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 them? 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.