Funny: there is no account of universality (indeed the word "logic" and certainly not abstracts are never used)in the bible.
Further, logic is conceptual in nature, immaterial for sure, but not as illusive as you want to make it seem. This will be explained further below.
Secondly, since an actual objective world exists (since denial is an action that can only occur if one exists), however unchanging and at times, unpredictable it may be, this is our underpinning. Things exist, we can interact with them as directly as the sense impressions they leave allow. This world may not be permanent or stable (funny, now you sound like a Buddhist like me), but there is still an external reality.
Next, now that we have a solid basis that can provide a stability of sorts - an objectivist might say "existence exists" - how do abstractions work? Concepts, in the Buddhist view, are meant to convey meaning through economy (this is why conventional reality is so close to being true, but that's more to do with perception, another discussion for another time), thus they need to be open-ended. This is their usefulness hence their "abstract invariance."
Concepts are formed by extrapolating from the specific to the general in all three times. "Human" comes to include all people in all times, who have lived, do live, and will live of all sorts of shapes and sizes. It does not need to specify a number of units since it is all potential(think set theory and the concept of infinity).
See "Theravada Nyaya" for a better treatment of this process.
Now you understand how logic is conceptual in nature. That is, it can be seen as a small guidebook for cognition whose norms are undertaken voluntarily.
Presuppositionalism needs to get it's facts straight first as I've seen two different presup "accounts" for logic.