Logic curriculums

[veggiegal]

The formal logic looks confusing if you've never studied it, but it's basically algebra for arguments. You learn symbolism rules, and rules for how those symbols can be legitimately manipulated. Just like you learned 2x = 8, and that x was a variable, and that a legitimate rule to use was to "do the same thing to both sides"--i.e., divide both sides by 2. IME, if you find algebra easy, you'll find logic--at least in the beginning stages--quite straight-forward.

[Spy Car]

Tarki's World is probably best used not in isolation -- there's a nice logic textbook called Language, Proof, and Logic, by Jon Barwise and John Etchemendy, that incorporates Tarski's World as well as a couple of other software packages (Fitch, for learning formal proofs; and Boole, for learning truth tables.)

 

LPL gives a very thorough introduction to formal quantified logic, eventually working its way up to topics like mathematical induction and basic set theory. It uses a nice natural deduction-type proof system, in which the primary proof rules are introduction and elimination rules for each connective (such as "And-Elimination", which allows the inferences from p /\ q to p, or "If-Elimination", which allows the inference from p and p => q to q (this is then the rule often known as modus ponens (or, if you like to show off your medieval bona fides, modus ponendo ponens))). Other rules like modus tollens are given as derived rules.

 

LPL doesn't have a huge amount of discussion of translation from English into formal logic (a very nice book for that is Meaning and Argument: An Introduction to Logic Through Language, by Ernie Lepore). Its strategy seems to be to teach students directly to think in the formal logical language, rather than focusing on translation skills. (That's the way I tend to teach logic, too -- otherwise, you can easily fill the whole semester dealing with idiosyncracies of English in translation.)

 

The "or" symbol is \/, which is inclusive "or" (that's the standards choice in formal logic, and then it's typically noted in passing that exclusive "or" can be defined as (p \/ q) /\ ~(p /\ q), if it's wanted).

 

Forgive a few ignorant questions, as I have some exposure to Formal (Aristotelian) Logic but none at all to this form of symbolic logic. Is this properly called "First Order" Logic"? Are the symbolic notations in Tarski's World common to all logic programs (of this sort) across various fields of study?

 

And is there a progression you might recommend if we (my son and I) wanted to begging playing around with learning some of this? He is proving to be very adept at picking up symbolic thinking and at using critical thinking--but until Monday he is still a six year old, so I would not want to overwhelm him. On the other-hand is there was a way to introduce this sort of thinking to a bright young mind I would be all ears :bigear:

 

Bill

 

 

 

Bill

[veggiegal]

While there are some minor differences in logic symbols between different books (or at least there used to be 20 years ago!), the symbols given by Tarski's world are common: Ax (some write this as an upside down capital A instead) for "All x"; "Ex" for "some x"--which in logic means there exists at least one x; the 'if-then' arrow -->, etc. The differences I know of are similar to the way multiplication can be indicated via the 'x' symbol or a dot '.' between numbers (as well as numbers next to each other in brackets). If your child learns the Tarski's world symbolism, they will have a headstart on any formal/propositional logic they do down the road.

[Spy Car]

While there are some minor differences in logic symbols between different books (or at least there used to be 20 years ago!), the symbols given by Tarski's world are common: Ax (some write this as an upside down capital A instead) for "All x"; "Ex" for "some x"--which in logic means there exists at least one x; the 'if-then' arrow -->, etc. The differences I know of are similar to the way multiplication can be indicated via the 'x' symbol or a dot '.' between numbers (as well as numbers next to each other in brackets). If your child learns the Tarski's world symbolism, they will have a headstart on any formal/propositional logic they do down the road.

 

Thank you.

 

On a side-note, I have enjoyed your posts (and looking around your blog), and look forward to getting to know you better :001_smile:

 

Bill

[veggiegal]

Thanks Bill. I've enjoyed several of your posts too and am looking forward to getting to know you and many more folks and their wealth of wisdom on this board. A friend of mine recommended this board to me, even though we're not exactly WTM homeschoolers (we're quite eclectic), because she thought I'd enjoy the in-depth discussion of curriculum, teaching methods and so on. She was right--I'm loving it! :D

[Emerald Stoker]

nm

[Michelle My Bell]

After reading what Bill had to say above, and gently picking on him once again, I was certainly disappointed to be on the logic book hunt again. I was not ready to give up on Fallacy Dectective. I wanted to know more. I had this in my basket to check out this Friday, but it is still there.

 

I thought that I had researched FD so well. :glare: I wanted to believe that Bill was just being Bill and that it could not be too bad.

 

I fired off an e-mail.

 

Here is the response:

We wrote our books to be appropriate for young children. It is hard to avoid all controversial topics in a logic book, given that the book is about how to talk about and resolve controversial issues. We've tried to avoid topics that might offend people or give the impression we are taking a side on a particular issue.

 

I replied back that I wanted him to be more specific. This was several days ago. I just wanted to let you all see the generic response. I was sorely disappointed. :confused: He finds abortion, even as a controversial topic, to be appropriate for third grade? What?

 

I don't believe that these books were ever intended for 3rd grade. It is my understanding they are for jr. high and up.

[Spy Car]

I don't believe that these books were ever intended for 3rd grade. It is my understanding they are for jr. high and up.

 

If the authors of Fallacy Dectives claim:

 

We wrote our books to be appropriate for young children. It is hard to avoid all controversial topics in a logic book, given that the book is about how to talk about and resolve controversial issues. We've tried to avoid topics that might offend people or give the impression we are taking a side on a particular issue.

 

Then I would say they are disingenuous at best, and bald-faced liars at worst.

 

Bill

[Michelle My Bell]

If the authors of Fallacy Dectives claim:

 

We wrote our books to be appropriate for young children. It is hard to avoid all controversial topics in a logic book, given that the book is about how to talk about and resolve controversial issues. We've tried to avoid topics that might offend people or give the impression we are taking a side on a particular issue.

 

Then I would say they are disingenuous at best, and bald-faced liars at worst.

 

Bill

 

Taken directly from their website:

 

Geared for ages twelve and older – we suggest using The Fallacy Detective before advancing onto more difficult logic programs.

[Spy Car]

Taken directly from their website:

 

Geared for ages twelve and older – we suggest using The Fallacy Detective before advancing onto more difficult logic programs.

 

They wrote to Chrissy that the materials were written to be "appropriate for young children." This is blatantly untrue. The claim that they have tried to avoid topics that "might offend" or "give an impression they are taking sides" is also blatantly untrue. They pick the most hot-button topics imaginable and make their positions very clear indeed. It is the point of the book--pushing the authors' well-known hard-line ideological and theological positions.

 

I do not respect people who make bald-faced lies.

 

Bill

[Donna T.]

I am reading The Fallacy Detective outloud to my 9 and 12 year olds. Both of them really like it. They are both able to understand the explanations and to follow along with the examples. We discuss each exercise outloud together. It is fun because we rarely agree on the "answers" and they love to find out who is right. They enjoy it so much that it is our current bedtime book and they never forget to remind me to read it to them before they go to sleep. We are learning from one another through our discussions. Just tonight my 9 year old said, "I love how this book makes us talk about things that we wouldn't normally think to talk about."

 

I do have to explain some of the vocabulary to my 9 year old. There are some things that are simply "over his head" and I don't get bogged down in explaining things that aren't important for now. So far, I have not run into anything that has offended me in any way. There are some Bible verses in the first few lessons, not a problem for us. They do reference abortion, murder, communism, obesity, reincarnation, politics, education... but they also have references to dogs, fleas, novels, baseball, cold symptoms, and gardening. It's not all heavy and we find the writing style to be humorous and entertaining. My children already know these things exist and I don't mind talking with them about such things.

 

The introduction to the book clearly states that they are writing this book to Christians. They write, "We have tried to interweave a genuinely Christian worldview into this book." However, I absolutely do NOT get the impression that they are trying to influence me... they are simply presenting things that I can relate to as a Christian, things that I am already thinking about and willing to think upon further. They aren't including such topics for the sake of telling me what I ought to believe about them. They are simply referred to within the context of examples of how people think about particular issues. They aren't focusing on the issues, but use the issues as topics for the purpose of illustrating both faulty and clear thinking. And, most often, they are pointing out fallacies in typical "Christian" thinking. I really see this as the whole point of the book... to help Christians to think about all kinds of things and to recognize their own faulty thinking in relation to those things. For example, if you are against capital punishment you need to know WHY you are against capital punishment, but they aren't telling me what I ought to believe about it in the first place.

 

FWIW, our family does not agree (in fact, we HIGHLY disagree :D) with some of the theology that the Bluedorns believe to be true, neither would we be considered as politically conservative; however, we are comfortable with the book.

 

We will be starting the Logic Countdown series this fall, and my oldest is currently using The Art of Argument. FD has been a fun and simple way for us to learn about the informal fallacies.

Edited July 9, 2011 by Donna T.

[FLW2003]

I don't intend to hijack this thread, but sine there are so many very knowledgable people participating in this conversation, I figured I would ask this question here.

 

In choosing curriculum, I always like to begin with the end in mind. Not having any experience in logic, and reading the suggestions in the WTM, I asked myself what the goal is. Since I have no knowledge of logic beyond Boolean Logic, I am not well versed in this topic. The first thing I thought about after reading the logic suggestions in the WTM is the LSAT logic questions. Could someone please speak to how these LSAT questions compare to the curriculums in the WTM or formal logic in general. My guess is that they are quite a bit different.

 

Steven

[wapiti]

I don't intend to hijack this thread, but sine there are so many very knowledgable people participating in this conversation, I figured I would ask this question here.

 

In choosing curriculum, I always like to begin with the end in mind. Not having any experience in logic, and reading the suggestions in the WTM, I asked myself what the goal is. Since I have no knowledge of logic beyond Boolean Logic, I am not well versed in this topic. The first thing I thought about after reading the logic suggestions in the WTM is the LSAT logic questions. Could someone please speak to how these LSAT questions compare to the curriculums in the WTM or formal logic in general. My guess is that they are quite a bit different.

 

Steven

 

I don't really remember the logic questions on the LSAT (it's been amost 20 yrs ;)), so you may be better off looking at a practice test to answer your question. I vaguely recall analogies, perhaps. (FWIW, I never had any official "logic" instruction and I did very, very well on the LSAT. A practice test book was my only preparation.)

[cjgrubbs]

Has anyone use Critical and Creative Thinking Activities by Evan Moor? I like the variety of activities in the samples I'm looking at but not sure if they would really be considered a good Logic curriculum. I'm looking mainly for a 6th grader, but possibly for my 3rd grader, too.

[Michele B]

DD10.5 used Mindbenders last year for 4/5 grade. (I'm not very good at official grades; we use the grammar and math books until we finish them which may or may not be exactly 1 year).

 

After reading this very interesting post, I have more options than I need! :lol:

 

I would like to order the Logic Countdown, Liftoff, Orbit set on Amazon. If Countdown is too simple, I will wait and use it for dd7.

 

I am also interested in Critical Thinking 1 and 2.

 

Do these series cover the same material, or could we use LC,LL, & LO and then use the Critical thinking series, or if I used LC, LL, & LO, would we go straight into Critical Thinking 2?

[Maverick_Mom]

I like Critical Thinking Press, but boy are they expensive.

 

Ugh. I hear you there.

[ChrissySC]

DD10.5 used Mindbenders last year for 4/5 grade. (I'm not very good at official grades; we use the grammar and math books until we finish them which may or may not be exactly 1 year).

 

After reading this very interesting post, I have more options than I need! :lol:

 

I would like to order the Logic Countdown, Liftoff, Orbit set on Amazon. If Countdown is too simple, I will wait and use it for dd7.

 

I am also interested in Critical Thinking 1 and 2.

 

Do these series cover the same material, or could we use LC,LL, & LO and then use the Critical thinking series, or if I used LC, LL, & LO, would we go straight into Critical Thinking 2?

 

Simple builds confidence too. This is a great idea for subjects where children struggle. Find a lesser resource to build self esteem and feelings of accomplishment.

[Jen500]

It's a software package. There's a FAQ sheet at that link that tells how to get it.

 

The books that come with Tarski's World would be too challenging for most children under high school; but our oldest dd had fun with the software at a younger age. Dh wants to start dd8 with it soon, but we have an old copy that isn't cooperating.

 

Wow, thanks for sharing this program.