Re:How many real numbers exist? New proof moves closer to an...
by rssoconnor on Saturday July 17, 2021 @09:40PM
(#27870173)
ZFC+¬Con(ZFC) proves "ZFC+¬Con(ZFC) is inconsistent".
So if were the case that ZFC+¬Con(ZFC) was sound then what it proves would be true, and "ZFC+¬Con(ZFC) is inconsistent" would be true. But that would mean ZFC+¬Con(ZFC) is actually inconsistent, and thus ZFC+¬Con(ZFC) would actually be unsound after all.
So if were the case that ZFC+¬Con(ZFC) was sound then what it proves would be true, and "ZFC+¬Con(ZFC) is inconsistent" would be true. But that would mean ZFC+¬Con(ZFC) is actually inconsistent, and thus ZFC+¬Con(ZFC) would actually be unsound after all.