Logic breakthrough: to introduce a universal, begin a universal proof as soon as the constant that you wish to replace with a universal variable appears in the main proof and do not within that universal proof permit any existential exploitation that replaces a variable with a constant that appears in the universal being proved. This simultaneously 1) grants access to the content of existential-universal sentences (and the like) without losing their strength and 2) forbids inappropriately strengthening universal-existential sentences and similar pitfalls. This replaces the rule that universal introductions simply cannot be done on sentences with constant(s) originally from existential exploitation(s), which gives only 2 and not 1. A result of many hours consideration and a great mental relief.
Posted on: Sun, 26 Oct 2014 17:27:21 +0000