Is every statement true?

correct in relation to what?
reality

Actually, no. Reasoning can be done correctly even with premises that bear no relation to 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.

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

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

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

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.

people use logic to arrive at all sorts of conflicting assertions, none of which need be true. it’s divorced from truth. logic is a meatgrinder - you get out what you put in, processed in a certain way. if you apply logic to bullshit, you end up with processed bullshit.

the proposal that there is no truth has meaning only in certain contexts, but it does have at least those meanings. invalid logic may be entirely beside the point if what someone is saying is useful in some way.

Logic rests on three axioms, which can themselves be formulated as statements:

  1. A equals A.
  2. A does not equal not-A.
  3. Not-A does not equal A.

Now how can logic determine the truth of any statements if it rests on statements which it assumes to be true?

Firstly, this is incorrect, Saully, on several grounds. Most saliently, no axiom of logic can be said to derive from another axiom. It’s easy to see that your 2. and 3. derive from your 1. Beyond that, as I have said, logic does not determine the truth of statements.

No, it wasn’t meant as an argument, just as a list. And I agree with you: my point is that logic cannot determine the truth of statements.

I realise it wasn’t an argument. My point is that no axiom can be called an axiom if it is derived from another axiom. Axioms must be independent of each other, or they’re not axioms.

In fact, there is no one set of axioms for logic - different systems use different axioms. What you have actually been trying at is an axiom of mathematics.

But where did I suggest that axioms be derived from other axioms?

And is there a single set of axioms for formal logic? And is formal logic what you meant when you used the word “logic” in this thread prior to my appearance in it?

You didn’t suggest it. Your second and third axioms are restatements of each other. They are the same statement. There are some other problems with “A does not equal not-A”, because an axiom of logic is a formula. It’s a long story, but “inequality” cannot, to my knowledge, be used as an operation in an axiom of logic. So I can only interpret your use of this operation as a restatement of your axiom A.

As I just said, there is no single set. In fact, the set of axioms is virtually unlimited quantitatively, but is limited qualitatively. And yes, I am using logic to mean formal logic, because that appears to be the context of the OP.

But Faust, surely you know which axioms I mean, seeing as you were the one who first told me about them. So how would you formulate those?

Okay, but aren’t there some axioms that all sets share, since there can be no logic without axioms, and those axioms are limited qualitatively?

In any case, how about the following contradiction?

Premise 1: “Logic presupposes certain axioms, i.e., assumes the truth of certain statements.”
Premise 2: “Logic can determine the truth of a statement.”

Doesn’t the fact formulated in premise 1 logically refute the hypothesis formulated in premise 2?

I’m not sure what you’re referring to. Gotta link?

We’re not talking about sets, but systems of logic. They are limited by the fact that they must all be independent of each other, for instance.

Yeah, it assumes the truth. I am agreeing with you, and have from the start. i have said this several times, now - logic does not determine the truth of any claim. It was not designed to, and it just doesn’t.

Truly, logical systems accept the truth of certain statements. That A = A is taken as self-evident. There have been those who have disputed the truth of that. Somehow. It is, strictly speaking, illiterate to do so.

I could perhaps look it up, but it should suffice to say that they are the laws of identity, of the excluded middle, and of non-contradiction.

Well, you introduced the word “set”. Anyway, are there more limitations to them? Or could we create a system of logic from any positive number (greater than 1?) of independent axioms?

Indeed, because anything follows from a contradiction. For instance, ihuoDUoniwni0.

Ahh. The three classical laws of thought. I didn’t remember talking to you about that. I thought you were maybe talking about Peano.

A = A (usually the triple bar “equivalence” sign is used)

Contradiction: ~(P . ~P) where the dot is the sign for conjunction and meaning that P is not both true and false.

Excluded middle: P v ~P where the v is the sign for “or” and read “P or not P”

These were Aristotle’s starting points, but to say that they are the basis for all logic is true only historically. Now i understand the context.

There are more limitations, but again, they are not quantitative. When we say that there are many systems of logic, we are saying that there are many sets of axioms. There are systems that have the very same parameters as other systems, but just use different sets of axioms.

May we get back on track to the original argument?

There’s little more to say about this at this point. It has been refuted.

The following is an argument for every statement being true that is similar to, but different from the opening argument.

Let s be a statement. By the law of excluded middle, s is true or not true.

Assume s is true. Then s is true. Discharge the assumption.

Assume s is not true. Then a true statement, the negation of s, contradicts s. So, a contradiction exists. By the principle of explosion, s is true. Discharge the assumption.

By disjunction elimination, s is true. This concludes the argument.

The content of the opening post of this thread I began is not original. According to timestamps, I had posted the same content earlier on another website in a thread I began. The other thread has the same name as the name of this thread, “Is every statement true?” That thread is located at able2know.org/topic/172914-1. I do not plan on posting in the other thread, for now at least. I believe this website is more trustworthy since it indicates whether and when posts have been edited.

So, the statement…

must be true, given that it is a statement.