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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: The philosophy of logic reformulates existing ideas on a new
 basis ---
Date: Fri, 8 Nov 2024 08:05:39 -0600
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On 11/6/2024 6:45 PM, Richard Damon wrote:
> On 11/6/24 12:10 PM, olcott wrote:
>> On 11/6/2024 10:45 AM, Alan Mackenzie wrote:
>>> Andy Walker <anw@cuboid.co.uk> wrote:
>>>> On 04/11/2024 14:05, Mikko wrote:
>>>>>>>>> [...] The statement itself does not change
>>>>>>>>> when someone states it so there is no clear advantage in
>>>>>>>>> saying that the statement was not a lie until someone stated
>>>>>>>>> it.
>>>>>>>>      Disagree.  There is a clear advantage in distinguishing those
>>>>>>>> who make [honest] mistakes from those who wilfully mislead.
>>>>>>> That is not a disagreement.
>>>>>>      I disagree. [:-)]
>>>>> Then show how two statements about distinct topics can disagree.
>>>
>>>>         You've had the free, introductory five-minute argument;  the
>>>> half-hour argument has to be paid for. [:-)]
>>>
>>>>         [Perhaps more helpfully, "distinct" is your invention.  One 
>>>> same
>>>> statement can be either true or false, a mistake or a lie, depending on
>>>> the context (time. place and motivation) within which it is uttered.
>>>> Plenty of examples both in everyday life and in science, inc maths.  
>>>> Eg,
>>>> "It's raining!", "The angles of a triangle sum to 180 degrees.", "The
>>>> Sun goes round the Earth.".  Each of those is true in some contexts, 
>>>> false
>>>> and a mistake in others, false and a lie in yet others.  English has 
>>>> clear
>>>> distinctions between these, which it is useful to maintain;  it is not
>>>> useful to describe them as "lies" in the absence of any context, eg 
>>>> when
>>>> the statement has not yet been uttered.]
>>>
>>> There is another sense in which something could be a lie.  If, for
>>> example, I empatically asserted some view about the minutiae of medical
>>> surgery, in opposition to the standard view accepted by practicing
>>> surgeons, no matter how sincere I might be in that belief, I would be
>>> lying.  Lying by ignorance.
>>>
>>
>> That is a lie unless you qualify your statement with X is a
>> lie(unintentional false statement). It is more truthful to
>> say that statement X is rejected as untrue by a consensus of
>> medical opinion.
> 
> But, in Formal System, like what you talk about, there ARE DEFINITION 
> that are true by definition, and can not be ignored.
> 

My basis expressions of language that are stipulated to be true
can only correct when they are coherent.

Truth preserving operations applies to these coherent set of
axioms also derived expressions defined to be true.

No other expressions of language of formal system L
are true in L.

> To make a statement that is contrary to those definitions, is to knowing 
> say a falsehood, which makes it a lie, at least after the error has been 
> pointed out, and that
> 

Contradictory axioms cannot be false because both sides of
the contradiction carry equal weight. Instead of false axioms
the formal system is incoherent thus incorrect.

>>
>> This allows for the possibility that the consensus is not
>> infallible. No one here allows for the possibility that the
>> current received view is not infallible. Textbooks on the
>> theory of computation are NOT the INFALLIBLE word of God.
> 
> But in Formal System, the definition ARE "infallibe".
> 

Not when they contradict other definitions. We could say that
Russell's Paradox is undecidable yet only within incoherent
naive set theory. When we get rid of the incoherence RP ceases
to exist.

> Yes, you might disagree with the definition, and form a competing 
> system, but you need to go to the effort to actually create that 
> definition, and make sure you are clear that you are working in an 
> alternate system.
> 

That my simple system of expressions stipulated to be true
combined with the application of truth preserving operations
seems simple does not mean it is simplistic.

Before we proceed to define the set of truth preserving
operations we must first see that the value of such a
system does eliminate undecidability and incompleteness.
Unless we do this first we boggle the mind with too many
details to see this.

>>
>>> Peter Olcott is likewise ignorant about mathematical logic.  So in that
>>> sense, the false things he continually asserts _are_ lies.
>>>
>>
>> *It is not at all that I am ignorant of mathematical logic*
>> It is that I am not a mindless robot that is programmed by
>> textbook opinions.
> 
> But, then make claims about things in a system, which REQUIRE the 
> following of the definitions of the system, that ignore the definitions 
> of the system.
> 
>>
>> Just like ZFC corrected the error of naive set theory
>> alternative views on mathematical logic do resolve their
>> Russell's Paradox like issues.
> 
> But, ZFC was a brand new system created, not a "fixing" of naive set 
> theory.
> 

A system that applies only truth preserving operations to a set
of expressions that have been stipulated to be true <is> by itself
a sufficiently complete system to be evaluated against my claims
about it.

Once it is understood that such a system does get rid of incompleteness
and undecidability thenn (then and only then) can we add details without
overwhelming the mind with too much detail

> We talk about what is true in ZFC, not what is true in the "fixed" naive 
> set theory.
> 
> Yes, the "default" lable of what system we are talking about when we 
> just use the term "Set Theory" changed, but, that was done by the 
> general consensus of the users of Set Theory (and not everyone actually 
> uses ZFC, but know enough to make it clear form context what system they 
> are in.
> 
> Snce you have yet to publish a formal definition of some alternate 
> system, just some loose ideas about what might be different, you can't 
> even make references to it, let alone try to assume that it is now the 
> "default" computaiton system.
> 
>>
>> (Incomplete(L) ≡  ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
>>
>> When True(L,x) is only a sequence of truth preserving operations
>> applied to x in L and False(L, x) is only a sequence of truth
>> preserving operations applied to ~x in L then Incomplete(L)
>> becomes Not_Truth_Bearer(L,x).
> 
> But, since Tarski showed that there are input to True(L, x) that can not 
> have a truth value, that means that 

Expressions that are not truth bearers wold be rejected as erroneous.
We really should not have to go over these same details 500 times.

That you keep "disbelieving" semantic tautologies is disingenuous at
best. Because people have continued to play trollish head games with
my work we may see the rise of the fourth Reich. This might have been
avoided if my system of dividing truth from lies was adopted earlier.

> True can not be a "predicate", since 
> Predicates are always truth bearers. True is defined such that:
> 
> If x is true in L, True(L, x) will be True.
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