Mako wrote:
Isn't the proposition (1) merely the same as saying "There are no transcendental facts," except it's phrased here as a set-theoretic proposition? Again, I'm tentatively agreeing with the proposition.

If we add a fourth definition and state for our purposes that "All definitions of 'god(s)' include properties of transcendence." ...

...can we not claim then that, according to our definitions, "There are no gods?," (i.e. The set of gods is empty?)

Going by our set of definitions in the op, claiming that there are no transcendental facts (or that there are no gods) is not the same as claiming "There are no red emeralds." The qualities of redness and emerald-ness are contingent/conditional qualities and do not imply a formal contradiction. But 180's set of definitions includes the way we define all facts and that we necessarily define them as being conditional states of affairs.. It's thus a categorical, limiting condition for facts, period. However it would seem (to my non-logician self) that the proposition should actually be an axiom and therefore that it is axiomatic that "there are no transcendental facts" or "the set of transcendental facts is empty."

reincarnated wrote:
I like this thread.
On a literal reading of 180 Proof’s definitions, “transcendent fact” would be a simple oxymoron (since “fact” is defined as denoting something conditional, whereas “transecendent” is defined as denoting something beyond conditions).
Hence these two sets (the set of things which are “transcendant”, and the set of things which are “facts”) are mutually exclusive, and the union of these two sets is thus by definition a null set.

There is a set of “bachelors”, and there is a set of “married people”. The set of “married people who are also bachelors” is defined as the union of these two sets – and the union of these two sets is empty. Now a “married bachelor” is just as non-existent as a “transcendent fact” (according to 180 Proof’s definitions), but nevertheless we can (logically) talk about the set of “married bachelors” even though it seems nonsensical in English.
But I doubt that the word “transcendent” is always used in the English language in exactly the way 180 Proof has defined it here.

What is a “correct definition”? In theology, transcendent simply means outside of the mortal world (in the sense that God’s existence is said to transcend our material world). In Mediaeval philosophy, transcendent simply meant outside of the Aristotelian categories of reality. Kant and Sartre also use the term “transcendent” (or transcendental) in their works, but I doubt whether their intended meanings are identical to the one suggested by 180 Proof. In colloquial usage, “transcendent” simple means “going beyond….” – which begs the question “going beyond what?”