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On 11/16/2024 02:22 AM, Jim Burns wrote:Let's recall an example geometrically of what'sOn 11/15/2024 9:52 PM, Ross Finlayson wrote:>On 11/15/2024 02:37 PM, Jim Burns wrote:>On 11/15/2024 4:32 PM, Ross Finlayson wrote:>>Ah, yet according to Mirimanoff,>
there do not exist standard models of integers,
If it is true that
our domain of discourse is a model of ST+PQ
then it is true that
our domain of discourse holds a standard integer.model.
What is Mirimanoff's argument that
it doesn't exist?
Mirimanoff's? Russell's Paradox.
ST+PQ does not suffer from claiming
that the set of all non.self.membered sets
is self.membered or claiming it isn't.
>
While I am at it,
ZFC does not suffer from claiming
that the set of all non.self.membered sets
is self.membered or claiming it isn't,
and
ordinal.theory=Well.Order
does not suffer from claiming
that the set of all non.self.membered sets
is self.membered or claiming it isn't.
>
Is it possible that you (RF)
have misunderstood Mirimanoff?
>That>
"If it is true that our domain of discourse
is a model of ST+PQ then it is true that our
domain of discourse holds a standard integer.model"
is a pretty long axiom - why not just say
"infinity", that's the usual approach.
I don't say "infinity" is an axiom
primarily because
"infinity" is not an axiom of ST+PQ
ST+PQ:
⎛ set {} exists
⎜ set x∪{y} exists
⎜ set.extensionality
⎜ plurality ⦃z:P(z)⦄ exists
⎝ plurality.extensionality
>
"Infinity exists" ==
"the minimal inductive plurality exists"
is a theorem of those axioms.
>
I said, in such a long.winded manner, that
"infinity exists" is theorem of ST+PQ
because,
although I know that claim is well.justified,
it sounded as though this person Mirimanoff
has shown that I am mistaken about that.
I wanted to put my justification out there
for his argument to attack.
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