Do our views of existing of non-real objects have common characteristics?

Question

If we come to the conclusion, as realists, that reality has a conscious-independent existence, we could extend our investigation to the question whether there are things outside reality that also exists, equally conscious-independent If so, my question is whether such things would have common characteristics in our - conscious - treatment.

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In the spirit of showing my “search for a solution” I present few cases below.

I take here two different candidates of non-real existence: Platonic mathematics and divinity. I take Platonic mathematics as being somewhat unproblematic in that I follow the treatment of Stanford Encyclopedia of Philosophy. I maintain that divinity is non-real and choose to follow the Christian faith, and specifically the protestant version with the Augsburg confession: “…there is one divine essence which is called and is God, eternal, without body, indivisible [without part], of infinite power,…” It is clear that the divine essence “has no body” and therefore qualifies for our investigation. Catholics may (or may not) accept this part of the confession.

Proofs and axioms

The proof for Gods existence were numerous during the middle ages, but later, with Kant and Kierkegård, the belief has gained ground that a proof cannot be produced and that the existence is a matter of faith. (Kant’s book “Critique of pure reason” was banned by the Vatican, indicator of some uncertainty regarding the later Catholic positions). It seems therefore that position of the (Protestant) faith comes close to what on the mathematical side would be called an axiom.

Further, on the Platonic mathematics, we note some of the more popular the arguments in support of existence comes from Frege. In the post “Frege's argument for the existence of abstract mathematical objects” there is a (general) comment about argument and proof by Allegranza: “user1 - an "argument for existence" is an argument... A proof is a valid (logically correct) argument starting with axioms assumed as true.”

In any case I assume the interpretation of abstract existence as an axiom in both cases is reasonable. The problem I see with this result is that the common characteristics can be discarded as being close to - and perhaps embedded - in the definition itself, and therefore perhaps not really a new finding.

Counterarguments

I therefore go on to present the characteristics of some of the counterarguments, beginning with the religious side: The Swedish philosopher Ingemar Hedenius, received his doctorate in 1936 with a thesis on Berkeley and his sensationalism. Thirteen years later, in 1949, he published a collection of essays entitled "Faith and Knowledge" which rejected The Church of Sweden and the truth in the teachings of Christianity. This broadside was not fired by any leftist activist. It was a representative of the Uppsala philosophy, a son of the king's physician and grandson of Per Hedenius, rector of Uppsala University 1871-72. The debate that followed has been described as one of the most intense cultural debates in Sweden..

The debate was all the more remarkable as some of the arguments presented were a thousand years old. It was, among other things, the existence of metaphysical assumptions and the so-called theodicy problem (why a good God allows the manifestation of evil). Another was related to the resurrection, said to be in contradiction to what Hedenius calls "the linguistic theoretical postulate" which requires faith to be able to be transferred in modern scientific terms to unbelievers.

His beliefs are summarized by Wikipedia (Eng.) which contain the “language-theory postulate”: It must be possible to communicate the religious comprehension and experience even to non-believers. On the mathematical side, the Stanford Encyclopedia notes: “The most influential objection is probably the one inspired by Benacerraf (1973). What follows is an improved version of Benacerraf’s objection due to Field (1989). This version relies on the following three premises.

Premise 1. Mathematicians are reliable, in the sense that for almost every mathematical sentence S, if mathematicians accept S, then S is true. Premise 2. For belief in mathematics to be justified, it must at least in principle be possible to explain the reliability described in Premise 1. Premise 3. If mathematical platonism is true, then this reliability cannot be explained even in principle.”

We note here that the both objections have strong connotation to linguistics. This is a less obvious consequence of the initial definition of abstract existence.

Answer 1

If you are asking whether there are similarities between mathematical Platonism and organized religion, you may have an ally in Edward Nelson, who wrote a few texts in this direction. Nelson viewed Platonism as originating with the Pythagorean school, and speaks of a Pythagorean brotherhood, with purportedly many members today. You may want to consult

Confessions of an Apostate Mathematician

Mathematics and Faith

There are additional related texts on his website.

Answer 2

OP : "If we come to the conclusion, as realists, that reality has a conscious-independent existence"

"Do our views of existing of non-real objects . . ."

Before we get to non-real objects let's consider first if there are even any real objects in conscious-independent existence. Presumably this refers to objects that exist before any eye has ever laid sight on them. But as Bertrand Russell observes in Portraits From Memory And Other Essays (1950) objects (things) are human inventions.

“things” have been invented by human beings for their own convenience. This is not obvious on the earth's surface because, owing to the low temperature, there is a certain degree of apparent stability. But it would be obvious if one could live on the sun where there is nothing but perpetually changing whirlwinds of gas. If you lived on the sun, you would never have formed the idea of “things,” ... In such an environment, even Hegel's philosophy would seem to be common sense, and what we consider common sense would appear as fantastic metaphysical speculation.

Granted that in phenomenology the existence of the world is given à priori, but objects themselves are not yet brought into apperception where their probable, objective existence is determined. The realist position seems to be that one has observed objects, defined them as say, planets, and now declares that planets exist even if there had never been any humans. But 'planet' is a human-made determination. Without this determination planets, moons and atoms are as undifferentiated plasma. Before we can get to real mind-independent objects, let alone non-real mind-independent objects, a clear definition of what constitutes existence for a mind-independent 'thing' is necessary.