/sci/ - Science & Math

>>8216702
>http://steve-patterson.com/cantor-wrong-no-infinite-sets/

It looks to me like his argument is similar to one of Wittgenstein's arguments. Essentially it boils down to something like
>Cantor's diagonolization argument ends in a contradiction. The usual way to resolve this is by claiming that the set is uncountable, however the correct way to resolve it is actually by realizing that infinite sets don't exist (i.e. the true contradiction lies with a different assumption further up the tree).

He seems to argue that instead one should fall back on a system of set theory/mathematics(?) analogous to computability.

I haven't read all of his work but it looks like he definitely does not believe in potential infinity (strict or otherwise).

>>8216789
Both of your descriptions about arithmetic are bad and you should both feel bad.

>>8216810
This is formally correct if you approach math from a proof theory perspective. At best one could accept countable infinity (either potential or actual).

>>8216831
>>8216855
I have a question for you.

Regarding the use of the [math]\forall[/math] quantifier, do you believe that one should be able to quantify over an infnite number of things? If so, how do you justify this?

On a sidenote, stating that there is always more is the argument of potential infinity, not the argument of actual infinity.

>>8216930
If all your statements and all your proofs are restricted to finite length then how can you justify the existence of actually infinite sets or worse uncountably infinite sets?

>>8217388
>>8217402
>having a literally a high school tier understanding of these concepts.

>>5030177