Manhattan NA Drill Question Forum

[P.J.Fry]

4th edition of the Manhattan LR book page 113 (solution page 116)

Can I post the problem verbatim here, or is that against the rules? I'll edit it out and paraphrase if it's not cool.

5. An automatic bell above the front door rings whenever a customer enters the front door of The Town Convenience Store. Therefore, one can accurately determine the number of customers who enter Town Convenience on any given day simply by counting the number of rings from the front door bell.

The drill then goes on to ask which of the following are sufficient assumptions, necessary assumptions, or neither.

__ The bell rings each time a customer leaves the store through the front door.

Solution: Neither - This hurts the argument! If the bell rings each time the customers leave, then our counting would get messed up. We need to assume that the bell does NOT ring when customers leave. This assumption does the exact opposite of what we want.

I don't feel it ringing when a customer leaves would hurt the argument. You could still effectively count the number of customers who entered. For example, if we count the bell rings 100 times throughout the day then we could say that 50 customers entered. A similar principle was applied in PT30 S2 Q22 - the rattlesnake molting. Answer choice A in that question was determined not to be necessary because you could still accurately count a rattlesnakes age if it molts more than once a year as long as it were on regular intervals.

I felt it was actually a necessary assumption. To me, the logical negation would be "The bell DOES NOT ring each time a customer leaves through the front door." This could imply that it rings sometimes, and does not ring other times when a customer leaves. which would absolutely destroy the argument.

Is that too much of a stretch imagine it could imply only ringing sometimes when a customer leaves? Am I incorrectly negating ie. is the logical negation actually "The bell NEVER rings each time a customer leaves through the front door."?

[Colonel_funkadunk]

4th edition of the Manhattan LR book page 113 (solution page 116)

Can I post the problem verbatim here, or is that against the rules? I'll edit it out and paraphrase if it's not cool.

5. An automatic bell above the front door rings whenever a customer enters the front door of The Town Convenience Store. Therefore, one can accurately determine the number of customers who enter Town Convenience on any given day simply by counting the number of rings from the front door bell.

The drill then goes on to ask which of the following are sufficient assumptions, necessary assumptions, or neither.

__ The bell rings each time a customer leaves the store through the front door.


Solution: Neither - This hurts the argument! If the bell rings each time the customers leave, then our counting would get messed up. We need to assume that the bell does NOT ring when customers leave. This assumption does the exact opposite of what we want.

I don't feel it ringing when a customer leaves would hurt the argument. You could still effectively count the number of customers who entered. For example, if we count the bell rings 100 times throughout the day then we could say that 50 customers entered. A similar principle was applied in PT30 S2 Q22 - the rattlesnake molting. Answer choice A in that question was determined not to be necessary because you could still accurately count a rattlesnakes age if it molts more than once a year as long as it were on regular intervals.

I felt it was actually a necessary assumption. To me, the logical negation would be "The bell DOES NOT ring each time a customer leaves through the front door." This could imply that it rings sometimes, and does not ring other times when a customer leaves. which would absolutely destroy the argument.

Is that too much of a stretch imagine it could imply only ringing sometimes when a customer leaves? Am I incorrectly negating ie. is the logical negation actually "The bell NEVER rings each time a customer leaves through the front door."?

The premise and conclusion is about what happens when a customer enters. So negating what happens when the customer leaves the store does not destroy the argument.

[P.J.Fry]

The premise and conclusion is about what happens when a customer enters. So negating what happens when the customer leaves the store does not destroy the argument.

Sure it does. If the bell rings every time a customer enters (50 times) and sometimes when the customer leaves (maybe 2 times, maybe 36 times) we have no way of accurately counting how many customers entered by counting the number of times the bell rings.

We can only accurately know how many entered if we know how often the bell rings when they leave (eg. it never rings when they leave, it always rings when they leave, it rings every 2nd time a customer leaves).

[Colonel_funkadunk]

The premise and conclusion is about what happens when a customer enters. So negating what happens when the customer leaves the store does not destroy the argument.

Sure it does. If the bell rings every time a customer enters (50 times) and sometimes when the customer leaves (maybe 2 times, maybe 36 times) we have no way of accurately counting how many customers entered.

We can only accurately know how many entered if we know how often the bell rings when they leave (eg. it never rings when they leave, it always rings when they leave, it rings every 2nd time a customer leaves).

Think about it this way. If the negation is "the bell never rings when the customer leaves the store", then that negation actually strengthens the argument. Because if the bell never rings when customers leave the store, that makes it more likely that you can count the number of people that entered simply by counting the rings when they enter. Also, when it says "simply by counting the rings" means just by counting the rings when they enter. Not by counting them then dividing them in half if it rings when they exit. That's why that statement hurts the argument "the bell sometimes rings when they leave the store"

[gavaga1]

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[P.J.Fry]

Think about it this way. If the negation is "the bell never rings when the customer leaves the store", then that negation actually strengthens the argument. Because if the bell never rings when customers leave the store, that makes it more likely that you can count the number of people that entered simply by counting the rings when they enter. Also, when it says "simply by counting the rings" means just by counting the rings when they enter. Not by counting them then dividing them in half if it rings when they exit. That's why that statement hurts the argument "the bell sometimes rings when they leave the store"

If that is the correct negation, then I agree with you completely.

I took it this way: "The bell rings each time a customer leaves the store through the front door." where the bolded 'each time' means '100% of the time.' The logical negation of '100% of the time' is not '0% of the time' or 'never.' It is 'not 100% of the time' which could be 0% or 99%. Am I wrong?

As for simply counting, if we knew the bell rang 100% of the time when the customer left, could we not simply count +1 every second ding and still reliably determine the number of customers? The Rattlesnake problem mentioned above allows for that when it says "So if they were not so brittle, one could reliably determine a rattlesnake's age simply from the number of sections in its rattle, because a new section forms each time a rattlesnake molts." Answer choice A (snakes molt exactly once a year) is not a necessary assumption because we could still determine the age if it molted twice a year, or three times etc..

[Colonel_funkadunk]

Think about it this way. If the negation is "the bell never rings when the customer leaves the store", then that negation actually strengthens the argument. Because if the bell never rings when customers leave the store, that makes it more likely that you can count the number of people that entered simply by counting the rings when they enter. Also, when it says "simply by counting the rings" means just by counting the rings when they enter. Not by counting them then dividing them in half if it rings when they exit. That's why that statement hurts the argument "the bell sometimes rings when they leave the store"

If that is the correct negation, then I agree with you completely.

I took it this way: "The bell rings each time a customer leaves the store through the front door." where the bolded 'each time' means '100% of the time.' The logical negation of '100% of the time' is not '0% of the time' or 'never.' It is 'not 100% of the time' which could be 0% or 99%. Am I wrong?

As for simply counting, if we knew the bell rang 100% of the time when the customer left, could we not simply count +1 every second ding and still reliably determine the number of customers? The Rattlesnake problem mentioned above allows for that when it says "So if they were not so brittle, one could reliably determine a rattlesnake's age simply from the number of sections in its rattle, because a new section forms each time a rattlesnake molts." Answer choice A (snakes molt exactly once a year) is not a necessary assumption because we could still determine the age if it molted twice a year, or three times etc..

Oh okay well I misread the statement from the original post. I thought it was "the bell sometimes rings when the customer leaves the store" which would lead to "the bell never leave". But I definitely get where you are getting at, but I think the issue is that when it says "simply by counting the rings" this means of it rings 12 times, count to 12, twelve people entered the store. If we have to divide the number of rings or something to figure out the number of people, that is not simply counting the rings. I mean I could be off base, but that's what I'm gathering as the central issue.

[BillPackets]

Think about it this way. If the negation is "the bell never rings when the customer leaves the store", then that negation actually strengthens the argument. Because if the bell never rings when customers leave the store, that makes it more likely that you can count the number of people that entered simply by counting the rings when they enter. Also, when it says "simply by counting the rings" means just by counting the rings when they enter. Not by counting them then dividing them in half if it rings when they exit. That's why that statement hurts the argument "the bell sometimes rings when they leave the store"

If that is the correct negation, then I agree with you completely.

I took it this way: "The bell rings each time a customer leaves the store through the front door." where the bolded 'each time' means '100% of the time.' The logical negation of '100% of the time' is not '0% of the time' or 'never.' It is 'not 100% of the time' which could be 0% or 99%. Am I wrong?

As for simply counting, if we knew the bell rang 100% of the time when the customer left, could we not simply count +1 every second ding and still reliably determine the number of customers? The Rattlesnake problem mentioned above allows for that when it says "So if they were not so brittle, one could reliably determine a rattlesnake's age simply from the number of sections in its rattle, because a new section forms each time a rattlesnake molts." Answer choice A (snakes molt exactly once a year) is not a necessary assumption because we could still determine the age if it molted twice a year, or three times etc..

Oh okay well I misread the statement from the original post. I thought it was "the bell sometimes rings when the customer leaves the store" which would lead to "the bell never leave". But I definitely get where you are getting at, but I think the issue is that when it says "simply by counting the rings" this means of it rings 12 times, count to 12, twelve people entered the store. If we have to divide the number of rings or something to figure out the number of people, that is not simply counting the rings. I mean I could be off base, but that's what I'm gathering as the central issue.

You're both missing that two people could walk thru the door at once. The bell ringing on the way out is nothing.

[Colonel_funkadunk]

Think about it this way. If the negation is "the bell never rings when the customer leaves the store", then that negation actually strengthens the argument. Because if the bell never rings when customers leave the store, that makes it more likely that you can count the number of people that entered simply by counting the rings when they enter. Also, when it says "simply by counting the rings" means just by counting the rings when they enter. Not by counting them then dividing them in half if it rings when they exit. That's why that statement hurts the argument "the bell sometimes rings when they leave the store"

If that is the correct negation, then I agree with you completely.

I took it this way: "The bell rings each time a customer leaves the store through the front door." where the bolded 'each time' means '100% of the time.' The logical negation of '100% of the time' is not '0% of the time' or 'never.' It is 'not 100% of the time' which could be 0% or 99%. Am I wrong?

As for simply counting, if we knew the bell rang 100% of the time when the customer left, could we not simply count +1 every second ding and still reliably determine the number of customers? The Rattlesnake problem mentioned above allows for that when it says "So if they were not so brittle, one could reliably determine a rattlesnake's age simply from the number of sections in its rattle, because a new section forms each time a rattlesnake molts." Answer choice A (snakes molt exactly once a year) is not a necessary assumption because we could still determine the age if it molted twice a year, or three times etc..

Oh okay well I misread the statement from the original post. I thought it was "the bell sometimes rings when the customer leaves the store" which would lead to "the bell never leave". But I definitely get where you are getting at, but I think the issue is that when it says "simply by counting the rings" this means of it rings 12 times, count to 12, twelve people entered the store. If we have to divide the number of rings or something to figure out the number of people, that is not simply counting the rings. I mean I could be off base, but that's what I'm gathering as the central issue.

You're both missing that two people could walk thru the door at once. The bell ringing on the way out is nothing.

Well you're missing that OP specifically asked about the effect of a phrase that has nothing to do with two people walking in the door at once.

[P.J.Fry]

Yes, I'm referring to the specific necessary assumption about the bell not ringing each time a customer leaves the store.

There are infinite other necessary assumptions you could come up with such as "no one enters the back door," "two customers do not enter the store at the same time," "a poltergeist does not cause the bell to ring at random intervals" etc.