Jatopian
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Trickster wrote:

rman wrote:

Someone Else wrote:
Oh, it's quite simple. There is no king of France. So is it a true statement that the king of France is bald, or not?

I think it’s true.

You are correct, sir.

Wrong, both of you. It was not said, "If there is a king of France, he is bald." The way it was stated, the existence of a king of France was not a conditional, it was simply predisposed.

This is why I'm suspicious of logicians. Anyone that devoted to a subject that can be thoroughly learned in only one semester is probably having to look too hard for things that aren't there - or make them up.

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Tahnan
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Trickster wrote:

rman wrote:

Someone Else wrote:
Oh, it's quite simple. There is no king of France. So is it a true statement that the king of France is bald, or not?

I think it’s true.

You are correct, sir.

Does that mean that you would both also accept that "The king of France is not bald" is true, there being no king of France? Because that would leave you in the odd situation of believing both "P" and "not P", and I don't envy you that. (Or else, to cite Bertrand Russell, you're Hegelians who, loving a synthesis, believe the king wears a wig.)

TripleM
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Personally, with 'the' being a definite article, I would translate 'the King of France is bald' as 'there exists a King of France and the King of France is bald', which is false, rather than 'if there exists a King of France, the King of France is bald' or 'every King of France is bald', which are vacuously true.

But that's just me. And Bertrand Russell, who came up with this in the first place, it seems.

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[Last edited by TripleM at 08-16-2012 04:59 AM]

Trickster
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Tahnan wrote:
Does that mean that you would both also accept that "The king of France is not bald" is true, there being no king of France? Because that would leave you in the odd situation of believing both "P" and "not P", and I don't envy you that.

That's not what's happening here, though it's easy to be confused by it. My example above with the fact that, "If the sky is pink, then the sky is not pink," was intended to highlight such a seeming contradiction.

"The king of France is not bald" is in natural language, which is ambiguous. It depends on how you parse the article "the" with respect to the order of binding the operations implied by the rest of the sentence.

"There is a King of France and that person is also not bald," is one interpretation. This one is false, but it's not the interpretation I was parsing.

"Assume the King of France exists; if so, then that King is not bald," is the interpretation I was taking. The idea is that in natural language, when we speak a subject we imply existence in most cases. "The King of France" implies existence of the King. If I wanted to say the former version, I'd instead say, "There is a King of France, and that King is not bald," to be clearer.

The second parse (the one I was taking) is true, because the precondition is false. "If there is a King of France, then P equals not P," is even true, because the part before the implication is false. An implication can only be false if the postcondition is false and the precondition is true.

Ultimately, however, the flaw is that English is not rigorous. If I say "Every boxer loves a woman," you use context to determine whether "every" binds first (in which case, I mean for every boxer, there exists some woman which that particular boxer loves), or whether "a" binds first (in which case, I mean there is one particular woman beloved by every boxer out there).

In this case, you can read the subject (the King of France) as an integral part of the statement of fact being subject to testing (i.e., a claim that "subject is true and predicate is true") or you can read the subject as assumption (i.e., a claim that "if subject is true this implies predicate is also true"). The first is false because the subject is false, and the second is true because the subject is false.

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[Last edited by Trickster at 08-16-2012 05:32 AM]

Trickster
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TripleM wrote:
But that's just me. And Bertrand Russell, who came up with this in the first place, it seems.

Again, it's a somewhat ambiguous parse. I'm not butting heads with Russell by claiming this, as most of English is ambiguous the moment you add articles to nouns being compared (among other times).

(English was also a bit of a different language back then, which sounds a bit ridiculous to say since it was so recent, but try reading a National Geographic from 1900 and see if you can understand what the hell they're saying.)

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Trickster
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Jatopian wrote:
It was not said, "If there is a king of France, he is bald." The way it was stated, the existence of a king of France was not a conditional, it was simply predisposed.

I don't agree that this is the only valid interpretation. The reason this form is often called a "complex question" in forensics is that it assumes something as a precondition rather than making it part of the refutable statement.

If I ask: "Have you stopped doing cocaine yet?" this is clearly not a fair yes or no question. It implies that you have at one point in time done cocaine, but that fact isn't part of the refutable question (as phrased). Saying the above question is not the same as saying, "Have you at one time done cocaine, and since that time, also stopped doing it?" Our reaction to either is simply to respond, "No," because we don't agree with the implication; but there are multiple ways to translate it formally (because it isn't formally composed in the first place).

You can't apply formal logic to a situation where the meaning changes to suit your needs. Hence, legal documents have a lot of template jargon which are used to formalize legal arrangements, for one non-mathy example.

Jatopian wrote:
This is why I'm suspicious of logicians. Anyone that devoted to a subject that can be thoroughly learned in only one semester is probably having to look too hard for things that aren't there - or make them up.

I've spent much longer than a single semester on the study of logic, but I do appreciate the observation of how I've wasted my time and education.

I mean, of course those of us who like discrete math are all armchair philosophers who "make up" stuff to deceive everyone else, but I don't expect someone as savvy as you to fall for our BS.

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[Last edited by Trickster at 08-16-2012 05:54 AM]

Tahnan
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Trickster wrote:
"The king of France is not bald" is in natural language, which is ambiguous. It depends on how you parse the article "the" with respect to the order of binding the operations implied by the rest of the sentence.

There is no order of binding in this sentence. There is no ambiguity. There is a sentence with a presupposition.

In truth, everything you're saying suggests that you fundamentally understand this but don't have the vocabulary to express it, which unfortunately makes it come out, from where I'm sitting, incoherent. (Bear in mind that I have taught graduate-level courses on this subject.)

Y'all've been using a variety of terms--precondition, implication, predisposition--but if you'll allow a technical term, a presupposition of a sentence is something that must be true for that sentence to even be true or false. The reason that neither "You have stopped doing cocaine" nor "You have not stopped doing cocaine" is true is that both of them presuppose that you at one point did cocaine. It's more than merely implied: if I tell you "I saw Trickster duck into the bathroom, and she came out a lot more energetic and she had this white powder under her nose", then I'm certainly implying she was doing cocaine, but the sentence I said is still either true or false. But that's not the case with "Trickster has stopped doing cocaine": this goes beyond mere implication. (Even more technically: this latter sentence carries the presupposition, regardless of my intentions. Implying something is all about the speaker's intentions.)

Anyway, the point being that "The king of France is bald" can't be evaluated as true or false, because that evaluation depends on--presupposes--there being a king of France. Bertrand Russell held it to be merely false, on the grounds that the sentence itself says "There is a single individual who is the king of France, and that individual is bald"; but Russell very much wanted it to be the case that either a sentence is true or its negation is true, which forced him into the corner of calling this one false (and "The king of France is not bald" true, on the grounds that it's not the case that there is a single individual who is the king of France and who is bald).

No paradox at all; no ambiguity; just a feature of language.

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Trickster wrote:
He sidestepped the problem by changing "truth" to "provability". If you have a statement that says, "this statement is not provably true", then such a statement must be true (falsity would imply truth, which is a contradiction). But such a statement is also out of reach of any proof system humans can devise. Thus mathematics is incomplete.

If I'm understanding this right, that statement can be proven to not be false, in as much as if it were false, then it would be provable to be true. And if you do 'prove' it to be true, then your proof by the very nature of the statement you have proved that it is false. And thus it isn't a proof of it being true.

As for the Cynical Child, Zeno's father didn't say Zeno would be surprised by when the gift would be given, just surprised. Though because Zeno 'knew' that his father would not give the gift on any day, Zeno would not know. At least not for certain.

I don't really get the "If X is true, then X is not true." All it seems to me is disconnected logic. Though I am reminded of the "Colorless green dreams sleep furiously" sentence, in terms of useless sentences.

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Presenting a paradox of my own construction,

When you have the perfect excuse to be causing trouble, someone really smart will see that it's the perfect excuse and get suspicious because it means you can be up to anything. If he suspects you, then the excuse isn't really perfect, but if your excuse is only pretty good, but not perfect, he wont suspect you as much because you're not hiding behind as large of an excuse.

Therefore to have the perfect excuse is to have an imperfect excuse, and to have an imperfect excuse is to have the perfect excuse.

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averagemoe wrote:
someone really smart will see that it's the perfect excuse

If someone can see that, then it isn't the perfect excuse.
Unless that person is perfect, and if they are perfect, they will be able to spot any excuse, but then the excuse would not be perfect, so if this was the case, one of them would have to be imperfect.

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azb
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Bumping to present a paradox.

"I will never say never!"

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Someone Else
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I think that's just false. I don't see any paradox resulting from that statement.

skell
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Someone Else wrote:
I think that's just false. I don't see any paradox resulting from that statement.

Right, because with "I will never say never!" you declare to forbid yourself from saying never, but until you end the declaration (that is you end the sentence) you are free to say never however many times you see fit, so this would be okay too:

"I will never say never as never never has helped in neverending neverstream of nevertask never yo."

But this would be bad (although still not a paradox because per wiki A paradox is a statement that apparently contradicts itself and yet might be true and as human beings we can say one thing and do another, it's called hypocrisy:

"I will never say never. Never, suckers!"

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Jacob
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Even if you say "This sentence does not contain the word "Never" ", it's still false and not a paradox. You don't even need to make reference to further utterances of the word "Never".

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