It is notoriously difficult to settle ontological issues. Part of the challenge consists in formulating, without begging any questions, what needs to be established. What are the things that exist: objects, properties, structures? Part of the challenge also consists in determining, in a non-question-begging way, what it takes to settle the relevant issues: How are such problems supposed to be decided? On the basis of arguments based on theoretical virtues, indispensability considerations, explanatory power?To formulate an ontological issue involves understanding the presuppositions required to express the problem and the sorts of allowable answers to the corresponding questions. After all, certain problems cannot be posed unless certain presuppositions are in place: "Are there numbers?" cannot be answered unless some conception of numbers is specified. Whether the conception is correct or not is often related to the way in which the problem is conceived, and different conceptions yield different problems, given that they raise different questions about what there is. To ask whether there are numbers understood as certain properties is not to ask whether there are numbers characterized as certain sets. One is then concerned with whether different things, in accordance with the corresponding conceptions, exist or not.

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