Is formal logic worth our time?

[MIch elle]

I just bought Traditional Logic I and I'm only on chapter 2 but looking ahead it seems that this is a set of rules for a game I've never played and probably will not play in my lifetime.

 

Can someone help me out and tell me what's the point of formal logic and how it's going to help us? I've read SWB's logic chapter in revised TWTM but it's still not clicking for me.

 

Anyone been through Traditional Logic and can say it's been well worth it?

 

Thanks!

[Laura Corin]

I'll be interested to hear the answers. We just hit a little logical notation at the end of Logic Liftoff and I'm having a hard time seeing the point. To me it's like the rules of accountancy: useful for accountants - arcane and painful for the rest of us (I speak as an MBA). I'm wondering if something like The Fallacy Detective would be a good direction for us.

 

Laura

[Ali in OR]

I have a feeling this formal logic course you mention goes way beyond my experience, but thought I would share a little about symbolic logic.

 

When I was teaching high school math at an excellent ps, we started the honors geometry course for 9th graders with a month of symbolic logic. We used Patrick Suppes book. Kids learned how to symbolize arguments like:

If it is raining, Mom will drive me to school.

It is raining.

Therefore Mom will drive me to school.

 

or

 

A-->B

A

therefore B

 

And you learn some nice Latin (I think!) names for logical rules--this is ponendo ponens. It's a way of learning logical reasoning. You can talk about how if you know A is true, B will always be true, but just because B is true doesn't mean A will be. Your mom might drive you to school because you slept late--it's not necessarily raining just because your mom drives you to school. There are of course a bunch of these logic rules and you get to the point where you can prove much more complicated statements.

 

A month of this before geometry also introduced the kids to the idea of how to prove something before we started Euclidean geometry proofs. I think it is a great topic of study to include in a classical education. But as I said, I don't have any experience with the Traditional Logic book.

[Charon]

The problem with informal logic is its lack of formality. I wish I had a nickel for every time someone has tried to bust out a fallacy on me when arguing over the internet -- "ad hominem" has to be the most over-used string of letters on the entire world wide web. A good example of how informal fallacies aren't always fallacies might be arguments from authority. Sometimes, it is appropriate to use an authority, and sometimes it isn't. That 9 out of 10 medical doctors say a treatment is necessary makes a strong argument that the treatment is, indeed, necessary all things being equal. If, on the other hand, some one comes along and says that the poster citing these statistics is just trying to sell their drugs (used in the treatment) and has cherry picked the doctors or is otherwise not representing the facts in an unbiased manner, then you have to doubt their argument from authority, after all. (This counter, by the way, is ad hominem.) Just because "they are fallacies" doesn't mean they don't figure into the rational consideration of the matter. And that is because, as informal fallacies, they aren't always fallacies.

 

But, such fallacies and informal logic, in general, is really based on the facts of formal logic along with a few other philosophical positions (including the position that the laws of excluded middle and non-contradiction are actually true, for instance). And, math is, too. So, that's probably why, for instance, apparently graduate students in philosophy all over the place have to demonstrate their proficiency with it to be allowed to stay in the graduate school and pursue their PhDs. So, it's not a minor thing. I you go to graduate school in math, though you may not have to pass a specific qualifying exam on that topic, every qualifying exam you take will make heavy use of your ability to use that kind of logic. There is simply no way you can pass an analysis qualifying exam and not know what how to properly negate something like, for instance: "For every epsilon greater than zero, there exists an integer N such that whenever n>N, |a(n)-a|<epsilon." (Of course, when you actually get to writing this down in practice, you will be using the "upside down As" and "backwards Es" and so on.) So, if for no other reason than that, I think it is safe to say that it is absolutely central to both fields. (And these two fields are pretty central to all intellectual life.)

 

My main problem with studying formal logic is that it tends to be just that -- studying it and not doing it. You learn, as one poster mentioned, what "ponendo ponens" means. But, I don't really care if you know that. I want you to be able to negate the definition of a limit in under a nanosecond. You will have to constantly do stuff like that to pass your qual. It doesn't matter if you know that the upside down A is called a "quantifier". It doesn't really matter if you know how to prove Godels Incompleteness theorem. You just have to be super fast and accurate at manipulating that kind of formal statement -- and above all, accurate -- you really have to get it exactly right. And, you have to do it super fast or it will take you days to figure out a problem that you only have a few hours to solve. And, I think that philosophers do it probably for similar reasons. It is not only in their area to know about symbolic logic, but this one topic above all others strikes directly at a person's ability to reason. Your practice with formulating, negating and otherwise manipulating complex logical statements is your experience with reason. There isn't a special kind of reason for liberal arts majors, here. There is just one kind of reason. And formal logic lies at the center of it. (Don't get me wrong -- I'm not saying that informal logic is inferior to formal logic or something like that. And, it isn't knowing terminology or recognizing symbols that really matters, either. But, the practice with and direct instruction of things like that the contrapositive of an implication is equivalent to the implication and the converse is not equivalent, for instance, certainly is very important -- the training to actually do the logic well.)

 

Formal logic isn't about the symbols or the terminology. It's about being able to handle "all", "some", and "none" properly and things like that. Just because a lot of people might implicitly assume the converse or improperly negate statements in their writing all the time, that doesn't mean that it is now some sort of legitimate mode of reasoning -- "logic for the liberal arts". Formal logic, like math, is a tool you will not use only if you don't have it and a tool you probably use, at least intuitively, all the time without realizing it. In reality, it should form the glue with which all informal arguments are strung together as well as just the actually correct entire argument in lots of cases. You should be able to translate regular English into formal statements and formal statements into regular English as well as properly negate complex formal statements at will without having to think too hard about it. If you have to spend a long time just getting the logic of one statement down, then how will you ever be able to string a multitude of them together into an article or a proof or something meaningful like that?

[Charon]

nt =no text

[Laura Corin]

What texts would you recommend? Logic Liftoff didn't explain the logic (!) of the notation well enough. Calvin and I could do it mechanically, but didn't know why we were doing it - it really didn't mean anything to us.

 

Laura

[Chris in VA]

Wow, that is a great post. Thanks so much.

[Julie in GA]

This is an excellent post, Charon. People are using faulty logic all the time. Where do we begin to unravel the threads? Like you said, informal logic is a good start, but it has its weaknesses. Formal logic is where we have to begin in order to build logical thinking, and clear, logical language.

 

I was reading an article by Michael Horton, who was using the terms "univocal" and "equivocal" quite a bit. He was talking about how people interpret Scripture passages that describe God or His attributes. Anyway, I was not following his argument very well at all, until I read the Trad. Logic chapter on univocal, equivocal and analogous terms. Then the light bulb went on. For the umpteenth time as a homeschooler, I asked myself, "Why wasn't I taught this stuff in school?"

 

Press on, Michelle!

[Kathie in VA]

I'm looking forward to doing formal logic with my kids (?next year?). I've done some in College so it's not totally foreign to me. Right now we are doing Fallacy Detective, having done Mindbenders A & B. Perhaps we'll get to Teaching Toolbox also. However I agree that just learning formal logic won't be enough. I'd really like to find ways to utilize that knowledge... like taking our math into word problems to really put it to use. Then there is also 'Symbolic logic' but I hear that's for after formal logic... so I'll see if we have time/energy for that later.

 

One place I've found so far that I think will help here is the Classical Writing program.... I believe in the later books they intend to work thru and make use of formal logic.

 

It would be nice if we can apply our fomal logic skills to our discussions on history and literature.. but I don't know if there is a program out there (yet) made to help us homeschool moms through such a discussion. If there is one, PLEASE let me know!

[Holly IN]

This post is very interesting since we shelved our logic book last year. I got fed up with doing it. Hmmm this has spured me on to get back to doing this. Thanks

Holly

[Charon]

What texts would you recommend? Logic Liftoff didn't explain the logic (!) of the notation well enough. Calvin and I could do it mechanically, but didn't know why we were doing it - it really didn't mean anything to us.

 

Laura

 

...Classical Euclidean Geometry is such a big deal and undoubtedly the motivation for Plato's motto: "Let no one enter without geometry." You can teach a course on logic, but that doesn't directly condition the student to think logically. It just identifies what logical thinking is, in the first place (a related matter to be sure but not exactly to the point). A reasonably interesting subject that makes heavy use of logic is a better choice, and for a long time, Euclidean Geometry was kind of the only one. It may still be, to a large extent, for school aged children.

 

I have a couple of logic books by Nance. I have an introductory college freshman philosophy text. I have several advanced math texts. All of them either already assume a certain level of ability with logic, or they don't exactly directly build that aptitude up. What I really want is something like the Sequential Spelling of logic -- a series of about 3000 worksheets that start at a super low level that a 2nd or 3rd grader can handle and then gradually climb to the level of negating a series of statements like the definition of a limit I gave above. The student just does a couple worksheets a day consisting of truth tables and negations. Or, I also have this idea of an "assertion table" -- instead of filling out a truth table with T's and F's you fill it out with English sentences asserting the correct statement for the given cell of the truth table.

 

That would be great, but I don't know of such a program. I do have the best of intentions of doing Nance, though, and moving up from there. But really, as I say, it is built into our proof-oriented math program. I think that programs like Nance's are helpful, but, truly, my best personal recommendation is don't skip geometry. Incidentally, the guy Ali mentioned, Patrick Suppes, is a very important person from the New Math era. I believe he also ran the Stanford EPGY for some time. And, he is also a serious professional philosopher and big contributor to the the philosophy of science. He's probably not a bad author to look into. (Maybe it is work on distributive justice that is blocking me from wanting to use him.)

[MIch elle]

I'll press on with Traditional Logic I on my own and see where I get with it before I attempt to do it with my dc.

 

 

Shalom,

[Guest Martin Cothran]

I hope it is okay for me to take a shot at this question…

 

Logic is one of the liberal arts. The liberal arts are the generalizeable, universal intellectual skills: they are used in all other disciplines. The whole point of studying the liberal arts is to acquire the central academic skills that are common to all learning. The trivium is the term used for the first three of these liberal arts which have to do with language.

 

Logic (at least traditional logic—modern logic is really a mathematical logistical system) is one of the three central language arts, along with grammar and rhetoric. Grammar is the most basic because it teaches you the structure of language—any language, and undergirds all other language study. The others are the use of language for some purpose: logic for the purpose of argument, and rhetoric for the purpose of persuasion (which assumes you know the logical skill of argument). Aristotle would add poetics to these, where the student studies the structure and meaning of literature and poetry.

 

The reason you study logic is simply because it under girds all persuasive speech. We spend most of our life using language—with those in authority over us, with those who are under our authority, and with our peers. We use it in our families and in our jobs and at school. And a good part of the time we are using it for persuasive purposes.

 

Formal logic is simply training in how to use reason properly. It is like doing scales in music or katas in martial arts or calisthenics in sports. You don’t use it directly, but it enables you to do those things better. Can you do those things without it? Yes, but more likely than not you will suffer if you have not done them—or at least you will be at a disadvantage if you are competing with others who have done those things.

 

The thing I hear more than anything else about kids that go off to college is this: they can’t write a persuasive paper. In every course outside of the sciences, they will be asked to do this repeatedly, and most are not prepared for it because they don’t know how to write and they don’t know how to reason.

 

Studying logic solves at least half of this problem.

 

The bottom line is that most people reason a whole lot more than they do most everything else--including all those things that most people think are more important than logic.

[mcconnellboys]

Thanks for the post, Mr. Cothran!

 

Regena

[VanessaS]

This is such an interesting thread...

[Rhondabee]

Hey, Charon! Glad to see you about. You and your dear wife have been in my thoughts and prayers lately, though I have lost your blogs and don't really know what's up. Just please tell her & know that positive vibes are being sent your way.

[Jean in Wisc]

We waded through it...and then my children started using it:

 

Mom, did you hear what they said? They need a class in logic.

 

Mom, look at this paragraph--they are wrong. We learned in logic class that..."

 

Mom, did you hear that advertisement?

 

Mom, in college class today...I really think they should teach logic in public school!

 

It goes on and on in my home. The class of logic has changed how they think, how they reason, how they see things. Formal logic is one class I would never willingly drop from my high school class list. I have heard several people say that the logic class they took in college was the one class they took that was worth the tuition.

 

Jean

[Amber in AUS]

Interesting reading!

[Hoggirl]

We waded through it...and then my children started using it:

 

Mom, did you hear what they said? They need a class in logic.

 

Mom, look at this paragraph--they are wrong. We learned in logic class that..."

 

Mom, did you hear that advertisement?

 

Mom, in college class today...I really think they should teach logic in public school!

 

It goes on and on in my home. The class of logic has changed how they think, how they reason, how they see things. Formal logic is one class I would never willingly drop from my high school class list. I have heard several people say that the logic class they took in college was the one class they took that was worth the tuition.

 

Jean

 

 

Are those the courses you did?

Thanks!

[Jean in Wisc]

Traditional Logic Book 1 and 2 by Martin Cothran, Memoria Press.

 

And, yes (I'm reading minds here), I used and liked the boring DVDs. LOL! Child #1 only had them for book 2, which was fine. I got the book 1 DVDs for child #2 and did them all. Child #3 will use them all. I just like sitting in on them so that I don't have to read the chapter and figure it out in my own head. :D They could be done without the DVDs. I'm getting lazy in my old age.

[Spy Car]

I hope it is okay for me to take a shot at this question…

 

 

Both the Memoria Press website and Amazon in the descriptions of your work say it teaches formal logic "along with a basic understanding of Christian theory of knowledge".

 

Can you clarify this last point? I feel highly aggrieved by what I consider a perversion of logic materials to pursue ideological aims by other authors such as Nance/Wilson and the Blundorns. So (despite any informal fallacy which may be entering my thinking process) when I see "Christian" and logic used in the description I get worried.

 

Does your work assume the student shares your faith? Are there reasons someone seeking a purely "secular" logic book might not be comfortable with Traditional Logic? Are theological (as opposed to logical) issues discussed in your work? Is it a specifically "Christian" oriented work?

 

I'm hope to find a formal logic curriculum, but have thus far been very unhappy with the admixture of logic and apologetics I've experienced in "home school" oriented works.

 

Please excuse the "directness" of my questions. Welcome to the forum.

 

Bill

Edited March 8, 2009 by Spy Car

[Hoggirl]

Traditional Logic Book 1 and 2 by Martin Cothran, Memoria Press.

 

And, yes (I'm reading minds here), I used and liked the boring DVDs. LOL! Child #1 only had them for book 2, which was fine. I got the book 1 DVDs for child #2 and did them all. Child #3 will use them all. I just like sitting in on them so that I don't have to read the chapter and figure it out in my own head. :D They could be done without the DVDs. I'm getting lazy in my old age.

 

Okay, I am so confused now! :lol: I thought I saw on the high school board that you did Intro and Intermediate Logic. Are these the Nance books? Did you do the MP materials first and THEN the Nance materials? I am just trying to get the proper scope and sequence.

 

Thanks, again.

[Snickerdoodle]

:lurk5:

[Jean in Wisc]

Just guessing here, without going off and looking to see what I wrote...

 

I refer to a number of our classes as intro/interm/advanced: algebra, logic--anything thing that progresses. So....I probably referred to logic in those terms which no doubt was a big blunder simply because there is a logic program with that name.:sad:

 

My fault. I own both programs. I never ended up using Nance's books (could never convince myself I wanted to sit through the program with my kids). I hope it did not cause too many problems for anyone.

 

In elementary grades we used that series with the Logic Liftoff book and those Mindbenders...

 

I'm too tired to go look for the exact titles. My mom has been in the hospital this week. I took my son back to the surgeon Wednesday for a 6 week check up on his spinal fusion, and I've had a naaaasty cold and ache from head to toe. (Pity party here!)

 

Maybe I should:lurk5: when I feel like this rather than trying to type! LOL! Don't forget to turn your clocks ahead.

 

Jean

[Hoggirl]

I am sorry you are having such a rough week. Why does it seem that things like that always come all at the same time????

 

It sounds like the TL from Memoria Press worked well for you. I appreciate your taking time to share.

[laughing lioness]

We did Intro and Intermed Logic by Nance first and are doing Traditional Logic this year. Sure wish that we had done it the other way around. The Nance logic is symbolic math and traditional logic is about words.

My kids have enjoyed the DVD's- maybe not the most entertaining DVD's they've ever watched but clear and concise. They GET it and they understand it.

[admin]

Guys, this thread had been resurrected by a spammer. No one had posted on it for a year, so don't be disappointed if no one responds to your questions.

[Spy Car]

Guys, this thread had been resurrected by a spammer. No one had posted on it for a year, so don't be disappointed if no one responds to your questions.

 

Thank you for the heads up :001_smile:

 

Bill (who was Waiting for Godot :D)

[platosacademy]

Formal Logic is valuable for evaluating arguments. It's also valuable for the LSAT, GRE and other standardized tests. Most importantly, a strong foundation in both informal and formal logic is necessary in order to write persuasive arguments during the rhetoric stage. It might be fun to have your child go through the opinions column of the newspaper and pick out the fallacies and the invalid arguments during logic time.