• Welcome to the new Internet Infidels Discussion Board, formerly Talk Freethought.

Logic and self referential statements

A statement of paradox will violate the law of self-contradiction. Statements of paradox are often self-referential, although you can get statements that are simply self-contradictory, by referencing two categories that are mutually exclusive.

However, I'm not sure why all self-referential statements would be said to violate the law of non-contradiction. There are plainly some that don't. "This sentance is a statement" for example.

My suspicion is that someone is thinking of paradoxes, the most famous of which tend to be self-referential, and incorrectly generalising to all self-referential statements.

Paradoxes in general cause a great deal of excitement from philosophers who want to tie language to truth in some way.
 
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.
 
Togo said:
A statement of paradox will violate the law of self-contradiction. Statements of paradox are often self-referential, although you can get statements that are simply self-contradictory, by referencing two categories that are mutually exclusive.

However, I'm not sure why all self-referential statements would be said to violate the law of non-contradiction. There are plainly some that don't. "This sentance is a statement" for example.

My suspicion is that someone is thinking of paradoxes, the most famous of which tend to be self-referential, and incorrectly generalising to all self-referential statements.

Paradoxes in general cause a great deal of excitement from philosophers who want to tie language to truth in some way.
Click to expand...

I did not pose the question properly in the O.P. My mistake. I did not mean to say that all self referential sentences violate the law of non-contradiction.
Can a statement (not sentence) be both true and untrue? Or can two contradictory statements be both true? Or can A be non A ? Example?
 
dx713 said:
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.
Click to expand...

How about LNC is:-

A is not ~ A
 
fast said:
ontological_realist said:
Do self referential statements invalidate the law of non-contradiction?
Click to expand...
My guess is no. It's a law, and it's going to take a whole heap to muck it up.
Click to expand...

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).
 
ontological_realist said:
fast said:
My guess is no. It's a law, and it's going to take a whole heap to muck it up.
Click to expand...

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).
Click to expand...
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.
 
fast said:
ontological_realist said:
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).
Click to expand...
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.
Click to expand...
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
 
You must log in or register to reply here.
Back
Top Bottom