Something We Can All Agree On

[David Sklansky]

It seems so obvious that it is surprising that I haven't heard this suggested before.

Starting with second or third grade, one day a year should be devoted to teaching, and then reminding kids, this one simple point:

Just because, If A is true, B is true

It doesn't mean that If B is true, A is true

Or that If A is not true, B is not true

But it does mean that if B is not true, A is not true.

I believe that at least half of the stupid ideas that people have, stem from not fully realizing those simple statements above. Yet those statements are usually taught only as part of more techinical classes that only some of the older students take. There is no reason for that.

Let's persuade schools to devote one day a year to making sure that kids realize the above. We could call it the Two Plus Two Initiative.

[Kimbell175113]

I know you know this already, but a big problem is that people never really form the statement "if a, then b" in the first place. They just intuitively realize that a and b are connected in some way, and go from there without further thought.

[tarheeljks]

i agree, but 2nd or 3rd grade seems a little early. some children don't reach the concrete operational stage until as late as puberty, so i think a concept like this should be addressed in middle school at the earliest. my vote is to introduce this in geometry b/c (i think) geometry is the first course i took that explicitly made use of logic and b/c i think almost all students take geometry.

[PairTheBoard]

[ QUOTE ]
It seems so obvious that it is surprising that I haven't heard this suggested before.

Starting with second or third grade, one day a year should be devoted to teaching, and then reminding kids, this one simple point:

Just because, If A is true, B is true

It doesn't mean that If B is true, A is true

Or that If A is not true, B is not true

But it does mean that if B is not true, A is not true.

I believe that at least half of the stupid ideas that people have, stem from not fully realizing those simple statements above. Yet those statements are usually taught only as part of more techinical classes that only some of the older students take. There is no reason for that.

Let's persuade schools to devote one day a year to making sure that kids realize the above. We could call it the Two Plus Two Initiative.

[/ QUOTE ]

That's a good idea. I remember logic lessons when I went to school although I'm not sure when they gave them. Maybe not that early but I think fairly early. The lessons can be a lot of fun for kids.

All houses in the Enchanted City are painted Red. Jimmy the squirel lives in a Red House. Does that mean Jimmy lives in the Enchanted City?

Stuff like that.

PairTheBoard

[.Alex.]

I was under the impression that this concept was thoroughly covered in 10th grade geometry classes across the country. I think that most people understand this and know what it means, but they don't apply it often enough when forming ideas because they let their emotions control them. Not sure if your suggestion is enough to change the status quo.

[ALawPoker]

But would it really help? I think even people with "stupid ideas" realize that what you say about A and B is indeed true, if it's called to their attention.

I think they come up with their stupid ideas because that's just their way of stereotyping thought (which we all do to some degree). I think teaching people not to do this is more complicated than just reminding them of the obvious.

EDIT: Oops, sort of repeated Alex.

[tarheeljks]

[ QUOTE ]
I was under the impression that this concept was thoroughly covered in 10th grade geometry classes across the country. I think that most people understand this and know what it means, but they don't apply it often enough when forming ideas because they let their emotions control them. Not sure if your suggestion is enough to change the status quo.

[/ QUOTE ]

this was not covered explicitly in the geometry class that i took. the implications of "if a is true then b is true" can be inferred relatively easily, but i don't think i saw these implications in print before i took computer science. of course there will be children who can figure this out on their own, but that doesn't mean it isn't worth teaching.

[Silent A]

Actually, I don't think this will do much good because I don't think people make this error as often as David implies. What I think is far more common is the "co-relation means causation" error. Or, to be more precise, people tend to see co-relation and then apply the causation arrow based on personnal pre-dispositions.

A common example of this in politics is people who argue that marajuana is a gateway drug to cocaine/crack/heroin but never argue that alcohol is too (even though the "logic" would be identical).

I think it would help if David could present some examples of "stupid ideas" that involve the logic error he describes. I'm having trouble thinking of a single non-trivial example.

[soon2bepro]

I believe some people may have a problem with this because of the common wording:

"If A, then B"

If you interpret this as a consecuence that happens within a timeline, like: "If A is true, B will happen in the future", then clearly B being false doesn't mean A is false.

[PLOlover]

[ QUOTE ]
If you interpret this as a consecuence that happens within a timeline, like: "If A is true, B will happen in the future", then clearly B being false doesn't mean A is false.

[/ QUOTE ]

?

[FortunaMaximus]

[ QUOTE ]
[ QUOTE ]
If you interpret this as a consecuence that happens within a timeline, like: "If A is true, B will happen in the future", then clearly B being false doesn't mean A is false.

[/ QUOTE ]

?

[/ QUOTE ]

Cause and effect.

[LooseCaller]

he's saying this isnt the correct way to interpret it. there is no temporal relationship implied by "If A, then B."
assume A means "human male" and B means "has Y chromosome." this is an example of a time where establishing not B also means not A.

[bigmonkey]

[ QUOTE ]

All houses in the Enchanted City are painted Red. Jimmy the squirel lives in a Red House. Does that mean Jimmy lives in the Enchanted City?

Stuff like that.

PairTheBoard

[/ QUOTE ]

I agree with David's sentiment but I think propositional logic should be taught at the same age as basic arithmetic, say about 4 years old. I studied philosophy as an undergraduate degree and when we went to the open day for the course while we were still at school one of the professers addressed us with this question:

There are 4 cards (he drew them on the board). If there is an even number on one side then there is a heart on the other side. How many hearts are there? We can see 4 cards with the numbers 2, 4, 5 and 7 on them.

I thought the answer to this question was blatantly 2 but I didn't stick my hand up to answer because I thought there would just be no credit gained from answering something so obvious. Someone answered that there's between 2 and 4 and we cannot know, at which point I'm thinking "Oh my God. If you were that stupid why would you try to answer this question?" Of course they were right, and I immediately understood after having it explained to the whole room. I think myself and most of the people who misunderstood were not stupid. About half of the group had studied philosophy at school and must've learned this there. For the rest of us the concept of "If A then B" was identical to our concept for "Iff A then B" or "If A then B and if B then A", simply because we'd never encountered situations where they might be different. We were all 17/18 then so not exactly new to the world of common sense. I expect many people go to their graves believing that "If A then B" and "Iff A then B" are the same thing. I think if you went into a bar and said to someone "I'll wager my $10 to your $10 that if I can throw a dart blindfold from across the whole bar and hit the dartboard, it will hit the bullseye", and then demand $10 when my dart lands in someone's pint they would be very annoyed. They would either refuse to pay up because their conception of the bet was that I had to both hit the dartboard and the bullseye, or they would feel like they had been hustled, and probably still not pay. If they understood the hustle they'd probably not learn anything from this about the nature of conditional statements because they'd be too set in their ways to change.

(I would love it though if they said something like "Let us apply the Ramsey Test to the proposition you bet on, or use Adams' logic of indicative conditionals, and I think you'll owe me $10" I would then proceed to pay them.)

[m_the0ry]

This is basic logic that, sadly, a good three quarters of people do not realize or understand.

"B if A"

means we can infer B when A is true. When B is true we can make no inference.

"B iff a" (double f is not a type, read as 'B if and only if A')

means we can infer B when A is true. We can also infer A when B is true.

[cgrohman]

Its supposed to be. It also forms the basis for most of the questions on the LSAT.

[tarheeljks]

[ QUOTE ]
[ QUOTE ]

All houses in the Enchanted City are painted Red. Jimmy the squirel lives in a Red House. Does that mean Jimmy lives in the Enchanted City?

Stuff like that.

PairTheBoard

[/ QUOTE ]

I agree with David's sentiment but I think propositional logic should be taught at the same age as basic arithmetic, say about 4 years old. I studied philosophy as an undergraduate degree and when we went to the open day for the course while we were still at school one of the professers addressed us with this question:

There are 4 cards (he drew them on the board). If there is an even number on one side then there is a heart on the other side. How many hearts are there? We can see 4 cards with the numbers 2, 4, 5 and 7 on them.

I thought the answer to this question was blatantly 2 but I didn't stick my hand up to answer because I thought there would just be no credit gained from answering something so obvious. Someone answered that there's between 2 and 4 and we cannot know, at which point I'm thinking "Oh my God. If you were that stupid why would you try to answer this question?" Of course they were right, and I immediately understood after having it explained to the whole room. I think myself and most of the people who misunderstood were not stupid. About half of the group had studied philosophy at school and must've learned this there. For the rest of us the concept of "If A then B" was identical to our concept for "Iff A then B" or "If A then B and if B then A", simply because we'd never encountered situations where they might be different. We were all 17/18 then so not exactly new to the world of common sense. I expect many people go to their graves believing that "If A then B" and "Iff A then B" are the same thing. I think if you went into a bar and said to someone "I'll wager my $10 to your $10 that if I can throw a dart blindfold from across the whole bar and hit the dartboard, it will hit the bullseye", and then demand $10 when my dart lands in someone's pint they would be very annoyed. They would either refuse to pay up because their conception of the bet was that I had to both hit the dartboard and the bullseye, or they would feel like they had been hustled, and probably still not pay. If they understood the hustle they'd probably not learn anything from this about the nature of conditional statements because they'd be too set in their ways to change.

(I would love it though if they said something like "Let us apply the Ramsey Test to the proposition you bet on, or use Adams' logic of indicative conditionals, and I think you'll owe me $10" I would then proceed to pay them.)

[/ QUOTE ]

at this age i don't think children's brains have developed enough to comprehend propositional logic

[m_the0ry]

[ QUOTE ]
at this age i don't think children's brains have developed enough to comprehend propositional logic

[/ QUOTE ]


Actually, this logic is incredibly intuitive at the venn diagram level. The same principles lay the foundation for set theory. It's a generally important philosophy for the sciences and it should be required in general education.

[tarheeljks]

[ QUOTE ]
[ QUOTE ]
at this age i don't think children's brains have developed enough to comprehend propositional logic

[/ QUOTE ]


Actually, this logic is incredibly intuitive at the venn diagram level. The same principles lay the foundation for set theory. It's a generally important philosophy for the sciences and it should be required in general education.

[/ QUOTE ]

good point, but venn diagrams are too advanced for most 4 year olds right. we are talking mid to late elementary school at the earliest?

[bigmonkey]

It's really not complicated at all. I think the reason some college students find it tough is because they've already gone past the stage where they would learn it easily. They say that young children can learn two (possibly three?) languages at once and learn quicker than teenagers. As far as I can see, the fact that having A and the fact that having B entailing A&B is about as easy to comprehend as 1+2=3.

[PairTheBoard]

[ QUOTE ]
It's really not complicated at all. I think the reason some college students find it tough is because they've already gone past the stage where they would learn it easily. They say that young children can learn two (possibly three?) languages at once and learn quicker than teenagers. As far as I can see, the fact that having A and the fact that having B entailing A&B is about as easy to comprehend as 1+2=3.

[/ QUOTE ]

The difference between "And","Or", and "XOR" is one everybody should learn better early too. Kids should get comfortable and fluent in the logic of breaking things up into Cases. Lots of simple intuitive exercises should be done to familiarize them with this process. We saw right here in a recent SMP thread the difficulties someone had solving (x-3)(x+3)<0 through the logic of Cases.

Students are generally so bad at conceptualizing Cases that many places have virtually given up hope getting to see the logic for why the solution is -3<x<3. Instead they settle for the Rote method of solving for the zeros of (x-3)(x+3) then plugging a point from each of the three intervals defined by those zeros to see if they work in the inequality. Everyone learns the algorithm for solving the inequality but nobody understands why it works. When they see new kinds of problems where they haven't learned a Rote method they have no idea how to approach it by breaking it down into Cases if possible.

Breaking a problem down into Cases is almost a fundamental strategy in analyzing things yet the method is completely foreign to a lot of people.

PairTheBoard

[bigmonkey]

[ QUOTE ]
[The difference between "And","Or", and "XOR" is one everybody should learn better early too. Kids should get comfortable and fluent in the logic of breaking things up into Cases. Lots of simple intuitive exercises should be done to familiarize them with this process. We saw right here in a recent SMP thread the difficulties someone had solving (x-3)(x+3)<0 through the logic of Cases.

Students are generally so bad at conceptualizing Cases that many places have virtually given up hope getting to see the logic for why the solution is -3<x<3. Instead they settle for the Rote method of solving for the zeros of (x-3)(x+3) then plugging a point from each of the three intervals defined by those zeros to see if they work in the inequality. Everyone learns the algorithm for solving the inequality but nobody understands why it works. When they see new kinds of problems where they haven't learned a Rote method they have no idea how to approach it by breaking it down into Cases if possible.

Breaking a problem down into Cases is almost a fundamental strategy in analyzing things yet the method is completely foreign to a lot of people.

PairTheBoard

[/ QUOTE ]

I didn't see that straight away but it is maybe because I have been up since 4:30 a.m and am pretty knackered now, although I suspect I wouldn't have made that connection immediately normally. The worst thing is I know for a fact 4 years ago I would've made that inference immediately, and it's not as if I am getting Alzheimer's or anything, being only 20. I was good at mathematics all my life, better than any one of my peers (although I've met people at university, particularly professors, who I know are much better than I ever was), but when I stopped studying mathematics my mental arithmetic slowed down so badly I was worried about it. It must be about as good now as it was when I was 10. Pretty sad really, but maybe it suggests that things like this are related to use and habit rather than a causal tracking of common sense.

[PLOlover]

[ QUOTE ]
It's really not complicated at all. I think the reason some college students find it tough is because they've already gone past the stage where they would learn it easily. They say that young children can learn two (possibly three?) languages at once and learn quicker than teenagers. As far as I can see, the fact that having A and the fact that having B entailing A&B is about as easy to comprehend as 1+2=3.

[/ QUOTE ]

I think I was 11 when I learned the distance equation for you know graphing and of course already knew the pythagorean theorum, but it wasn't until 12 that I realized they were the same thing, so bassed on that i would say start teaching it around 12.