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Sep 14, 2019 at 14:16 comment added Frank Hubeny @avraham I think what you have in the first line is "I believe that P". If I added that then you would get by reiteration "I believe that P". I agree that I don't think the three propositions would entail "I believe that P" nor would the assumption "I believe that P" entail these three propositions. Also my first one included "I believe that P" because I assumed that was the antecedent of all of these propositions. I am not sure what it is the argument is trying to show so I offered a paraphrase of what I thought it meant.
Sep 14, 2019 at 13:44 comment added avraham Your set of propositions doesn't entail that I believe anything because all of its propositions have "if I believe that P" at their start and it could be that for any P I don't believe that P. I'm going to assume that in proposition number 1 you meant to write: "I believe that I exist.". Even then your set of propositions doesn't entail that I don't believe that cats exist, whereas my set of proposition entails that I don't believe that cats exist (Subtitute P by "cats exist" in the contrapositive of my first proposition.)
Sep 13, 2019 at 20:16 history answered Frank Hubeny CC BY-SA 4.0