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

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.
If x is false in L (and thus ~x is true) then True(L, x) will be false
and if Truth_Bearer(L, x) is false, then True(L, x) will be False.
 

x = "what time is it?"
True(English,x) == false
True(English,~x) == false
∴ x is not a truth-bearer in English

Note, True(L, x) is not the same as Truth(L, x) which returns the truth value of x, but is a full predicate that just rejects (returns false) for any statement that is not actually true.
 Tarski shows that that such a predicate can not exist in a Formal Logic system that meets certain minimal requirements.
 

>
This is not any lack of understanding of mathematical logic.
It is my refusing to be a mindless robot and accept mathematical
logic as it is currently defined as inherently infallible.

 No, it *IS* your refusal to understand what formal logic actually is, and thus your repeated LYING about what is true.
 

That I am correcting Tarski's and you construe Tarski
as infallibe is your mistake not mine.

>

-- Andy Walker, Nottingham.
    Andy's music pages: www.cuboid.me.uk/andy/Music
    Composer of the day: www.cuboid.me.uk/andy/Music/Composers/Peerson

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