M'incompleteness

see

Is this a correct interpretation of Gödel's Incompleteness Theorems?

That was a mathematical assumption done by mathematicians.

It's a consequence of them, but it really needs a huge footnote to state it like that.

No, I'm rarely sure of anything. Which post are you?
This follows from Russell's paradox, mathematics cannot be reduced to formal logic.

In which case, what is a correct interpretation/reading?

>This follows from Russell's paradox
wat
>mathematics cannot be reduced to formal logic.
You really need to be cautious there. Is not exactly like that. They were looking for a simpler system to base math. Russell wrote the whole Principia based on that precept. Russell's paradox demonstrated that the system Frege was working on was not sustainable. At least 15 years before the Principia, and 40 years before Gödel.

That, given a formal logic system (and here we have to be cautious, because there are complete systems) strong enough to have some properties (that I'm not defining, but they are enumerated in the first page of the paper), there is always a proposition that you can't prove it's true inside that system. Math is complex enough to be part of that system. Therefore there are mathematical propositions that you cannot demonstrate true or false. That's why it is incomplete. There are systems that are complete, but they are not very complex.

Thank you for clarifying, I was misreading (obviously), I only have a small amount of background in the philosophy of mathematics.

>starves to death
What did he mean by this?

The logicists were after him

Is mathematics not purely a logic based language, is in code? Cause and effect, if, else, then, etc..?

I can't remember who he thought wanted to poison him. The fact is that he had that thought for a really long time, and he only accepted food from his wife. She died, he starved.

That was the logicists premise, but it seems that there are mathematical inferences and objects that are more basic and universal than that.

Wouldn't the incompleteness theorems point to mathematical objects being less universal?

No. Why?

Because don't the incompleteness theorems essentially prove that, if we think of statements of mathematical logic as a set and statements of formal logic as another, there isn't a bijection between them? If this is so, they cannot be equal in cardinality. If we assume consistency (injective), then there are less statements in the set of mathematical logic. So the other case is inconsistency, which seems itself flawed to define a mathematical logic system as also inconsistent, but if I'm wrong in that, please enlighten me.

After a quick moment of thought it also could simply be a complete misunderstanding of Gödel.

I don't know what cardinality has anything to do with this.
And I don't know what are you trying to do with functions.
You can create as many propositions has you want. They are free. Take two and put a conjunction in between. There you have more. There is not a definite set of logical statements, unless you are comparing two specific sets. And this is not the case.

I'm not entirely sure what I was trying to do either. I was confused as to why mathematics being more general meant that it couldn't be reduced to formal logic. It came from a fundamental misunderstanding of reduction and the incompleteness theorems. Thank you for putting up with and actually responding to my post.
Do you have any literature recommendations for someone trying to get into the philosophy of mathematics?

The original papers are quite technical and you need to read the logical notations. And they have change a lot.
If you have a lot of time to lose (and you are very serious) read: From Frege to Gödel by J. van Heijenoort, but that's a compilation of the most important papers.
But, actually, the best recommendation is to read the Stanford Encyclopedia of Philosophy articles and look on their bibliography what interests you. They are peer reviewed articles, and even thought I hate those fuckers, they are well written.

I'm a mathematics undergrad and the topic has been fascinating to me since I started studying philosophy in my free time, thank you for the recommendation, I'll add it to the running list I've got.

>I'm a mathematics undergrad
Then you are gonna get good at it quite fast. Don't lose your interest in logic, and don't forget to read philosophy from time to time.

Oh, and before I forget, because you are a math undergrad, try to read as much as you can on category theory and bother your teachers about it. You might unlock the last boss with that.