[...]... senses Paradoxes have both shaped and been shaped by the classic debate between rationalists and empiricists A faithful portrayal of paradoxes situates them in their natural intellectual environments Without this background, they take on the appearance of circus animals I concede that paradoxes sometimes ought to be studied in isolation Logicians and mathematicians routinely assemble paradoxes in a clinical... by asserting, “Anaximander was the first Greek to map the stars.” In a fill-in-theblank question, such as “What is the ratio of the earth’s height to its diameter?” you are presented with an infinite range of 6 A B RI E F H I S TOR Y O F TH E P A RAD OX values Anaximander chose The ratio of the earth’s height to its diameter is 1:3.” (Anaximander thought that the earth had the shape of a dog’s water... for instance, defines a paradox as a statement that conflicts with a conceptual truth His example is the Stoic doctrine that those and only those are free who know that they are not free Most philosophers agree arguments play an essential role in paradox R M Sainsbury identifies the paradox with the unacceptable conclusion of an argument that has acceptable premises and an acceptable inference pattern... no idea of what the answer is Neither did the creator of the Mad Hatter, the logician Lewis Carroll The poser of a paradox need not drape its meaning behind ambiguities and metaphor He can afford to be open because the riddle works by overburdening the audience with too many good answers Consider the folk paradox, “Which came first, the chicken or the egg?” The egg answer is backed by an apparently... Like has gone to like Similarly, the earth arose from watery beginnings through a process of sedimentation As the water receded, land was exposed Anaximander drew the first world map of these land masses Herodotus describes the map in such detail that scholars have redrawn it Anaximander invokes balance to explain why the earth does not fall endlessly into space The nature of this equilibrium has received... destiny and predicted that Polycrates would soon fall into grave misfortune And indeed, when Polycrates sailed to Magnesia at the invitation of the Persian governor, he was brutally murdered A NA X I MA N D E R A N D TH E RI D D LE OF ORI G IN 15 Did Amasis commit the gambler’s fallacy? This is the mistake of assuming that the law of averages works by compensation rather than by swamping A fair coin... to accept the reality of contradictions He thinks the paradoxes are out there This line of thought has been extended by P RE F A CE xiii Hegel, Marx, and nowadays, by the dialethic logicians of Australia At the other extreme are those who trace our inconsistency to reliance on our senses Parmenides dismisses the appearance of there being many things that are changing and moving He conceived of reality... fascinated by antagonistic struggle They admired questions that are sustained by a balance of power between rival answers Their playwrights became adept at smelting the ore of paradoxes The paradox lover delights in an unexpectedly even match—especially when his audience can foretell the rightful outcome Children know the answers to Zeno’s paradoxes of motion: Can you walk out of a room? Can an arrow travel... They trace paradoxes to shortages of a priori insights With the rise of science, empiricists have driven a hard bargain in the opposite direction They trace paradoxes to a glut of misinformation If we could cleanse ourselves of superstition and subtler contaminants, we would gain the patience needed to answer what riddles can be answered and the maturity to admit ignorance when at the outer range of. .. healthy amoeba On the other hand, amoeba reproduction seems like suicide because there is nothing to survive as It would be arbitrary to identify the mother amoeba with just one of her daughters And to say that the mother amoeba continues as the pair of daughters conflicts with the idea that organisms are unified individuals Typically, the case for one solution to a paradox looks compelling in isolation The . class="bi x0 y0 w0 h1" alt="" A BRIEF HISTORY of the Paradox This page intentionally left blank A BRIEF HISTORY of the Paradox PHILOSOPHY AND THE L ABYRINTHS OF THE MIND Roy Sorensen 2003 Oxford. intentionally left blank Preface Mathematicians characterize prime numbers as their atoms because all numbers can be analyzed as products of the primes. I regard paradoxes as the atoms of philosophy because. the mother amoeba with just one of her daughters. And to say that the mother amoeba continues as the pair of daughters conflicts with the idea that organ- isms are unified individuals. Typically,