On 11/8/24 9:05 AM, olcott wrote:
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.
Which just shows your ignorance.
If the statements of language are stipulated to be true in some formal logic system, then they ARE true in that formal logic system.
If the statements are incoherent, then the system becomes incoherent, but that doesn't affect the statements themselves in the sytsem.
Truth preserving operations applies to these coherent set of
axioms also derived expressions defined to be true.
Right, and that includes expressions that are defined to be true after an INFINITE sequence of steps
No other expressions of language of formal system L
are true in L.
So?
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.
Right, so if you want to claim a system is incorrect because of incoherence, you need to be able to demonstrate that contradiction.
>
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.
No, they are still infallible. Contradictory definitions just make the system contradictory (and thus mostly worthless).
You can't "get rid of" Russell's Paradox in a system that allows it to be formed. You don't ban Russell's Paradox just by saying it isn't allowed, you need to build a set of rules that make it impossible to constuct the Paradox.
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.
Which you can't show is part of the existing system, nor have you fully defined an alternate system, so you can't use what you want to, because there is no system they are defined in.
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.
No, you have the cart before the horse. You can't see if a system has eliminated undecidability or incompleteness until you know what the system might be.
You might investigate the sources of it in the standard system to think what you might change, but you can't actually see the results of the change until you build the system.
This is how most system are developed, with a cycling like that of trial and error. Most of which, rarely gets published, only when they find something that seems to actually be promising. Like the stages to ZFC, where ZF preceded it.
>
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.
Like every classical Formal Logic.
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
But it doesn't, not if the system allows sufficiently expressive operations, like mathematics.
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.
The probem is that you don't seem to understand the terms you are using.
The predicate "True" that Tarski talks about, can't "reject" a statement, except by saying it isn't true (since non-truth-bearers aren't true).
If the system can build as a grammatical statement in system L that
x is defined to be the expression ~True(L, x), then we find that the system can't define a proper value for True(L, x) and thus can't define the needed predicate "True".
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.
That you keep on putting forward false and illogical statements as semantic tautologies, you just show your utter stupidity.
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
So?
Tarski didn't use True(L, ~x) he used ~True(L, x), and there is a difference.
If x is a non-truth-bearer, then so is ~x, and True can return false for both.
But True(L, x) will always be a truth-bearer for all expressions x by its definition as a predicate, and just false if x isn't a truth-bearer.
That means that ~True(L, x) will also be a truth-bearer for all expressions x by its definition as a predicate, and the properties of the negation operator.
That means that if x IS the expression ~True(L, x) then we have a problem with the figuring out what value True(L, x) will have for that expression.
The key to Tarski's proof, that you just skip over, likely because you can't understand it, it the part where he shows that such an expression *IS* part of the language L, and thus an input that True(L, x) needs to handle.
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.
No, you are just not understanding Tarski.
You claim things he has proven as just "assumptions", showing your ignorance of what he talks about.
That you continue after having it pointed out, just show that you are nothing but a pathological liar.
>
-- 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
>
>
>
>
A different perspective on undecidability
Re: A different perspective on undecidability