Aristotle's distinction between potential and actual infinity, while influential, was rejected by Cantor and subsequent mathematicians as a contingent conceptual limitation, not a necessary truth.
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actual infinity(Contrasted with 'potential infinity'; generally rejected by intuitionists)
An infinity treated as a completed, existing totality rather than an ongoing process
necessary truth(Mill's empiricist reinterpretation of modal concepts)
A proposition whose denial seems inconceivable, explained by Mill not as a metaphysical fact but as a result of psychological association making the proposition deeply ingrained.
potential infinity(Contrasted with 'actual infinity'; intuitionists typically accept only potential infinities in the Aristotelian tradition)
An infinity understood as an ongoing, never-completed process of extension, as opposed to a completed totality