Hello John D.
I’ve just tuned in to your original question. I see it has generated quite a response but without any disrespect intended to your other interlocutors, let me begin by trying to answer your original question.
You ask what my opinion is regarding the ontology of abstract objects – do they really exist? are they fictions? etc.
As I’m sure you are aware, there are 3 basic positions on this question: 1. what are called abstract objects (numbers, properties) are as real if not more real than the objects of our sensory experience [metaphysical realism]; 2. abstract objects do not exist except as a function of our language – to think otherwise is to make the mistake of thinking that our language and reality are correlated in a kind of one-to-one relationship [metaphysical nominalism/(sometimes conceptualism]; and 3. abstract objects do exist in a sense (answering to certain aspects of reality) but not in the same way as your cat exists [modified metaphysical realism].
If I had to choose a position on this issue, it would be modified metaphysical realism. As the responses to your original post demonstrate, this seemingly abstruse issue has theological ramifications. If you or any of the other contributors to this thread would like to repeat questions of interest, I will do my best to respond. To make sure I respond reasonably quickly, it helps to send me an email alert to gerard.casey@ucd..ie
All the best,