🚀 go-pugleaf

On May 6, 10:40 am, Charlie-Boo <shymath...@gmail.com> wrote:
> On May 4, 10:47 am, Newberry <newberr...@gmail.com> wrote:
>
> > We will utilize the following three definitions.
>
> > Definition 1: A sentence is meaningful if and only if it is a picture
> > of a possible state of affairs.
>
> > Definition 2: A sentence is true if and only if it corresponds to an
> > actual state of affairs.
>
> > Definition 3: A sentence is false if its negation corresponds to an
> > actual state of affairs.
>
> The problem isn't mapping  SENTENCE => {true,false}.  The problem with
> the Liar is when you assume a given sentence is true or false, you can
> map that to a contradiction.  The above definitions can be used to
> decide if a simple sentence e.g. "Snow is white." is true or not.  But
> the Liar has nothing to do with that.  It has to do with formal
> implication producing falsehood.
>
> 1. Any solution to the Liar must be formal.
> 2. Any formalism can be used to generate variations of anything that
> it is used to formalize.
> 3. Thus any solution to the Liar must be able to generate variations
> of the Liar.
>
> And when you do this, you see what the real problem is.
>
> The Liar is not that hard - it really isn't.  It is simply 4
> properties of systems that are (a) desirable, (b) easy to have in a
> system by themselves, and (c) contradictory to have all 4 of them.
>
> Formalized (1), we have (2) variations of "This is not true." and (3)
> a theorem that applies to other systems - e.g. Turing Machines, Set
> Theory, Axiomatic Theorem-Proving.
>
> "This is not true." uses 4 words, and each word provides a capability
> of English.  These 4 capabilities are common in formal systems, and a
> simple (though not trivial) theorem shows they are not compatible.
> Applied to other systems, we get theorems about Turing Machines, sets,
> etc.
>
> BTW You are right that "This is not true." has no truth value.  That
> is the property that you have to give up in English: "Every sentence
> is true or false." does not hold.
>
> Here are some variations (I posted 1,000 generated ones once):
>
> 1. It is true.
> 2. It is not true.
> 3. It is false.
> 4. It is not false.
> 5. "It is true" is true of "This is false."
> 6. "It is not true of itself." is true of "It is not true of itself."
>
> # 6 is the direct application of the contradiction that exists in
> every system that has the 4 properties, in the case of English.  It
> reduces to "This is not true."
>
> C-B
>
>
>
> > To further characterize possible we can say that it means imaginable.
> > Ludwig Wittgenstein says something very similar. He alludes to
> > imaginability a few times: If I can imagine objects combined in states
> > of affairs, I cannot imagine them excluded from the possibility of
> > such combinations. [TLP 2.0121], We picture facts to ourselves. [TLP
> > 2.1] A picture is a model of reality. [TLP 2.12] Finally he says: A
> > picture represents a possible situation in a logical space [TLP 2.202]
> > But what does "possible" mean? What is thinkable is possible too. [TLP
> > 3.02] So we have: A picture represents a thinkable situation in a
> > logical space. What is thinkable? 'A state of affairs is thinkable':
> > what this means is that we can picture it to ourselves. [TLP 3.001] So
> > finally we have: A situation in a logical space is a state of affairs
> > we that can picture to ourselves.  ...
>
> >http://xnewberry.tripod.com/SentencesLackTruthValues.html- Hide quoted text -
>
> - Show quoted text -

"This sentence is not true" is not a picture of any possible state of
affairs.