Saturday, December 27, 2008

Logic - Truth Tables and Truth Trees

Be sure to listen to my 1SmartMama radio archive where I verbally explain this topic on Saturday, December 27, 2008 at 11am.

Over Christmas, Challenge B students are required to memorize the appendices from Nance's Intermediate Logic. My William and I took the tables and simplified them for easier memorization. Each morning over the holiday, he copied Appendix A and C.

Here is the original from the book for clarity. You may want to scroll back to it occasionally during this lesson.

To make it easier to remember, we just write the things that change. The things that are the same, are the same and easy. So we only filled in the letter F for false, since the T F table never changes and the empty boxes indicate T or True. Below are my notes. The words and, or, if/then and equal just remind us of the symbols meanings APPROXIMATELY. Also, we abbreviated the column labels to a rhyme: Neg, Con, Dis, Con, Bi.

Here is Appendix C from the book. I don't like how the printer made it look different than the Appendix A. We noticed that they used the same terms as A, so we made it into our form of a table. Even though memorizing is a grammatical process, notice it takes dialectic skills to reform someone else's info into your own tool.

We put C right under A, and now have reduced the two charts to one easy chart. Notice that both charts have a simple Negative column. So we write that first and it's easy to memorize. Then we just repeated the original p and q chart and wrote a check mark after each.

Then we write the exact same row in the Negated column, except we add parenthesis and a ~ before each pq relationship.

Now that the headings are listed, we have to fill in the chart. There are only 3 that have just a p over a q so we do them first. Then we draw the slants and the p and qs for the rest of the table, noticing that the Bi column is different too. So, they are either p over q, p before q, or pp over qq. We say these lind of things out loud to remind us.

Lastly we look at the negatives for patterns. We notice the p over q has no negative, both neagtives, and one negative. We notice the pp over qq has all right negative and split negative. The rest we just memorize. I know it is all memorization, but if you look for patterns and differences and say the story while you write it becomes easier.

Now that we've thought through the chart, we write it neatly, and proceed to copy it daily.

Here's William at the end of filling in a chart. Messy board and boy in PJs but that's the beauty of home centered ed. Logic is done before breakfast.

Now that we have A and B memorized, we will tackle Appendix B, which is the longest.
To spend a weekend with adults practicing your own logic skills, join my longtime Tutor, Jody Harvey, in Winston-Salem, NC for a Latin in a weekend retreat register at
Please comment on how this was or wasn't helpful.


RockerWife said...

I want to say first off I am a great fan of Classical ED and think you are brilliant and amazing. I wish I had known the tiny bit I know now when my older kids were in home centered ed (I like that term). But I am going to be honest with you. I find it very difficult to even follow some of your more simple ideas and/or posts. I'm sure part of this is due to the face that when you post, there is the assumption that the ppl reading know what you are talking about. Or, at least they have enough information to understand where to "place" the information you are sharing. This post was greek to me even though I am starting to learn about the challenge programs.

I hope as Classical Ed gets off the ground thru the US, you will be able to hire someone to work with you and help you to point out areas where it would be helpful to have some detail explanation along with the information you are providing.

I share my thoughts with you in a spirit of kindness and as much humbleness as I can pull together. (ok, I'm being totally honest here!) Thanks so much for all your work and I look forward to learning more about the challenge program for 2009.

Anonymous said...

Thanks for you honesty Rocekrwife...It's just the kind of feedback I want. I'm messing around with this communication - It's all new to me. I packed in too much info into too little time. Trying to find the balance between "meat' and "handholding" while learning new technologies. If folks don't tell me these things on posts, I'll assume I'm doing better than I think. Leigh!

Anonymous said...

See, it says Anonymous in the comment above as I'm stll trying to figure out the right button to push. I'll try a different one this time. I want my struggles with editing, technology, or anything I am learning to be apparent to my audience. I do not know everything, but I can learn anything. Figuring things out in front of folks may cause me occasional embarassment (like did I just spell that word correctly? I'll get a dictionary..nope rr, ss makes it embarrassment, still looks funny to me), but it also encourages others to at least try. If I can do it, obviously anyone else can do it. PLEASE keep posting RockerWife.

Now let's see how the next sign off button works..

Anonymous said...


Anonymous said...

just finishing a logic course by james b nance and was looking for the most simple, brain relieving method of learning all about truth trees. no matter how i look at it though, OUCH!

Gabriel said...

I, too, took a class on logic a while ago. I thought it was a lot of fun so I created a web application to generate truth trees. Check it out:

I'm using a slightly different notation though.

Gabriel said...

Hello again,

I think there's a typo towards the end of this post: "Now that we have A and B memorized" should read "Now that we have A and C memorized". Shouldn't it?

Also, if I may offer a constructive criticism, I think you focus too much on learning the tables by heart. Logic is about reasoning and inference mainly, not memorization (although of course you need a minimum now and then). I think a better exercise would have been to understand why the rules of Logic are what they are.

For example, start by choosing the simplest rule of all: double negation and try to understand why we can infer p from ~~p. Then do the same for conjunction and disjunction.

One more thing is that you don't speak of the concept of metavariable. What is p? What is q? Does William already know? (maybe I missed an earlier post about Logic, I couldn't find any).

The concept of operator (also called connective) is also very abstract. I'd suggest another approach. Start with real world sentences first like "It's sunny today!", then make sure that William knows what negating a sentence mean. When the child is able to say that the negation is "It's not sunny today!", do it with other sentences. Continue the exercise with negating an already negated sentence. We should get something like "It is not... not sunny today!", or "It is not the case that it is not sunny today!". The child should see that this awkward sentence really just means that "It is sunny today!". That's just one instance of why "p" can be infered by "~~p".

On the plus side, I like how you make William remember only what changes, and how you make him see the patterns, i.e. p over q, p before q, pp over qq. With that sort of tricks, memorization is so much easier!

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