12/04/2014, 09:31 AM

I respect the philosophical points of view... but i really think that this drag us off topic... is not the place to discuss about this...

Is like if I start a new thread where I ask how old are the users of the forum and you start to argue about the existence of the time itself and conclude sayng that time doesnt exist thus everyone is 0 years old (QED)...

Really, I appreciate the philosophical threads but... but...

We are talking about Cardinal arithmetic, that is defined inside a set theory (ZFC)...

you can't come here with a mysterious proof that use other deduction rules and that uses an implicit rejection of the set theory framework.

Anyways I should note that this sentence is wrong...

Doner and Tarski completely extended the Hyperoperations in to the transfinite ordinals!

That's because Hos are defined via recursion, so they just used the transfinite recursion over the ordinals.

At the end.. I recognize the existences of the constructivism and the finitism near the classical mathematical frameworks such as ZFC, NBG, MK ecc. ecc.

The russel paradox and the fall of the Cantor's theory originated a wide range of solutions including some that refuse the existences of cardinalities bigger than (like constructivism) and some that totally refuse actual infinity (like intuitionism for example).

Said that...I still feel this wide range of differences as ideological and philosophical differences.

That's why I guess that we are going off topic and that the original thread was started to talk about the Cardinals defined inside a theory that admits different cardinality as ZFC.

Is like if I start a new thread where I ask how old are the users of the forum and you start to argue about the existence of the time itself and conclude sayng that time doesnt exist thus everyone is 0 years old (QED)...

Really, I appreciate the philosophical threads but... but...

We are talking about Cardinal arithmetic, that is defined inside a set theory (ZFC)...

you can't come here with a mysterious proof that use other deduction rules and that uses an implicit rejection of the set theory framework.

Anyways I should note that this sentence is wrong...

Quote:and the "evil" set theorists say tetration is nonsense as defense.

Doner and Tarski completely extended the Hyperoperations in to the transfinite ordinals!

That's because Hos are defined via recursion, so they just used the transfinite recursion over the ordinals.

At the end.. I recognize the existences of the constructivism and the finitism near the classical mathematical frameworks such as ZFC, NBG, MK ecc. ecc.

The russel paradox and the fall of the Cantor's theory originated a wide range of solutions including some that refuse the existences of cardinalities bigger than (like constructivism) and some that totally refuse actual infinity (like intuitionism for example).

Said that...I still feel this wide range of differences as ideological and philosophical differences.

That's why I guess that we are going off topic and that the original thread was started to talk about the Cardinals defined inside a theory that admits different cardinality as ZFC.

MathStackExchange account:MphLee