## Is every statement true?

Half-formed posts, inchoate philosophies, and the germs of deep thought.

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### Re: Is every statement true?

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.
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### Re: Is every statement true?

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.

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?
"Someone may object that the successful revolt against the universal and homogeneous state could have no other effect than that the identical historical process which has led from the primitive horde to the final state will be repeated. But would such a repetition of the process--a new lease of life for man's humanity--not be preferable to the indefinite continuation of the inhuman end? Do we not enjoy every spring although we know the cycle of the seasons, although we know that winter will come again?" (Leo Strauss, "Restatement on Xenophon's Hiero".)

Sauwelios
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### Re: Is every statement 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.

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### Re: Is every statement true?

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.

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.
"Someone may object that the successful revolt against the universal and homogeneous state could have no other effect than that the identical historical process which has led from the primitive horde to the final state will be repeated. But would such a repetition of the process--a new lease of life for man's humanity--not be preferable to the indefinite continuation of the inhuman end? Do we not enjoy every spring although we know the cycle of the seasons, although we know that winter will come again?" (Leo Strauss, "Restatement on Xenophon's Hiero".)

Sauwelios
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### Re: Is every statement true?

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.

Faust
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### Re: Is every statement true?

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?
"Someone may object that the successful revolt against the universal and homogeneous state could have no other effect than that the identical historical process which has led from the primitive horde to the final state will be repeated. But would such a repetition of the process--a new lease of life for man's humanity--not be preferable to the indefinite continuation of the inhuman end? Do we not enjoy every spring although we know the cycle of the seasons, although we know that winter will come again?" (Leo Strauss, "Restatement on Xenophon's Hiero".)

Sauwelios
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### Re: Is every statement true?

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.

Faust
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### Re: Is every statement true?

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.

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?

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.

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?
"Someone may object that the successful revolt against the universal and homogeneous state could have no other effect than that the identical historical process which has led from the primitive horde to the final state will be repeated. But would such a repetition of the process--a new lease of life for man's humanity--not be preferable to the indefinite continuation of the inhuman end? Do we not enjoy every spring although we know the cycle of the seasons, although we know that winter will come again?" (Leo Strauss, "Restatement on Xenophon's Hiero".)

Sauwelios
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### Re: Is every statement true?

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.

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### Re: Is every statement true?

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?

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.

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.

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?

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.

Indeed, because anything follows from a contradiction. For instance, ihuoDUoniwni0.
"Someone may object that the successful revolt against the universal and homogeneous state could have no other effect than that the identical historical process which has led from the primitive horde to the final state will be repeated. But would such a repetition of the process--a new lease of life for man's humanity--not be preferable to the indefinite continuation of the inhuman end? Do we not enjoy every spring although we know the cycle of the seasons, although we know that winter will come again?" (Leo Strauss, "Restatement on Xenophon's Hiero".)

Sauwelios
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### Re: Is every statement true?

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.

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?

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.

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### Re: Is every statement true?

May we get back on track to the original argument?
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### Re: Is every statement true?

browser32 wrote: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.
"Someone may object that the successful revolt against the universal and homogeneous state could have no other effect than that the identical historical process which has led from the primitive horde to the final state will be repeated. But would such a repetition of the process--a new lease of life for man's humanity--not be preferable to the indefinite continuation of the inhuman end? Do we not enjoy every spring although we know the cycle of the seasons, although we know that winter will come again?" (Leo Strauss, "Restatement on Xenophon's Hiero".)

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### Re: Is every statement true?

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 https://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.
Paul E. Mokrzecki
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### Re: Is every statement true?

So, the statement...
Not all statements are true

must be true, given that it is a statement.
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### Re: Is every statement true?

That's correct; as a statement, "not all statements are true" is also true.
Paul E. Mokrzecki
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### Re: Is every statement true?

browser32 wrote:That's correct; as a statement, "not all statements are true" is also true.
So every syllogism is correct. Why bother demonstrating something?
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### Re: Is every statement true?

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.
Paul E. Mokrzecki
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### Re: Is every statement true?

It makes you wonder why would someone be committed to the obviously absurd idea that evwry statement is true (a.k.a. trivialism.)
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### Re: Is every statement 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.)

A statement is true until found to be untrue. It is only a proposition, and as propositions go, many a proposed idea has taken a long long time to be proven or disprove. They can be true in one sense, at one time, or false in a certain time. Descartes' Cogito waa true to the times it pertained to so was Newton absolutely true to his time. Einstein is mostly right up to this time.
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### Re: Is every statement true?

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.
It could be, by why is it being done, here, by you?
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### Re: Is every statement true?

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.

It's being done here because I apparently started this thread over 6 years ago and felt it was best to keep things organized by keeping related interests in trivialism in the same thread. The argument I recently provided in my post at viewtopic.php?p=2699033#p2699033 can be thought of as an improved version of my argument in the original post of this thread. With neat features and timestamps for posts and edits, this website is reliable enough to receive my thoughts and efforts.
Paul E. Mokrzecki
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### Re: Is every statement true?

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.
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.
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