Logic and self referential statements

[Juma]

Can you give an example?

"This sentence is false"

What sentence?

 

[Togo]

The sentance that is being referred to seems pretty clear, and you could certainly produce whole paragraphs attempting to define the location and identification of a particular sentance, without removing the central paradox.

An ambiguous sentance could possibly be both true and untrue, because it may be two or more different meanings, which in turn have two different truth values.

e.g. I have a row every morning.

Do I go rowing every morning - yes
Do I have an argument every morning - no.
The sentance is both true and false, but only because it has two possible meanings.

Appreciate that's essentially a cheat, but it's worth bearing in mind that the contradiction comes from the meaning of the sentance, and not from the structure.

 

[Bomb#20]

"This sentence is false"

What sentence?

Are you proposing to get out of the bind using an argument to the effect that the referent of "This" is ambiguous? "This" is inessential to the problem.

"preceded by itself in quotation marks is an untrue sentence." preceded by itself in quotation marks is an untrue sentence.

 

[Kharakov]

"False."

Is the definition of false true?

 

[Testy Calibrate]

Ceci n'est pas une déclaration auto-référentielle.

Isn't this a joke about rhetorical questions?

What if there were no rhetorical questions?

 

[Testy Calibrate]

anyway, re: the OP, I assume you are referring to the liar's paradox. (I always lie.) That's kind of an interesting question.

 

[Kharakov]

I took the sentence in to a quantum mechanic to have them look at it.

 

[Testy Calibrate]

Did they say you won't know the answer until you look at it?

 

[Juma]

What sentence?

Are you proposing to get out of the bind using an argument to the effect that the referent of "This" is ambiguous? "This" is inessential to the problem.

"preceded by itself in quotation marks is an untrue sentence." preceded by itself in quotation marks is an untrue sentence.

No, that didnt fix it. It actually got worse.

 

[Kharakov]

I took the sentence in to a quantum mechanic to have them look at it.

Did they say you won't know the answer until you look at it?

Back to the "paradox".

Duplicitous or metaphorically "two faced" statements are both true and false at the same time.

This sentence is duplicitous. <duplicitous>
This sentence is both true and false. <duplicitous>
This sentence is false. <duplicitous>

 

[fast]

The sentance that is being referred to seems pretty clear, and you could certainly produce whole paragraphs attempting to define the location and identification of a particular sentance, without removing the central paradox.

An ambiguous sentance could possibly be both true and untrue, because it may be two or more different meanings, which in turn have two different truth values.

e.g. I have a row every morning.

Do I go rowing every morning - yes
Do I have an argument every morning - no.
The sentance is both true and false, but only because it has two possible meanings.

Appreciate that's essentially a cheat, but it's worth bearing in mind that the contradiction comes from the meaning of the sentance, and not from the structure.

The sentence, "I'm standing by the bank" is true while the sentence, "I'm standing by the bank" is false, and it only appears contradictory because it's appears that I'm expressing contradictory propositions;however, because this is an instance where things are not as they appear via using the ambiguous term, "bank", I'm actually expressing the fact that I'm standing by the bank (a financial institution) while also expressing that I'm not standing by the bank (at the waters edge).

 

[fast]

I'm not going to be so quick to think that every self-referential sentence expresses a proposition. If a sentence doesn't express a proposition, then the sentence is not true, and no sentence that is not true because of that is a false sentence, for only sentences that express propositions can be true or false.

Yes.

And, to be explicit, I don't accept that "This sentence is false" expresses a proposition.

I would also say that people saying that the sentence is meaningless are also correct. The sentence is linguistically acceptable and can be accepted as having a certain kind of meaning, namely that a syntactic machine could correctly reply to certain pointed questions about the sentence, such as "What sentence is said to be false?" etc. But precisely because the sentence is neither true nor false, we are unable to form a belief, however tentative, as to whether what it means is true or false, hence it has no meaning for us beyond its being syntactically acceptable.
EB

That sounds good to me.

If someone said, "this sentence is false," I'd ask what sentence, as it's indicative of referencing a different sentence, but if I found out they were referencing that very sentence, then I'd interpret the 'statement' as: the sentence, "this sentence is false" is true, but because there's no truth or falsity, as indicated by no apparent proposition expressed, I'd be inclined to think that although the sentence is not true, it is not therefore false, but then I'd have to remember the interpretation which is to say of the sentence that it's true; after all, if I say, the sky is blue, are I not saying that the sentence, "the sky is blue" is true? Either way, there's no truth or falsity to the original sentence in question.

 

[ontological_realist]

I don't know about academic logic but it seems to me that if the law of non-contradiction (A is not ~ A) is untrue even in a single case, then every thing anybody claims becomes nonsense, meaningless and gibberish. Because then if you say that there is a table in this room it would also mean that you are saying that there is not a table in this room. etc. (because then table means table and also non table).

I'm not going to be so quick to think that every self-referential sentence expresses a proposition. If a sentence doesn't express a proposition, then the sentence is not true, and no sentence that is not true because of that is a false sentence, for only sentences that express propositions can be true or false.

I agree. If a sentence is not a proposition, then it has no truth value. Then it can not be false or true.

Sorry, I have not studied formal logic. That is why I wanted every body's input.

I was disturbed after reading of self referential sentences.

--

 

[Bomb#20]

Are you proposing to get out of the bind using an argument to the effect that the referent of "This" is ambiguous? "This" is inessential to the problem.

"preceded by itself in quotation marks is an untrue sentence." preceded by itself in quotation marks is an untrue sentence.

No, that didnt fix it. It actually got worse.

That was kind of the point -- it's a self-contradictory sentence where the liar's paradox doesn't depend on a sentence being able to point to itself with a construction like "This sentence".

 

[dx713]

Godel proved that any language developed enough to express arithmetics is necessarily incomplete, i.e. you can form in it sentences whose thruth value can't be determined.
(and trying to assign a truth value to that sentence leads to an inconsistent language, where most sentences can be demonstrated both true and false)
He did use a self-referencing statement to prove that.

Apart from that, I can't discuss more the OP, because I don't know what the "law of non-contradiction" is.

How about LNC is:-

A is not ~ A

In that case, I'd say that the kind of self-referential sentence you refer to in the OP does not violate the law of non-contradiction.
This kind of sentence has an undecided truth value, not meaning that it's both true and false but that it's neither.
(caveat: note that I'm not a philosopher, but approaching that on a mathematics angle. I might be completely off base for this forum)

 

[Juma]

No, that didnt fix it. It actually got worse.

That was kind of the point -- it's a self-contradictory sentence where the liar's paradox doesn't depend on a sentence being able to point to itself with a construction like "This sentence".

I understand that what is what ypu tried to do. But you failed. The example is not what you think it is.

Reflect on what "itself" refers to.

 

[Togo]

That was kind of the point -- it's a self-contradictory sentence where the liar's paradox doesn't depend on a sentence being able to point to itself with a construction like "This sentence".

I understand that what is what ypu tried to do. But you failed. The example is not what you think it is.

Reflect on what "itself" refers to.

It would be far more efficient to actually state the point you're trying to make, rather than trying to get other people to guess.

 

[Speakpigeon]

(caveat: note that I'm not a philosopher, but approaching that on a mathematics angle. I might be completely off base for this forum)

Do you really mean "mathematics angle" or do you mean "logical angle"?
EB

 

[dx713]

I did math studies.
For me, logics were a subset of mathematics.

 

[Horatio Parker]

I did math studies.
For me, logics were a subset of mathematics.

I know Bertrand Russell tried to prove that math was a subset of logic.

Is that your personal feeling, or a teaching?