Menu
Jump to content

What's with the ads?

cintinative

Help with this logic problem please!

Recommended Posts

According to the publisher, this is invalid. 

 

I can't wrap my mind around why. Please help. TIA!

 

"Since all mothers are parents, and all parents have children, then all children have mothers."

Share this post


Link to post
Share on other sites

I am thinking that it's not invalid because it's not true, but because it's not a direct consequence of the first two statements.  All mothers being parents and all parents having children doesn't, according to the way it's written, lead to all children having mothers.  All mothers can be parents and have children, and all parents can have children, but those don't mean that ALL children have mothers.  SOME children could have mothers, but the sentence doesn't allow for the fact that SOME children might not have mothers.  We know that all children have mothers because we know basic biology, but that statement doesn't make that true.

 

If it were written, "Since all beeps are dots, and all dots have squirts, then all squirts have beeps," you would say, "Well, no.  There could be some squirts that don't have beeps, even if the first two statements are true."  At least I think that's what it means.

  • Like 4

Share this post


Link to post
Share on other sites

That sort of makes sense. I think it is the biology bit that is tripping me up.  The beeps and dots argument makes sense.

 

For example, this statement was valid (and is the question before the one I asked about):

 

"Since all mothers are parents, and all parents have children, therefore, all mothers have children."

Share this post


Link to post
Share on other sites

It's checking your understanding of the law of syllogism.

 

m => p,

 

and

 

p => c

 

Therefore,

 

m => c.

 

But see how there's no arrow leading from c to anything else? This means we can't conclude "Children have...".

  • Like 3

Share this post


Link to post
Share on other sites

It says all mothers are parents and all parents have children, but it doesn't say that all parents are mothers or that all children have parents.

  • Like 1

Share this post


Link to post
Share on other sites

"Since all mothers are parents, and all parents have children, then all children have mothers."

 

Not all parents are mothers.  Not all children have parents.

Share this post


Link to post
Share on other sites

It's tricky because we know that in fact, all children do have mothers, and we tend to forget to separate the idea of a parent and a mother in the second  statement - we intuitively think of "parents" as "a mother and a father".  But that is not part of the statement.

 

Although - it's interesting - I wonder if we could say that in fact, "parents" does necessarily mean, at least with humans, a mother and a father?

 

But that is rather outside of what they are trying to demonstrate!

Share this post


Link to post
Share on other sites

"Since all mothers are parents, and all parents have children, then all children have mothers."

 

I think the problem is that we know all children have mothers as a true biological fact, and it is hard to separate the truth of that from the faulty logic of the statement.

Substitute something else:

 

"Since all poodles are dogs, and all dogs have four legs, then all four legged creatures are poodles." is obviously not correct.

  • Like 1

Share this post


Link to post
Share on other sites

I'm curious what people think of the purpose of the problem. Obviously, it's to test the student's knowledge of syllogisms, which is clearer when the problem can be revealed through common sense or when it uses nonsense concepts like the example given above. But I wonder if it's also to push students to understand how logic will be incomplete without more complete information. If you start with limited information, your conclusions will also be limited in their scope, maybe even to the point of being misleading, which I think is the case here. Again, logically, it's not misleading because the conclusion is limited. We cannot say from this information that all children have mothers. But in an argument, it makes it sound to the casual listener like maybe some children don't have mothers or like the science on that is still out and can't be concluded, which would be a false assumption.

  • Like 1

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

SUBSCRIBE TO OUR NEWSLETTER & RECEIVE A COUPON FOR
10% OFF
We respect your privacy.You’ll hear about new products, special discounts & sales, and homeschooling tips. *Coupon only valid for first-time registrants. Coupon cannot be combined with any other offer. Entering your email address makes you eligible to receive future promotional emails.
0 Shares
Share
Tweet
Pin
×