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 they constitute the basic points of departure for disciplined speculation.
Philosophy is held together by its questions rather than by its answers. The basic philosophical questions come from troubles within our ordinary conceptual scheme. These paradoxes bind generations together with common problems and an accumulating reservoir of responses.
Philosophy is generally presented in terms of its issues or in terms of its history. A study of the history of paradoxes provides an opportunity to practice both approaches simultaneously.
This book is guided by an anthropological hypothesis: paradoxes developed from the riddles of Greek folklore (as did the oracles of Delphi, Christian catechisms, and the game of charades). Accordingly, I begin classically with the Greek philosophers. They refined informal verbal dueling into “dialectic,” the procedure best known through Plato’s dialogues. The efforts of the Greeks were improved in turn, yielding contemporary logic and dialectical conceptions of history and science.
Paradoxes are questions (or in some cases, pseudoquestions) that suspend us between too many good answers. When an amoeba divides in two, does it go out of existence? On the one hand, organisms can survive the loss of half of their bodies. The only problem with the mother amoeba is that she has been too successful; instead of losing half her body as a dead tissue, she has created a second 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 question is kept alive by the tug of war between evenly matched contestants. The Greeks were intrigued by surprising, enduring oppositions such as these.
Common sense may seem like a seamless, timeless whole. But it really resembles the earth’s surface; a jigsaw puzzle of giant plates that slowly collide and rub against each other. The stability of terra firma is the result of great forces and counterforces. The equilibrium is imperfect; there is constant underlying tension and, occasionally, sudden slippage. Paradoxes mark fault lines in our common-sense world.
Do these fissures reach into reason itself? Many philosophers urge us to follow the argument wherever it leads; in the case of Socrates, even to death. But what do we do when compelling arguments lead us in conflicting directions?
One radical response, pioneered by Heraclitus, is to accept the reality of contradictions. He thinks the paradoxes are out there. This line of thought has been extended by 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 as a single, unified whole. Zeno’s paradoxes were intended to reinforce Parmenides’s conclusion by extracting absurdities from common sense.
Most philosophers are moderates who try to reconcile perception with reason. Democritus’s compromise was a changing universe of complex objects built up from unchanging, indivisible atoms moving about in the void. Rationalists pitch the negotiation in reason’s favor. 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 our 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 setting. Antinomies, paralogisms, and sophisms are stood before the reader like draftees at a mass medical screening. Much has been learned by analytical methods that ignore the bigger picture. But why always ignore the bigger picture?
In any case, I am interested in the developmental and antiquarian aspects of paradoxes. Consequently, my approach is more leisurely. Although I have my own theory of paradoxes, my general intent is to have the paradoxes enter at their own initiative and in their original order.
The deepest paradoxes are extroverts, naturally good at introducing themselves. These challenges to compulsory, universal beliefs are self-illuminating; they stimulate us to draw distinctions and formulate hypotheses that bear on the issue of how we ought to react to paradoxes. Is common sense ever mistaken? Are paradoxes symptoms of the frailties of human reason? Do they point to ineffable truths? When is it rational to ignore arguments?
When Aristotle’s nephew Callisthenes volunteered to record the expedition of Alexander the Great, he had to follow the impetuous Alexander into situations that invited miscalculation. The discoverers of paradoxes expose their historians to a parallel danger. From what appears to be a safe distance, I see the inquirer crane his head for a better look, eventually placing one foot on one solid-looking principle and the other foot on a second principle that is actually incompatible with the first. In my eagerness to document his insecure footing, I risk misstep myself. In the following pages, I take this chance over and over, across two millennia. Sooner or later, I must share the fate of those I chronicle. I apologize for these errors but am grateful to those who led me up to a position to make them.
I also have more specific acknowledgments. I thank the editor of Mind for permission to reprint, in chapter one, a portion of “The Egg Came Before the Chicken,” Mind 101/403 (July 1992): 541-42. I am grateful to V. Alan White for permission to quote “Antinomy” from his website devoted to philosophy songs at www.manitowoc.uwc.edu/staff/awhite/phisong.htm. Finally, I thank colleagues and my students at Dartmouth College for their comments and suggestions on earlier drafts of this book.