Re: Replacement of Cardinality

Am 24.08.2024 um 06:30 schrieb Jim Burns:

On 8/23/2024 8:05 PM, Moebius wrote:

Am 24.08.2024 um 00:04 schrieb Jim Burns:

 

x = 1/0  :⇔  0⋅x = 1
¬∃x ∈ R: x = 1/0

>
Nonsense.

 | 1.3 Stipulative definitions
|
| A stipulative definition imparts a meaning to the defined term,
| and involves no commitment that
| the assigned meaning agrees with prior uses (if any) of the term.
| Stipulative definitions are epistemologically special.
| They yield judgments with epistemological characteristics that
| are puzzling elsewhere.
| If one stipulatively defines a “raimex” as, say,
| a rational, imaginative, experiencing being
| then the judgment “raimexes are rational” is assured of
| being necessary, certain, and a priori.

Concerning *predicates*, NOT "names" (referring to non-existing objects), man.
Hint:
          raimex(x) :<-> rational(x) & imaginative(x) & experiencing(x) & a_being(x)
          "x is a raimex iff ..."
After stating this definition we may claim:
          Ax(raimex(x) -> rational(x))
          “All raimexes are rational.”

https://plato.stanford.edu/entries/definitions/

Seems you really don't get it. (*sigh*)
Without proof of
          1. Ex(raimex(x))
and
2. AxAy(raimex(x) & raimex(y) -> x = y)
we may not use the "definition"
          x = the_raimex :<-> rational(x) & imaginative(x) & experiencing(x) & a_being(x)
In other words, we are not allowed to talk about _the_ raimex (not having a proof that there is exactly one such such being, i.e. exactly one x such that x is a raimex).
Hence, no this is NOT a proper definition:

x = 1/0  :⇔  0⋅x = 1

...just nonsense.

Lemma.

More nonsense. Are you you one of the multiple personalities of Mückenheim by any chance?