Is Anselm of Canterbury venerated by the Eastern Orthodox Church, or is he accepted as a saint only by the Western churches? Similarly, is his Satisfaction Theory of atonement accepted at large within the EOC (if at all)? If not, which theory of atonement tends to bear prominence in her teaching/liturgy (such as the Ransom Theory, Moral Influence Theory, or the *Christus Victor* Theory)?

This question is related to https://christianity.stackexchange.com/questions/97517/objections-to-natural-theology-at-the-time-of-vatican-i In contrast to the observance of natural phenomena in order to arrive at the conclusion that God exists, an [*ontological argument*](https://en.wikipedia.org/wiki/Ontological_argument) is one which draws the same conclusion from some source other than observation of the world; e.g., from reason alone. The first such well-known argument, I believe, is the one attributed to St. Anselm, which (though multiple versions exist) I paraphrase as: "God is that Being Whom nothing greater can be conceived" — the proof of which can be assembled by reading his *Proslogion*. His argument which one may infer therein became famous; and then criticized a century or so later by St. Thomas Aquinas. Many variations of Anselm's demonstration, as well as many criticisms, followed throughout the centuries. In the twentieth century, the great logician Kurt Gödel (probably following the writings of Leibniz rather than that of Anselm), formalized a logical argument (with parallels to Anselm) which has been hailed as correct. For those familiar with logical symbols, see, for example, [*Gödel Says God Exists and Proves It*](https://mindmatters.ai/2021/06/godel-says-god-exists-and-proves-it/) ; and his proof is this: Of course, the validity of [Gödel's argument](https://en.wikipedia.org/wiki/G%C3%B6del%27s_ontological_proof) (which is now widely accepted) depends on acceptance of his definitions (the Df.'s) and the inherent truth of his axioms (the Ax.'s). QUESTION: What (if anything) has the Catholic Church declared (by say, either Council or papal encyclical) about affirming God's existence by reason alone; i.e., by some (apparently correct) ontological argument?

In *Cur Deus Homo*, Anselm provides an argument primarily in natural theology (as I understand it, anyway) for the proposition that the divine nature assumed a human nature for itself, without confusion of natures (modulo the Chalcedonian credo, then). The argument goes something like: 1. Humanity should redeem itself. 2. Only God can redeem humanity. 3. Should-implies-can (roughly; you could also say, "If something to be done is right/good, then there is a way to do it"). 4. Therefore God could in some way exist also in human form. I personally like and accept this line of reasoning, owing greatly to my preconversion acceptance of (3). In fact, my conversion came about in part because of the above reasoning. Now I say "in part," in part(!) because I thought there was a way to adapt Anselm's argument to the question of the Resurrection. First, sometimes John 3:16 is translated such that it says "shall not perish" instead of "will not perish." I don't know the original Greek words there, so this is a gap in my reasoning, but the idea is that the Bible is saying there that there are circumstances in which we can say that someone **should** be resurrected. (The Bible also talks about a "right to be the children of God": John 1:12.) Secondly, then, let us suppose (this is a hypothetical, but we who believe would discharge the antecedent re: Jesus Christ) that there was someone who was very good, perfect in fact. If this perfect person died, would we be able to say that this person *should* be resurrected? That it would be right and good for this person to come back from the dead? Then via (3) from Anselm's argument, we would get, "Therefore, it is possible for this perfect being to be resurrected." And if it was possible, and appeared to be actual, why would we think it was untrue that it had turned out to be actual? Or is Anselm's kind of reasoning too flawed in general? He was, after all, as far as I know, the one who came up with the first [ontological argument](https://plato.stanford.edu/entries/ontological-arguments/) . But I am attracted to that argument, too, so I don't know...

The following is paraphrased from *A Passion for Mathematics* by Clifford A. Pickover (read in Kiefer Sutherland's voice): (mathjax here ) **Theorem**: The axiom of choice is equivalent to the existence of a unique God (St. Anselm, Aquinas, and others). > Proof: > > First, suppose the axiom of choice. Partially order the set of subsets > of the set of all properties of objects by inclusion. This set has > maximal elements. God is by definition (due to Anselm) a maximal > element set. > > We prove existence: God $\subseteq$ God $\cup$ $\{$existence$\}$, so > God $=$ God $\cup$ $\{$existence$\}$. Therefore, God exists. > > We prove uniqueness: Let God and God′ be two gods, then God $\cup$ > God′ $\supseteq$ God (due to Aquinas) $\implies$ God $\cup$ God′ = God > $\implies$ God $\subseteq$ God′ Similarly, God′ $\subseteq$ > God. Therefore, God is unique. > > Second, suppose the existence of a unique God, omnipotent, omniscient > and amoral (or omnibenevolent. It does not matter for this context). > Given an index set $R$ and collection of sets > $\{A_{\alpha}\}_{\{\alpha \in R\}}$, pray that the unique God picks, > by omnipotence, $x_{\alpha} \in A_{\alpha}$ for each $\alpha \in A$. > Then $$\{x_{\alpha}\}_{\alpha \in R} \in \prod_{\alpha \in R} A_{\alpha}$$ as required. Questions: 1. What is a "maximal element set"? I could not find this online. I do not remembering learning this in philosophy of religion class when I was in bachelor's. 2. In existence, how does God $\subseteq$ God $\cup$ $\{$existence$\}$ imply God $=$ God $\cup$ $\{$existence$\}$? I guess that we have somehow already had God $\supseteq$ God $\cup$ $\{$existence$\}$. 3. In uniqueness, why do we have have that God $\subseteq$ God′ instead of God $\supseteq$ God′? 4. Is uniqueness required for the second direction? I can think of only the unique choice of $x_{\alpha}$ or something of the sort. I think I am fine with the second direction. Update: I think [this link](http://ion.uwinnipeg.ca/~currie/logic.pdf) might have some answers.

Upon which Bible verses did [Anselm](https://en.wikipedia.org/wiki/Anselm_of_Canterbury) base his [satisfactory theory of atonement](https://en.wikipedia.org/wiki/Satisfaction_theory_of_atonement) ?