Abstract

AbstractIn the philosophy of science, Weak Structural Realism (WSR) offers a promising priority-based strategy to avoid the main objection to eliminative Ontic Structural Realism (OSR). On that view, quantum particles depend for their identity on quantum entanglement structures but are defined as not entirely structural thin physical objects. A similar approach can be applied to mathematical structuralism, where Weak Mathematical Structuralism (WMS) provides a novel, more moderate interpretation of ante rem structuralism. WMS is articulated in terms of grounding: numbers are grounded for their identity in the abstract structure they belong to. However, they are not completely reduced to their structural features and are re-conceptualized as thin mathematical objects, endowed with both structural and non-structural properties. The introduction of such objects in the structural ontology allows to escape some typical objections to ante rem structuralism without abandoning the priority of structures.KeywordsScientific structuralism Mathematical structuralismOntological dependenceMetaphysical groundingThin objectsIndividuation

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