Re: Replacement of Cardinality

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.
|  See Frege 1914 for a defense of the austere view that,
| in mathematics at least,
| only stipulative definitions should be countenanced.
| Frege, G., 1914, “Logic in Mathematics,”
| in _Gottlob Frege: Posthumous Writings_
| edited by H. Hermes, F. Kambartel, and F. Kaulbach,
| Chicago: University of Chicago Press (1979), pp. 203–250.
https://plato.stanford.edu/entries/definitions/
Stipulate.
x = 1/0  :⇔  0⋅x = 1
Lemma.
¬∃x ∈ R: x = 1/0