| Summary: | In this text, an analysis of the argument that Peirce formulates against nominalism in his New Elements of Mathematics is presented. In order to accomplish this task, a brief historical review of the problem will be carried out to locate Peirce's proposal. In this way, we can evaluate if there is a novelty or not in his proposal with respect to the previous ones. Later, we will present the argument within the Peircean theory of Firstness, Secondness and Thirdness at metaphysical, semantic and logical levels. Finally, from elements of analytic metaonthology, we will evaluate whether this argument is enough to solve the problem or if, rather, the debate between nominalists and realists about the existence of universals is "purely verbal" and, therefore, the discussion in which Peirce is framed becomes infertile. It will be concluded that Peirce does manage to overcome the discussion. However, for this it will be necessary to specify the meaning of the concepts like 'existence' and 'reality'.
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