If God is dead, then everything is permitted, worried Dostoevsky. Without a realm of moral facts independent of our minds, objective moral truth seemed impossible. Yet, argues Justin Clarke-Doane, moral anti-realism is perfectly compatible with objective moral truth. Conversely, if we insist on realism about mathematics – the idea that our mathematics tracks a reality outside of our minds – then we must give up on the idea that mathematical claims are objectively true. Realism and objectivity, far from always going together, seem here to be in tension.

Realism and objectivity