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According to Platonists, entities such as numbers, sets, propositions and properties are abstract objects. But abstract objects lack causal powers and a location in space and time, so how we could ever come to know of the existence of such impotent and remote objects? In this text, Colin Cheyne presents a systematic and detailed account of this epistemological objection to the Platonist doctrine that abstract objects exist and can be known. Since mathematics has such a central role in the acquisition of scientific knowledge, he concentrates on mathematical Platonism. He also concentrates on our knowledge of what exists, and argues for a causal constraint on such existential knowledge. Finally, he exposes the weaknesses of recent attempts by Platonists to account for our supposed Platonic knowledge.