Traditional vs symbolic logic: homeschoolers need them BOTH

When we first started homeschooling our daughter, our affinity toward classical education programs was clear. Choosing a curriculum, however, was less straightforward.

The first curriculum provider we chose to work with was Memoria Press. Memoria Press is based out of Louisville, Kentucky, and operates classical schools out of local churches around the country. We ended up dropping it in the middle of first grade, and I mostly regard purchasing their materials as an expensive mistake.

Memoria Press’ idea of teaching grammar is to have young children write out the rules of grammar over and over and over again. Then they get to recite them. It is the same way with Latin, though at least with their early books children can learn the Latin Mass. It is a brilliant way to make your child hate doing school work to the point of tears.

But the worst aspect of their curriculum was that their math and science education was virtually non-existent. In fact, I would say their math curriculum is actually below the standards found in public schools. That’s kind of difficult to achieve.

This is a problem that I have noticed with a lot of classical and Charlotte Mason homeschoolers, however. They love teaching literature, poetry, and history. They hate teaching math and higher levels of science. Thus, most of them ignore math and long for the days when they can read The Screwtape Letters as a family. That’s no way to prepare your child to thrive in a thoroughly modern world.

At any rate, I still receive Memoria Press’ catalogs and find great humor in reading the articles they publish. The latest has an article on teaching logic that I feel compelled to share with readers here.

In Logic Is Not Math, Martin Cothran offers a polemic suggesting logic is a “language art” unrelated to the field of mathematics. It torments him, he confesses,. that so many publishers include logic materials under their math section. He blames those dastardly logical positivists for this unfortunate development. According to Cothran, symbolic logic did not exist until the early 20th century, when it was invented by Bertrand Russell and Alfred North Whitehead.

As someone who studied philosophy in both my undergraduate and graduate years and aced both traditional and advanced symbolic logic, this article had me rolling. It reinforced for me that we made a good decision about what curriculum to use for our daughter. I cannot intellectually process someone claiming that mathematical logic is of no use for children, except if you really, really, really suck at every STEM field and want an excuse for why you are not prepared to provide such an education.

From Cothran’s piece:

The question I want to ask and answer here is this: If logic is not math, then what is it? The answer is that logic is a language art. It is the study of right reasoning. I cannot stress this point strongly enough. For classical educators, this point is absolutely crucial because it will determine the very makeup of the curriculum.

In the old listing of the liberal arts, there were two basic classes of subjects: the three language arts (the trivium) and the four math arts (the quadrivium). Logic was always considered to be the second of the language subjects, after grammar and before rhetoric.

Grammar is the prerequisite for logic, since the ability to argue and reason rightly assumes the ability to communicate competently. And logic is the prerequisite for rhetoric, since logic is one of the three persuasive appeals: to the will (ethos—the appeal to the speaker’s character), to the imagination (pathos—the appeal to the audience’s emotions), and to the intellect (logos—the appeal to truth).

In fact, modern symbolic logic is the creation of modern philosophers (such as Bertrand Russell) and didn’t even exist until the turn of the twentieth century. Russell and Alfred North Whitehead wrote a book called Principia Mathematica that attempted to create a logical calculus that could be used to solve scientific problems. To this was added “truth tables,” a procedure that purported to be able to resolve any meaningful statement into a set of symbols and determine its truth value.

This was at a time when philosophers in the English world were experiencing science envy. They wanted their discipline to have the same objectivity and accuracy as the hard sciences. For these people Principia Mathematica became a sort of totem, and for many years it was required reading for English and American philosophy students. This was, of course, a daunting task, since most students were not mathematically sophisticated (or patient) enough to even understand the book, with its complex technical formulas and turgid explanations.

It helped give rise to the school of philosophy known as “logical positivism,” which claimed that the only meaningful statements were statements which could be scientifically verified, a belief that persisted into the late twentieth century. But the close connection between modern logic and philosophical positivism has turned into something of a curse given the steep fall of positivism since the late twentieth century.

Logical positivism was in one sense a victim of its own criterion. Its adherents believed that there were only two kinds of meaningful statements: logical statements that were true by definition (the ones we see in modern logic) and factual statements that could be empirically verified. Statements that were neither logical nor factual (like the statement “God exists,” which is neither true by definition nor empirically verifiable) were dismissed as meaningless.

But the central criterion of logical positivism does not meet its own criterion. The statement “There were only two kinds of meaningful statements: logical statements and factual statements” is neither a logical nor a factual statement, and is therefore meaningless.

As these and other issues arose inside and outside the movement, confidence in the movement began to erode, and, along with it, the original basis for modern logic.

What a bunch of poppycock.

Symbolic logic is not dead. In fact, it is thriving. Anyone who has been well trained in symbolic logic can easily learn any programming language they want. It is the single best preparation there is for landing a gig in the technology industry and breaking into the top 1% of earners in this country. The operating system of your computer, the apps you use on your phone, all of it, are constructed using the principles of symbolic logic. Do you think these operations work because the system is an accurate way of describing what is true and consistent?

Symbolic logic has not been some strange form of entertainment in the modern world. It physically built the modern world. It is the functional expression of intelligence.

It’s also not factually accurate to suggest that mathematical logic was “invented” by Brits in the 20th century. Elaborate systems of logic emerged across the millennia in the Far East, Greece, and in the Islamic world. It was the latter that gave the world mathematical logic, although the Greeks did use predicate logic to some extent in their work. It’s kind of hard to argue that symbolic logic was foreign to them. The Greeks loved the idea of proof.

It hardly took until the 20th century for mathematical logic to reach Europe, either. Leibniz, Lambert, Boole, De Morgan, Peacock, Peirce, and Frege all predated Russell and Whitehead.

Studying logic involves a lot more than merely knowing what ad hominem means. Thinking logically is not equivalent to being persuasive. It is the structural ordering and manipulation of ideas. It involves being able to test and prove concepts.

I think it is fine to suggest that children should study traditional logic during their K-12 years and save symbolic logic for college if their parent is not willing or able to teach it. But that’s not ideal. Teaching symbolic logic and math together is ideal. Beyond that, symbolic logic will likely improve your child’s ordinary quantitative reasoning skills. It’s certainly an odd prejudice to suggest that symbolic logic should be ignored because we are past its alleged decline and fall.

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