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

On 2024-11-16 14:21:44 +0000, olcott said:

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.

That is just an attempt of a straw man deception. Not a good attempt
as it is so obvious.

The principle of explosion is not a truth preserving operation.

Of course not. A principle is not an operation.

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)

We believe that reduction preserves truth because nobody has ever
presented an example where both A ∨ B and ¬A ∨ C are true and B ∨ C
is false.
As another example, we believe that tautologies of propositional logic
are true because nobody has ever presented an example of false tautology.
--
Mikko