On Saturday, January 21, 2023 at 10:29:32 AM UTC-6, Jeffrey Rubard wrote:
> On Friday, January 20, 2023 at 5:24:00 PM UTC-8, Richard Damon wrote:
> > On 1/20/23 7:29 PM, olcott wrote:
> > > On 1/20/2023 4:54 PM, Richard Damon wrote:
> > >> On 1/20/23 5:16 PM, olcott wrote:
> > >>> On 1/20/2023 4:09 PM, Richard Damon wrote:
> > >>>> On 1/20/23 5:02 PM, olcott wrote:
> > >>>>> On 1/20/2023 2:46 PM, Richard Damon wrote:
> > >>>>>> On 1/20/23 2:31 PM, olcott wrote:
> > >>>>>>> On 1/19/2023 8:34 PM, Richard Damon wrote:
> > >>>>>>>> On 1/19/23 2:12 PM, olcott wrote:
> > >>>>>>>>> On 1/17/2023 5:44 PM, Richard Damon wrote:
> > >>>>>>>>>> On 1/17/23 11:39 AM, olcott wrote:
> > >>>>>>>>>>> On 1/16/2023 7:51 PM, Richard Damon wrote:
> > >>>>>>>>>>>> No, because I am showing that G is TRUE, not PROVABLE. Truth
> > >>>>>>>>>>>> can use infinte sets oc connections, proofs can't. Only YOU
> > >>>>>>>>>>>> have perposed that we think about infinite proofs.
> > >>>>>>>>>>>>
> > >>>>>>>>>>>
> > >>>>>>>>>>> Formal systems cannot ever use infinite connections from their
> > >>>>>>>>>>> expressions of language to their truth maker axioms thus
> > >>>>>>>>>>> eliminating
> > >>>>>>>>>>> these from consideration as any measure of true "in the system".
> > >>>>>>>>>>>
> > >>>>>>>>>>>
> > >>>>>>>>>>
> > >>>>>>>>>>
> > >>>>>>>>>> Source? or is this just another of your made up "Facts"
> > >>>>>>>>>>
> > >>>>>>>>>
> > >>>>>>>>> You can't even remember that you said this?
> > >>>>>>>>
> > >>>>>>>> No, I said they can't have infinite PROOFS, not infinite
> > >>>>>>>> connections to Truth.
> > >>>>>>>>>
> > >>>>>>>>>> WHERE in the definition of a "Formal System" does it say that
> > >>>>>>>>>> the connecti0on must be finite.
> > >>>>>>>>>
> > >>>>>>>>> You said that formal system cannot have infinite proofs.
> > >>>>>>>>> Did you change your mind?
> > >>>>>>>>
> > >>>>>>>> Right ***PROOF*** not ***TRUTH***
> > >>>>>>>>
> > >>>>>>>> Truth can be based on an infinite chain of connections, proofs
> > >>>>>>>> can not.
> > >>>>>>>
> > >>>>>>> Truth *in a formal system* cannot be based on infinite
> > >>>>>>> connections because formal systems are not allowed to have
> > >>>>>>> infinite connections.
> > >>>>>>
> > >>>>>> Says Who ***FOR TRUTH***
> > >>>>>>
> > >>>>>> You reference does not provide that data, so I guess you are just
> > >>>>>> making it up, and thus showing you to be a LIAR.
> > >>>>>>
> > >>>>>>>
> > >>>>>>> Haskell Curry establishes that truth in a theory (AKA formal
> > >>>>>>> system) is anchored in the elementary theorems (AKA axioms) of
> > >>>>>>> this formal system.
> > >>>>>>
> > >>>>>> Right, ANCHORED TO, not limited to. Statments other than the
> > >>>>>> elementary theorems are True, and they are true if they have a
> > >>>>>> connection (not limited to finite) to these Truths.
> > >>>>>>
> > >>>>>> Where does he say True statements must have a FINITE connection to
> > >>>>>> the elementary theorems.
> > >>>>>>
> > >>>>>>>
> > >>>>>>> A theory (over (f) is defined as a conceptual class of these
> > >>>>>>> elementary
> > >>>>>>> statements. Let::t be such a theory. Then the elementary statements
> > >>>>>>> which belong to ::t we shall call the elementary theorems of::t;
> > >>>>>>> we also
> > >>>>>>> say that these elementary statements are true for::t. Thus, given
> > >>>>>>> ::t,
> > >>>>>>> an elementary theorem is an elementary statement which is true. A
> > >>>>>>> theory
> > >>>>>>> is thus a way of picking out from the statements of (f a certain
> > >>>>>>> subclass of true statements.
> > >>>>>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
> > >>>>>>>
> > >>>>>>> Perhaps you believe that you are enormously much brighter than
> > >>>>>>> Haskell Curry ?
> > >>>>>>>
> > >>>>>>
> > >>>>>> You don't understand what he is saying,
> > >>>>>>
> > >>>>>> He is saying these statements are True in F, as a given.
> > >>>>>
> > >>>>> Wrongo !!!
> > >>>>>
> > >>>>> The terminology which has just been used implies that the
> > >>>>> elementary statements are not such that their truth and
> > >>>>> falsity are known to us without reference to::t.
> > >>>>>
> > >>>>>
> > >>>>
> > >>>> Right, they aren't just true in the Statement class, but are only
> > >>>> considerdd true because we are in the Theory F.
> > >>>>
> > >>>
> > >>> F is not the theory T is the theory.
> > >>>
> > >>>
> > >>
> > >>
> > >> Red Herring.
> > >>
> > >> F is the Theory in Godels descussion.
> > >
> > > It is not a red herring at all. Curry proves that the mathematical
> > > notion of incompleteness itself is incoherent in that Curry sustains
> > > Wittgenstein's notion of true in a formal system.
> > >
> > > That G is unprovable in F merely means that G is untrue in F a triviality.
> > >
> > Please point out WHERE in the page you have cited that he does this.
> >
> > Remeber, the CLASS of statemeents he talks about as "Elementary
> > Statments" that he talks about is NOT a "exhaustive" list of statements
> > that can be formed, but a base set to start from.
> >
> > This is clear from the line you have highlighted pointing out that these
> > statements of are called elementary statements to distinguish them from
> > other statements which we may form from them.
> >
> > Then the "Elementary Theorems" are a SUBSET of these, that are defined
> > to be True in the Theory. Thus, these also are not a complete listing of
> > all true statements in the Theory, but only the set a base truths that
> > we are working from (in addition to the contensive statements that are
> > true indepentent of the Theory).
> >
> > NOTHING on that page limits "True" statements to those things that are
> > provable or only having a FINITE connection to those Elemetary Theories..
> >
> >
> > All this shows is that you don't understand what you are reading, or are
> > just lying.
> "They're just lying?"

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