Is every statement true?

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.

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.

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.

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yeah, i think you’re muddying this convo up on purpose.

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.

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).

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.

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.

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.

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.

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.