It is worth noting that von Neumann only discovered the second incompleteness
theorem after having learned of the first from Gödel!
And from what I’ve read, the second is conceptually, if not technically,
a fairly immediate consequence of the first.
See e.g. this section in the SEP entry on the incompleteness results.
Wikipedia calls it an “extension oft the first”.
So don’t see how the independent discovery of the second incompleteness theorem by von Neumann
tells us much about the counterfactuality of the first.
It is worth noting that von Neumann only discovered the second incompleteness theorem after having learned of the first from Gödel!
And from what I’ve read, the second is conceptually, if not technically, a fairly immediate consequence of the first. See e.g. this section in the SEP entry on the incompleteness results. Wikipedia calls it an “extension oft the first”.
So don’t see how the independent discovery of the second incompleteness theorem by von Neumann tells us much about the counterfactuality of the first.