Sujet : Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct
De : polcott333 (at) *nospam* gmail.com (olcott)
Groupes : comp.theoryDate : 16. Nov 2024, 15:21:44
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vha9po$1md4$2@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 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.
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)
-- Copyright 2024 Olcott "Talent hits a target no one else can hit; Geniushits a target no one else can see." Arthur Schopenhauer