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. Today we have the second half of a Q&A with Shenefelt and White, who both teach Great Books at NYU’s Liberal Studies Program (read the first half here). In today’s half, Shenefelt and White explain their claim that, throughout history, the development of logic has reflected larger social changes happening in the world. And be sure to check out the book’s website!
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.