Statments - What are They?

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Purple Knight
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Statments - What are They?

Post #1

Post by Purple Knight »

Question for debate: What is a statement?

We've all seen this one:

"This statement is false."

Or this one:

"The following statement is false."
"The previous statement is true."

Now what we have here are paradoxes where the statements cannot have definite truth values. However, any statement being unable to have a definite truth value ruins the concept of a truth value.

The resolution is simple: None of these are statements.

Why not? Well, because statements must refer, ultimately, to facts which exist in the real world, not to other statements or to themselves. Statements that do not refer ultimately to facts can't be checked and don't have truth values, so they can't be statements, because a statement must be true or false.

Now, you can have a chain, but at the end of that chain must be a reference to a real fact, which can (at least, in theory) be checked.

"The next statement is true."
"The next statement is true."
"The next statement is true."
"It rained on Saturday."

Notice that all of these statements are reducible to, "It rained on Saturday." and whether it rained on Saturday or not is what we would check, to check the truth value of the statement.

You can also reference what someone said, which is different than referencing a statement.

"I ate the four horsemen of the apocalypse last Wednesday."
"Purple Knight said he ate the four horsemen of the apocalypse!"

When someone says something, makes that utterance, or puts those words down, that is now a fact that can be checked, a thing that happened (or didn't), not just a statement. I can type or utter that this statement is a lie, and then I did in fact say it, and then saying I said it is true. If, however, you say that what I said was true, you're reducing it to a statement again, removing from it the fact that I uttered it and addressing its truth value, and it can't have a truth value unless it refers to a fact that can, at least in theory, be checked.

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Re: Statments - What are They?

Post #2

Post by Miles »

Purple Knight wrote: Tue Oct 05, 2021 12:54 am Question for debate: What is a statement?
state·ment
/ˈstātmənt/
noun: statement; plural noun: statements

a definite or clear expression of something in speech or writing.
"do you agree with this statement?"

an official account of facts, views, or plans, especially one for release to the media.
"the officials issued a joint statement calling for negotiations"

a formal account of events given by a witness, defendant, or other party to the police or in a court of law.
"she made a statement to the police"
Source: Oxford Languages

any statement being unable to have a definite truth value ruins the concept of a truth value.
Why?

. . . statements must refer, ultimately, to facts which exist in the real world, not to other statements or to themselves.
I contend the following is a statement: "the Earth is flat."

Statements that do not refer ultimately to facts can't be checked and don't have truth values, so they can't be statements, because a statement must be true or false.
Statements like, "Jesus was the son of god" I imagine.

Now, you can have a chain, but at the end of that chain must be a reference to a real fact, which can (at least, in theory) be checked.

"The next statement is true."
"The next statement is true."
"The next statement is true."
"It rained on Saturday."

Notice that all of these statements are reducible to, "It rained on Saturday." and whether it rained on Saturday or not is what we would check, to check the truth value of the statement.
And, what if it might have rained on the tiny, (1.7 sq mi) uninhabited island of Jarvis in the South Pacific Ocean (Latitude: -0.374350 Longitude: -159.996719), and I said "It rained on Jarvis Saturday," however, there is no way to check its truth value. Is my claim not a statement?.


When someone says something, makes that utterance, or puts those words down, that is now a fact that can be checked, a thing that happened (or didn't), not just a statement.
Fact: "Noah took all the dinosaurs aboard the ark, but he and the other seven got hungry and ate them all."



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Re: Statments - What are They?

Post #3

Post by Purple Knight »

Miles wrote: Tue Oct 05, 2021 2:51 am
Purple Knight wrote: Tue Oct 05, 2021 12:54 am Question for debate: What is a statement?
state·ment
/ˈstātmənt/
noun: statement; plural noun: statements
I'm sure you're aware that formal logic often as different definitions of terms than the dictionary. Note though that one of your definitions - the first one - mentions definite and clear, which I have to agree with. Now, a poem might express an emotion or something which is still definite and clear but lacks reference to fact, but when we're talking about a logical statement, if it has no truth value, it is not definite and clear. It is not definite or clear whether, "This statement is a lie." is true or false.

Miles wrote: Tue Oct 05, 2021 2:51 am
any statement being unable to have a definite truth value ruins the concept of a truth value.
Why?
Because a truth value must be binary, either true or false, to be optimally useful logically. If something is not false, we can say it's true, and vice-versa. If indeterminate is a possible truth value, that drastically decreases the use and value of the concept. If you're happy with a logical system that's less useful, by all means, have trinary or quaternary or even septuple truth values. Statements can be true, false, indeterminate, blerb (which means both true and false), twerb (both true and indeterminate), flerb (both false and indeterminate) or nerb (none of the above). There's nothing saying you can't have that system, it's just not as useful.
Miles wrote: Tue Oct 05, 2021 2:51 am
Statements that do not refer ultimately to facts can't be checked and don't have truth values, so they can't be statements, because a statement must be true or false.
Statements like, "Jesus was the son of god" I imagine.
Notice I keep saying statements can at least in theory be checked. Give me a 23 and me kit, a time machine, and God's dead body (fresh if possible), and I can help you out. If it rained on a tiny uninhabited island, then it rained. However, if it's really and truly completely impossible to ever check, then after all our checking we will believe it didn't rain and treat the statement "It rained on Saturday." as false, and the fact that our knowledge might be incomplete doesn't break logic. What breaks logic (here meaning, makes it drastically less useful) is if truth values don't have to be binary, either true, or false.
Miles wrote: Tue Oct 05, 2021 2:51 am
When someone says something, makes that utterance, or puts those words down, that is now a fact that can be checked, a thing that happened (or didn't), not just a statement.
Fact: "Noah took all the dinosaurs aboard the ark, but he and the other seven got hungry and ate them all."



.
What I mean is that, the fact that Miles said there were dinosaurs on the arc is now something that actually happened in reality. If I say you said it, that's true. I am making a distinction between referring to statements and referring to people having made statements.

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Re: Statments - What are They?

Post #4

Post by Miles »

Purple Knight wrote: Tue Oct 05, 2021 3:40 pm
Miles wrote: Tue Oct 05, 2021 2:51 am
Purple Knight wrote: Tue Oct 05, 2021 12:54 am Question for debate: What is a statement?
state·ment
/ˈstātmənt/
noun: statement; plural noun: statements
I'm sure you're aware that formal logic often as different definitions of terms than the dictionary. Note though that one of your definitions - the first one - mentions definite and clear, which I have to agree with. Now, a poem might express an emotion or something which is still definite and clear but lacks reference to fact, but when we're talking about a logical statement, if it has no truth value, it is not definite and clear. It is not definite or clear whether, "This statement is a lie." is true or false.
So you don't include remarks like "What a beautiful day," an exclamation, or "shut the door" an imperative, but rather things like "1 is a prime number." So your Title question might be better stated as "Logical Statements - What are They?" Gotcha. ;)

Miles wrote: Tue Oct 05, 2021 2:51 am
any statement being unable to have a definite truth value ruins the concept of a truth value.
Why?
Because a truth value must be binary, either true or false, to be optimally useful logically. If something is not false, we can say it's true, and vice-versa. If indeterminate is a possible truth value, that drastically decreases the use and value of the concept. If you're happy with a logical system that's less useful, by all means, have trinary or quaternary or even septuple truth values. Statements can be true, false, indeterminate, blerb (which means both true and false), twerb (both true and indeterminate), flerb (both false and indeterminate) or nerb (none of the above). There's nothing saying you can't have that system, it's just not as useful.
But you're talking about a concept here. An abstract idea; a general notion, which in this case is the attribute assigned to a proposition in respect to its truth or falsehood. So I fail to see how some mere statement such as "shut the door," which lacks any truth value, would ruin this concept.

Miles wrote: Tue Oct 05, 2021 2:51 am
Statements that do not refer ultimately to facts can't be checked and don't have truth values, so they can't be statements, because a statement must be true or false.
Statements like, "Jesus was the son of god" I imagine.
Notice I keep saying statements can at least in theory be checked. Give me a 23 and me kit, a time machine, and God's dead body (fresh if possible), and I can help you out.
???? Are you saying there are some theoretical principles by which you could determine truth value of "Jesus was the son of god"? If so, what are they?

If it rained on a tiny uninhabited island, then it rained. However, if it's really and truly completely impossible to ever check, then after all our checking we will believe it didn't rain and treat the statement "It rained on Saturday." as false,
Why? What does your belief have to do with establishing a truth value?

quote=Miles post_id=1052017 time=1633416661 user_id=4854]
When someone says something, makes that utterance, or puts those words down, that is now a fact that can be checked, a thing that happened (or didn't), not just a statement.
Fact: "Noah took all the dinosaurs aboard the ark, but he and the other seven got hungry and ate them all."
What I mean is that, the fact that Miles said there were dinosaurs on the arc is now something that actually happened in reality. If I say you said it, that's true. I am making a distinction between referring to statements and referring to people having made statements.
:approve: Gotcha.


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Re: Statments - What are They?

Post #5

Post by Purple Knight »

Miles wrote: Tue Oct 05, 2021 6:13 pmSo you don't include remarks like "What a beautiful day," an exclamation, or "shut the door" an imperative, but rather things like "1 is a prime number." So your Title question might be better stated as "Logical Statements - What are They?" Gotcha. ;)
I think you should look at the section where I made the topic. But this is a flaw with this particular definitional nitpick, and you can certainly come up with another.
Miles wrote: Tue Oct 05, 2021 6:13 pmBut you're talking about a concept here. An abstract idea; a general notion, which in this case is the attribute assigned to a proposition in respect to its truth or falsehood. So I fail to see how some mere statement such as "shut the door," which lacks any truth value, would ruin this concept.
Again, you're going pure definitional, including "shut the door," as a statement. I could accept your proposal that I specify logical statements, but then you'd just have some definitional problem with that.

It's still true that paradoxes and indeterminate truth values ruin a lot of the use of the concept of a truth value, and it's still true that we can solve that by simply not including statements that don't reference facts, that can't even in theory be checked against some reality, in the category of statements, and putting them into the same category of imperatives like, "shut the door." which don't make a claim as to a fact.
Miles wrote: Tue Oct 05, 2021 6:13 pmAre you saying there are some theoretical principles by which you could determine truth value of "Jesus was the son of god"? If so, what are they?
I'm saying that in theory, with the proper instruments and data, you could check this. Some of the instrumentation might not exist, or we might not have it, but that's qualitatively different than "this statement is a lie," which doesn't reference reality and could never be checked against reality.
Miles wrote: Tue Oct 05, 2021 6:13 pm
If it rained on a tiny uninhabited island, then it rained. However, if it's really and truly completely impossible to ever check, then after all our checking we will believe it didn't rain and treat the statement "It rained on Saturday." as false,
Why? What does your belief have to do with establishing a truth value?
Nothing. I didn't say it did. I said the fact that we will sometimes determine truth value wrongly doesn't break the concept of truth value or the concept that truth value must be, at least in theory, checkable against reality. The concept is still useful even if some of our determinations are wrong.

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Re: Statments - What are They?

Post #6

Post by Gracchus »

[Replying to Purple Knight in post #1]

"This statement is false." is correctly stated as "If this statement is true, then this statement is false."
Let us use "stroke" notation. Nand or Sheffer stroke notation. https://en.wikipedia.org/wiki/Sheffer_stroke0
A statement must always be in the form of p|q where p and q are statements. Any symbolic argument can be reduced to this single operator. Let p, q be statements. Then p|q indicates that both statements cannot be true. If either is true, then the other must be false, and if p is false and q is false then the negation of the false statement is true and so p|q is true. And p|p is a statement that if p is true then p is false and so "This statement is false" is saying if this statement is true then this statement is false, and by definition p|p is false. QED

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Re: Statments - What are They?

Post #7

Post by Purple Knight »

Gracchus wrote: Fri Oct 08, 2021 5:31 pm"This statement is false" is saying if this statement is true then this statement is false, and by definition p|p is false. QED
Regardless of whether I agree with this resolution, regardless of whether I think this "this statement is false" is equivalent to any sort of if-statement, a statement that points to itself, or to another statement, and not ultimately to some actual fact that can at least in theory be checked against reality, doesn't have any real meaning. It describes nothing.

"This statement is true." doesn't have the same irresolvability problems as "This statement is false." but it has the same problem in that it points nowhere, to nothing, to a construction of language and not to a fact.

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