If you wish to be formal, it’s “Dr”. If you prefer informality that’s fine.
Take, for example, mathematical facts. They just “are” if you want. But what uses can you assert for mathematical truths that are not accessible?
I can assert them as axioms and use them to generate new formal systems. Consider Euclid’s fifth, for example, which two millennia of geometers have failed to prove from smaller axiomatic systems; but which yields any number of theorems when taken as an axiom, or when either of its negations are so taken.
The mere fact that the mathematical truths are before they are accessible (Again, godel’s incompleteness theorem) says that mathematical truths exist, and therefore so do the parts that they are comprised of.
Again, I do not understand this usage of the word ‘exists’. You cannot prove Euclid’s fifth axiom, or at any rate nobody has succeeded in doing so. Is it true? But its negations yield equally fruitful formal systems. What then is the sense in which it exists? Do you just mean that you can write it down on paper? Then likewise the adventures of Frodo Baggins exist. Are we to take it that the competing facts “Exactly one parallel line through a point not on a line”, “Exactly zero lines”, and “An infinite number of lines” all exist at the same time? What does this mean?
And even that aside, I object even more strongly to saying that a god exists in this same undefined sense. From an axiom you can at least derive theorems; an axiom is part of a formal system. Of what formal system is your god a part?
If you wish to be formal, it’s “Dr”. If you prefer informality that’s fine.
I can assert them as axioms and use them to generate new formal systems. Consider Euclid’s fifth, for example, which two millennia of geometers have failed to prove from smaller axiomatic systems; but which yields any number of theorems when taken as an axiom, or when either of its negations are so taken.
Again, I do not understand this usage of the word ‘exists’. You cannot prove Euclid’s fifth axiom, or at any rate nobody has succeeded in doing so. Is it true? But its negations yield equally fruitful formal systems. What then is the sense in which it exists? Do you just mean that you can write it down on paper? Then likewise the adventures of Frodo Baggins exist. Are we to take it that the competing facts “Exactly one parallel line through a point not on a line”, “Exactly zero lines”, and “An infinite number of lines” all exist at the same time? What does this mean?
And even that aside, I object even more strongly to saying that a god exists in this same undefined sense. From an axiom you can at least derive theorems; an axiom is part of a formal system. Of what formal system is your god a part?