Abstract Objects Are Merely Useful Fictions, This I Know.
For The Abstract Objects Tell Me So!
Whenever someone argues that abstract objects don't really exist, remember that they are USING abstract objects as their intellectual and logical authority to adjudicate the reality of those same objects!
I wonder how abstract objects got that kind of supervisory authority to arbitrate their own existence, when they don't even really exist themselves!
If you clearly understand this post, its an easy analogy to understanding why rationalist-objectivist atheism is necessarily theistic about reason and logic, as we all are in reasoning about universals---including the universals that make up general reason and logic themselves.
The boot-strapping problem of abstract objects being used to ontologically self-adjudicate still remains, and I haven't seen anything yet that even mentions it---much less actually deals with it.
Abstract objects and universals are necessarily real, the sine qua nons of all possible knowledge of contingent reals. If they are necessary for adjudicating ontological status, they themselves must have an even higher supervisory ontological status, which means they are *necessarily* more real than any other objects we ordinarily take as real. There's simply no way around this without ending up in the old self-referential cul-de-sac.
Objector: I'm not sold on the necessity of abstract objects since I think that necessarily existing entities existing independently of God impugn the doctrines if divine aseity and creation ex nihilo. However, I'll throw in with the Thomists and say it's clear that universals located in the divine intellect are necessary and exist necessarily.
Response: They are all necessarily components of the divine mind, and their absolute inescapable necessity is what guarantees this. Knowledge of divine aseity itself necessarily depends logically on them.
If you examine closely what you mean by universals, abstract objects, irreducibly basic categories, and so on---that examination itself would not be possible without those same categories already operating in advance at the highest cognitive levels.
As Boyle proved, Thomistic metaphysics is necessarily self-referential metaphysics at its logical base. Russell's prohibition of self-referencing statements is an instance of what it prohibits, and so on. It's all about self-reference and ultimate universal criteria and standards of analysis, which are already there logically prior to any actual analysis of anything including reasoning about current preferences.
That system is already in place and we're always trying to approximate it in some sense and degree, even regardless of prior misses of goals.
The bottom line is that if you give reasons for God, those reasons are already assumed to have an ultimate God-level authority in order to adjudicate the knowledge and claims about the possible reality of God.
Why does faith have to be reasonable or smart or even plausible? Why does it still try to be rational about what it declares itself to be exempt from? Why must there be any intellectual defense at all? If reason is not God-level already, why must theistic or Christian belief have reason and logic's seal of approval in the first place in the slightest? The entire discussion is a submission to reason's authority, whether one is a believer or an atheist.
In fact, the whole issue about the relationship between faith and reason is itself just one big cognitive worship-fest dedicated to reason.
Artwork: Until Now by Ralph Hertle. Available at: