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Our aim is thus to present some novel forms of abstractionist mathematical pluralism which can be modeled on parallel ways of substantiating logical pluralism (also in connection with logical anti-exceptionalism). To do this, we start by discussing the Good Company Problem for neo-logicists recently raised by Paolo Mancosu (2016), concerning the existence of rival abstractive definitions of cardinal number which are nonetheless equally able to reconstruct Peano Arithmetic. We survey Mancosu\u2019s envisaged possible replies to this predicament, and suggest as a further path the adoption of some form of mathematical pluralism concerning abstraction principles. We then explore three possible ways of substantiating such pluralism\u2014<jats:italic>Conceptual Pluralism<\/jats:italic>,<jats:italic>Domain Pluralism<\/jats:italic>,<jats:italic>Pluralism about Criteria<\/jats:italic>\u2014showing how each of them can be related to analogous proposals in the philosophy of logic. We conclude by considering advantages, concerns, and theoretical ramifications for these varieties of mathematical pluralism.<\/jats:p>","DOI":"10.1017\/s1755020321000113","type":"journal-article","created":{"date-parts":[[2021,3,22]],"date-time":"2021-03-22T07:18:15Z","timestamp":1616397495000},"page":"268-297","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":4,"title":["FOR BETTER AND FOR WORSE. 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