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

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