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Logic and self referential statements

Juma said:
I understand that what is what ypu tried to do. But you failed. The example is not what you think it is.
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Why not?

Reflect on what "itself" refers to.
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Reflect on what "itself" refers to in which sentence? By itself, it doesn't have a referent. And it doesn't appear in my example sentence, so how would its referent induce failure?

Togo said:
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.
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Yeah, what he said.
 
Bomb#20 said:
Reflect on what "itself" refers to in which sentence? By itself, it doesn't have a referent. And it doesn't appear in my example sentence, so how would its referent induce failure?
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Really? I count to two "itself":
Bomb#20 said:
"preceded by itself in quotation marks is an untrue sentence." preceded by itself in quotation marks is an untrue sentence.
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Juma said:
Really? I count to two "itself":
Bomb#20 said:
"preceded by itself in quotation marks is an untrue sentence." preceded by itself in quotation marks is an untrue sentence.
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Gaah! Looking at the wrong sentence. Clearly senility is starting to set in. Sorry, let's try that again...

Reflect on what "itself" refers to.
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The first "itself" doesn't refer to anything since it's mentioned rather than used. The second "itself" refers to the head of the subject of the sentence, just as any "itself" would in a sentence with the structure (<head> <verb>ed by itself <prepositional phrase> <predicate>). The subject of the sentence is the following sentence fragment:

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

Reflecting on that hasn't produced any enlightenment. Care to help me out?
 
Bomb#20 said:
Juma said:
Really? I count to two "itself":
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Gaah! Looking at the wrong sentence. Clearly senility is starting to set in. Sorry, let's try that again...

Reflect on what "itself" refers to.
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The first "itself" doesn't refer to anything since it's mentioned rather than used. The second "itself" refers to the head of the subject of the sentence, just as any "itself" would in a sentence with the structure ( ed by itself ). The subject of the sentence is the following sentence fragment:

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

Reflecting on that hasn't produced any enlightenment. Care to help me out?
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There are two instances of the same text. The "itself" refers to the one in citationmarks, not the other one. Thus a better version would be:
"followed by the same text results in a untrue sentence." followed by the same text results in a untrue sentence.

But then the question is: what sentence? To make it self refering we always must add extra information. The sentence itself is never enough.

The "this" is always there but even if it is explicitily added it is not enough.

So: no there are no self referring sentences. But there are self referring systems.

And a sentence is not true or false because it states that it is.
 
Horatio Parker said:
dx713 said:
I did math studies.
For me, logics were a subset of mathematics.
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I know Bertrand Russell tried to prove that math was a subset of logic.

Is that your personal feeling, or a teaching?
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Teaching, I suppose.
I mean that the only times I worked with logic were during math courses, so math is the only reference I have for logic.
 
dx713 said:
Teaching, I suppose.
I mean that the only times I worked with logic were during math courses, so math is the only reference I have for logic.
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I did formal logic as part of philosophy. The Maths students did formal logic as part of their mathematics course, but it was taught by the philosophy department. On a few occasions we all ended up in the same lecture hall.

Similarly, the compulsory statistics course for scientists was taught by the maths department.
 
Juma said:
There are two instances of the same text. The "itself" refers to the one in citationmarks, not the other one. Thus a better version would be:
"followed by the same text results in a untrue sentence." followed by the same text results in a untrue sentence.
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The point of quotation marks is to mark the text one is quoting. The marks are not quoting themselves. When I say you wrote "There are two instances of the same text.", that's not a claim that you put quotation marks around those words. What your proposed better version asserts is that the construction:

followed by the same text results in a untrue sentence. followed by the same text results in a untrue sentence.
​

results in an untrue sentence. Since that construction isn't a sentence at all, your version is simply false, rather than paradoxical.

But then the question is: what sentence? To make it self refering we always must add extra information. The sentence itself is never enough.
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That applies to any sentence, referring to anything. You always have to add the rules of the language. As far as I can see that's the only thing you have to add to my version. The subject of the sentence is (

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

). Going by the rules of English, what could that noun phrase refer to, other than a string of text assembled by starting with (

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

) and preceding that text with another copy of the same text, with the front copy in quotation marks? I.e., it must refer to the text (

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

). And the predicate my version asserts is true of that referent is that it is an untrue sentence. So the "this" isn't there. The sentence refers to itself only indirectly, by providing instructions for assembling a sentence, instructions that simply happen to generate a copy of the original sentence instead of some other sentence.

The "this" is always there but even if it is explicitily added it is not enough.
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Consider the sentence

You get an untrue sentence if you put together English's singular third-person copula, the U.S.'s title for its head of state, and Barry Goldwater's name, in alphabetical order.​

Would you claim that sentence has an implicit "this" in it? It seems to me that sentence is perfectly clear about what sentence it's talking about and it's doing it without any verbal pointing. So how could the presence or absence of an implicit "this" depend on the assembly instructions?

So: no there are no self referring sentences. But there are self referring systems.
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Okey-dokey. So the sentence+English is a self-referring system. Does calling it that instead of calling the sentence self-referential save it from being paradoxical?

And a sentence is not true or false because it states that it is.
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It doesn't state that it is. But the assembly instructions give you a sentence, and the sentence they give you is the subject of my sentence. Is the sentence true, false, or neither? Pick one. If you pick either "false" or "neither", then it's not a true sentence. So the subject of my sentence is an untrue sentence, and the predicate of my sentence asserts that its subject is an untrue sentence. So my sentence is true, not because it says so, but because what it asserts corresponds to reality. None of this would be in any way problematical, apart from the inconvenient circumstance that the sentence said to be untrue in the premise is verbatim the same sentence said to be true in the conclusion. And of course an equivalent problem arises with the contrary premise: if you pick "true".
 
fast said:
Speakpigeon said:
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
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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.
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"if I say, the sky is blue, am I not saying that the sentence, "the sky is blue" is true?"

I think that If you say that the sky is blue then you are saying that it is true that the sky is blue.
 
Togo said:
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.
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"it's worth bearing in mind that the contradiction comes from the meaning of the sentence, and not from the structure."

Yes it is important.
 
ontological_realist said:
fast said:
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.
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"if I say, the sky is blue, am I not saying that the sentence, "the sky is blue" is true?"

I think that If you say that the sky is blue then you are saying that it is true that the sky is blue.
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Almost on the first, and yes on the second.

If you say the sky is blue, you're saying it's true that the sky is blue. I agree with the underlying truth utterance implication. We just have to be careful that we keep that a separate issue from the subject matter. Yes, if the sky is blue; hence, if it's true that the sky is blue, then the sentence, "the sky is blue" is true, but the subject matter is about the sky, not the sentence. Technically, (I think), saying that it's true the sky is blue can convey more than merely that the sky is blue in certain contexts; for instance, if my truthfulness is brought into question, saying of something that it's true could be a denial of deceitfulness.
 
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fast said:
ontological_realist said:
"if I say, the sky is blue, am I not saying that the sentence, "the sky is blue" is true?"

I think that If you say that the sky is blue then you are saying that it is true that the sky is blue.
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Almost on the first, and yes on the second.
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Sorry, I am not clear what you say here. Could you please clarify.

I was quoting you saying, "if I say, the sky is blue, am I not saying that the sentence, "the sky is blue" is true?"

--
 
ontological_realist said:
fast said:
Almost on the first, and yes on the second.
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Sorry, I am not clear what you say here. Could you please clarify.

I was quoting you saying, "if I say, the sky is blue, am I not saying that the sentence, "the sky is blue" is true?"

--
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Clarification might be tedious, but suffice it to say that I agree with your response.

If the sky is blue, then a) it's true the sky is blue and b) the sentence, "the sky is blue" is true.
 
This sentence is true and false at the same time.

Is there a good article on duplicitous self referential statements?
 
Kharakov said:
This sentence is true and false at the same time.

Is there a good article on duplicitous self referential statements?
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The sentence, "this sentence is true and false at the same time" is not a true sentence, so anyone uttering that sentence in an attempt to convey a truth will fail.
 
fast said:
Kharakov said:
This sentence is true and false at the same time.

Is there a good article on duplicitous self referential statements?
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The sentence, "this sentence is true and false at the same time" is not a true sentence, so anyone uttering that sentence in an attempt to convey a truth will fail.
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It's duplicitous.
 
fast said:
ontological_realist said:
Sorry, I am not clear what you say here. Could you please clarify.

I was quoting you saying, "if I say, the sky is blue, am I not saying that the sentence, "the sky is blue" is true?"

--
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Clarification might be tedious, but suffice it to say that I agree with your response.

If the sky is blue, then a) it's true the sky is blue and b) the sentence, "the sky is blue" is true.
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O.K
 
Horatio Parker said:
dx713 said:
I did math studies.
For me, logics were a subset of mathematics.
Click to expand...

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

Is that your personal feeling, or a teaching?
Click to expand...

If I remember correctly, even before Russell, Gottlob Frege, a German mathematician and philosopher, showed that mathematics was a subset of logic and that logic as well as mathematics refer not to human thinking but to objective reality. This last part seems very interesting to me!
 
ontological_realist said:
Horatio Parker said:
I know Bertrand Russell tried to prove that math was a subset of logic.

Is that your personal feeling, or a teaching?
Click to expand...

If I remember correctly, even before Russell, Gottlob Frege, a German mathematician and philosopher, showed that mathematics was a subset of logic and that logic as well as mathematics refer not to human thinking but to objective reality. This last part seems very interesting to me!
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The last part seems wrong to me.
For me, maths are a tool. A very complex and fascinating tool, but their only connection with reality is when you choose a mathematical system whose axioms are modeling the scientific theories you want to expand on.
 
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