Re: Replacement of Cardinality

Am 04.08.2024 um 19:59 schrieb Jim Burns:

On 8/4/2024 11:44 AM, WM wrote:

Le 03/08/2024 à 19:42, joes a écrit :

 

[...]

>
The reversed quantification is nonsense

 ...because from ∀x∃u to ∃u∀x is unreliable.
  From ∃u∀x to ∀x∃u  is reliable.
 From ∃u∃x to ∃x∃u  is reliable.
 From ∀u∀x to ∀x∀u  is reliable.
However,
from ∀x∃u to ∃u∀x is unreliable.
 In some cases,
from ∀x∃u to ∃u∀x is not.only.unreliable,
it is incorrect.

Example (referring to FOPL= only):
     ∀x∃u x = u     (true)
     ∃u∀x x = u     (false)
for any universe of discourse with more than one "entity" (object).