Different positions in the [[philosophy of mathematics]] have different attitudes towards infinity. At one extreme, Platonists and formalists generally have no philosophical objection to any form of infinity than can be defined. At the other extreme, finitists and ultrafinitists deny the existence of infinity; to them, only finite quantities, and finite objects, actually exist. In the middle, many constructivists and intuitionists adopt a position of countablism - an acceptance of the existence of countable sets, but denying that uncountable sets exist. | Different positions in the [[philosophy of mathematics]] have different attitudes towards infinity. At one extreme, Platonists and formalists generally have no philosophical objection to any form of infinity than can be defined. At the other extreme, finitists and ultrafinitists deny the existence of infinity; to them, only finite quantities, and finite objects, actually exist. In the middle, many constructivists and intuitionists adopt a position of countablism - an acceptance of the existence of countable sets, but denying that uncountable sets exist. |