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### Is every statement true?

Posted: Fri Jun 03, 2011 1:28 am
Consider the following argument:

If a statement is true, then it is a member of the set of true statements.

If a statement is false, then it implies a contradiction (as we find in a proof by contradiction). Since anything follows from a contradiction, it follows that the statement is true. Thus the statement is a member of the set of true statements.

Since a statement is true or false, all statements therefore belong in the set of true statements. All statements are true, with the set of false statements being a subset of the set of true statements. A statement thus is either true and true only, or both true and false.

Does this mean that all statements are true?

### Re: Is every statement true?

Posted: Fri Jun 03, 2011 3:12 am
No, it doesn't. A false statement doesn't imply a contradiction. You'd need two statements to have a contradiction.

### Re: Is every statement true?

Posted: Fri Jun 03, 2011 3:26 am
In a proof by contradiction, we assume a statement, that is actually false although we don't know that yet at first, and derive a contradiction. The fact that a false statement allows us to derive a contradiction shows that a false statement implies a contradiction. Therefore since anything follows from a contradiction, the statement assumed is true and the statement assumed is false. Thus, it's true, by conjunction elimination on the previous statement.

### Re: Is every statement true?

Posted: Fri Jun 03, 2011 3:41 am
Not really, a false statement implies or states something inaccurate. It may cause a contradiction with other knowledge such as one's own observations but is not in itself a contradiction.

But as far as I'm concerned, nothing is true.

### Re: Is every statement true?

Posted: Fri Jun 03, 2011 4:13 am
browser32 wrote:If a statement is false, then it implies a contradiction (as we find in a proof by contradiction). Since anything follows from a contradiction, it follows that the statement is true. Thus the statement is a member of the set of true statements.

What in the world? Whattttt? What? What are you talking about?
Anything follows from a contradiction? What does that mean? And how does it imply that a contradictory statement is true?

Nigga's straight-up bonkers.

### Re: Is every statement true?

Posted: Fri Jun 03, 2011 6:15 am

browser - I'm trying to make this simple for you - in a proof, there is more than one statement. Think about this. A false statement, by itself, does not imply a contradiction. You can look this stuff up pretty easily.

### Re: Is every statement true?

Posted: Fri Jun 03, 2011 2:16 pm

Firstly, Faust, I asked what that means, and secondly I asked how it implies a contradictory statement is true.
You answered neither, just repeated the statement.

### Re: Is every statement true?

Posted: Fri Jun 03, 2011 2:41 pm
FJ - I am referring to "Nigga's straight-up bonkers."

That's not acceptable.

"Firstly, Faust, I asked what that means..."

Simply put, if A is both true and false, at the same time and in the same place, then truth values, as used in classical logic, have no meaning, so anything goes.

This does not, as I stated, imply that a contradictory statement is true, because there is no such thing as a (simple) contradictory statement to begin with. If I say "I am entirely black and entirely white, I have made two statements. The bare fact of the falsity of a simple statement is not relevant here.

browser is confusing a reductio argument with a mere statement.

Again, I'm trying to keep this simple.

### Re: Is every statement true?

Posted: Fri Jun 03, 2011 3:44 pm
Ah, so if you assume a contradictory statement is true then anything follows. That's what is meant. I needed that to be clarified to understand where he went wrong in his reasoning.

If a statement is false, then it implies a contradiction (as we find in a proof by contradiction). Since anything follows from a contradiction,

can be traslated to:
"Since anything follows [if you assume a contradiction is true]..." <- we don't assume that, so everything he said after that is based on an assumption that we're not making.

### Re: Is every statement true?

Posted: Fri Jun 03, 2011 4:03 pm
Ah, so if you assume a contradictory statement is true then anything follows.

No. Anything follows from a contradiction. I have explained the difference between your formulation and mine, above. It may seem like a minor discrepancy, but it is this very discrepancy that has led browser astray.

"Since anything follows [if you assume a contradiction is true]..." <- we don't assume that, so everything he said after that is based on an assumption that we're not making.

Not exactly. A true contradiction - a contradiction that is true - isn't part of classical logic. In classical logic, a contradiction occurs when two propositions are logically "incompatible." There is no truth value, per se, for a contradiction itself. Remember that contradictions are just relations between claims, so we can, of course, find contradictions.

### Re: Is every statement true?

Posted: Fri Jun 03, 2011 4:10 pm
You're being really vague and confusing my pants off bro. Be clear.

"Simply put, if A is both true and false, at the same time and in the same place, then truth values, as used in classical logic, have no meaning, so anything goes."
This is what you mean when you say anything follows from a contradiction, right?

It starts with "if A is both true and false," it starts with an "if". That's key. That "if," though...for his argument to work, we have to assume that that "if" is valid, that A is both true and false. If A is NOT both true and false simultaneously, then everything that you said after doesn't stand. The "anything goes" doesn't stand. You see? That's what I'm saying.

His whole argument rests on contradiction. It's circular. We have to assume contradictory statements are true to get to his conclusion that...lol...contradictory statements are true.

### Re: Is every statement true?

Posted: Fri Jun 03, 2011 4:20 pm
I am actually not being vague.

""Simply put, if A is both true and false, at the same time and in the same place, then truth values, as used in classical logic, have no meaning, so anything goes."
This is what you mean when you say anything follows from a contradiction, right?"

Yes.

"It starts with "if A is both true and false," it starts with an "if". That's key. That "if," though...for his argument to work, we have to assume that that "if" is valid, that A is both true and false. If A is NOT both true and false simultaneously, then everything that you said after doesn't stand. The "anything goes" doesn't stand. You see? That's what I'm saying."

Yeah.....the problem is that neither of you know the vocabulary of logic, which is what is causing the confusion. I don't know what it means for an "if" to be "valid". I think you're trying to say that the antecedent is true in "If A is both true and false, then every statement is true", but I'm not sure. What actually happens is this - if A can be both true and false, then truth values mean nothing - every statement is true, and every statement is false, as you wish.

What I think browser may also be doing is trying to make a claim about (Googling...) dialetheism, which is an entire 'nother can o' worms.

### Re: Is every statement true?

Posted: Fri Jun 03, 2011 4:20 pm
Let me try another approach.
I'm going to replace "Anything follows from a contradiction" with what you said that actually means, since that's such a vague phrase. GOD I HATE THAT PHRASE

browser32 wrote:Consider the following argument:

If a statement is true, then it is a member of the set of true statements.

If a statement is false, then it implies a contradiction (as we find in a proof by contradiction). If A is both true and false, at the same time and in the same place, then truth values, as used in classical logic, have no meaning, so anything goes, and it follows that the statement is true.

You see what I did there? I translated his statement into something that I can actually make sense of. That's important: when you cloud your ideas in vague phrases it becomes hard for anyone else to pick out what's wrong with it. Now that I translated it, via Faust's help, to something less vague, it's quite simple to see what's wrong with it. "If A is both true and false..." <- but it's not...so that's it. That's where it ends. The proof fails right there.

Anything goes if A is both true and false, sure, but why do we assume that A is both true and false? We don't.

You see what I'm saying? We have to assume contradictions can be true to get to his conclusion that contradictions are true. Circular. That's what I'm getting at.

### Re: Is every statement true?

Posted: Fri Jun 03, 2011 4:35 pm
I think it's something more along the lines of drawing a logical conclusion, or proposition, from a contradiction. If something is asserted as both true and not true, it can become a 'wild card', so to speak, in any logical conclusion drawn from it.

In other words something asserted as both true and false says nothing because anything can be said about it, regardless if the statement is true, false, or anywhere in between.

And Faust is right. There must conflicting statements [ex. something is both true and false] in order for a contradiction to take place.

A statement thus is either true and true only, or both true and false.

I think this may be a source of confusion as well. The statement which you consider both "true and false" is just false. The only truth to it is that it's false. But that is a redundant statement about the contradiction itself.

To say a claim is false because it is contradictory is the same as saying it is true that the claim is false. However, the former addresses the claim, whereas the latter addresses the contradiction.

### Re: Is every statement true?

Posted: Fri Jun 03, 2011 4:36 pm
I'm going to replace "Anything follows from a contradiction" with what you said that actually means, since that's such a vague phrase. GOD I HATE THAT PHRASE

Ahh, I see, FJ. It's an emotional thing. Okay.

"If a statement is true, then it is a member of the set of true statements."

I'm fine with that.

"If a statement is false, then it implies a contradiction (as we find in a proof by contradiction)."

This is incorrect. A false statement does not imply anything. It does not imply a contradiction. There is no logical contradiction is this: "I am handsome." Here's why. To say that there is a contradiction confuses the technical and everyday (or extended) usages of the word "contradiction". Logic is about statements only. While the statement "I am handsome" contradicts observation, that makes it only untrue, and not a logical contradiction, but a "contradiction" between the claim and the empirical observation. It's not a logical contradiction. A logical contradiction is a condition that is logically impossible. It could be true that i am handsome - it just doesn't happen to be true.

If A is both true and false, at the same time and in the same place, then truth values, as used in classical logic, have no meaning, so anything goes, and it follows that the statement is true.

Correct, but a statement never is "in the same place" as an observation. Statements, once subject to verification, can turn out to be false, but a simple statement is never contradictory - for it would need another statement to contradict. Now, paradoxes, which a bit different, can be apparently self-contradictory, but "I am handsome" is not paradoxical. I hope we can leave paradoxes aside, as this would only cloud the waters more.

Anything goes if A is both true and false, sure, but why do we assume that A is both true and false? We don't.

Again, I don't think browser made a bad assumption. i think he is confounding two sense of the word "contradiction", as I stated above.

"

### Re: Is every statement true?

Posted: Fri Jun 03, 2011 4:43 pm
yeah, i think you're muddying this convo up on purpose.

### Re: Is every statement true?

Posted: Fri Jun 03, 2011 4:47 pm
I assure you, I am not. Logic neither begins nor ends with truth. Logic is concerned only with validity. We can, in a reductio argument, demonstrate a contradiction, which is, of course, the purpose of a reductio argument. A reductio argument is not concerned with truth at all, but with finding that contradiction. Within this context, the phrase "true contradiction" has no meaning. "Contradiction" has meaning.

### Re: Is every statement true?

Posted: Fri Jun 03, 2011 4:52 pm
The context is given by the OP. You're saying the context is out of context...
I don't think it's useful to divorce logic completely from truth like that, because logic doesn't just exist in a vacuum. It's used to determine what's true and what isn't. Truth and logic are inextricably linked, and if they're not then logic is pointless and self-referential (I don't think it is, but you seem to, which makes it extra-weird that you insist on keeping this convo about logic in itself and not about truth, as that would make the whole conversation likewise pointless).

### Re: Is every statement true?

Posted: Fri Jun 03, 2011 4:54 pm
Mind you, I understand that a valid argument doesn't necessarily provide a true conclusion, I'm not saying that logic is synonymous with truth, but I am saying that it's really kinda pointless to talk about logic if logic can't be used to determine what's true.

### Re: Is every statement true?

Posted: Fri Jun 03, 2011 6:44 pm
The context is given by the OP. You're saying the context is out of context...
I don't think it's useful to divorce logic completely from truth like that, because logic doesn't just exist in a vacuum. It's used to determine what's true and what isn't.

What can i tell you? I can't lie to Jesus, Flannel or otherwise. Logic does not determine what is true. It just doesn't. You can look this up. It's a tool, devised for a purpose, and finding out what is true is just not that purpose. This is why I nitpicked about the difference between truth and validity. The purpose of logic is to establish the validity of an argument. here's a little snippet from Wiki:

"Logic (from the Greek λογική logikē)[1] is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science. Logic examines general forms which arguments may take, which forms are valid, and which are fallacies."

Logic is not about truth, but about reasoning. I don't make the news - I only report it.

Truth and logic are inextricably linked, and if they're not then logic is pointless and self-referential (I don't think it is, but you seem to, which makes it extra-weird that you insist on keeping this convo about logic in itself and not about truth, as that would make the whole conversation likewise pointless).

Logic is self-referential, in that it is based upon axioms that are taken to be self-evident. I'm sorry to be the one to tell you. But I have studied logic for quite a while, and this is pretty much the straight dope.

Mind you, I understand that a valid argument doesn't necessarily provide a true conclusion, I'm not saying that logic is synonymous with truth, but I am saying that it's really kinda pointless to talk about logic if logic can't be used to determine what's true.

It's used to preserve truth, if there is truth to be preserved. It doesn't determine truth. So there is a relationship between truth and logic - it's just not the one you claim it to be.

I know this may all seem like nitpicking, but I have seen, over many years now, small mistakes, in nomenclature or in understanding, multiply to the point of nonsense, when people who do not know anything about logic get talking about it. It's vital to get the basics down first, because logic is not a body of knowledge, it's a method. I completely understand if you think I am obfuscating, or emphasising trivial elements of logic - many people here have. But you have to be precise about logic, or you get on a very slippery slope, very quickly.

### Re: Is every statement true?

Posted: Sat Jun 04, 2011 4:00 am
Faust wrote:...correct reasoning.

correct in relation to what?
reality

### Re: Is every statement true?

Posted: Sat Jun 04, 2011 2:16 pm
Actually, no. Reasoning can be done correctly even with premises that bear no relation to reality.

### Re: Is every statement true?

Posted: Sat Jun 04, 2011 4:12 pm
Flannel Jesus wrote:
Faust wrote:...correct reasoning.

correct in relation to what?
reality

The "logic" (and also reasoning) Faust is talking about is not the same thing as many people may imagine with the word.
It's more strict, restricted compared to what general public think of "logic" (and reasoning).
And he is taking the time and well explaining.

viewtopic.php?f=1&t=171862&start=0

and quote (from other site) like this might be helpful to understand.

formal logic

Definition

Classical or traditional system of determining the validity or invalidity of a conclusion (inference) deduced from two or more statements (premises). Based on the theory of syllogism of the Greek philosopher Aristotle (384-322 BC) systematized in his book 'Organon,' its focus is not on what is stated (the content) but on the structure (form) of the argument and the validity of the inference drawn from the premises of the argument-if the premises are true then the inference (also called logical consequence) must also be true. The basic principles of formal logic are (1) Principle of identity: if a statement is true then it is true. (2) Principle of excluded middle: a statement is either true or false. (3) Principle of contradiction: no statement can be both true and false at the same time. Also called Aristotelian logic. See also fuzzy logic and symbolic logic.

Personally, I think it's a fault of Aristotle if the focus of "formal logic" is narrow.
viewtopic.php?f=1&t=171919

### Re: Is every statement true?

Posted: Sat Jun 04, 2011 4:13 pm
i understand that, you misunderstood what i meant.
the reasoning itself is correct because it works in reality. i'm not talking about specific premises or specific conclusions.

the reason logic is even something people consider is because it can be used to take true premises and reach true conclusions in reality. if logic couldn't do that, nobody would give a shit about logic because it wouldn't mean anything or matter at all in reality.

### Re: Is every statement true?

Posted: Sat Jun 04, 2011 4:35 pm
i understand that, you misunderstood what i meant.
the reasoning itself is correct because it works in reality. i'm not talking about specific premises or specific conclusions.

the reason logic is even something people consider is because it can be used to take true premises and reach true conclusions in reality. if logic couldn't do that, nobody would give a shit about logic because it wouldn't mean anything or matter at all in reality.

This is correct, in the main, but not entirely. Many people have cared about logic to "prove" the existence of God, for instance. It's not entirely clear if such proofs have anything to do with reality.

Also, it's not entirely clear if the OP does, either.