by then wouldn't be neither sad nor happy if our species was replaced.
Not to disagree, but a large part of the human experience is about "making things work when nothing's going right." I've yet to see any sort of machine which can cope with a large degree of chaos in its operations.
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Re: The Old Liar Paradox

Post by bobbo_the_Pragmatist » Thu Feb 14, 2019 2:43 am

landrew wrote:
Thu Feb 14, 2019 2:19 am
Not to disagree, but a large part of the human experience is about "making things work when nothing's going right." I've yet to see any sort of machine which can cope with a large degree of chaos in its operations.
Every one I've ever seen reboots and asks for your password.
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Re: The Old Liar Paradox

Post by landrew » Thu Feb 14, 2019 3:07 am

I doubt we'll ever make an AI machine that we can't shut down, but it's conceivable that some form of self-serving sentience may eventually form within the internet.
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Re: The Old Liar Paradox

Post by bobbo_the_Pragmatist » Thu Feb 14, 2019 3:20 am

I agree...........caveat...........how to tell the difference between "self serving sentience" ((relatively harder to develop)) and preventing itself from being shut down ((relatively easy to develop???)).
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Re: The Old Liar Paradox

Post by Poodle » Thu Feb 14, 2019 5:07 am

To be frank, I don't believe there is any paradox here. Pinocchio's nose is in one of two states ... either it is growing or it is not growing. A simple series of measurements establishes the fact. Absent the measurements, the truth of the original statement is not establishable. With the measurements, the truth or falsity of the statement is indisputable.

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Re: The Old Liar Paradox

Post by landrew » Thu Feb 14, 2019 7:48 pm

bobbo_the_Pragmatist wrote:
Thu Feb 14, 2019 3:20 am
I agree...........caveat...........how to tell the difference between "self serving sentience" ((relatively harder to develop)) and preventing itself from being shut down ((relatively easy to develop???)).
Natural selection could conceivably create such a creature. It's "instinct" for survival would have been developed from the fact that it has survived, and if it didn't have that impulse, it wouldn't exist. An analog to biological evolution.
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Re: The Old Liar Paradox

Post by Wordbird » Sat Mar 16, 2019 4:20 am

Upton_O_Goode wrote:
Mon Dec 24, 2018 4:47 pm
"If Pinocchio were to say, 'My nose is growing,' would he be telling the truth?"
Let's step back and examine the subject of magical truth curses.

This is not the liar's paradox. This is a magical truth curse.

We're going to assume magical truth curses exist but make them as little ridiculous as possible.

What truth curses can't do:
1. Truth curses can't create information. The curse does not make Pinocchio omniscient, or even potentially omniscient. He can't check to see if god exists. He can't gain knowledge from his curse, especially knowledge that may be impossible to access otherwise.

2. Truth curses that explicitly punish for a lie rather than prevent one can't trigger until you have finished your intended statement, because adding a word could change the truth-value of the statement. The statement receives a period, or possibly an and. Then, if the statement is false, when it is finished, the curse triggers. (Truth curses that prevent lies must activate on what someone intends to say; if the cursed subject intends a lie, he can't speak, but it's possible that such a curse actually prevents a true statement. "Will not prevent true statements" is not on that box label. "Prevents all intentional lies" is.)

The curse can punish you for spouting random garbage you have no reason whatsoever to believe is true. There's no contradiction or absurdity in that. In fact, a curse that doesn't punish for this is next to useless, because Pinocchio could just join this forum and make himself into a skeptic to get out of it. He doesn't know for an absolute fact that what he said was a lie, you see, because he's smart and uppity now and he's given Socrates a fair shake and he actually knows naught.

So here's your answer: Assuming Pinocchio makes the statement, "My nose is growing," when he hasn't previously just triggered his curse with a different lie, the statement is a lie, and after it is finished, the curse triggers. An onlooker might say the curse malfunctioned, but it didn't.

On the subject of the old liar's paradox, there is no paradox, because, "This statement is a lie," is not even a statement. Statements refer to something other than themselves. Statements say something about the world, not words. Statements that refer to other words must eventually, somewhere down the line, refer to facts. "Pinocchio is made of wood," is a statement. It takes one thing and puts it in a category of things - categorisation. Very important. If there is no thing to which the statement refers, there is no statement. There is no meaning. It's basically just flatulence pretending to be a statement.

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Re: The Old Liar Paradox

Post by Gord » Sat Mar 16, 2019 12:51 pm

You play Dungeons and Dragons, don't you?

I can sense a DM when I meet one!
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Re: The Old Liar Paradox

Post by Wordbird » Sat Mar 16, 2019 8:51 pm

Gord wrote:
Sat Mar 16, 2019 12:51 pm
You play Dungeons and Dragons, don't you?

I can sense a DM when I meet one!
*rolls a d20*

d20: 1

Uhm... not very well apparently.

But I would have said that about magical truth curses regardless. It's ludicrous to think that because Pinocchio is cursed, he has access to the correct information concerning whether or not god exists.

A curse that prevents lies rather than punishing them would be forced to prevent a true statement in at least one instance. If the cursed liar intends to say, "My curse will stop me from saying this," he intends to get it out, and therefore he intends to lie, because if he gets it out, it's a lie. The curse will stop him, and in so doing, prevent a true statement. It's not a contradiction or paradox because such curses must work on what the person intends to say.

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Re: The Old Liar Paradox

Post by Gord » Sun Mar 17, 2019 7:35 am

Now, see, back in the olden days, you could have at least two different types of curses: There was the one that just happened, and it always happened the same way so you could work around it or find something useful it could do; and then there was the one that had an intelligence behind it, to foil all your attempts to find a workaround.
"Knowledge grows through infinite timelessness" -- the random fictional Deepak Chopra quote site
"Imagine an ennobling of what could be" -- the New Age BS Generator site
"You are also taking my words out of context." -- Justin
"Nullius in verba" -- The Royal Society ["take nobody's word for it"]
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Is Trump in jail yet?