Re: Replacement of Cardinality (infinite middle)

On 8/19/2024 8:08 PM, Ross Finlayson wrote:

On 08/19/2024 04:18 PM, Jim Burns wrote:

[...]

>
Then, about that
the class of ordinal is an ordinal

True because of what we mean by 'ordinal'
⎛ which leaves open the other question about
⎜ whether that class or finite ordinals or
⎝ inaccessible cardinal or ... _exist_

and needn't be given by axiom or relation to an axiom,
yet instead as a matter of comprehension over the class,

...if the class exists.
How we know that a class exists is by axiom.
It's an abstract object.
What other way could we know?
This need for some axiom to start off the existing
is harder to paper over in a formal language.
But, with either a formal or natural language,
it's inherent in exploring Plato's realm of Forms.
How else do we enter that realm?