Paradoxes

Ranging from the preface paradox which purports to show that we can rationally hold contradictory beliefs to the determinist paradox which proposes that we have no genuine choices in our lives, we explore those paradoxes which have cast doubt on some of our most fundamental metaphysical, logical and mathematical beliefs.
We begin in ancient Greece with Zeno’s arguments for the impossibility of motion. By arguing that motion is impossible regardless of whether we view space as infinitely or finitely divisible, we are left with the implausible conclusion that motion is an illusion. Moving to the 13th century we consider the paradox of the unliftable stone, which casts doubt on the possibility of an all-powerful entity, and finish our exploration of metaphysical paradoxes with the modern-day paradox of how to reconcile scientific determinism with our deep-seated belief that we make free choices in our lives.
Moving on to paradoxes that call into question some of our fundamental beliefs on knowledge and evidence, we examine Goodman’s ‘grue’ paradox which argues that, contrary to scientific practice, empirical evidence equally confirms an infinite number of hypotheses, and the preface paradox which casts doubt on the common assumption that it’s irrational to have contradictory beliefs.
Finally, we explore logical and mathematical paradoxes, concentrating on the Russell paradox which threatened the very foundations of set theory and mathematics, along with casting doubt on the reliability of mathematical intuition, and the liar paradox, the king of paradoxes, which has defied an agreed solution for over two thousand years.