If A, Then B

If A, Then B: How the World Discovered Logic

Copyright Date: 2013
Pages: 352
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    If A, Then B
    Book Description:

    While logical principles seem timeless, placeless, and eternal, their discovery is a story of personal accidents, political tragedies, and broad social change. If A, Then B begins with logic's emergence twenty-three centuries ago and tracks its expansion as a discipline ever since. It explores where our sense of logic comes from and what it really is a sense of. It also explains what drove human beings to start studying logic in the first place.

    Logic is more than the work of logicians alone. Its discoveries have survived only because logicians have also been able to find a willing audience, and audiences are a consequence of social forces affecting large numbers of people, quite apart from individual will. This study therefore treats politics, economics, technology, and geography as fundamental factors in generating an audience for logic -- grounding the discipline's abstract principles in a compelling material narrative. The authors explain the turbulent times of the enigmatic Aristotle, the ancient Stoic Chrysippus, the medieval theologian Peter Abelard, and the modern thinkers René Descartes, David Hume, Jeremy Bentham, George Boole, Augustus De Morgan, John Stuart Mill, Gottlob Frege, Bertrand Russell, and Alan Turing. Examining a variety of mysteries, such as why so many branches of logic (syllogistic, Stoic, inductive, and symbolic) have arisen only in particular places and periods, If A, Then B is the first book to situate the history of logic within the movements of a larger social world.

    eISBN: 978-0-231-53519-9
    Subjects: Philosophy

Table of Contents

  1. Front Matter
    (pp. I-VI)
  2. Table of Contents
    (pp. VII-X)
    (pp. XI-XVI)
    (pp. 1-18)

    WE LIVE in a world of constant change: armies collide, empires decline, sometimes whole civilizations slide into oblivion. Does anything last forever? The Apostle Paul says three things last (faith, hope, and love), but we would suggest a fourth constant in our lives: the laws of logic.

    We all have a sense of logic; it shapes us every day. Yet its nature is deeply mysterious. Logic isn’t like language, varying from culture to culture. Logic is like arithmetic—tricky yet objectively true. Just as the number seven has always been prime to every culture that has ever defined prime numbers,...

    (pp. 19-32)

    MODERN LOGIC is, in many ways, an elaboration of ancient Greek logic, but Greek logic depended ultimately on an extraordinary landscape—a landscape of narrow valleys and rugged mountains surrounded by an expansive sea.

    Specifically, Greek logic was an indirect consequence of two geographical accidents (and we shall be talking about the social effect of these accidents for some time). First, the mountains of Greece, along with the many small islands of the Aegean, separated the classical Greeks into hundreds of politically independent communities. Second, the water nevertheless tied these communities by an easy method of transportation: seafaring. These two...

  6. 2 ARISTOTLE: Greatest of the Greek Logicians
    (pp. 33-48)

    THE STYLE of Aristotle’s treatises is so clinical and detached that it is easy to forget how close he was to the relentless violence of his time. In fact, Aristotle was intimately connected to one of the Mediterranean world’s most violent political machines: the regime of the kings of Macedon. His father had been court physician to Philip II’s father,¹ but Aristotle was packed off at around the age of seventeen to the turbulent city of Athens, where he entered the school founded by Plato, the Academy. The Academy must have seemed a tranquil oasis amid the perils of the...

  7. 3 ARISTOTLEʹS SYSTEM: The Logic of Classification
    (pp. 49-72)

    THE ATHENIAN Assembly often disappointed the classical Greeks, but geometry deeply impressed them. Euclid’s Elements was composed about a generation after Aristotle, but geometry handbooks were already in circulation by the time Aristotle taught. What most impressed the Greeks about geometry was its certainty and finality. Unlike the vagaries of politics, which often tempt us with a bad argument or force us to rely ultimately on an intelligent guess, the geometry of the ancients seemed to offer conclusive proof. Once the definitions, postulates, and axioms were laid out, the theorems appeared to follow as a matter of logical necessity. It...

  8. 4 CHRYSIPPUS AND THE STOICS: A World of Interlocking Structures
    (pp. 73-98)

    WE LIVE our lives across space and time, but we can extend our logic across space and time too. One way to see how we can do this is to think for a moment about geometry and arithmetic.

    When we look at a geometrical figure, we obviously think about space, but the figure we are looking at, if printed on a page, is essentially timeless—it is static and unchanging. When we carry out an operation in arithmetic, on the other hand, we typically think of a “before” and an “after.” And our use of the operation represents a change....

  9. 5 LOGIC VERSUS ANTI-LOGIC: The Laws of Contradiction and Excluded Middle
    (pp. 99-122)

    WE LIVE in an age that is prone to relativism, but so did the classical Greeks. Truth and falsity became matters of deep perplexity to them as they began to encounter other cultures through trade. As commerce accelerated and linked ever larger parts of the Mediterranean world together, the more sophisticated of the Greeks soon realized that what one society took to be true, another often took to be false. Many began to wonder, who can know for sure what is true—and what does “truth” even mean? As a result, alternative theories of truth began to proliferate in the...

    (pp. 123-156)

    FEW THINGS seem less logical than war, and yet war can have profound effects on logic. Among the most profound of all such effects came during Europe’s wars of religion, which lasted from 1524 to 1648 and which gave the world a grand new variety of fanatical systems of belief. What the wars showed above all was that fanatics can be logical, at least if you grant them their premises. They, too, can validly infer one proposition from another; they can often supply premises that, if true, would prove their conclusions.

    This quality is typical of fanatics. Fanatics of the...

  11. 7 WILL THE FUTURE RESEMBLE THE PAST? Inductive Logic and Scientific Method
    (pp. 157-184)

    THE SEVENTEENTH century was an age of turmoil and blood, but it was also a time of rising trade, growing cities, insurgent middle classes—and tremendous scientific advance.

    The period opened with the extraordinary assertions of the priest Giordano Bruno, who said stars were suns and the universe was infinite; he was burned at the stake by the Roman Inquisition in 1600.¹ By 1609, Johannes Kepler in Germany had determined that the planets traveled around the sun in elliptical orbits. Kepler escaped the violence of his time, but his mother was imprisoned for thirteen months on a charge of witchcraft, and...

    (pp. 185-204)

    PLATO REMARKED that arguments, like men, are often pretenders.¹ Shoddy reasoning can deceive us just as people do. The classical Greeks made a special point of studying the shoddy reasoning that emerged from the simple democracies of their time; they wanted to know how large numbers of fellow citizens were being bamboozled and hoodwinked. Likewise, in modern times, the great stimulus to the study of poor reasoning has been the growth of representative democracy and the escalating force of public opinion. From the late eighteenth century onward, public opinion has increasingly influenced lawmaking. The result has been greater attention to...

    (pp. 205-234)

    THE INDUSTRIAL Revolution, beginning in the late eighteenth and early nineteenth centuries, has given the world new conveniences, factories, and cities—and also a new kind of logic. For good or ill, the visible effects of industrialism are now everywhere around us, but the abstract effects of industrialism are around us too. One of the most profound of these abstract effects is symbolic logic, which is a consequence of an age of machinery. Symbolic logic emerged from a nineteenth-century world of mass production and large mechanical operations, and in the twentieth and twenty-first centuries it has given rise, in turn,...

  14. 10 FAITH AND THE LIMITS OF LOGIC: The Last Unanswered Question
    (pp. 235-250)

    MANY MEDIEVAL thinkers found logic useful and edifying, but others found it distressing because its consequences seemed to challenge their faith. And for a time, the greatest of all such logical challenges came from Peter Abelard, who was young, shrewd, frequently arrogant, and deeply threatening to religious conservatives in twelfth-century France.

    Abelard applied himself to many philosophical controversies, especially to what philosophers call the problem of universals, but he always styled himself first and foremost a “dialectician,” which was the medieval term for logician.¹ And the basic problem for Abelard and his followers was that they were being asked by...

    (pp. 251-272)
  16. NOTES
    (pp. 273-320)
    (pp. 321-326)
  18. INDEX
    (pp. 327-334)