You’re comparing the soundness of the second argument with the validity of the first. Yes, Euclid and lots of mathematicians have proved that “argument’s conclusion completely follows from euclid’s axioms” but that just means the argument is valid. Similarly, the second argument’s conclusion follows from its premises.
The first premise of the first argument is an assumption. I have no idea how one would show that to be true. E is described by Euclid’s axioms because we’ve decided thats a helpful way to describe it. Usually, the first two premises of the second argument are taken to be assumptions also but we can come up with very good empirical reasons for believing them to be true if we have to. I don’t really think either argument is more sound except that question the truth of the first premise of the first argument is probably a category error.
In any case 13 year-old atheists usually screw up the arguments. Do you think a 13 year-old atheist would win a debate with say Alvin Plantinga?
You’re comparing the soundness of the second argument with the validity of the first. Yes, Euclid and lots of mathematicians have proved that “argument’s conclusion completely follows from euclid’s axioms” but that just means the argument is valid. Similarly, the second argument’s conclusion follows from its premises.
The first premise of the first argument is an assumption. I have no idea how one would show that to be true. E is described by Euclid’s axioms because we’ve decided thats a helpful way to describe it. Usually, the first two premises of the second argument are taken to be assumptions also but we can come up with very good empirical reasons for believing them to be true if we have to. I don’t really think either argument is more sound except that question the truth of the first premise of the first argument is probably a category error.
In any case 13 year-old atheists usually screw up the arguments. Do you think a 13 year-old atheist would win a debate with say Alvin Plantinga?