## Sunday, October 16, 2011

### Do false statements exist?

Commenter Anthony questions whether false statements exist, and says
In order for me to concede that false statements exist, I would need clarification of what is meant by "statements" and what is meant in saying that they "exist". If the answer I receive is "they just do" or "most people accept that they do", you can argue all you want about "burden of proof", but I will not be convinced, any more than I would be convinced by the same "arguments", that "red unicorns exist".
OK then.  Starting with the definitions.  There are various definitions of 'statement' but I will go with 'declarative sentence' for this one.  As for 'exists', I will read 'false statements exist' as equivalent to 'some statements are false'.  See my earlier remarks about Brentano equivalence.

So we need to demonstrate to Anthony's satisfaction that some declarative sentences are false.  That is easy.  The sentences "The sky is red" is a declarative sentence, and it is false.  So, some declarative sentences (i.e. at least one) are false.  If Anthony denies that "The sky is red" is false, there is an equally easy reply.  If you deny something, you are denying that it is true. But if you are right in denying this, it must be false. So in order to make the objection at all, you have to concede that at least one declarative sentence, in this case "'The sky is red' is false" is false, and thus concede the point.  More generally, to affirm "no declarative sentence is false" is to deny "some declarative sentence is false". But if that denial is right, "'some declarative sentence is false' is false" is true, and so at least one declarative sentence is false, namely "no declarative sentence is false".  Slightly more formally:

(1) No declarative sentence is false (assumption)
(2) "Some declarative sentence is false" is false (E and I are contradictory opposites)
(3) "Some declarative sentence is false" is a declarative sentence (definition)
(4) Some declarative sentence is false (substitution)

I doubt this will be the end of the matter.

Anthony said...

Your proof assumes that all declarative sentences are either true or false, right?

I could ask you to define "declarative sentence", "true declarative sentence", and "false declarative sentence", but maybe it would be clear if you answer whether or not the following are declarative sentences, and if so, whether they are true or false.

"Red unicorns exist."
"Red unicorns do not exist."
"Non-red unicorns exist."
"Non-red unicorns do not exist."
"All unicorns are red."
"All unicorns are not red."
"No unicorn is red."
"All unicorns are non-red."
"Happiness is purple."
"Happiness is non-purple."
"Happiness is not purple."

Anthony said...

Another question. Does "some declarative sentences are false" imply that "false statements exist"?

Edward Ockham said...

>>Your proof assumes that all declarative sentences are either true or false, right?

Yes. We could quibble about whether 'false' is the same as 'not true', of course.

All the sentences in your list will count.

>>Another question. Does "some declarative sentences are false" imply that "false statements exist"?

You asked me to define 'exist', and I did so by means of Brentano's equivalence. You could quarrel with this if you want, and many have.

Anthony said...

Well, these are not quibbles. They are serious flaws in your reasoning. And you didn't answer my questions.

Edward Ockham said...

>>Well, these are not quibbles. They are serious flaws in your reasoning. And you didn't answer my questions.

No they are quibbles. Please explain why.

Oh I see, you want me to answer the true or false ones.

"Red unicorns exist." false
"Red unicorns do not exist." true
"Non-red unicorns exist." false
"Non-red unicorns do not exist." true
"All unicorns are red." false in traditional semantics, true in modern semantics
"All unicorns are not red." reading as 'not all unicorns are red' true
"No unicorn is red." true
"All unicorns are non-red." false
"Happiness is purple." false
"Happiness is non-purple." false
"Happiness is not purple." true

I don't see what these have to do with your claim that no statement is false, however.

Anthony said...

Two of the supposed "statements" you did not give an answer to. Are you using modern semantics or traditional semantics?

Alternatively, here's another question:

Is "This statement is false." a declarative sentence, and is it true or false?

Edward Ockham said...

>>Two of the supposed "statements" you did not give an answer to.

Which?

>>Are you using modern semantics or traditional semantics?

>>Alternatively, here's another question: Is "This statement is false." a declarative sentence, and is it true or false?

It is not true, nor is it false. Note that the possible fact that some sentences fail to have a truth value does not support the statement that no statement is false.

By the way, Anthony, are there any statement of mine - by which I mean, things I have said, that you disagree with? I have tried to answer all your many questions, I will go no further from now on unless you answer this question. Again: is there anything I have said which you disagree with?

Anthony said...
This comment has been removed by the author.
Anthony said...

You agreed that your proof assumes that all declarative sentences are either true or false. But then you agree that "This statement is false." is neither true nor false. Is "This statement is false." a declarative sentence?

I disagree with your purported definition of "statement". I disagree with your purported definition of "exist". I disagree with the validity of your "proof".

Edward Ockham said...

>> I disagree with your purported definition of "statement".

Thank you. Then you think my statement that ‘a statement is a declarative sentence’ is false?

Michael Sullivan said...

Is "This statement is false." a declarative sentence?

No. It doesn't assert anything. It has the grammatical form of an assertion but not the logical content. That's because "is" is a copula predicating "false" of "this statement", but "this statement" in the sentence is not a statement, but a term which does not actually refer to a statement.

Anthony said...

>> Then you think my statement that ‘a statement is a declarative sentence’ is false?

For me to think that I would have to think 1) that "A statement is a declarative sentence." is a statement; and 2) that it is false.

I'm not convinced of either.

But I've already told you that, when I told you that I wasn't convinced that false statements exist. Obviously if I'm not convinced that false statements exist, then I don't think that you've written a false statement!

---

Michael, I agree with you that "This statement is false." is not a statement, but I was under the impression that it was a declarative sentence. What is the definition of "declarative sentence"?

Michael Sullivan said...

I would define a declarative sentence as a sentence which declares something. Simple! So "This statement is false" has the grammatical form of a declarative sentence, but does not actually declare something.

I could as easily say "x is y", which is also grammatically well-formed, but so long as "x" and "y" have no positive content, the sentence "x is y" is neither true nor false.

Edward Ockham said...

>>I'm not convinced of either.

So you have said that you are not convinced of either. Does that mean that you think that "Anthony is convinced of either" is false?

Anthony said...

Michael, what is declared by a sentence which is not true? What about one where the predicate does not match the subject (e.g. "Happiness is purple.")? What about one where the subject is nonexistent (e.g. "Unicorns are red?").

"This statement is false." claims that it is a statement, and that it is false. It doesn't *declare* this, in that it is not valid. But neither is "Dogs are cats.".

Anthony said...

>> So you have said that you are not convinced of either. Does that mean that you think that "Anthony is convinced of either" is false?

I don't know, does it? Is that what "false" means? Is a string of words in the form "A is B" false simply because it is not true? Obviously not since you agreed that "This statement is false." is neither true nor false.

Anthony said...

>> Does that mean that you think that "Anthony is convinced of either" is false?

In order for me to truthfully say yes, I would have to be convinced of either. But if I were convinced of either, it would be true, not false.