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.

Building a Homeschooling Science Curriculum

For classical homeschoolers, locating high-quality education materials in languages, history, and literature is easy. I have agonized over what history series to use for an academic year because there are so many excellent alternatives and I passionately want them all.

But for mathematics and science… not so much. I think there are several reasons for this: (1) Parents with liberal arts backgrounds tend to emphasize other subjects over math and science because that’s their comfort zone. (2) Traditional schools do not become deeply invested in science until students are in late middle school, or even high school, age. This means there is no economic incentive for publishers to produce high-quality content in these subjects for younger children. (3) People in STEM-oriented pursuits tend not to go into education. There’s a lot more money to be made working for a tech company or Wall Street than in writing textbooks.

(Though the latter would not be a bad idea for STEM companies to invest in. Imagine if the folks at Google created a rigorous K-12 homeschooling / afterschooling program with all the bells and whistles their own technology platforms could provide. They could offer a certificate for having passed through it that would trump diplomas and they would have unparalleled intelligence into the pipeline of available talent. What a brilliant way to train future engineers… the next generation of Google. But I digress.)

Since we are a STEM-oriented household, this was very disappointing for us when we started homeschooling. Our daughter has grown up immersed in science-related hobbies. When it came time to sorting out her academic year, I had to go all the way up to 8th/9th grade materials to find any content whatsoever that our seven-year-old daughter would not find facile and tedious. She helped me build a massive telescope when she was five, so growing a seed in a sandwich bag was not exactly her idea of a fun science project.

While she is a gifted child intellectually, I don’t think this is an extraordinary problem. Most children in the United States can handle much more than what education standards prescribe these days. Kids are getting a better education on YouTube than in traditional classrooms because there are resources on YouTube that do not treat them like idiots (as the Common Core crowd does).

So what do you do when traditional options bite? For us, the answer has mostly been make a lot of trips to the library and build a science lab off of Amazon. While we have built an enormous home library, I have long given up trying to buy everything we want to read. There is just too, too much.

We pick some general topics to organize the academic year around. This year, for example, we are studying ecology, botany, and water and marine life. From there, we divide up our weeks into more specific subjects. One week, we will study relationships among animals in ecosystems. Another week, we will study pollution. And so on.

Once we have the topic, we treat the topic as one giant research project and scavenger hunt. We go to the library and check out as many books as possible on that topic and request more from other libraries if necessary. Everyone in our household has a library card and can check out up to 20 books. It is not uncommon for us to go to the library and come home with 40 books on ocean currents and oil spills or whatever we are studying that week. Then we read and discuss and write about several books a day.

I prioritize two kinds of science books: (1) books that have ideas about science projects or experiments, and (2) books that integrate math and technology into their discussions. You would be amazed at how many children’s / young adult nonfiction books there are with experiments on specific topics. We found an entire book devoted to experiments involving erosion. It was geektastic.

From there, we search out other resources that fit our topic. If we are studying oil spills, we would go to YouTube and Curiosity Stream for videos. We look for news articles online about current events. Ten years after an environmental disaster, what is life like in the region?

So how do you get the resources you need to do lab work with a child? Thanks to Amazon and Google, homeschoolers have a lot more resources than they did decades ago.

(Some of these resources add up in cost, but you are still spending nowhere near what private schools charge for tuition. This is my preferred metric on spending, and one of the big reasons we choose to homeschool. Tally up private school tuition for K-12 cumulatively and then consider what kind of garage science lab you can build with that money instead. If science brings your child great joy, this is a serious consideration.)

Amazon has a page for Carolina Biological Supply Company, which has a lot of the tools you need to build a biology lab. I have ordered a lot of stuff from this company, and it is wonderful. You can seriously order frogs and fetal pigs to dissect off of Amazon now. (Except for weeks afterward, my husband would tease me whenever an Amazon box landed on our doorstep. “Before I open this, are there going to be any dead animals in here?”)

Another awesome resource is the Home Science Tools website. They have lab kits for all ages and a tab with projects and experiments to try.

The American Academy of Mechanical Engineers has a wonderful series on How to Homeschool Engineering Students. That is part one and here is part two. There is also Teach Engineering K-12. We have a subscription to Kiwi Co.’s Tinker Crate series, which has been wonderful at E’s age. She has developed quite a love of engineering. (You will get some strange looks when your child starts going off on an adult about hydraulics, however. I suppose that is a measure of success.) And of course, there is Mindstorms.

For young coders, this a great YouTube channel, Coding Tech. We have started our daughter on a BitsBox subscription and (independently) coding some elementary games. (When your parents develop software for a living, computer science is an everyday subject in your house….)

Here is a list of 100 chemistry experiments for kids of all ages from The Homeschool Scientist.

Some universities have put together STEM-related content for home education. See Hofstra’s Center for STEM Research, MIT’s OpenCourseware, and Open Learning at Harvard.

We invested in a Curiosity Stream subscription and have not been disappointed. They have so many documentaries on so many subjects that you cannot find anywhere else. That app is a homeschooler’s dream.

I am okay with science education being more like drinking from an open fire hydrant than “be sure to underline keywords and answer the questions at the end of the chapter.” That is where passion and creativity and bona fide expertise come from. That is how you build a lifelong learner instead of someone who treats education as a means to an end. That is why we choose to homeschool in the first place.