Is there a specific word for "goes without being said"?
Solution 1:
I suggest the word implicit (implicitly, in the first example in the question):
- Suggested though not directly expressed: comments seen as implicit criticism of the policies
...
- (implicit in) Always to be found in; essentially connected with: the values implicit in the school ethos
Solution 2:
I think there is a bit of a disconnect between the question and the examples given. That being said I think there are several words that can be used depending on context.
One possibility is the word obvious with emphasis on the second definition.
Merriam-Webster
1 : easy to see or notice
2 : easy for the mind to understand or recognize
I think this can be used somewhat interchangeably with the phrase "goes without saying/being said".
Ex: After seeing the wreckage it goes without saying that the ship ran aground.
Ex: After seeing the wreckage it was obvious that the ship ran aground.
Also take a look at this post on Grammarist.
Goes without saying
It’s easy to be hard on goes without saying—if something goes without saying, why say it?—but the phrase sometimes works well as a wordy way of saying obviously, and it can be useful for emphasis or transition.
Also, as pointed out by Mark the word implicit can be used in the examples given by the OP and also in many cases interchangeably with "it goes without saying/being said". I would emphasize the first definition since it captures the idea of something being known without being expressed.
implicit
adjective im·plic·it \im-ˈpli-sət\ 1 : understood though not clearly or directly stated
Solution 3:
I would say "self-evidently" works well in both cases. Similar to "obvious" and related synonyms, but with the added nuance of implying the obviousness requires no external or a priori knowledge of the subject at hand.