When you say that P({} and something) = P(something), you suppose the hypothesis (in addition to using several nontrivial consequences of coherence that So8res mentioned, like P mapping equivalent statements to the same thing).
More importantly, “{} and something” isn’t a syntactically correct sentence. I don’t think most authors consider the empty sentence syntactically correct either. (Marker, the textbook I used, doesn’t.)
When you say that P({} and something) = P(something), you suppose the hypothesis (in addition to using several nontrivial consequences of coherence that So8res mentioned, like P mapping equivalent statements to the same thing).
More importantly, “{} and something” isn’t a syntactically correct sentence. I don’t think most authors consider the empty sentence syntactically correct either. (Marker, the textbook I used, doesn’t.)
Whoops, you’re right.