Hi,
Mostowski Collapse has left the building, his successor
is Mild Shock. But you might be interested in:
What if Singularities DO NOT Exist?
https://www.youtube.com/watch?v=HRir6-9tsJsBye
P.S.: Not to be confused with this singularity, but
maybe nevertheless the same creative motivation?
AI Scientist Ben Goertzel Explains the Singularity
https://www.youtube.com/watch?v=m90buK0tFysRoss Finlayson schrieb:
> On 07/28/2024 09:04 AM, Ross Finlayson wrote:
>> On 04/10/2020 03:11 PM, Ross A. Finlayson wrote:
>>> On Friday, April 10, 2020 at 10:55:46 AM UTC-7, Mostowski Collapse wrote:
>>>> Its gibberish, since most of your
>>>> sentences lack a verb. Whats is this
>>>> pile of words:
>>>>
>>>> "structure, in sets, for of course all the formality
>>>> of all the structure of the sets **usually** "mechanically",
>>>> then what a "reality" embodies for a "mathematical universe"
>>>> a model of a universe of ZF set theory."
>>>>
>>>> Do you mean **usually** **is**?
>>>> Since when is it chick to drop verbs
>>>> in english sentences?
>>>>
>>>> On Friday, April 10, 2020 at 7:06:20 PM UTC+2, Mostowski Collapse wrote:
>>>>> Gibberish makes ZFC being a model of
>>>>> reality? Yeah if your reality is brain cancer.
>>>>>
>>>>> LoL
>>>>>
>>>>> On Friday, April 10, 2020 at 5:51:35 PM UTC+2, Ross A. Finlayson wrote:
>>>>>> On Friday, April 10, 2020 at 3:34:05 AM UTC-7, Mostowski Collapse
>>>>>> wrote:
>>>>>>> Corr.:
>>>>>>> But pretty sure ZFC is **not** postulating
>>>>>>> some reality here. Unless you are that
>>>>>>>
>>>>>>> A theory of anything, is not really
>>>>>>> a theory of something. Calling ZFC a model
>>>>>>>
>>>>>>> of reality is pretty crank.
>>>>>> No, it's the same as "there exists causality"
>>>>>> (there exists a theory, there exists A-Theory),
>>>>>> then that the model universe, ZF's, sees in other
>>>>>> theories that "the universe of ZF is its own powerset",
>>>>>> encompassing all relation.
>>>>>>
>>>>>> The "Pure" part of set theory is two things:
>>>>>> structure, in sets, for of course all the formality
>>>>>> of all the structure of the sets usually "mechanically",
>>>>>> then what a "reality" embodies for a "mathematical universe"
>>>>>> a model of a universe of ZF set theory.
>>>>>>
>>>>>> Then this "mechanically pure" and "totally pure",
>>>>>> help to reflect that applied set theory is descriptive.
>>>>>>
>>>>>> Applied set theory is descriptive. The "naive" set
>>>>>> theory is often best - for where it's true.
>>>>>>
>>>>>> "The proof strength of ZFC", is where, these days,
>>>>>> univalency, as an example, is basically a naive
>>>>>> universal.
>>>>>>
>>>>>> I.e. "for theorems in mathematics" "the proof
>>>>>> strength of ZFC" suffices for quite a work.
>>>>>>
>>>>>> Results in theorem proving?
>>>
>>> The "Pure" part of set theory is two things:
>>> (1) structure, in sets,
>>> for of course all the formality
>>> of all the structure of the sets
>>> usually "mechanically",
>>>
>>> then what a "reality" embodies
>>> for a "mathematical universe" :
>>> (2) a model of a universe of ZF set theory.
>>>
>>>
>>> Verb? This is: "is" a structure and "is" a model.
>>>
>>> The diagrammatical sentence diagram, you'll find in
>>> my style, is often both explicit, and encompassing
>>> parenthetical reference.
>>>
>>> About the universe being its own powerset,
>>> a similar result of Russell's made Frege
>>> abandon his completeness results, which is
>>> important because Goedel's both "completeness"
>>> and "incompleteness" results about arithmetization
>>> of structure reflect truisms.
>>>
>>> So, ..., "gibberish" here is only as received -
>>> i.e. you're a very excellent English speaker
>>> and apparently quite fluent in the concepts,
>>> it's too bad that some idiomatic grammar
>>> leaves you at a loss. Don't get me wrong -
>>> I'm not perfect.
>>>
>>>
>>> Also of course there's an importance of context,
>>> and a usual coherency and constancy in narrative.
>>>
>>> Then, "pure mathematics" in "philosophy of mathematics"
>>> and for "foundations of mathematics" is quite "mathematics".
>>>
>>> To your question of "what universe of ZF? V? L?",
>>> it's appreciated. Here of course you already know
>>> that there's Cantor's, Russell's, and Burali-Forti's
>>> results with that of course the universe of ZF is in
>>> a theory that is extra-ZF (here "stronger/weaker",
>>> in the results/axiomatics).
>>>
>>> Then, even just looking at ordinals and as that
>>> "powerset is order type is successor" and that
>>> for example "diagonalizing the finite ordinals
>>> makes an infinite one", notes that Russell would
>>> have to apply a resolution to the paradox that
>>> there's an infinite ordinal at all, consistently
>>> (as for example is defined as the second constant
>>> in the language of ZF besides empty: omega,
>>> or an inductive set, those two sets, the rest
>>> following expansion and restriction of comprehension).
>>>
>>> I.e., ZF to be accepted _does_ have "truly infinite" things.
>>>
>>
>
Roger Penrose versus Roy Kerr (Was: Mathematics and the singularity, let's discuss it)