Philosophy: (Seven Paradoxes) Paradox 1: The Man who Spoke the Truth but Didn't

(Seven Paradoxes) Paradox 1: The Man who Spoke the Truth but Didn't

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2005/07/20 12:02:31 PST by PegasusHoplite28
Edited at 2005/07/20 13:31:54 PST

A traveller was walking one day when he met an old man sitting beside the road smoking a pipe.
'The first thing said to you by the first person you meet today will not be true,' said the old man. 'Trust me - don't believe what he says!'
'OK,' said the traveller. 'But hang on a minute: you're the first person I've met today.'
'Exactly!' said the old man.

You may have spotted something funny going on here. If the old man speaks the truth, then the first thing he says is not true. But if the first thing he says is not true, then the first thing he says is true.
This is a version of the famous liar paradox, a paradox first formulated in ancient Greece over 2,000 years ago.
The traveller thought he saw a way out of the paradox: claim that what the old man first said is neither true nor not true. After all, why does every such sentence have to be either true or not true?

'Old man, you're trying to trick me,' said the traveller. 'It's obvious that what you said is neither true nor not true.'
'Aha,' said the old man. 'You're suggesting that it is not true that what I said is true, and also not true that what I said is not true?'
'That's exactly right,' said the traveller.
'Well, then, if it's not true that what I said is true, then what I said is not true!'
The traveller was starting to get a headache. The old man continued: 'And if it's not true that what I said is not true, then what I said is true! For what I said is precisely that what I said is not true!'
The traveller was starting to feel like ramming the old man's pipe down his throat.
'So you see,' said the old man, 'your suggestion is wrong: it's not true that what I said is neither true nor not true. In fact, it's both true and not true!'

But that's impossible. Isn't it?

Comments, opinions?

2005/07/20 12:26:36 PST by seanan

Maybe paradoxes are nonsense.

2005/07/20 17:34:37 PST by Goyen

Seanan there's a problem with that. Our great and beloved teacher always used paradox in such a "profound" way that the definition would often be forgotten.

A paradox is something that seems untrue at first glance but in actuality is true (supposedly).
One common example is "Alone in a crowd."

That appears to be contradictory, but actually is speaking in a profound way about feelings and such. Anyways, so if something that is a "paradox" presupposes that it is true, then you just said that anything true is nonsense.

----------------------------------------------------------------------------------------------
Now, this statement is neither "true" nor "false" because admitting either would be contradictory. Now, let us show the types of these "liar paradoxes".

1) Self-Statement: This one is when a statement talks about itself, such as "This sentence is false.". This one can easily be beaten because it is like a tautology (p v ~p) in nature, and tautologies never prove anything. Therefore, this "self-statement" is meaningless.
(another form of this is "I am telling the truth that this sentence is false", because the statement still talks about itself)

2) Statement of self: This much like self-statement, except the one who introduces the sentence uses it to talk about him or herself. One example is the example used in the first post.
Oh, dear, it seems he edited it since I last saw it. No matter.

The old man tries to trick this traveller when he finds out it is neither true nor not true. The old man says that "not true" would become "false" and that "not not true" would become "true", since we often use such logic. Ah! There is the problem! This is much like the statement "robots can't think", where it means that thinking CANNOT apply to robots.

Therefore, although the traveller nor the old man realized it, that line of reasoning does not work because the realm of truth and falsity can't apply to that statement! If it could, then it would EITHER be true OR false! But we already realized in advance that truth and falsity cannot work for that statement!

Hence forth, both types of "liar paradoxes" are worthless in any sort of logic because they are beyond logic.

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2005/07/20 17:56:33 PST by Croato

"But that's impossible. Isn't it?"

This is where you're wrong: there's the true, there's the false, and then there's the metaphysical.

Let's first re-examine the primary statement: "The first thing said to you by the first person you meet today will not be true,"

The first task necessary is to classify the statement made. Because the fact that the statement is not true is a quality added by the content of the statement (as opposed to being implied in the concept of "the first thing said"), it is a synthetic statement (as opposed to analytic). Now, according to Kant, there are then two types of synthetic statements: a posteriori and a priori. A synthetic statement a posteriori is one gathered from experience. Normally, when declaring whether a statement is true or false, one obtains this knowledge from experience. HOWEVER, in this particular case, because the statement is neither true or untrue, it cannot be proven through experience. And because it can't be proven through experience, it simply falls with all other synthetic statements that cannot be proven through experience, such as '2,000 angels can fit on the head of a nail'.

The statement is therefore a a synthetic statement a priori DISGUISED as a synthetic statement a posteriori! The statement is therefore not true, not untrue, but metaphysical. Case closed.

2005/07/20 18:47:04 PST by Goyen

It IS true that the statement is metaphysical, but seriously, don't tell me you're using that "law of empirical varifiability"!
The law doesn't even hold up to its own standards! D:<

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2005/07/20 20:54:12 PST by seanan

I agree with Goyen.

The "liar paradox" posted above is a self-statement.

Let's look at the statement:

"The first thing said to you by the first person you meet today will not be true."

The subject, [The first thing said to you by the first person you meet today], is really just [this sentence] in disguise, because, obviously, the sentence that the old man says is the first thing said to the traveller by the first person he meets.

Therefore, by the process of substitution, we get this sentence:

"[This sentence] will not be true."

We can change the tense here and get

"[This sentence] is not true."

And thus we clearly see that it is a self-statement, which I believe Goyen asserted earlier. Goyen also asserted that self-statements are tuatologies, which are, of course, NONSENSE.

So, I say again, paradoxes (at least the kind we are talking about, "liar paradoxes") are nonsense.

2005/07/20 22:43:53 PST by ajames
Edited at 2005/07/21 09:05:09 PST

Goyen has graciously pointed out that the word 'paradox' has been used in this class in a couple different ways. Although the word 'paradox' is a family resemblance term, it might be helpful to try to gloss some of the most general ways it has been used.

The first place we encountered this word was when studying McDowell. There 'paradox' meant a wildly implausible conclusion that appeared to follow from seemingly true premises. There are always a number of different ways to cope with such paradoxes. One can either (1) deny the truth of any one of the premises, or (2) show that the conclusion does not actually follow from them, or (3) show that accepting the conclusion is not so bad after all.

If 'paradox' were to be defined merely in the way Goyen would have it, i.e., as a statement or conclusion that seems false but actually is true, then it would be hard to get into view what McDowell means when he describes his problems as paradoxes. After all, McDowell does not think the conclusions of his paradoxes are true. The way he chooses to resolve his paradoxes is to deny the truth of a hidden assumption that makes it seem as though the premises, which he wants to preserve, lead to the absurd conclusions.

The second place we encountered this word was when studying Kierkegaard. Kierkegaard uses the word 'paradox' to describe the various objects of faith of the religious life. Christ, miracles, revealed Holy Scripture, and apostolic authority are all described as paradoxes and Christianity as a paradox-religion. For Kierkegaard the paradoxical is opposed the rational, and so by calling these various items paradoxes, Kierkegaard is suggesting that there is no way to appropriate them rationally, e.g., scientifically or philosophically. This doesn’t mean that to appropriate them one must be irrational (a common misconception), but only that one must come to them through faith alone.

The third place we have encountered the word 'paradox' is here on the website in Kyle’s recent post of the Liar Paradox. The Liar Paradox can be put in the form of a single statement, e.g., “I am lying” or “This statement is false,” which seems to contradict itself; for if it’s true, it’s false, and if it’s false, it’s true, etc. One way philosophers (including Wittgenstein) have dealt with such statements is simply to say that they are nonsensical (so you aren’t alone Seanan), while other philosophers have felt that response to be too simple.

I hope this helps to clear up some of the confusion regarding the use of this word, and thanks again Goyen for encouraging me to do this.

2005/07/24 19:15:50 PST by admin

I must say I sort of agree with Seanan in that it's nonsensical; I believe it to be a loophole of sorts which should be thrown out as a logical statement. In addition, this old man needs to get a job rather than just spend his life acting as a human sphinx, with crazy paradoxes instead of riddles. What was with jobless old men in Greek times? (i.e., Socrates). In addition, Goyen, your definition of a paradox makes it seem too simple; if a paradox were simply somehting that seemed false but was actually true, they wouldn't require such thought. I believe an important aspect of a paradox is that its truth or falsity is unclear, i.e., you dont know either way. That's what make them brain-busting. For example, I say, my computer is broken. "THAT'S NOT TRUE, YOU'RE MAKING A POST ONLINE!" My statement seems false. So I respond, "I'm using a friend's." BOOM! PARADOX. Seems false, but true. Kinda sketchy, I think. And also Seanan, you said what I was planning to say, which is that the old man is basically saying "I am lying."

"wow, this place is almost as big as cartman's ass!"
cartman: "no it isn't, you guys."

2005/07/25 10:02:05 PST by seanan

I think that the definition for paradox as "a statement that seems false but is actually true" is the literary definition, like what you learn in English class. So Goyen is not totally wrong there, but I'm not sure that definition applies to philosophy.

2005/07/25 21:51:16 PST by Goyen

Quote from admin:

In addition, Goyen, your definition of a paradox makes it seem too simple; if a paradox were simply somehting that seemed false but was actually true, they wouldn't require such thought. I believe an important aspect of a paradox is that its truth or falsity is unclear, i.e., you dont know either way. That's what make them brain-busting.

Actually, the difference between the paradox and the "Philosophical paradox" is that the 2nd word has an adjective!

Paradox = at first glance, the statement appears false or nonsensical, but in actuality is true.

Philosophical Paradox = At first glance, the conclusion statement itself appears false and nonsensical, but the premises show that the conclusion appears to follow from them.(It is stated in the philosophical paradox that it "appears" to follow because the conclusion denies our normal thinking about the universe. Thus, we are not wanting to believe something that goes against our "common sense".)

Quote:

For example, I say, my computer is broken. "THAT'S NOT TRUE, YOU'RE MAKING A POST ONLINE!" My statement seems false. So I respond, "I'm using a friend's." BOOM! PARADOX.

Umm.. no that's not a paradox. Why would it appear "seemingly false" that you're using your friend's computer because yours broke down?

A paradox would be if you said your screen is completely broken but you're still making posts. Since we usually associate our screen with our computer, we think we need the screen to do things on our computer. But in actuality, we don't.

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2005/07/26 02:27:47 PST by Dr3w

Sentence 1: 'The first thing said to you by the first person you meet today will not be true'

This is statement of self like what Goyen's definition of paradox is.

Let's call this sentence 1.

SUPPOSITION #1
let's suppose sentence 1 is true. ---
then what sentence 1 is proposing is true.
However, sentence 1 said that it is not true.
So.....sentence 1 is not true, opposing our initial supposition.
we can say that "sentence 1 is not true".

SUPPOSITION #2
let's suppose sentence 1 is not true --
then what sentence 1 is proposing is not true
However, sentence 1 said that it is not true
So....sentence 1 is not not true , opposing our initial supposition.
we can say that "sentence 1 is not not true". (like what Goyen said).

But I agree with ya'll that this seems to contradict, which is impossible.....

(Now I thought of a sentence that do not contradict) Perhaps, let's say

Sentence Z: Sentence Z is true......

this doesn't contradict if we say that is is true, because it just adds to that it IS true. If we say it's not true, then it just confirms that it's not true.....so is it true or not true? we have no freaking idea and we need extra info to help us decide....but if we can say that it is just some meaningless junk, it doesn't proposes anything........ Maybe this is the case with Sentence 1....(but it is not nice to say that Sentence 1 is neither true nor not true, but just some meaningless junk!!!!)

so...let's take for example another sentence....

Sentence Y: Zebras are black....

Okay...we might say that this is both neither true and not true because...
It's not true because Zebras are ONLY partly black (there's another color...white)
It's not not true because Zebras are partly black

I don't think there's a contradiction....we have no definite definition of black. If we say that black would mean that ALL black, then Sentence Y is not true. If we say black would mean partly black, then Sentence Y is true...we will not face a contradiction here if we stick to only 1 single definition...

maybe this is the case with Sentence 1.....what we mean of the word "true" is unclear.

(I know you're tired of this, but let's take another sentence..)

Sentence X: white hope flies above slowness

Sentence X true or not true? let's have two definitions of the word true (i could come up with two for now...im sooo sleepy!!):

A) true means that it states a correct proposition.
---If we use this definition, then Sentence X is not true, since, being meaningless, it doesn't state any proposition at all........

B) true means not stating an incorrect proposition.
---If we use this definition, then Sentence X is true since it does not state an incorrect proposition, since it doesn't express any proposition at all....

Even if Sentence X is meaningless doesn't mean we can't prove if it's true or not, as long as we define the definition of "true"

Okay now in this case, let's use definition A since that is what we normally would suggest as the meaning of "true".

Remember we supposes that Sentence 1 is neither true nor not true, but some meaningless junk!!! with Definition A, we can see that meaningless is not a possibility. it is a form of "untruth"....so if Sentence 1 is meaningless, then with Definition A, Sentence 1 is not true.....look back and see that we are back to where we started....so saying that Sentence A is meaningless gets us nowhere!! UGH

Now suppose that sentence A is meaningless and not true. We have seen earlier that this sentence envelopes a contradiction.

So look back on SUPPOSITION#2, on the second part of it. It says "then what sentence 1 is proposing is not true". If Sentence 1 is meaningless then it doesn't have any proposition AT ALL....so saying that "then what sentence 1 is proposing is not true" doesn't hold, which means SUPPOSITION#2 doesn't hold...and there's no contradiction. SUPPOSITION#2 refers to a proposition that is stated by Sentence 1, but Sentence 1 doesn't state any proposition......

SUPPOSITION#3:
So what we're saying is that
- Sentence 1 is either not true or not not true, BUT not both
- Sentence 1 is not true (SUPPOSITION#1 holds, while SUPPOSITION#2 does not)
- If Sentence 1 is meaningful, then Sentence 1 is not not true......(contradict's above statement)
- Therefore, Sentence 1 is meaningless....

OMG, Jeez!!! we're back with meaningless and where we started UGH...

another try.....
- Sentence 1 is a meaningless sentence.
- Sentence 1 is not true......

huh...why don't we substitute this...so the above 2 statements is saying
"Sentence 1 is not true" is a meaningless sentence.

When we look back on SUPPOSITION#3, let's examine the second part of it....it's saying "Sentence 1 is not true". So how is it the sentence that the same SUPPOSITION proves is meaningless (look back on "Sentence 1 is not true" is a meaningless sentence)....I don't think it can...and now believe it, but I have no idea where to go to.

Dangit! It was a nice ride on this roller coaster, I thought I was going to throw up .And literally (in real life, I would as I'm not roller coaster friendly). It's 3:30 am right now, I tried so hard to study but UGH, paradoxes should just get a kick in the butt as well as that old man ^_^. The above post is long and pointless, I think I made so many contradictions about my statements here as I'm soooooo sleepy!! LOL

2005/07/26 13:07:32 PST by Goyen

Quote from Dr3w:

Sentence Z: Sentence Z is true......
This doesn't contradict if we say that is is true, because it just adds to that it IS true. If we say it's not true, then it just confirms that it's not true.....so is it true or not true? we have no freaking idea and we need extra info to help us decide....but if we can say that it is just some meaningless junk, it doesn't proposes anything........

No no no this is different. Sentence Z is EITHER true OR false. The liar paradox is where the sentence is NEITHER true NOR false. There's a big difference.

Quote:

Sentence Y: Zebras are black....

Well there's only one defintion of black. -_-
The difference is that people need adjectives to understand your underlying concept of the word "black" for the given situation, since you could mean partly black, or completely black.

Quote:

Sentence X: white hope flies above slowness

Sentence X true or not true? let's have two definitions of the word true (i could come up with two for now...im sooo sleepy!!):

A) true means that it states a correct proposition.
---If we use this definition, then Sentence X is not true, since, being meaningless, it doesn't state any proposition at all........

Even if Sentence X is meaningless doesn't mean we can't prove if it's true or not, as long as we define the definition of "true"

Ok now you're being a smart-allic.

1) If you mean "no proposition", you must be talking about opinions. Now come on, opinions aka value judgements can't have truth or falsity in them!

2) You're also making this rash and arrogant statement that nonsense has truth or falsity. If I say "asgpasghoih" to you and I have no actual meaning behind that phrase, then how can you say it's either true or false?

Quote:

Get some sleep! :P

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2005/07/26 21:56:55 PST by Dr3w

Okay Goyen, you have great counter points...but I have to say I do have many flawed points as well. It was a nice try on my part...but just a little info.

I use Sentence Y to make a point. You're right, people need adjectives to UNDERSTAND the concept of the word. I used it as to imply that we also need something to UNDERSTAND the concept of true ^_^. And as for Sentence X, I'll have to agree that this was made carelessly. However, I tried making the Sentence Z to jump to an assumption to make Sentence 1 meaningless. With that in hand, I took out supposition#2, and it's still meaningless. But like I imply that using Sentence X, Y, Z makes a roller coaster and we're back to where we started. So I just tried to have a subjective reasoning to make another attempt.

- Sentence 1 is a meaningless sentence.
- Sentence 1 is not true
"Sentence 1 is not true" is a meaningless sentence....

I thought that this would work, but I don't think prove the sentence that the same SUPPOSITION proves is meaningless. UGH. Oh well

2005/07/27 10:00:01 PST by Goyen

Argh.. my head hurts! :P Could you better explain your three "sentence 1"'s?

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2005/07/27 11:09:03 PST by seanan

I still say it's nonsense and let's leave it at that. :)