In If A, Then B: How the World Discovered Logic, Michael Shenefelt and Heidi White track the emergence and expansion of logic as a field of study. The following is an interview with Shenefelt and White, who both teach Great Books at NYU's Liberal Studies Program. The two authors discuss the origins of logic, look at some of logic's many uses, and give a convincing case for why studying logic is a valuable thing to do. And be sure to check out the book's website!
Question: Why do you say logic comes out of politics?
Heidi White: Formal logic began as a reaction to political failure in ancient Athens in the fifth and fourth centuries B.C. Many Athenians blamed the city’s defeat in the long war with Sparta on tricky and deceptive reasoning in the Athenian Assembly; they believed demagogues had misled the voters into endorsing a disastrous military campaign. Sounds kind of familiar, doesn’t it? The philosopher Plato complained about this tricky and deceptive reasoning all the time. He was relentless in insisting on the difference between persuasion that relied on dubious reasons or a lack of evidence and persuasion that was well reasoned and well supported. And in the end, he came to the view that good government had to rely on genuine knowledge, and knowledge had to be based on sound argument. His student Aristotle then zeroed in on formal deductive logic as a crucial part of sound reasoning.
Q: So do you need to know something about ancient history to understand logic?
Michael Shenefelt: Not at all. Logic is something we all use every day. And the most common methods of reasoning are hardwired in us. They appear in all cultures. The only difference is that logicians study these methods instead of just using them. It’s like walking. Most people walk, but not everyone studies it.
Q: But if we all use logic anyway, why study it in the first place?
HW: Because you can get better at it. If you study common forms of argument, you learn to spot them faster—especially the deceptive ones. You can pinpoint a fallacious argument, and you know why it’s fallacious; you’ve seen it before. This is the lesson the Athenians had to learn the hard way. They didn’t spot the deceptive ones, and it cost them dearly.
Q: What about logic in ancient Indian and ancient China?
MS: Philosophers in both ancient India and China studied argument and debate, but in a different way. They studied argument as a mix of logic and rhetoric, and without a distinction between deduction (which is reasoning in which the conclusion follows necessarily from the premises) and induction (where the conclusion is merely probable). All the Greek thinkers before Aristotle also studied argument in this same way—as a mix of logic and rhetoric, and without a distinction between deduction and induction. What set Aristotle apart was that he saw the logical force of an argument as depending on an abstract structure, like “All As are Bs, and all Bs are Cs; therefore all As are Cs.” And then he began studying the structures themselves. It’s structures like these that run your computer—deductively valid inferences—but they also play a crucial role in sound reasoning.
HW: As we say, everyone uses these structures. But it’s not until you start studying how they work that you’re doing what professional logicians do.
Q: Why should political failure have encouraged this kind of study?
HW: All peoples draw a distinction between what they see as reasonable and what they see as unreasonable. But the Athenians had a more intense interest in the distinction when it was specifically applied to argumentation. This was because many of them believed that faulty arguments had undermined the state. The Athenian Assembly had ruled an empire, and when the Assembly made foolish decisions, it was often because of sophistical arguments—arguments that looked good, but weren’t really logical in the first place. Plato dwelled on this problem a lot, the problem of faulty argumentation. And a whole generation of his students heard him complain about it—including Aristotle, and some of the people who ultimately would have attended Aristotle’s lectures.
MS: We should also add here that the Athenians had voted to execute Plato’s friend and inspiration, Socrates. This, too, had the effect of causing Plato and his students to focus on public argumentation and to seek ways of distinguishing reasonable arguments from faulty ones. Even Socrates had been accused of arguing sophistically—an accusation that Plato regarded as both false and galling. The accusation was part of what got Socrates killed. So Plato and his students had plenty of reasons to investigate argumentation.
Q: So the Athenian Assembly was an important factor in the development of logic?
MS: Yes. And the Assembly was itself an effect of the geography of the region.
Q: How was the Assembly an effect of geography?
HW: The mountains and islands of Greece cut the classical Greeks into very small states. Yet the smoothness of the Mediterranean Sea supported a large sea trade. This caused their little states to fill up with many citizens who came from the commercial classes, and these commercial classes then took political control from the hereditary elites of the past.
MS: The only way they could govern themselves was by mass meetings, and this made public argumentation crucial. The Assembly was the meeting. Commercial people tend to be argumentative and litigious, and it was against this background that the historical Sophists emerged as teachers of public speaking. The trouble was that many of them taught you how to win the argument by any means necessary, fair or foul. And so you ended up with a lot of sophistical reasoning. Plato and Aristotle were reacting against this.
Q: Why didn’t ancient societies in other parts of the world have the equivalent of the Athenian Assembly?
HW: Because elsewhere the states were larger and the sea trade was less extensive. So the commercial classes were surrounded by a much larger population of peasants, ruled by hereditary warlords. That was the usual pattern throughout the ancient world. The Athenian Assembly and the other Greek assemblies of the time were the glaring exceptions. Unlike other states, they were ruled by mass meetings because this was where the commercial classes had finally taken over. Logic was ultimately a consequence of this larger social change.
Q: When you stress geography, you sound like Jared Diamond.
MS: Yes, but we think Diamond has pointed to the wrong mechanism. In his book Guns, Germs, and Steel, he invokes the geography of landmasses. He thinks what mattered in the ancient world was the ease of moving goods and people—and consequently inventions and discoveries—over land. This makes a lot of sense if you’re talking about the Stone Age, but from the Bronze Age onward, most goods and people, and diseases too, moved over water. This didn’t start to change until the invention of railroads in the 19th century. So what really mattered was the geography of waterways.
Q: Is this emphasis on waterways your own idea?
MS: No. It’s Adam Smith’s idea. Smith makes the same point in the first three chapters of his Wealth of Nations. He points out that urban civilizations in the ancient world almost always planted themselves along waterways. And this was just as true of the Aztecs—whose capital was laced with canals—as it was for the peoples of the Mediterranean. The Mediterranean is effectively the world’s largest lake. In ancient times, it was much easier to navigate the Mediterranean than the oceans. This made a huge difference for urban civilizations, and it also affected anything in intellectual history or the arts that came out of an urban environment. It affected sculpture, architecture, philosophy, and theater. And it affected logic.
Q: All your discussion of the historical roots of logic makes it sound like logic is all a consequence of the ancient world’s history.
Michael Shenefelt: It’s also a consequence of the modern world’s history. Consider the Industrial Revolution of the 19th and 20th centuries. That’s what finally generated the logic that runs your computer—symbolic logic. The first fully symbolic systems came from George Boole and Augustus De Morgan in England in 1847, just as the Industrial Revolution was in full swing. Both thinkers said explicitly that they were seeking a way to make reasoning “mechanical.” Industrialization showed a whole generation of thinkers the immense power of mechanical operations, especially in the manufacture of cloth, and some wanted to achieve a similar effect in reasoning. A similar impulse also led to the development of abstract algebra, and this so-called mechanical effect in algebra was much stressed by John Stuart Mill. Later in the century, when Germany industrialized, you see the eminent figures of Gottlob Frege, George Cantor, and Richard Dedekind—great names in logic and mathematics. And when the Fiat automobile company was manufacturing cars in Turin, Italy, Giuseppe Peano started working at the University of Turin; Peano’s notation still underlies a lot of symbolic logic. Industrialization and symbolic logic were intimately connected. And then there’s the case of the United States. When the United States industrialized in the wake of the Civil War, Charles Sanders Peirce worked out a symbolic logic of his own and pointed out that logic problems might be solved using electrical switches.
Q: So logic reflects a larger social world.
Heidi White: Yes. This is the story we try to tell in our book. We look first at the historical forces that led to logical discoveries and then we try to explain these discoveries with what you might call short logic lessons, mixed into the narrative, so you can see what the logicians of the time were doing. We also have an appendix that lists the most common logical fallacies, along with some advice on how to spot these fallacies and how to expose them.
Q: Are there other examples of this—of social forces at other times in history that led to logical discoveries?
HW: Many. Think of the wars of religion in the 16th and 17th centuries, when thousands of Protestants and Catholics murdered one another over whose version of Christianity was theologically correct. Each side claimed to know for sure that God was on its side, and in reaction many thinkers, like René Descartes, paid much more attention to the question of when a belief was well founded and when it wasn’t. Descartes realized that a fanatic can construct a logical argument too—except that the premises of the argument are not well founded in the first place. So Descartes insisted that our reasonable beliefs need reliable foundations. And he saw these foundations as the premises of logical reasoning. He also insisted that circular reasoning could never be rationally persuasive. Many fanatical arguments turn out to be circular.
Q: Logic’s history seems to be bound up with many kinds of history—political, economic, and social. But how does logic matter to those who aren’t historians?
HW: Today, logic is also a basic part of citizenship. It’s essential to democracy. In a democracy, we vote on the basis of public argumentation. Much of this argumentation takes place on television, or in newspapers, or on the internet. If the argumentation is then sophistical, we risk undermining justice, and we risk undermining the public good.
MS: Think for a moment of a political commentator on a cable news channel who never goes into the field, never interviews witnesses, and never studies crucial documents. Instead, think of him just sitting behind a big desk and attacking political opponents personally—what logicians call the “ad hominem.” Think of him exaggerating opposing opinions so they all look ridiculous from the start—the so-called straw man. These are the methods of sophistry. If you then have large numbers of viewers who never ask, “Is this argument well-founded?” or “Is that inference actually logical?” you’re encouraging voters to make foolish decisions. And you’re courting disaster. This is how democracies of the past have talked themselves into tragic mistakes.
Q: Has this problem increased with the rise of the cable news channels?
HW: The same basic methods were used in the Athenian Assembly, and in American history, they were also used by Joe McCarthy in the 1950s. In fact, they were such a large problem in 19th-century England that Jeremy Bentham wrote a whole book about rhetorical fraud in politics. It was called The Book of Fallacies. Logicians and journalists have been analyzing additional sophistries ever since. It’s a constant battle. The crucial point is that, in a democracy, the fate of your country ultimately depends on whether you’re really willing to fight this fight. We live in a world of change and chance, of storm and strife, and of right and wrong. These are the lessons of the past that can help us to be better citizens in the future.