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

MoeBlee wrote:
On Aug 15, 1:47 pm, Nam Nguyen <namducngu...@xxxxxxx> wrote:
Nam Nguyen wrote:

Now that has settled, we can take a note that the definitions mentioned
right above ignore words like "tautology/validity" and "contradiction"!
Ignore the words do they. And my (good) intention is to move definitions
of tautology and contradiction to syntactical-provability base.

'contradiction' is already a syntactical term.

Good: then it'd exact zero-effort to make 'contradiction' syntactical.

'tautology', in the
exact sense such as in Enderton, is semantical.

I didn't say Enderton et al stated otherwise.


If your personal project is to get all the definitions moved over to
the syntactical, then by all means enjoy yourself. Then when you're
finished, and I've agreed to abide by your definitions, I'll make up a
new set of definitions, with new words like "latlology' and define
them with regard to semantics.

People do have projects *all* the time. Hilbert had one, Godel had one,
who knows you might have been in advanced stage of "latlology" (project)
already, and, one can never tell, 1000 years from now one might come up
with a project in which mathematical truths might be validated only
through Zen's Satori.

But I don't think that's the point. The point is we should *discuss* and
compare them for strengths and weakness, in a way that wold help us to better
reasoning, moving forward. Wouldn't you think so?


MoeBlee


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

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