The central philosophical question about abstract objects is: Are there any? An affirmative answer – given by Platonists or Realists – draws support from the fact that while much of our talk and thought concerns concrete (roughly, spatiotemporally extended) objects, significant parts of it appear to be about objectswhich lie outside space and time, and are therefore incapable of figuring in causal relationships. The suggestion that there really are such further non-spatial, atemporal and acausal objects as numbers and sets often strikes Nominalist opponents as contrary to common sense. But precisely because our apparent talk and thought of abstracta encompasses much – including virtually the whole of mathematics – that seems indispensable to our best attempts to make scientific sense of the world, it cannot be simply dismissed as confused gibberish.

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