ionism is the view that Fregean abstraction principles underlie our knowledge of the existence of mathematical objects. It is often assumed that the abstractionist proof for the existence of such objects requires ‘negative free logic’ in which all atomic sentences with empty terms are false. I argue that while negative free logic is not indispensably needed for the proof of abstract existence, there is a motivation for it—along broadly Fregean lines. The standard motivation for negative semantics rests on the explanation of truth in terms of reference. This line of reasoning, however, is not available in a context in which the reference of abstract terms must be proved, and not presupposed. I reverse the direction of explanation, thereby offering a novel motivation, Truth Priority, for the use of negative semantics. Some of the implications of Truth Priority for the abstractionist conception of ontology and reference will also be explored.

中文翻译：

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抽象、真理和自由逻辑


离子主义认为弗雷格抽象原理是我们对数学对象存在的认识的基础。人们通常认为，此类对象存在的抽象主义证明需要“否定自由逻辑”，其中所有带有空项的原子句子都是假的。我认为，虽然否定自由逻辑对于证明抽象存在来说并不是必不可少的，但它是有一个动机的——大致沿着弗雷格的路线。否定语义的标准动机依赖于根据指称对真理的解释。然而，这种推理方式在抽象术语的指称必须被证明而不是预设的上下文中不可用。我扭转了解释的方向，从而为否定语义的使用提供了一个新颖的动机，即真理优先。还将探讨真理优先对本体论和指称的抽象主义概念的一些影响。