Evolving Religion in America

Boon, Coel
Re Godel, in the method of proof of lack of consistency of real number theory (as a sufficiently high class of axiomatic system), he proved there existed an infinite number of statements that were clearly true, contradictory, and yet not produced by the production system (axiom plus rules). More subtly, they are ambigouous, and thus equally true.

This outcome is a condition of sufficient complexity of the system. So much for the mathmatical "truth" issue.

Coel
What is this objective reality of which I speak? I'm speaking from the perspective of philosophical "realism".

There is of course a limitation truth in this definition, related to things physical, their relations, and logical implications. This leaves out great classes of "truths" that are important to humans and have been raised in this discussion. Things like justice, beauty, goodness, etc. ("Your protege don't care about art....")

I don't have a definition of truth for these classes. I guess I'm post modern. Or, white trash.

About the degree of fidelity, of course you are right there. Descriptive theories will vary in fidelity by some degree, however small (unless there is no observational test). Newtonian mechanics vs General Relativity, for example. The latter is currently viewed as "more true". Both are broadly viewed as "justifiably true".

Less clearly differentliable as examples are the various "interpretations" of quantum pheonmena: Compenhagen school, many worlds view, etc. Its hard to say which are "more true". Each appear to have equal fidelity to observations.

There is the mathmatical example, and the physical example.
 
Godel proved that for any system of enough complexity,you cannot complete the system (have every true statement provable from within the system) without introducing inconsistency. What you're describing does not make sense to me. how is the 'truth' of these contradictory statements established if not within the system? by some metasystem? but then this metasystem would be inconsistent and therefore meaningless.
 
Boon
Like I said, he proved there exists an infinite number of theorems that appear clearly true but can't be produced by the system. A subset of these are inconsistent, i.e. contradictory, but that subset is also infinite. That's that.

Example, a mathmatical version of: "this statment is false". and "the prior statement is false".

We have the same understanding, just a different interpretation. You might read Godel, Esher, Bach for more detail, or "Incompleteness", a biography of Godel and an examination of his theory. This is from where I formed this view.
 
we are bombarded with so much propoganda from both sides, it is difficult to know who to believe. i find it silly when people try to say the earth is 6000 years old or that a small group of particles suddenly appeared, blew up and created the universe.
 
Coel
As I said, I speak from the perspective of "realism", that there exists a reality of which we can gain some understanding (to contrast with anti-realism). That reality is the truth standard of which I speak when I speak of fidelity.

I will refer you to the Godel references I offered, and there are more, for the deeper understanding you seek on this front. I am assuming you understand, if not agree, with my basic point. If I'm wrong, apologies, but my explanations are feito.

The physics point, to restate what seems to me to be obvious, is that there are competing quantum level theories that have equal fidelity to all data yet are fundamentally different. This situation confounds the "degree of fidelity" distinction offered in the Newton vs Relativity comparison.

Bottom line, its tough to say what's true, even for a realist. The anti realist says there is no truth.

Back to the math issue, that is independent of reality. Its a different class of truth. Then there is the matter of beauty and justice, and God, and all that. Other classes altogether. Again, I have no approach for truth in these cases, and conjecture that there is no unarbitrary guide. Not that this is a bad thing or an insurmountable problem of humanity. Workarounds are clearly available, well used, and not widely lamented.

Finally, I'm not pursuing rhetorical or argumentative superiority. I'm sharing my thoughts. If you have thoughts on the matter, share them, please. Without question marks, if possible.
 
thanks nb. i've read GEB awhile back. it was good, but i remember thinking not deserving of the hype imo.

i think what coel is getting at is what has troubled logicians for a long time, and the root is the liars paradox as you alluded to (or russell's paradox in mathematics), and reflexivity, or self-reference. Tarski had some theorem, of which i claim no real knowledge, that showed the notion of truth cannot be defined within the system (again for sufficiently complex system.) Anyhow, i think it is hardly a settled issue in some logicians minds.

where is wittgenstein?
 
Boon
Wittgenstein never supported Godel's theorem, so, he lost credibility with the mathmatician community.

Yes, the issue within the proof was related to self reference.
 
wittgenstein is regarded as either a charlatan or a genius (russell thought him a genius at first and a quack later.) philosopher.
yes, mathematicians dismiss him(not all) because of some of the stuff he wrote on the foundations (i can't remember exactly). i invoked the name because he struggled with the same questions about the limitations of language tgo express truth, but in a different way from most

anyway, i've gone way off the topic so i'll leave nolw
 
Coel
Understood. I am also looking for improved understanding, nothing else (despite examples otherwise).

From this perspective, the questioning (only) approach comes across, perhaps inaccurately, as an unwillingness to contribute one's share. That looks like and probably is an arbitrary value judgement on my part.
 
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