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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct
Date: Sat, 16 Nov 2024 11:11:55 +0200
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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. 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.

-- 
Mikko