Manifold potentially reaching absolute infinity?

[bigjoe]

While just looking the Downstreamers wiki page I came across this quote,

"Now he understood. This was the purpose. Not the long survival of humankind into a dismal future of decay and shadows, the final retreat into the lossless substrate, where nothing ever changed or grew. The purpose of humankind - the first intelligence of all - had been to reshape the universe in order to bud others and create a storm of mind. We got it wrong, [...] By striving for a meaningless eternity, humans denied true infinity. But we reached back, back in time, back to the far upstream, and spoke to our last children - the maligned Blues - and we put it right. This is what it meant to be alone in the universe, to be the first. We had all of infinite time and space in our hands. We had ultimate responsibility. And we discharged it. We were parents of the universe, not its children."

The biggest reason to assume that this true infinity is absolute infinity is due to the downstreamers immense knowledge about the manifold, and their nigh omniscience pre FVC, and how they "Think the same thoughts and live the same life's". It also is reasonable to believe that the downstreamers know about smaller infinities such as countable and Inaccessible Cardinals, and strive to reach the absolute infinity.

Is it reasonable to assume that the true infinity that they speak of is absolute infinity? If so would this warrant an upgrade to tier 0 or upgrade to possibly tier 0?

 

[Timeless]

No

 

[Timeless]

This is quite a big stretch to assume such things and two, absolute infinity is just like omnipotence. It doesn’t qualify for any tier.

 

[Cat275]

1. Even an axiom of infinity can qualify for true infinity.
(Which only proves the existence of aleph null)

2. Cantors absolute infinite fails to contain all sets in existence and it's tier varies on how much axioms are proven to exist or conceptually exist as an idea.

3. This is an outlier and commits many fallacies.

4. Numbers don't really have a tier by itself.

 

[bigjoe]

1. Even an axiom of infinity can qualify for true infinity.
(Which only proves the existence of aleph null)

2. Cantors absolute infinite fails to contain all sets in existence and it's tier varies on how much axioms are proven to exist or conceptually exist as an idea.

3. This is an outlier and commits many fallacies.

4. Numbers don't really have a tier by itself.

With the all things that are logically possible I manifold will happen, couldn't you still make the assumption they scale to inaccessibles cardinals?

 

[Cat275]

With the all things that are logically possible I manifold will happen, couldn't you still make the assumption they scale to inaccessibles cardinals?

No, logically possible doesn't include inaccessible and such you literally need to use new axioms to consider they are consistent.

(Also this large cardinals are not really possible..)

 

[bigjoe]

No, logically possible doesn't include inaccessible and such you literally need to use new axioms to consider they are consistent.

(Also this large cardinals are not really possible..)

They actually are logically possible within a Grothendieck universe, and it's the same reason why mathiverse scales to tier 0 because everything logically possible can happen.

 

[Timeless]

They actually are logically possible within a Grothendieck universe, and it's the same reason why mathiverse scales to tier 0 because everything logically possible can happen.

The difference is that the Mathiverse has a lot more evidence back it up. Manifold can only reach such tiers by highballing many things and I think it is better to be accurate. If you highball Twin Peaks for example, it would become the most powerful verse, even above the Mathiverse.

 

[Cat275]

They actually are logically possible within a Grothendieck universe, and it's the same reason why mathiverse scales to tier 0 because everything logically possible can happen.

That's adding a new axiom to the plate, which would already exceed the Zfc formalism and uses a new and extended logic. Also the difference here is that you need evidence of this large cardinals rather than just this, we're obviously reaching nlf territory since we don't consider things like modal realism to have large cardinals without any given concrete evidence.

(I don't really believe in mathiverse tier 0 as well.)

 

[bigjoe]

Although it might be a stretch it is still logically possible, and thus must be a part of manifold, one could already make the argument that a type 4 multiverse should already be tier 0 without other evidence needed.

Edit:I forgot to mention that most set theorists do agree that strongly Inaccessible cardinals can exist within a Grothendieck Universe, so to say they aren't a logical possibility is ridiculous. Remember even if the odds are 1/100000¹⁰⁰⁰⁰ they will still unfold within the infinite manifold.

 

[bigjoe]

The difference is that the Mathiverse has a lot more evidence back it up. Manifold can only reach such tiers by highballing many things and I think it is better to be accurate. If you highball Twin Peaks for example, it would become the most powerful verse, even above the Mathiverse.

That's why I believe it should be labeled as possibly tier 0 not flat tier 0.

 

[Timeless]

Nothing about this is tier 0 at all. There's no evidence of any absolute infinity, and absolute infinity is unquantifiable. Just because it's logically possible doesn't mean it would happen. Plus I don't see any evidence that the Grothendieck Universe is in Manifold

 

[bigjoe]

Actually because it is logically possible means it must happen in Manifold, https://photos.app.goo.gl/qgcJyPp5Hd2D2pd16 this quote sums it up perfectly. The fact that we take the exact same statements from mathiverse to put them at tier 0, but we won't put the downstreamers at tier 0 despite them blatantly transcending the manifold cosmology is ridiculous

 

[Timeless]

Actually because it is logically possible means it must happen in Manifold, https://photos.app.goo.gl/qgcJyPp5Hd2D2pd16 this quote sums it up perfectly. The fact that we take the exact same statements from mathiverse to put them at tier 0, but we won't put the downstreamers at tier 0 despite them blatantly transcending the manifold cosmology is ridiculous

Concat Ultima or Jibz or someone. They know a lot more about tier 0 then I do.

 

[Timeless]

Actually because it is logically possible means it must happen in Manifold, https://photos.app.goo.gl/qgcJyPp5Hd2D2pd16 this quote sums it up perfectly. The fact that we take the exact same statements from mathiverse to put them at tier 0, but we won't put the downstreamers at tier 0 despite them blatantly transcending the manifold cosmology is ridiculous

There's no way of knowing what's logically possible from this quote alone. You need verifiable proof that the "all logically possible" thing applies to inaccessible cardinals. It'd be like upgrading everyone who is omnipotent in their verse to tier - because they can do all logically possible things, which would include inaccessible cardinals. You just don't that they aren't that powerful. Unless to have explicit conformation or multiple quotes that imply that same EXACT thing, we cannot consider this to be true

 

[Cat275]

Anyways what's the proposal again? Absolute infinite for the reason of all possible things right..?

Well Absolute infinite is actually illogical to mathematicians by the burali-forti paradox.

Quoting:

The idea that the collection of all ordinal numbers cannot logically exist seems paradoxical to many. This is related to Cesare Burali-Forti's "paradox" which states that there can be no greatest ordinal number. All of these problems can be traced back to the idea that, for every property that can be logically defined, there exists a set of all objects that have that property. However, as in Cantor's argument (above), this idea leads to difficulties.

More generally, as noted by A. W. Moore, there can be no end to the process of set formation, and thus no such thing as the totality of all sets, or the set hierarchy. Any such totality would itself have to be a set, thus lying somewhere within the hierarchy and thus failing to contain every set.

The problem with a all containing set is also impossible since this set will not be contained by itself.

Anyways again numbers don't have tiers unless if it's something like the beth numbers and such and I wouldn't really use set theory logic in scaling since it really depends from fiction to fiction, in this wiki you need explicit statement of the large cardinals in the verse than just theologies like the multiverse hypothesis type 4 and etc. Though I don't plan on debating any longer.

There's no way of knowing what's logically possible from this quote alone. You need verifiable proof that the "all logically possible" thing applies to inaccessible cardinals. It'd be like upgrading everyone who is omnipotent in their verse to tier - because they can do all logically possible things, which would include inaccessible cardinals. You just don't that they aren't that powerful. Unless to have explicit conformation or multiple quotes that imply that same EXACT thing, we cannot consider this to be true

Also this^

 

[Livinmeme]

Anyways what's the proposal again? Absolute infinite for the reason of all possible things right..?

Well Absolute infinite is actually illogical to mathematicians by the burali-forti paradox.

Quoting:

The idea that the collection of all ordinal numbers cannot logically exist seems paradoxical to many. This is related to Cesare Burali-Forti's "paradox" which states that there can be no greatest ordinal number. All of these problems can be traced back to the idea that, for every property that can be logically defined, there exists a set of all objects that have that property. However, as in Cantor's argument (above), this idea leads to difficulties.

More generally, as noted by A. W. Moore, there can be no end to the process of set formation, and thus no such thing as the totality of all sets, or the set hierarchy. Any such totality would itself have to be a set, thus lying somewhere within the hierarchy and thus failing to contain every set.



Anyways again numbers don't have tiers unless if it's something like the beth numbers and such and I wouldn't really use set theory logic in scaling since it really depends from fiction to fiction, in this wiki you need explicit statement of the large cardinals in the verse than just theologies like the multiverse hypothesis type 4 and etc. Though I don't plan on debating any longer.



Also this^

Eh, kinda hard to put into words, but isn't absolute infinity the idea of all numbers and cardinality (also 0>1 is pretty inconsistent)

 

[NHTkenshin2]

I mean it seems like the manifold verse believes in such a concept

 

[Savior]

Eh, kinda hard to put into words, but isn't absolute infinity the idea of all numbers and cardinality (also 0>1 is pretty inconsistent)

Thats Cantor's view which is contradicted by Burali-Forti Paradox

 

[Ovy7]

Just some random mention of true infinity is waaaaay to vague for tier 0, let alone that high.

 

[Guardian_Doge]

snip

Cantor's view can just be associated with a reflection principle in asserting that Ω is a class then using a set's definition to accommodate a class being another element of a greater class and skirt the paradox, the actualist view of a Universe of sets via the reflection principle is just more difficult to justify not illogical thankfully.

But yeah for this particular thread, I see no mention of absolute infinity, soooo how we would define the framework of all logically possible universes is just something that requires the proper objects to construct a tier.