eprintid: 14044 rev_number: 6 eprint_status: archive userid: 5 dir: disk0/00/01/40/44 datestamp: 2016-12-01 10:50:06 lastmod: 2021-08-27 17:41:40 status_changed: 2016-12-01 10:50:06 type: book_section metadata_visibility: show item_issues_count: 1 creators_name: Hansson, B. title: Paradoxes in a Semantic Perspective ispublished: pub divisions: prog_sds abstract: Let us take Russell’s set of all sets that do not contain themselves as a paradigm of paradox. We assume that there is such a set, and if so, it has to be either a member of itself or not. But, as we know, either way leads to a contradiction. However, this is not the paradox. So far, the argument is just like a reductio ad absurdum proof, and the conclusion to draw is that our assumption was wrong, i.e. there is no such set. The paradox enters when we nevertheless insist that there has to be one — our intuitions about the existence of sets are so strong that we are not prepared to give them up even if they lead to a contradiction. And we cannot deny that they do — the logic of that part is impeccable. date: 1979 date_type: published publisher: Springer id_number: 10.1007/978-94-009-9825-4_19 full_text_status: none series: Synthese Library volume: 122 place_of_pub: Dordrecht, Nethrlands pagerange: 371-385 refereed: TRUE isbn: 978-94-009-9825-4 book_title: Essays on Mathematical and Philosophical Logic editors_name: Hintikka, J. editors_name: Niiniluoto, I. editors_name: Saarinen, E. coversheets_dirty: FALSE fp7_type: info:eu-repo/semantics/bookPart citation: Hansson, B. (1979). Paradoxes in a Semantic Perspective. In: Essays on Mathematical and Philosophical Logic. Eds. Hintikka, J., Niiniluoto, I., & Saarinen, E., pp. 371-385 Dordrecht, Nethrlands: Springer. ISBN 978-94-009-9825-4 10.1007/978-94-009-9825-4_19 .