Logic curriculums

[AimeeM]

Logic Blastoff series or Fallacy Detective?

Anybody who has used either, can you tell me what you liked (or disliked) about them?

Trying to make a decision between the two for my fifth grade daughter having had no prior formal instruction in logic.

[robsiew]

We have used Logic Liftoff and I have Logic Countdown for my upcoming 5th grader. I think they are great. They have a variety of activities and teach concepts well. Another bonus is you can photocopy them for in-family use so I don't have to keep rebuying them.

 

My 10 year old zoomed through Mind Benders A-B and went into C last year. While he liked them, they got a little old because they are all the same type of puzzle. I'll have my 4th grader do some this next year, but probably not as many as my older did (unless she really likes them, which is doubtful knowing her!)

 

Those are the only things we've really had experience with. I'm eager to see any other feedback you get as I'm looking for some more things for my 10 y/o. :lurk5:

[sagira]

Tinman Press items look really fun and varied. I requested a catalog from them today. I like Critical Thinking Press, but boy are they expensive.

[Spy Car]

The aims of Logic Liftoff and Fallacy Detective are totally different.

 

Logic Liftoff (which I have not used) is a gentle introduction to Formal Logic and includes things like syllogisms and deductive reasoning.

 

Fallacy Detective purports to teach Informal Logic, which involves fallacious thinking in argumentation, things like: Red Herrings, Straw-men arguments, Invalid Appeals to Authority, and other invalid arguments and uses of propaganda.

 

Unfortunately the authors of Fallacy Detective do not stick to the purported purpose of their book and instead interject their extremely conservative political and theological views on hot-button issues (such as abortion) into the text. My copy went into the trash.

 

Bill

[Farrar]

We haven't gotten up to the Logic Liftoff books yet, but we've done Lollipop Logic and Logic Safari by the same author and really liked them. I feel like they were, indeed, a gentle introduction, as Bill said.

[~Amanda~]

The aims of Logic Liftoff and Fallacy Detective are totally different.

 

Logic Liftoff (which I have not used) is a gentle introduction to Formal Logic and includes things like syllogisms and deductive reasoning.

 

Fallacy Detective purports to teach Informal Logic, which involves fallacious thinking in argumentation, things like: Red Herrings, Straw-men arguments, Invalid Appeals to Authority, and other invalid arguments and uses of propaganda.

 

Unfortunately the authors of Fallacy Detective do not stick to the purported purpose of their book and instead interject their extremely conservative political and theological views on hot-button issues (such as abortion) into the text. My copy went into the trash.

 

Bill

Oh, gosh, don't tell me that. I'm waiting on my copy to come in the mail :(

[Spy Car]

Oh, gosh, don't tell me that. I'm waiting on my copy to come in the mail :(

 

Sorry. My advice is to pre-read the book before you hand to a child. I used to be pretty naive about the degree of "world-view" intrusion that sometimes shows up in homeschool materials and I was shocked when I read Fallacy Detective.

 

I'm a lot more jaded (and wary) now.

 

Bill

[radiobrain]

Logic liftoff etc. and logic safari, are good. The safari books only deal with logic grid puzzles, the other ones have varying subjects.

 

I decided to use the Critical Thinking, Critical Thinking 1 book this year.

[Mommy22alyns]

The aims of Logic Liftoff and Fallacy Detective are totally different.

 

Logic Liftoff (which I have not used) is a gentle introduction to Formal Logic and includes things like syllogisms and deductive reasoning.

 

Fallacy Detective purports to teach Informal Logic, which involves fallacious thinking in argumentation, things like: Red Herrings, Straw-men arguments, Invalid Appeals to Authority, and other invalid arguments and uses of propaganda.

 

Unfortunately the authors of Fallacy Detective do not stick to the purported purpose of their book and instead interject their extremely conservative political and theological views on hot-button issues (such as abortion) into the text. My copy went into the trash.

 

Bill

 

 

Yikes. Thanks for the heads up!

[ChrissySC]

The aims of Logic Liftoff and Fallacy Detective are totally different.

 

Logic Liftoff (which I have not used) is a gentle introduction to Formal Logic and includes things like syllogisms and deductive reasoning.

 

Fallacy Detective purports to teach Informal Logic, which involves fallacious thinking in argumentation, things like: Red Herrings, Straw-men arguments, Invalid Appeals to Authority, and other invalid arguments and uses of propaganda.

 

Unfortunately the authors of Fallacy Detective do not stick to the purported purpose of their book and instead interject their extremely conservative political and theological views on hot-button issues (such as abortion) into the text. My copy went into the trash.

 

Bill

 

Really now, I like Fallacy Detective. And, anything written by man will have a purposeful bias. I think this has something to do with that we all have opinons - and men mostly feel the need to assert them?:lol: (poke, poke, LOL)

 

But, I am very fond of a formal introduction too. At what age do you think that Logic Liftoff is most appropriate or serves a purpose well?

 

Edit: http://www.amazon.com/Logic-Countdown-Bonnie-Risby/dp/1593630875/ref=pd_bxgy_b_img_b It would seem that the first book is Countdown, and there are three. While FD is more purposeful in what I would consider life logic maybe, this is more formal. I like the workbook format too. Anyone use all three ... is it reasonable to start the first in 4th grade? too remedial for 5th?

Edited June 29, 2011 by ChrissySC

[wapiti]

I'm using Logic Liftoff with my rising 5th grader. I'm also planning on using this tiny unit that was posted on the Logic board from MEP http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7_1.pdf (I have Harry Stottlemeier's Discovery but my intuition tells me that we may be better off looking at the subject mathematically first, and then with language. We'll see....)

[~Amanda~]

I'm using Logic Liftoff with my rising 5th grader. I'm also planning on using this tiny unit that was posted on the Logic board from MEP http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7_1.pdf (I have Harry Stottlemeier's Discovery but my intuition tells me that we may be better off looking at the subject mathematically first, and then with language. We'll see....)

Harry Stottlemeier's Discovery

 

I was just looking into this; I'm wondering if this will be better. I can't seem to find the TM though, except through the mail order forms.

[wapiti]

Harry Stottlemeier's Discovery

 

I was just looking into this; I'm wondering if this will be better. I can't seem to find the TM though, except through the mail order forms.

 

I got a used TM at Amazon - they don't show up very often. It still wasn't cheap (around 40 bucks). I'm on the fence as to whether it was worth it - we'll see later this year. DD enjoyed reading the story of Harry though (she'd prefer to read it through in one sitting rather than discussing it :lol::tongue_smilie:).

[zoo_keeper]

Yep, Fallacy Detective and the authors' Thinking Toolbox, I believe contain pervasive religious content. I remember raging to my husband when I encountered the abortion portion. How is that even remotely appropriate for children of this age? There were so many other topics they could have used. It was needless, IMO, propaganda. I didn't get any further in the book after that...

[Luckymama]

Wow Bill, thanks so much for the heads-up! Logic is the.last.thing I need to plan for this coming year.

[ChrissySC]

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?

 

 

Really now, I like Fallacy Detective. And, anything written by man will have a purposeful bias. I think this has something to do with that we all have opinons - and men mostly feel the need to assert them?:lol: (poke, poke, LOL)

 

But, I am very fond of a formal introduction too. At what age do you think that Logic Liftoff is most appropriate or serves a purpose well?

 

Edit: http://www.amazon.com/Logic-Countdown-Bonnie-Risby/dp/1593630875/ref=pd_bxgy_b_img_b It would seem that the first book is Countdown, and there are three. While FD is more purposeful in what I would consider life logic maybe, this is more formal. I like the workbook format too. Anyone use all three ... is it reasonable to start the first in 4th grade? too remedial for 5th?

[~Amanda~]

yeah, im still looking

[ChrissySC]

This kinda "sucks eggs" LOL

 

Not to derail - but I still need a Latin too!

 

I did look at Logic Countdown (there are two books to follow) and Logic Links (more pattern and mathematical I think).

[Camarell]

also looking for Logic that is more than just grid puzzles/games.

[freerange]

We're currently using logic countdown and a stack of mind benders, to be followed by log icliftoff and then perhaps The Snake and the Fox. I say 'perhaps' because although I have the book and like it, I don't yet have a feel for when she'll be ready for it.

[Mom0012]

also looking for Logic that is more than just grid puzzles/games.

 

I was just reviewing my WTM book last night for the logic stage to see if I was missing anything for my son. I do not have the most recent version of the book (waiting on that from the library), but her recommendations for 5th and 6th grade were:

 

5th grade: Logic puzzles: Mind Benders and Red Herrings (CTC)

6th grade: Critical Thinking, Book One and Book Two (CTC) (these aren't puzzles)

 

Somehow I missed the boat and did not do Mind Benders last year in 5th even though I bought them.

 

Lisa

[JudoMom]

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?

 

:confused: The book is for ages 12 & up.

 

Honestly, I'd get the book and read it for yourself.

[ChrissySC]

I was just reviewing my WTM book last night for the logic stage to see if I was missing anything for my son. I do not have the most recent version of the book (waiting on that from the library), but her recommendations for 5th and 6th grade were:

 

5th grade: Logic puzzles: Mind Benders and Red Herrings (CTC)

6th grade: Critical Thinking, Book One and Book Two (CTC) (these aren't puzzles)

 

Somehow I missed the boat and did not do Mind Benders last year in 5th even though I bought them.

 

Lisa

 

I used the MB and RH books. I really really do not like them. I have a hard time understanding them, LOL. I was taught formal logic and mathematical logic, as well as programming logic. I find them "puzzlish" for certain. I want how-to-think, or some such ...

 

I suppose I will finally hit checkout on FD though. I really want to know if it is as described. It would be worth the few dollars to discover what the heck is so disturbing. :lol:

[Spy Car]

 

I suppose I will finally hit checkout on FD though. I really want to know if it is as described. It would be worth the few dollars to discover what the heck is so disturbing. :lol:

 

Just don't say I (and others) didn't warn you ;)

 

Bill

[~Amanda~]

I didn't even look for the "disturbing" part, I couldn't get past all the bible quotes in the first few pages.

[Violet Crown]

Nobody ever takes this advice, but one can always ditch the homeschool materials and their Aristotelian logic, and join the Twentieth Century with logic as it is understood by modern logicians, philosophers, and mathematicians.

 

See for example

Tarski's World

(recommended by dh, who has taught many an Intro Logic course)

[~Amanda~]

I can't tell, from that link, if there is something to buy or...

[TheAutumnOak]

We have used Logic Liftoff and I have Logic Countdown for my upcoming 5th grader. I think they are great. They have a variety of activities and teach concepts well. Another bonus is you can photocopy them for in-family use so I don't have to keep rebuying them.

 

 

 

This is my answer exactly ;)...We used Logic Liftoff and will use Logic Countdown for my 5th grader...

 

ETA: I think this is reversed...We used Logic Countdown and will use Logic Liftoff...Countdown comes first...

Edited July 3, 2011 by TheAutumnOak
Wrong order

[veggiegal]

Nobody ever takes this advice, but one can always ditch the homeschool materials and their Aristotelian logic, and join the Twentieth Century with logic as it is understood by modern logicians, philosophers, and mathematicians.

 

See for example

Tarski's World

(recommended by dh, who has taught many an Intro Logic course)

 

:iagree:

 

My kids will be doing all kinds of logic / critical thinking materials, from puzzles to fallacies to modern propositional logic. (I won't ditch the homeschool materials entirely, just move beyond them). It kinda helps that teaching logic / reasoning classes at university is one of the many things I did in my life before kids. ;)

[Violet Crown]

I can't tell, from that link, if there is something to buy or...

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.

[robsiew]

This is my answer exactly ;)...We used Logic Liftoff and will use Logic Countdown for my 5th grader...

 

ETA: I think this is reversed...We used Logic Countdown and will use Logic Liftoff...Countdown comes first...

 

Yup, sorry I reversed those...

[Spy Car]

Nobody ever takes this advice, but one can always ditch the homeschool materials and their Aristotelian logic, and join the Twentieth Century with logic as it is understood by modern logicians, philosophers, and mathematicians.

 

See for example

Tarski's World

(recommended by dh, who has taught many an Intro Logic course)

 

Can you tell me more about Tarski's World?

 

Bill

[Farrar]

Nobody ever takes this advice, but one can always ditch the homeschool materials and their Aristotelian logic, and join the Twentieth Century with logic as it is understood by modern logicians, philosophers, and mathematicians.

 

See for example

Tarski's World

(recommended by dh, who has taught many an Intro Logic course)

 

Can you elaborate on that a little? Do you think doing things like analogies and logic grid problems is a waste of time? I have to say, if my kids didn't enjoy them, we probably wouldn't do them, but I do see that they encourage them to stop and think and reason and they seem like a worthwhile thing to do. And if this is the only suggestion you have for materials, then are you saying we shouldn't bother with logic until kids are in high school?

 

As someone who doesn't know much about logic, I'm just curious.

[Violet Crown]

I don't think analogies, grid problems, etc. are a waste of time. Neither does dh, our resident logician. It's the eventual memorization of various valid syllogistic forms down the road that's a little like memorizing rules for retrogrades so that you can make the orbit of the heavenly bodies around the Earth make sense.

 

Dh wrote up this as a response to questions about Aristotelian logic vs contemporary logic. The Barwise & Etchemendy book he mentions at the bottom is the source of the Tarski's World software.

 

--------------------------------

 

What is contemporary logic?

The study of logic was given its original form by Aristotle in the Prior Analytics. The resulting syllogistic logic retained its basic shape for the next two thousand years or so. But starting in the nineteenth century, and especially in the early twentieth century, there were considerable advances in logic.

Syllogistic logic provides tools for checking the logical validity of certain patterns of reasoning, but its scope is quite narrow. Consider the following line of reasoning:

(Premise 1) Someone admires someone.

(Premise 2) Everyone someone admires admires everyone.

(Conclusion) Everyone admires everyone.

This reasoning is logically valid. Take any two arbitrary people A and B. From Premise 1, we know that there are two people C and D such that C admires D. D is thus a person someone admires. From Premise 2, it follows that D admires everyone. So, in particular, D admires A. A is thus a person someone (namely, D) admires. Again by Premise 2, it follows that A admires everyone. So, in particular, A admires B. Since A and B were arbitrary, it follows that everyone admires everyone.

But syllogistic logic cannot capture or explain the validity of this reasoning. This is just one example – in general, there are large classes of patterns of reasoning that fall outside the scope of syllogistic reasoning. Contemporary logic gives a much more expansive collection of tools that captures these forms of reasoning while at the same time giving a simpler and more elegant explanation of the validities that are captured by syllogistic logic.

Contemporary logic is typically formal. This means that arguments are represented and analyzed in a formal, artificial language meant to bring out key logical features more clearly. If you see logic with lots of backward Es and upside-down As, you’re looking at contemporary logic. The use of formalism allows contemporary logic to give simpler explanations of complex phenomena in natural languages, and to integrate more easily with the tools of mathematics.

The advances of contemporary logic are one of the great intellectual accomplishments of the twentieth century – at the same level, for example, as the advances in physics of general relativity and quantum mechanics. Just as general relativity and quantum mechanics preserve the older Newtonian mechanics as a special case while providing additional explanation of other cases, contemporary logic preserves syllogistic logic as a special case while providing additional explanation of other cases. And contemporary logic, unlike general relativity and quantum mechanics, is actually simpler and easier to learn than the theory it replaces.

Contemporary logic is deeply intertwined with a number of important intellectual disciplines. Much that happens in computer science, linguistics, philosophy, and certain branches of mathematics cannot be well understood without a grasp of contemporary logic.

 

Why should you learn contemporary logic rather than syllogistic logic?

1. Contemporary logic does everything that syllogistic logic does, and does it more simply. In syllogistic logic, mastering the tools for checking the validity of syllogisms means either memorizing a lengthy and arbitrary-seeming list of valid forms, or learning a complicated set of techniques for transforming one syllogism into another. But contemporary logic uses three or four simple rules to make the same determinations.

2. Contemporary logic also provides tools for analyzing many arguments that are outside the scope of syllogistic logic. Traditional syllogistic logic, for example, provides only limited tools for working with combinations of connectives like "if" and "or", and no tools for dealing with sentences with multiple quantifiers. The sentence "Someone is mugged in New York City every fifteen minutes" is ambiguous – there is a natural reading on which it says that for each fifteen minute period, there is a mugging in New York City, and a less natural reading on which it says that there is a single unfortunate person in New York City who is repeatedly mugged. Contemporary logic gives tools that immediately and elegantly explain this ambiguity; syllogistic logic has nothing to say about it.

3. Contemporary logic developed largely as an attempt to formalize the reasoning of mathematicians. This means that it is a powerful and useful tool for improving mathematical reasoning. The standard mathematical definition of the claim that f is a continuous functions, for example, is:

 For every x, given any ε>o, there is a δ>0 such that for all y such that |x-y|<δ, |f(x)-f(y)|<ε.

Syllogistic logic gives no tools for understanding and working with complex claims like this, but contemporary logic does. A grasp of contemporary logic substantially improves students’ ability to master intricate mathematical concepts.

4. Because of the mathematical orientation of contemporary logic, it integrates thoroughly with math. One consequence of that is that contemporary logic features many mathematical tools for the analysis of logical languages. The theory of algorithm verification in computer science, for example, is an offshoot of this aspect of contemporary logic.

5. Contemporary logic is the form of logic that will be presupposed in any university-level study of logic and logically-influenced fields. Introductory logic courses will use contemporary, rather than syllogistic, logic. And more advanced subjects that require a background in logic, such as certain courses in computer science, mathematics, and linguistics, will make sense only with a background in contemporary logic, and not with a background in syllogistic logic.

6. Because of its use of formal languages, contemporary logic is an excellent tool for developing abstract reasoning techniques. Multiple studies show that people find highly abstract reasoning very difficult. Consider the following example. There is a deck of cards, each of which has a digit from 0 to 9 on one side, and a letter of the alphabet on the other side. Four cards are set in front of you, so that you can see one side of each card. You see an A, a 7, a G, and a 4. You are then asked to determine whether the claim "Every card with a vowel on one side has an odd number on the other side" is true or false. Which cards do you need to turn over to make this determination? Only 15-20% of people can perform this reasoning task correctly. Performing abstract reasoning of this sort can, for example, lead to substantial improvements in scores on the LSAT and GRE exams.

How should you go about learning contemporary logic?

There are a number of excellent textbooks in contemporary logic. Barwise and Etchemendy’s book The Language of First-Order Logic is a particularly thorough introduction that also includes software tools that are very helpful for mastering the material. Some other good texts:

 Allen and Hand, Logic Primer

 Mates, Elementary Logic

 Bonevac, Deduction

 Lambert and Van Fraassen, Derivation and Counterexample

 Lemmon, Beginning Logic

Edited July 3, 2011 by Sharon in Austin

[Violet Crown]

Can you elaborate on that a little? Do you think doing things like analogies and logic grid problems is a waste of time? I have to say, if my kids didn't enjoy them, we probably wouldn't do them, but I do see that they encourage them to stop and think and reason and they seem like a worthwhile thing to do. And if this is the only suggestion you have for materials, then are you saying we shouldn't bother with logic until kids are in high school?

 

As someone who doesn't know much about logic, I'm just curious.

As with the advances linguists have made in the field of grammar, the advances in logic seem to have coincided with a cessation of teaching the subject at a pre-college level. So no, there just isn't much out there. Other than playing with Tarski's World a bit, we have held off doing anything beyond playing with the old-fashioned logic puzzles until the high school level. We don't consider logic/critical thinking to be a "subject" at the primary level.

[Mom0012]

I used the MB and RH books. I really really do not like them. I have a hard time understanding them, LOL. I was taught formal logic and mathematical logic, as well as programming logic. I find them "puzzlish" for certain. I want how-to-think, or some such ...

 

I suppose I will finally hit checkout on FD though. I really want to know if it is as described. It would be worth the few dollars to discover what the heck is so disturbing. :lol:

 

Yes, the Mindbenders and Red Herring books are puzzles, but I don't think the Critical Thinking 1 and Critical Thinking 2 books are.

 

I do like Mindbenders. IMO, they are really good for increasing reading comprehension and making the kids think things through. I haven't tried Red Herrings (and don't really plan to).

 

Lisa

[ChrissySC]

Just don't say I (and others) didn't warn you ;)

 

Bill

 

 

Ugghhh... If you just just hadn't said anything, LOL.

 

*sigh*

 

If it sits in my cart, then I still don't have a logic book.:lol:

 

I really did spend some time looking at the three books that start with Logic Countdown. I also looked at Logic Links too.

 

Do I have to do something puzzlish? I really really don't like MB and RH. I want to, but I can't.

 

Do you think those books would do it?

 

I have to do something. I have put off formal logic study and latin for far far tooooooo long!

 

Edit: I'll look at these ... Critical Thinking 1 and Critical Thinking 2

[~Amanda~]

Anyone have an opinion about art of argument? discovery of deduction? argument builder?

 

what age/grade is appropriate to start art of argument?

[Chris in VA]

Ds did Fallacy Detective in 9th grade (he's older than is typical--he was 15). We don't mind Christian materials. There is a lot of worldview in there, in my opinion. It was our first intro into logic, and it is very clearly written and understandable, and we liked the examples that illustrate each type of fallacy.

 

I wouldn't, however, start there if I had to do it all over again. I wish we had used Critical Thinking 1 and 2, as recommended for Jr Hi in WTM. We could have added in FD later, and it would have made more sense to us (although it's very clear, as I said, we didn't get the whole "logic thing" very well just from FD and needed more depth).

[Farrar]

As with the advances linguists have made in the field of grammar, the advances in logic seem to have coincided with a cessation of teaching the subject at a pre-college level. So no, there just isn't much out there. Other than playing with Tarski's World a bit, we have held off doing anything beyond playing with the old-fashioned logic puzzles until the high school level. We don't consider logic/critical thinking to be a "subject" at the primary level.

 

Thanks for that. I appreciated that long post of explanation too. :001_smile: We also don't do it as a "subject" per se. It's just a fun extra. I had a lot of this sort of analogies, logic puzzles sort of stuff in elementary school, but no formal logic later on so it was interesting to read.

[robsiew]

I really did spend some time looking at the three books that start with Logic Countdown. I also looked at Logic Links too.

 

Do I have to do something puzzlish? I really really don't like MB and RH. I want to, but I can't.

 

Do you think those books would do it?

 

I have to do something. I have put off formal logic study and latin for far far tooooooo long!

 

Edit: I'll look at these ... Critical Thinking 1 and Critical Thinking 2

 

Why not just keep it fun with Logic Countdown and some online free puzzles or board games that emphasize strategy? It promotes the kind of thinking that will be great practice for more formal Logic in a couple years. My 5th grader loves logic and I believe will do really well, but we're not going too deep too fast. He LOVES many of the strategy board games and many of the puzzles online or for his ipod touch. Why not start there? We're planning on the CT books when he gets a bit older....

[ChrissySC]

Why not just keep it fun with Logic Countdown and some online free puzzles or board games that emphasize strategy? It promotes the kind of thinking that will be great practice for more formal Logic in a couple years. My 5th grader loves logic and I believe will do really well, but we're not going too deep too fast. He LOVES many of the strategy board games and many of the puzzles online or for his ipod touch. Why not start there? We're planning on the CT books when he gets a bit older....

 

Valid - consideirng ....

[Violet Crown]

Can you tell me more about Tarski's World?

 

Here's a quick overview of Tarski's world:

 

Tarski's World allows you to construct and describe a miniature world. The world is a 3x3 grid, on which you can place triangles, squares, and pentagons, each of which can be small, medium, or large. You can also put names (a, b, etc.) on the shapes.

 

You then learn to use a formal logical language to describe the world you've created. The language has basic predicates Triangle, Square, Pentagon, Small, Medium, Large, Smaller, LeftOf, and others. These predicates can be used to form basic sentences that can then be combined with logical operations to form more complex sentences. You can then check to see if your sentence is true or false in the world you have created.

 

For example, the sentence:

 

Ax(Square(x) => Ey(Triangle(y) /\ LeftOf(x,y))

 

says that "Every square is to the left of some triangle". The sentence:

 

Ex(Triangle(x) /\ Ay(Square(y) => LeftOf(y,x))

 

says that "Some triangle has every square to the left of it". By experimenting with rearranging the contents of the worlds, you can start to get a clear sense of how these two sentences differ, and in general of what sentences in the logical language mean, and how the logical operations affect meaning.

[robsiew]

Here's a quick overview of Tarski's world:

 

Tarski's World allows you to construct and describe a miniature world. The world is a 3x3 grid, on which you can place triangles, squares, and pentagons, each of which can be small, medium, or large. You can also put names (a, b, etc.) on the shapes.

 

You then learn to use a formal logical language to describe the world you've created. The language has basic predicates Triangle, Square, Pentagon, Small, Medium, Large, Smaller, LeftOf, and others. These predicates can be used to form basic sentences that can then be combined with logical operations to form more complex sentences. You can then check to see if your sentence is true or false in the world you have created.

 

For example, the sentence:

 

Ax(Square(x) => Ey(Triangle(y) /\ LeftOf(x,y))

 

says that "Every square is to the left of some triangle". The sentence:

 

Ex(Triangle(x) /\ Ay(Square(y) => LeftOf(y,x))

 

says that "Some triangle has every square to the left of it". By experimenting with rearranging the contents of the worlds, you can start to get a clear sense of how these two sentences differ, and in general of what sentences in the logical language mean, and how the logical operations affect meaning.

 

This is very interesting! Logic is something completely new to me (don't laugh too hard... my dh would agree! :lol:) I'm loving this thread! It's giving me some good things to research! How come I've NEVER been exposed to this? What did they teach me in HS/College/Graduate school????:confused:

[Spy Car]

Here's a quick overview of Tarski's world:

 

Tarski's World allows you to construct and describe a miniature world. The world is a 3x3 grid, on which you can place triangles, squares, and pentagons, each of which can be small, medium, or large. You can also put names (a, b, etc.) on the shapes.

 

You then learn to use a formal logical language to describe the world you've created. The language has basic predicates Triangle, Square, Pentagon, Small, Medium, Large, Smaller, LeftOf, and others. These predicates can be used to form basic sentences that can then be combined with logical operations to form more complex sentences. You can then check to see if your sentence is true or false in the world you have created.

 

For example, the sentence:

 

Ax(Square(x) => Ey(Triangle(y) /\ LeftOf(x,y))

 

says that "Every square is to the left of some triangle". The sentence:

 

Ex(Triangle(x) /\ Ay(Square(y) => LeftOf(y,x))

 

says that "Some triangle has every square to the left of it". By experimenting with rearranging the contents of the worlds, you can start to get a clear sense of how these two sentences differ, and in general of what sentences in the logical language mean, and how the logical operations affect meaning.

 

Thanks for this. The meaning of the parameters as symbolic expressions is not immediately obvious, but I suppose learning these is part of the process.

 

As I've rooting around to find out more, I see the program described as starting out easy and having an incremental build. Do you think this is something a smart almost 7 year old could grasp?

 

Bill

[Violet Crown]

Thanks for this. The meaning of the parameters as symbolic expressions is not immediately obvious, but I suppose learning these is part of the process.

 

As I've rooting around to find out more, I see the program described as starting out easy and having an incremental build. Do you think this is something a smart almost 7 year old could grasp?

 

Bill

 

[sorry for the delay, Bill; dh has been out of town. Post below is from him.]

 

Most undergraduates are able to pick it up after a semester of work or so. So yes, I'd say a smart almost 7 year old would be exactly the right audience.

 

Quick summary of the symbols used:

 

/\ = and

=> = if

A = all

E = there exists

 

So "Ax(Square(x) => Ey(Triangle(y) /\ LeftOf(x,y))" is, in pseudo-English, "For all x, if x is a square, then there exists a y such that y is a triangle and x is to the left of y".

Edited July 8, 2011 by Sharon in Austin

[veggiegal]

 

Quick summary of the symbols used:

 

/\ = and

=> = if

A = all

E = there exists

 

So "Ax(Square(x) => Ey(Triangle(y) /\ LeftOf(x,y))" is, in pseudo-English, "For all x, if x is a square, then there exists a y such that y is a triangle and x is to the left of y".

 

I'm intrigued. A few questions:

 

Does Tarski's world focus on translating everyday English into symbols? ('unless', 'if and only if', etc.). IME experience students need a LOT of time and practice with translation between English and symbolic logic, just as they need time translating English to math symbols/diagrams/equations.

 

Is there a symbol for 'or'? Is there any discussion of inclusive (the 'or' of logic) vs exclusive 'or' (arguably the most common 'or' in English)?

 

Are any deductions done, with simple rules / strategies illustrated (Modus Ponens, Modus Tollens, Reductio Ad Absurdum, etc.)?

[Violet Crown]

I'm intrigued. A few questions:

 

Does Tarski's world focus on translating everyday English into symbols? ('unless', 'if and only if', etc.). IME experience students need a LOT of time and practice with translation between English and symbolic logic, just as they need time translating English to math symbols/diagrams/equations.

 

Is there a symbol for 'or'? Is there any discussion of inclusive (the 'or' of logic) vs exclusive 'or' (arguably the most common 'or' in English)?

 

Are any deductions done, with simple rules / strategies illustrated (Modus Ponens, Modus Tollens, Reductio Ad Absurdum, etc.)?

 

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).

[veggiegal]

 

Thanks for the reply. I'll have a look into those other books you mentioned--this sounds like some stuff that would be both right up my 9 year old's alley, as well as a nice stretch in places. I absolutely loved the text I used when I took my first logic class some 20+ years ago, but cannot for the life of me remember the title. The one's you suggested look promising, and I like the idea of having a book more focused on translation issues, and one more on the deductions and rules.

 

 

[DragonFaerie]

The formal logic is waaayyyy over my head. Luckily, my kiddos are just 8 and 9 so I can avoid that for a little while. :lol:

 

In the meantime, we're doing puzzles. I have Logic Countdown, Mindbenders and analogies books for them. We'll rotate each week to keep it interesting.