Can you get Tier High 1-A to 0 Cosmology By simply using "Mathematical Realism" ?

[Andika_CL_atmadja]

Assume some verse used mathematical realism as a very foundation of their cosmological structures.

https://www.rep.routledge.com/artic... view,human activities, beliefs or capacities.

Platonism in the Philosophy of Mathematics (Stanford Encyclopedia of Philosophy)

plato.stanford.edu

Mathematical realism is the view that the truths of mathematics are objective, which is to say that they are true independently of any human activities, beliefs or capacities. As the realist sees it, mathematics is the study of a body of necessary and unchanging facts, which it is the mathematician’s task to discover, not to create. These form the subject matter of mathematical discourse: a mathematical statement is true just in case it accurately describes the mathematical facts.

An important form of mathematical realism is mathematical Platonism, the view that mathematics is about a collection of independently existing mathematical objects. Platonism is to be distinguished from the more general thesis of realism, since the objectivity of mathematical truth does not, at least not obviously, require the existence of distinctively mathematical objects.

and this cosmological structures encompass infinite higher cardinal or infinite higher order logic.

https://compass.onlinelibrary.wiley.com/doi/full/10.1111/phc3.12756

Can you get high 1-A tier to 0 Cosmology with this ? also please give elaboration don't just say yes or no.

 

[Cat275]

1st question before answering, are we assuming the mathematical realism is true here? Since gödels incompleteness theorem here comes in play.

 

[Cat275]

Anyways firstly we have this:

Mathematical platonism can be defined as the conjunction of the following three theses:

Existence.
There are mathematical objects.

Abstractness.
Mathematical objects are abstract.

Independence.
Mathematical objects are independent of intelligent agents and their language, thought, and practices.

I guess we won't have to worry about the problem of a concept of a number here, now assuming we are using the higher order logic here as well we can probably reach tier 0 if the measure sets etc etc exist, since a measure set is equal to kappa at most cases.

(And some measure sets help on making some woodin theorems and the michador schimell theorem but we won't tackle this topic.)

But point here is that if the 1st measure set exist a Löwenhein number of a second order logic would already be bigger than it.
(Which would be H1-A, since it's most likely greater than the 1st or normal kappa number)

Then we have the 3rd order logic to even bigger order logic so with the case of mathematical object in mathematical platonism we can probably assume it can reach tier 0.

Edit:
Oh yeah I was skimming through the threads and found this so i also gotta add the detail that a second order logic and it's codomains and domains etc are already that of inaccessible in size (or atleast bigger than alephs or worldly cardinals) and can go even bigger, since the 1st order logic is the formalism of zfc without any additional axiom.

(To quote:

First-order logic is the standard for the formalization of mathematics into axioms, and is studied in the foundations of mathematics. Peano arithmetic and Zermelo–Fraenkel set theory are axiomatizations of number theory and set theory, respectively, into first-order logic. No first-order theory, however, has the strength to uniquely describe a structure with an infinite domain, such as the natural numbers or the real line. Axiom systems that do fully describe these two structures (that is, categorical axiom systems) can be obtained in stronger logics such as second-order logic)

 

[Andika_CL_atmadja]

Anyways firstly we have this:

Mathematical platonism can be defined as the conjunction of the following three theses:

Existence.
There are mathematical objects.

Abstractness.
Mathematical objects are abstract.

Independence.
Mathematical objects are independent of intelligent agents and their language, thought, and practices.

I guess we won't have to worry about the problem of a concept of a number here, now assuming we are using the higher order logic here as well we can probably reach tier 0 if the measure sets etc etc exist, since a measure set is equal to kappa at most cases.

(And some measure sets help on making some woodin theorems and the michador schimell theorem but we won't tackle this topic.)

But point here is that if the 1st measure set exist a Löwenhein number of a second order logic would already be bigger than it.
(Which would be H1-A, since it's most likely greater than the 1st or normal kappa number)

Then we have the 3rd order logic to even bigger order logic so with the case of mathematical object in mathematical platonism we can probably assume it can reach tier 0.

very nice answers cat. I will respond it later.......