Sommers' proof that something exists

SOMMERS' PROOF THAT SOMETHING EXISTSGEORGE ENGLEBRETSENIn the concluding remarks of [4] I mentioned that in [8] Sommers hadgiven a proof to the effect that necessarily something exists and that laterin [5] this proof was shown to be wrong in principle. Sommers' proof wentlike this:1. Something is possible.2. Whatever is not a categorially possible thing is not a possible thing.3. Suppose there were nothing (i.e., nothing exists).4. By definition D-things are categorially impossible if and only if nothingis D and nothing is D.5. For any D, nothing is D and nothing is D. (by 3)6. For any D, D-things are categorially impossible, (by 4 and 5)7. For any D, D-things are not possible things, (by 2 and 6)Since 7 is inconsistant with 1, we must reject 1 or 2 or 3 or 4. 1, 2, and 4seem certain. Thus we must reject 3. This gives us the negation of 3(Something exists). Q.E.D.Guerry attacked Sommers' proof by showing that 4 allows counter-examples and must be rejected rather than 3. What bothered Guerry about4 was that it allowed Sommers to "derive a necessity (the impossibility ofD-things) from a contingency (the nonexistence of D- and D-things)."Nevertheless, a simple reformulation of this definition (4) can be used torender the proof immune to Guerry's attack. The reformulation is simplywhat I think Sommers had actually intended by 4. However, this reformu-lated argument can be shown to be simply invalid requiring Sommers tofind a completely new argument for his purposes.Definition 4 is unclear because the phrases "nothing is D" and"nothing is D" are ambiguous. Sommers has failed to make a distinctionexplicit which he happens to hold (implicitly). The distinction to be made isthat which holds between spans and is predicable of. This distinction hasbeen reinforced in [l], [2], [3], and [6]. A term D spans a thing if and onlyif any sentence used to affirm D of that thing is category correct. Ofcourse, D and D will always span the same things. (See [7], pp. 329 andReceived August 19, 1972