What does paradox reveal about the nature of truth?

@fresco,

Actually, Fresco, I haven't played golf in almost three weeks. It is killing me...and add to that the fact that Nancy has been laid off and is around the house interrupting me while I am writing...things are rather edgy at moments.

But, you know me...always relatively happy and content.

Thanks for asking. Sorry some of my recent comments seem biting. I truly do not mean them that way.

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@fresco,

By the way...this is probably THE most understandable post I've ever read of yours.

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@fresco,

fresco wrote:

Does your "inconsistent mathematics" paper deal with Paul Cohen's "proofs" that there both IS and IS NOT an infinite set lying between between Cantor's first two infinities? I seem to remember he received the Field's Medal for this, and that Godel was one of the referees.

It is primarily a survey on the topic, here is the link:
http://www.iep.utm.edu/math-inc/

Cantor's paradox is mentioned, but Paul Cohen's proofs are not mentioned.

Interestingly, Graham Priest's model of inconsistent arithmetic offers a collapsed version of arithmetic, which is free of that paradox.

What I enjoyed most in the article was the reflection back on calculus.
Specifically how the development of it required a treatment of the "infinitesimal" as both both zero and not zero and knowing or intuiting when to use it as which.

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@MattDavis,

You have to first define what is false. "This sentence is false" is incomplete.

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@Frank Apisa,

Frank Apisa wrote:

You are not stupid, Matt.

Oh stop it Frank!... You're making me blush.

Sorry about your wife's job and the no golf.
No wonder you are such a crotchity old man Wink

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@cicerone imposter,

cicerone imposter wrote:

You have to first define what is false. "This sentence is false" is incomplete.

OK.
So for the purposes of this example,
"Truth" as it applies to a proposition (or sentence) means that the content of the proposition (sentence) is an accurate reflection of the state it purports to reflect.
"False" as it applies to a proposition (or sentence) means that the content of the proposition (sentence) is NOT an accurate reflection of the state it purports to reflect.

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@MattDavis,

No, it doesn't, because "truth" itself is subjective.

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@cicerone imposter,

cicerone imposter wrote:

No, it doesn't, because "truth" itself is subjective.

If you are saying that all "truth" is subjective, no matter how strictly it is defined and no matter how carefully it is contextualized to mean something only within a specific system,
then I think we are going to to have to either "agree to disagree" or not "agree to disagree".
I would be agreeable to the former.
But I am certainly in agreement that we truly disagree.

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@MattDavis,

I never stated it applied to "all" truths.

That's not the issue; it only applies to issues that can be translated by individuals that has no scientific evidence/proof.

Provide some examples of what you are talking about that can be determined as a paradox?

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@cicerone imposter,

cicerone imposter wrote:

Provide some examples of what you are talking about that can be determined as a paradox?

I have already provided Gödel's incompleteness theorems as demonstrating that propositions analogous to the Liar's paradox exist in number theory. It has been more thoroughly explained previously at least twice by me in previous posts on this thread.
Were the previous explanations lacking?
Do you want me to try again?
Do you want me to provide you with a specific Gödel numbered proposition that is paradoxical within number theory?

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@cicerone imposter,

Actually Russell's paradox is much easier to express mathematically and "translate" into English.

http://1.bp.blogspot.com/-6Xsr1RWgUdA/UEYRjObakqI/AAAAAAAAAPw/1zCBz6vumJA/s1600/Russell%27sparadox.png

"English" meaning:
Let R be the set of all sets that are not members of themselves.
it then follows that [R is a member of itself] and [R is not a member of itself].

Conceptually:
If you take the set of all sets that are not members of themselves [R],
then [R] cannot be in [R] since [R] cannot be a "member of itself",
however,
if [R] is not within [R] then it qualifies to be in [R] since it is a set that is "not a member of itself".

1 Reply

@MattDavis,

That's gobligook! We decide what is "truth" by what is being described. If it's scientific truth, most will conclude that it's true most of the time. With other claims, it depends on one's perception and interpretation of what is being described. In other word, truth is in the eye of the beholder.

Math models of logic doesn't explain these differences.

Try explaining to a religious person that god doesn't exist.

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@MattDavis,

Quote:

Quote:
Re: Frank Apisa (Post 5249000)
Frank Apisa wrote:
You are not stupid, Matt.

Oh stop it Frank!... You're making me blush.

Sorry about your wife's job and the no golf.
No wonder you are such a crotchity old man

Me??? Crotchity???

Maybe a bit...but only a bit.

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@cicerone imposter,

cicerone imposter wrote:

If it's scientific truth, most will conclude that it's true most of the time.

Ok.
I'll play.
What makes something scientifically "true".

cicerone imposter wrote:

Try explaining to a religious person that god doesn't exist.

Ok.
Make a forum for it and I'll give it a shot.
Especially if you are able to provide me with a strong definition of "scientific truth".

1 Reply

@MattDavis,

You,

Quote:

Ok.
I'll play.
What makes something scientifically "true".

It's true until somebody can refute its findings, and past repeated experiments have shown it to be true. Science continues to seek truth. The ability of science to continue on the path to truth makes it more reliable than other beliefs.

You,

Quote:

Ok.
Make a forum for it and I'll give it a shot.

There are already plenty of forums/threads on a2k about religion and gods.

1 Reply

@cicerone imposter,

cicerone imposter wrote:

It's true until somebody can refute its findings, and past repeated experiments have shown it to be true. Science continues to seek truth. The ability of science to continue on the path to truth makes it more reliable than other beliefs.

This is incomplete. You must establish what is meant by "refute its findings".
Refuted how?
You must also establish what is meant by "experiments have shown it to be true".
Established how?

cicerone imposter wrote:

Science continues to seek truth.

Ok. So does logic. So does Buddhism. So does every other method of attempting to establish truth. Stating the goal of something doesn't establish how good it is at getting there.

cicerone imposter wrote:

The ability of science to continue on the path to truth makes it more reliable than other beliefs.

You haven't established yet that science IS on the path to truth. In fact you haven't even established what you mean by "truth".

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@MattDavis,

You're the one using the word "truth," so it's up to you to define it. I've already stated that "truth" is subjective to the eye of the beholder. Prove my statement wrong, if you can.

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@cicerone imposter,

Prove it how?
You mean assign a truth value to your assertion?
What methods of proof do you hold to be valid?
I thought you were claiming that "scientific truth" had validity, so I invited you to tell me what "scientific truth" is, so that I may make my "proof" in a form that you will accept.

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@MattDavis,

I already explained what I meant by "scientific proof." They are theories that have consistently produced the same results or have been corrected by new information. It continues to pursue truth, and is reliable to that extent.

I rely on its findings to be the truth until such time it's proven wrong or is modified.

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@cicerone imposter,

cicerone imposter wrote:

I already explained what I meant by "scientific proof."

No you actually haven't.

cicerone imposter wrote:

They are theories that have consistently produced the same results or have been corrected by new information.

Doesn't any theory always produce the same result?
Or is what you mean that 'a theory's predictions consistently matches some other result' ?
Are you describing a theory matching the results that agree with your perceptions?
What reason do you have to trust those perceptions?

cicerone imposter wrote:

I rely on its findings to be the truth until such time it's proven wrong or is modified.

So what in your scientific view qualifies as "proving wrong"?

Finding a predicted result that does not correspond with your perceptions?
Finding a result that does not correspond with anyone's perceptions?
Finding a result that does not correspond with most people's perceptions?
Finding a result that does not correspond to everyone's perceptions?

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What does paradox reveal about the nature of truth?

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