On 9/10/2024 4:34 AM, Mikko wrote:
> On 2024-09-09 17:38:04 +0000, olcott said:
>
>> On 9/7/2024 3:46 AM, Mikko wrote:
>>> On 2024-09-06 23:41:16 +0000, Richard Damon said:
>>>
>>>> On 9/6/24 8:24 AM, olcott wrote:
>>>>> On 9/6/2024 6:43 AM, Mikko wrote:
>>>>>> On 2024-09-03 12:49:11 +0000, olcott said:
>>>>>>
>>>>>>> On 9/3/2024 5:44 AM, Mikko wrote:
>>>>>>>> On 2024-09-02 12:24:38 +0000, olcott said:
>>>>>>>>
>>>>>>>>> On 9/2/2024 3:29 AM, Mikko wrote:
>>>>>>>>>> On 2024-09-01 12:56:16 +0000, olcott said:
>>>>>>>>>>
>>>>>>>>>>> On 8/31/2024 10:04 PM, olcott wrote:
>>>>>>>>>>>> *I just fixed the loophole of the Gettier cases*
>>>>>>>>>>>>
>>>>>>>>>>>> knowledge is a justified true belief such that the
>>>>>>>>>>>> justification is sufficient reason to accept the
>>>>>>>>>>>> truth of the belief.
>>>>>>>>>>>>
>>>>>>>>>>>> https://en.wikipedia.org/wiki/Gettier_problem
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> With a Justified true belief, in the Gettier cases
>>>>>>>>>>> the observer does not know enough to know its true
>>>>>>>>>>> yet it remains stipulated to be true.
>>>>>>>>>>>
>>>>>>>>>>> My original correction to this was a JTB such that the
>>>>>>>>>>> justification necessitates the truth of the belief.
>>>>>>>>>>>
>>>>>>>>>>> With a [Sufficiently Justified belief], it is stipulated
>>>>>>>>>>> that the observer does have a sufficient reason to accept
>>>>>>>>>>> the truth of the belief.
>>>>>>>>>>
>>>>>>>>>> What could be a sufficient reason? Every justification of every
>>>>>>>>>> belief involves other belifs that could be false.
>>>>>>>>>
>>>>>>>>> For the justification to be sufficient the consequence of
>>>>>>>>> the belief must be semantically entailed by its justification.
>>>>>>>>
>>>>>>>> If the belief is about something real then its justification
>>>>>>>> involves claims about something real. Nothing real is certain.
>>>>>>>>
>>>>>>>
>>>>>>> I don't think that is correct.
>>>>>>> My left hand exists right now even if it is
>>>>>>> a mere figment of my own imagination and five
>>>>>>> minutes ago never existed.
>>>>>>
>>>>>> As I don't know and can't (at least now) verify whether your left
>>>>>> hand exists or ever existed I can't regard that as a counter-
>>>>>> example.
>>>>>>
>>>>>>>> If the belief is not about something real then it is not clear
>>>>>>>> whether it is correct to call it "belief".
>>>>>>>
>>>>>>> *An axiomatic chain of inference based on this*
>>>>>>> By the theory of simple types I mean the doctrine which says
>>>>>>> that the objects of thought (or, in another interpretation,
>>>>>>> the symbolic expressions) are divided into types, namely:
>>>>>>> individuals, properties of individuals, relations between
>>>>>>> individuals, properties of such relations, etc.
>>>>>>>
>>>>>>> ...sentences of the form: " a has the property φ ", " b bears
>>>>>>> the relation R to c ", etc. are meaningless, if a, b, c, R, φ
>>>>>>> are not of types fitting together.
>>>>>>> https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
>>>>>>
>>>>>> The concepts of knowledge and truth are applicable to the knowledge
>>>>>> whether that is what certain peple meant when using those words.
>>>>>> Whether or to what extent that theory can be said to be true is
>>>>>> another problem.
>>>>>>
>>>>>
>>>>> The fundamental architectural overview of all Prolog implementations
>>>>> is the same True(x) means X is derived by applying Rules (AKA truth
>>>>> preserving operations) to Facts.
>>>>
>>>> But Prolog can't even handle full first order logic, only basic
>>>> propositions.
>>>
>>> The logic behind Prolog is restricted enough that incompleteness cannot
>>> be differentiated from consistency. It seems that Olcott wants a logic
>>> with that impossibility.
>>
>> It is not that incompleteness cannot be differentiated
>> from inconsistency it is that the inconsistency of
>> self-contradiction has been mistaken for undecidability
>> instead of invalid input.
>
> Of course incompleteness can be differentiated from incosistency.
Self-contradictory expressions are incorrect deemed to be
undecidable expressions instead of invalid expressions.
Is this "actual piece of shit" "a rainbow" or "a car engine"?
I can't decide, therefore the formal system is incomplete.
(The correct answer is neither, yet the correct answer is not allowed).
> An incosistent theory cannot be incomplete, at least if any ordinary
> logic is used. If you want to use a paraconsistent logic then you
> must be very careful with terms of ordinary logic.
>
> The basic theory behind Prolog is Horn Clauses, where incompleteness
> cannot be differentiated from consistency. Standard Prolog has features
> that break the logic if used but the terms "incompleteness" and
> "consistency" are only defined for logic, not programming.
>
Tarski's Liar Paradox from page 248
It would then be possible to reconstruct the antinomy of the liar
in the metalanguage, by forming in the language itself a sentence
x such that the sentence of the metalanguage which is correlated
with x asserts that x is not a true sentence.
https://liarparadox.org/Tarski_247_248.pdf
Formalized as:
x ∉ True if and only if p
where the symbol 'p' represents the whole sentence x
https://liarparadox.org/Tarski_247_248.pdf
"this sentence is not true" is not a truth bearer
that must be rejected as invalid input and not the
basis for the undecidability theorem.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer
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