Re: The philosophy of logic reformulates existing ideas on a new basis ---

On 11/8/2024 12:05 PM, Alan Mackenzie wrote:

olcott <polcott333@gmail.com> wrote:
 [ .... ]
 

That formal systems that only apply truth preserving
operations to expressions of their formal language
that have been stipulated to be true cannot possibly
be undecidable is proven to be over-your-head on the
basis that you have no actual reasoning as a rebuttal.

 So it's uncalled for insults now, is it?  The above paragraph is
incoherent.

Have you every heard of axioms and axiom schemas?
https://www.liarparadox.org/Haskell_Curry_45.pdf
These are very similar to Haskell Curry
"an elementary theorem is an elementary statement which is true."
AKA Olcott expressions of language that are stipulated to be true.
Have you every heard of the much more generic term for
inference rules called "truth preserving operations"?
None of what I say is all that difficult unless one's
primary purpose is to be disagreeable.

 Formal systems are not "undecidable".  Propositions in them
may or may not be.
 But in any formal system that is powerful enough to do anything with,
there are undecidable propositions.  That is a fact on a par with 2 + 2 =
4.  It is a fact that any non-specialist with a decent amount of humility
would accept from an expert.
 It is high time that you recognised that you are not an expert in this
field, your level of understanding is low, and that you could perhaps
learn things from others who know and understand more.
 

-- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

 

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer