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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: The philosophy of logic reformulates existing ideas on a new
 basis ---
Date: Fri, 8 Nov 2024 12:01:12 -0500
Organization: i2pn2 (i2pn.org)
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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.
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