Conventionalism about mathematics has much in common with two other views: fictionalism and the multiverse view (aka plenitudinous platonism). The three views may differ over the existence of mathematical objects, but they agree in rejecting a certain kind of objectivity claim about mathematics, advocating instead an extreme pluralism. The early parts of the paper will try to elucidate this anti-objectivist position, and question whether conventionalism really offers a third form of it distinct from fictionalism and the multiverse view. The paper then turns to anti-objectivism about logic, and suggests that here too conventionalism offers no distinct alternative, and that there are limits on the extent of pluralism/anti-objectivism. It also argues that these limits can't be used to argue for more extensive objectivity within mathematics, and also that they do allow for more limited pluralism within logic, e.g. as regards resolution of semantic and property-theoretic paradoxes.

中文翻译：

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关于数学和逻辑的约定主义

关于数学的传统主义与其他两种观点有很多共同点：虚构主义和多元宇宙观点（又名丰盛柏拉图主义）。这三种观点可能对数学对象的存在存在分歧，但他们一致拒绝某种关于数学的客观性主张，转而提倡极端的多元主义。本文的前半部分将试图阐明这种反客观主义的立场，并质疑约定主义是否真的提供了不同于虚构主义和多元宇宙观点的第三种形式。然后本文转向关于逻辑的反客观主义，并表明在这里约定主义也没有提供明显的替代方案，并且多元主义/反客观主义的程度也受到限制。它还认为这些限制不能用来论证数学中更广泛的客观性，而且它们确实允许逻辑中更有限的多元性，例如在语义和属性理论悖论的解决方面。