Sure, but it remains your invention, logical or not. And thus a diversion.
It's not a diversion. It's an explanation. I'll try again. In argumentation (i.e., real world application of logic in debate), if your "opponent" claims X, in order to demonstrate her or him to be wrong, it suffices to show either ~X, or (if X was a conclusion reached using a series a series of propositions and inference rules as in proof or derivation such as the one the Strenger quoted, it suffices to show that any step in the deductive process was not justified). In other words, it suffices to show that the argument is invalid. If an argument is valid, it can still be false, because logical validity depends only on structure: an argument is logically valid if the conclusion "follows from" the premises (more formally, if the premises
were true, then the conclusion
must be true). In order to show that an argument is correct (sound), it must be valid and the premises must be true.
Hence this is a valid argument:
The king of Spain rules the Moon
I am the King of Spain
Conclusion: I rule the Moon
It is completely false, because the premises are false, but it is valid.
This is the argument in question:
"(1) If God exists, then he is nonphysical.
(2) If God exists, then he is a person (or a personal being).
(3) A person (or personal being) needs to be physical.
(4) Hence, it is impossible for God to exist (from 1-3)"
Now, from a strictly logical point of view, this entire proof is an assumption. Every time you see "if" (or ⊃, or →), it means "assuming [something] to be true, then...
Let Gx= "x is a god", Nx="x is nonphysical" (and there for ~Nx means "x is physical" or "x is not nonphysical"), Px="x is a person or personal being" (because of the parenthesis, I am taking as equivalent person and personal being; otherwise the argument is ambiguous as to what it asserts because the operator v ("or") in logic is always inclusive)
Then we have
(1) ∀x(Gx→~Nx) | Assumption (translation: "for all x, if x is a god, then x is nonphysical")
(2) ∀x(Gx→Px) | Assumption (translation: "for all x, if x is a god than x is a person")
(3) ~∃x(Px & Nx) | Assumption (translation: "there exists no x s.t. x is a person and x is nonphysical")
(4) ∀x(Px→ ~Nx)| Equivalent to (3) (translation: "for all x, if x is a person then x is physical")
(5) ~∃x(Gx) |From (1), (2), & (3) or (4) by assumption and
reductio/contradiction
I threw in an extra line to show you an example of logical equivalence. Also, I have opted somewhat for clarity over rigor. Normally, I'd be working within a specific formal language/system such that I would have to ensure every line that wasn't assumed was properly justified according to that system. Because logic must be completely unambiguous, bracketing is not just essential for knowing which operator (such as "&" or "→") operates on what (more technically, operates on which well-formed formula or WFF, pronounced "woof"), but also for quantification scope. This means that in order to derive (5) I'd have to do things like use dummy variables for elimination and other things that you can learn about in the free sources I provided.
The point is that logically this argument rests entirely upon assumptions. It is valid (or would be if expressed according to some predicate calculus system), but the following "proof" is just as valid:
(1) If I exist, God exists
(2) I exist
(3) God exists
Now we have to see if the argument is sound. This is no longer a matter of strictly formal logic, because that is entirely unambiguous (your computer can tell you if an argument is valid, an in fact it works because it is a physical instantiation of Boolean logic- the processor uses logic gates). And immediately we run into a flaw: the equivocation fallacy. There is nothing that says a personal god must be physical (nothing to justify this assumption). Note that the argument doesn't assume that there are no non-physical beings, but uses equivocation in order to go from "personal god" as understood in the theological sense to an interpretation of "personal" in terms of a person. Formally, it is asserting in (2) ∀x{(Gx→Px) but in (3) and (4) we really have P'x (i.e., the P stands for a different predicate). The argument is not sound. Therefore it is false.