A thriving literature has developed over logical and mathematical pluralism – i.e. the views that several rival logical and mathematical theories can be equally correct. These have unfortunately grown separate; instead, they both could gain a great deal by a closer interaction. 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’s 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—Conceptual Pluralism, Domain Pluralism, Pluralism about Criteria—showing 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.

一个蓬勃发展的文学已经发展了逻辑和数学多元论——即几个相互竞争的逻辑和数学理论可以同样正确的观点。不幸的是，它们已经分开了；相反，他们都可以通过更密切的互动获益良多。因此，我们的目标是提出一些新形式的抽象主义数学多元论，它们可以模仿证实逻辑多元论的平行方式（也与逻辑反例外论相关）。为此，我们首先讨论 Paolo Mancosu（2016 年）最近为新逻辑学家提出的 Good Company Problem，该问题涉及基数的竞争性抽象定义的存在，但它们同样能够重构 Peano 算术。我们调查了 Mancosu 设想的对这一困境的可能答复，并建议采用某种形式的关于抽象原则的数学多元主义作为进一步的途径。然后，我们探索三种可能的方式来证实这种多元化——概念多元论、领域多元论、关于标准的多元论——展示了它们中的每一个如何与逻辑哲学中的类似建议相关联。我们通过考虑这些数学多元论的优点、关注点和理论分支来得出结论。