Re: Looking for Undecidable Propositions in Systems without a certainamountofarthimetic.

MoeBlee wrote:
On Aug 15, 3:08 pm, Nam Nguyen <namducngu...@xxxxxxx> wrote:
MoeBlee wrote:
I'll make up a new set of definitions, with new words like "latlology'
and define them with regard to semantics."
What say you to that?

Since you've not presented "latlology" in enough details, since face-prima
"latlology" truths seem isomorphic to canonical truths, since I've started
talking about my "project" first, why don't we compare the strengths and
weaknesses of my syntactical project (which isn't that different from the
syntacticalism part of Hilbert's program), and move on from there?

This is wearying. I don't see any point at all to your project. But I
at least offered the discussion point that if I agreed to all your new
definitions then I'd make new ones to replace the words you took over.
And I've asked you how that comfits with your project.

If you're
sincere about a conversation, then please address my question.

For what's it worth, in the context of public technical discussions
like this, my attitude is that sincerity is very much given; we don't
have to even mention it. That's why didn't even think of it and instead
have spent much time in the conversation to technically (with details)
do the mapping from canonical truths to my provability counterparts:
from tautological truths, from truth-based undecidability etc...
If I missed mapping anything else, by all means let me know; I'm confident
I could complete the mapping eventually.

But from your sincere part of the conversation here, what I've I got?
Not much! I've got:

"I'll make up a new set of definitions"
"with new words like 'latlology'"
"and define them with regard to semantics."

and then a question:

"What say you to that?"

How on Earth could I even evaluate your *new definition* when all relevant
information I got from you is "define them with regard to semantics"?

And now you question my sincerity in the conversation?

Your conversation has becomes weird indeed! (To say it mildly!).


Specifically, in the related thread "Godel cant tell us what makes a
mathematical statement true", you said:

> Of course, Those formulations of Godel's results that refer to 'truth'
> would of course have a different meaning if you changed the definition
> of 'true'.

Why don't we re-evaluate and compare Godel's results through the framework
he used (viz-a-viz the canonical arithmetic truth system) and my syntactical
truth system?

Because it's not interesting.

Apparently, your explanation is below.

It's not interesting to ponder what
happens to the statement, "All dogs are mammals" if we change the
definition of 'dog' to 'electric can opener'.

That's an erroneous analogy. Because "electric", "can", "opener" have
no relevance here to "dogs", and "mammal"! Otoh, My definition and the
canonical definition of truths, w.r.t. an underlying T, both have the
syntactical consistency of T as a key relevant part!

A correct analogy would be something like my defining "dogs" as:

"All dogs are mammals of a specific wolf-DNA-sequence that has existed
since 150,000 years ago."

With that new definition of mine, you don't have to ponder "what happens"
to *old knowledge* "All dogs are mammals": it's still the same knowledge.
But you'd better your knowledge about dog and know its ancestor is more
recent that than of a whale, which happens to be also in the wolf-family!

If I want to address the
question of whether all electric can openers are mammals, I can just
as well do that directly rather than first redefine the word 'dog'.

First, you don't have an evidence that's the kind of re-definition I've
been doing. Finally, perhaps you'd want to review both your knowledge
of biological evolution and your ways of making logical arguments.
From the conversation so far, they're either deficient or incoherent.

--
"To discover the proper approach to mathematical logic,
we must therefore examine the methods of the mathematician."
(Shoenfield, "Mathematical Logic")

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