The purpose of Gödel numbering is to represent an arbitrary-length string of symbols as a single integer which allows you to manipulate it using Peano arithmetic.

But it is not like Gödel invented binary as you seem to suggest. Baudot code (a 5-bit character encoding) was in use in 1870’s.

In any case, Gödel-numbering is the least interesting part of the the theorem. The groundbreaking idea is creating statements about theorems.

The “something” Gödels proof talks about is axiomatic systems. It doesn’t talk about physical objects.

What about describing an electrical circuit formally? Surely this was thought possible before Principia was published.

> could you encode in pure logic how a dog behaves

Assuming we knew enough about how a dog behaves (or less ambitiously, a more primitive organism) I would assume this could be described in a formal language. But why would Principia be needed for this? Math have been used to model natural phenomena a long time before Principia.

I doubt you have any reliable statistics about this, given how many victims keep silent out of fear.

But in any case, the moral failure of the church was not the existence of individual abusers (which indeed can exist anywhere in society), but how on an institutional level known abusers were protected by the curch. Everyone who was part of the cover-up (which went all the way to the top) is complicit.

Language-level safety only protect against trivial mistakes like dereferencing a null-pointer. No language can protect against logical errors. If you have untrusted people comitting unvetted code, you will have much worse problems.

C# also supports null-safety, although less elegantly and as opt-in. If enabled, it won’t let you deference a possibly-null reference.