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

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Sujet : Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct
De : polcott333 (at) *nospam* gmail.com (olcott)
Groupes : comp.theory
Date : 16. Nov 2024, 16:24:05
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vhadel$2jm4$3@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
User-Agent : Mozilla Thunderbird
On 11/16/2024 8:32 AM, Richard Damon wrote:
On 11/16/24 9:21 AM, olcott wrote:
On 11/16/2024 3:11 AM, Mikko wrote:
On 2024-11-15 23:49:17 +0000, olcott said:
>
On 11/15/2024 3:03 AM, Mikko wrote:
On 2024-11-14 23:40:19 +0000, olcott said:
>
When you start with truth and only apply truth preserving
operations then you necessarily end up with truth.
>
And if you don't you prove nothing.
>
>
That is the basic model of all correct proofs.
https://en.wikipedia.org/wiki/Syllogism#Basic_structure
>
No, it is not. There are truth preserving transformations that do
not follow that pattern.
>
There are zero truth preserving operations that are not truth
preserving operations. The principle of explosion is not a
truth preserving operation. The full semantics of natural
can be extended to only apply truth preserving operations
to its own statement of basic fact.
 But Syllogism is not the only form of "Truth Preserving Operations".
 
It is the foundation of necessarily correct reasoning.
True(L,x) ≡ Haskell_Curry_Elementary_Theorems(L) □ x
x is a necessary consequence of the expressions of the
language of L that have been stipulated to be true.
False(L,x) ≡ Haskell_Curry_Elementary_Theorems(L) □ ~x
~x is a necessary consequence of the expressions of the
language of L that have been stipulated to be true.
The above provides the basis for LLM AI systems to
distinguish facts from fictions.
That the provability operator has been replaced
with the necessity operator seems to require semantic
relevance. This prevents logic from diverging from
correct reasoning in many different ways such as
the principle of explosion.

IF that is all you accept, then be prepared for a very limited logic system.
 
>
For example, the reduction rule: if A,
B, and C are formulas, the recution rule permits that from
A ∨ B and ¬A ∨ C can be inferred B ∨ C.
>
>
That is the way the contradiction is supposed to work
A ∧ ¬A cancel each other out leaving B ∨ C.
A ∧ ¬A ∴ Trump is the Christ is proven (is nuts)
>
 Just shows you are the one that is NUTS.
 Your problem is it seems you only understand the most elementary of logic, but presume everyone one else is just using that most elementary of logic.
 Yes, With the most restricted set of rules, you can't get to incompleteness, but that is because you can't create the system with the power needed for the proof.
 The problem is that having the fullness of the logic of Natual Numbers is enough to cross the line, so your "Complete" Logic system can't have that, but you just are too stupid to undetstand that limit, because you don't know how any of your tools actually work.
When True(L,x) and False(L,x) are defined as above then
Truth_Bearer(L,x) ≡ (True(L,x) ∨ False(L,x))
eliminating the notion of Incomplete(L) previously defined by
Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

Date Sujet#  Auteur
10 Nov 24 * Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct54Alan Mackenzie
10 Nov 24 `* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct53olcott
10 Nov 24  `* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct52Alan Mackenzie
10 Nov 24   `* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct51olcott
10 Nov 24    `* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct50Alan Mackenzie
10 Nov 24     +* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct8olcott
10 Nov 24     i`* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct7Alan Mackenzie
11 Nov 24     i +* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct2olcott
12 Nov 24     i i`- Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct1Alan Mackenzie
11 Nov 24     i `* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct4olcott
11 Nov 24     i  `* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct3Richard Damon
11 Nov 24     i   `* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct2olcott
11 Nov 24     i    `- Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct1Richard Damon
13 Nov 24     `* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct41olcott
13 Nov 24      +- Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct1Richard Damon
13 Nov 24      +* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct3joes
13 Nov 24      i`* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct2olcott
14 Nov 24      i `- Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct1Richard Damon
13 Nov 24      +* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct23Mikko
14 Nov 24      i`* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct22olcott
14 Nov 24      i +- Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct1Richard Damon
14 Nov 24      i `* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct20Mikko
15 Nov 24      i  `* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct19olcott
15 Nov 24      i   +* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct9Richard Damon
15 Nov 24      i   i`* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct8olcott
15 Nov 24      i   i `* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct7Richard Damon
15 Nov 24      i   i  `* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct6olcott
15 Nov 24      i   i   +- Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct1Richard Damon
15 Nov 24      i   i   +- Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct1joes
15 Nov 24      i   i   `* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct3Richard Damon
16 Nov 24      i   i    `* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct2olcott
16 Nov 24      i   i     `- Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct1Richard Damon
15 Nov 24      i   `* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct9Mikko
16 Nov 24      i    `* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct8olcott
16 Nov 24      i     +- Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct1Richard Damon
16 Nov 24      i     `* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct6Mikko
16 Nov 24      i      `* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct5olcott
16 Nov 24      i       +* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct3Richard Damon
16 Nov 24      i       i`* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct2olcott
16 Nov 24      i       i `- Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct1Richard Damon
17 Nov 24      i       `- Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct1Mikko
13 Nov 24      `* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct13Alan Mackenzie
13 Nov 24       +* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct11olcott
13 Nov 24       i+* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct7joes
13 Nov 24       ii`* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct6olcott
14 Nov 24       ii `* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct5Richard Damon
14 Nov 24       ii  `* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct4Mikko
15 Nov 24       ii   `* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct3olcott
15 Nov 24       ii    +- Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct1Richard Damon
15 Nov 24       ii    `- Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct1Mikko
13 Nov 24       i+* Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct2Alan Mackenzie
13 Nov 24       ii`- Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct1olcott
14 Nov 24       i`- Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct1Richard Damon
14 Nov 24       `- Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct1Mikko

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