Inference versus consequence, an invited lecture at the LOGICA 1997 conference at Castle Liblice, was part of a series of articles for which I did research during a Stockholm sabbatical in the autumn of 1995. The article seems to have been fairly effective in getting its point across and addresses a topic highly germane to the Uppsala workshop. Owing to its appearance in the LOGICA Yearbook 1997, Filosofia Publishers, Prague, 1998, it has been rather inaccessible. Accordingly it is republished here with only bibliographical changes and an afterword.