Faust wrote: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.
Faust wrote: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.
Faust wrote: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?
Faust wrote:But where did I suggest that axioms be derived from other axioms?
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.
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?
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?
Faust wrote: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?
I'm not sure what you're referring to. Gotta link?
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?
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.
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?
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.
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?
browser32 wrote:May we get back on track to the original argument?
Not all statements are true
So every syllogism is correct. Why bother demonstrating something?browser32 wrote:That's correct; as a statement, "not all statements are true" is also true.
Magnus Anderson wrote:It makes you wonder why would someone be committed to the obviously absurd idea that evwry statement is true (a.k.a. trivialism.)
It could be, by why is it being done, here, by you?browser32 wrote:Karpel Tunnel:
It could be done for enlightenment purposes or for fun. Since every statement is true, there are infinitely many reasons. It could be done for each real number.
I postulate that no homo sapian can have all of his or her dreams come true or have his or her desires fulfilled if all of his or her skepticism is justified.browser32 wrote:Karpel Tunnel:
I want all my dreams to come true. I want all my desires to be fulfilled. Trivialism provides a solution to all of my problems. It fully and sufficiently justifies all skepticism I have of anything.
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