Something that seems not likely to be true because it wasn't justified by deriving it from the axioms and theorems of a logical system is called ad hoc1
Then a statement that isn't ad hoc is something that follows from / can be derived from a theory or logical system and doesn't contradict it.
For example, if our logical system said
For each positive integer n, n - 1 is the positive integer preceding it, if it exists2
Then a statement such as
except 5. 5 - 1 is 8
can be described to be ad hoc (and it is false as well, but ad hoc doesn't necessarily mean that something is wrong1)
And a statement such as
except 1. 1 does not have a positive integer that precedes it
may seem ad hoc, so we'll add that "this statement is not ad hoc and is consistent with the mathematics2"
I'm looking for a single word or a phrase that captures this meaning so that on rephrasing, my sentence above would become "this statement is _______."
- This may differ from usage of ad hoc with the meaning - "created or done for a particular purpose as necessary" because it carries a different connotation. See Ad hoc hypothesis.
Also, this makes my question different from Antonym for "ad hoc".
- Here, by "positive integer", I mean the numbers
1, 2, 3, 4, ....