Question about conditional logic Forum

[GAUL]

Does the argument A -> B require assuming B -> A?

At first I thought it was a illegal reversal, and the answer was of course a no.
But if we negate B -> A, then we would get B ->~A, which is exactly the negation of the original argument, i.e. it is a destoryer.
Therefore the answer seems to be a yes, but somehow I just feel it is not right.

Have I missed something?

[thevuch]

your first impression is right. if a then b does not entail if b then a UNLESS it is a biconditional. biconditionals on the LSAT are worded 'if and only if' but otherwise a reversal is a common logic mistake thrown in on wrong answer choices

[thevuch]

Does the argument A -> B require assuming B -> A?

At first I thought it was a illegal reversal, and the answer was of course a no.
But if we negate B -> A, then we would get B ->~A, which is exactly the negation of the original argument, i.e. it is a destoryer.
Therefore the answer seems to be a yes, but somehow I just feel it is not right.

Have I missed something?

and im not sure what you mean by 'negate' B then A, the contrapositive of A then B would be NOT B then NOT A (this is a valid inference). but B then NOT A is incorrect

when you 'negate' if i understand you correctly to get the contrapositive you have to flip and negate both.

[GAUL]

Does the argument A -> B require assuming B -> A?

At first I thought it was a illegal reversal, and the answer was of course a no.
But if we negate B -> A, then we would get B ->~A, which is exactly the negation of the original argument, i.e. it is a destoryer.
Therefore the answer seems to be a yes, but somehow I just feel it is not right.

Have I missed something?

and im not sure what you mean by 'negate' B then A, the contrapositive of A then B would be NOT B then NOT A (this is a valid inference). but B then NOT A is incorrect

when you 'negate' if i understand you correctly to get the contrapositive you have to flip and negate both.

Thanks for answering, by 'negate' I mean exactly how we usually treat the answer choice (the consequent) in a necessary assumption question, or I just cannot do that in question like this?

[GAUL]

Does the argument A -> B require assuming B -> A?

At first I thought it was a illegal reversal, and the answer was of course a no.
But if we negate B -> A, then we would get B ->~A, which is exactly the negation of the original argument, i.e. it is a destoryer.
Therefore the answer seems to be a yes, but somehow I just feel it is not right.

Have I missed something?

and im not sure what you mean by 'negate' B then A, the contrapositive of A then B would be NOT B then NOT A (this is a valid inference). but B then NOT A is incorrect

when you 'negate' if i understand you correctly to get the contrapositive you have to flip and negate both.

Thanks for noticing!

[thevuch]

Thanks for answering, by 'negate' I mean exactly how we usually treat the answer choice (the consequent) in a necessary assumption question, or I just cannot do that in question like this?

Actually the question comes from PT38-S1-Q14, basically the question is talking about one thing:

The British people travel abroad more now than 30 years ago, therefore British people must have more money now than 30 years ago.

It asks for a necessary assumption and the right answer says that if British people had more money 30 years ago, they would have travel abroad more 30 years ago.

oh i see. for me, conditional logic never really came into play on necessary assumption questions. here the 'negate' term as i understand it means that the correct answer choice can be revealed through the negate method. as in the right answer you listed above, if that were negated (if it were not the case) then the argument you listed above wouldnt work. for ex,XXXXXXXXXXXXXXXXXXXX" would not work because the amount of money people had 30 years ago is not a solid indicator anymore like the argument needs it to be, hence why the correct answer is correct.

the 'negate' term in necessary assumption questions has to do with the idea that you can recognize the correct answer choice by negating it, if the answer choice is NOT true, can the argument in the stimulus still be true? if not, then thats the correct answer

[thevuch]

youre not allowed to post questions because its LSAC copyright or some shit. delete it

[GAUL]

youre not allowed to post questions because its LSAC copyright or some shit. delete it

Thanks, both for the answering and noticing.

[Christine (MLSAT)]

This is a great question, actually, because it's something that a lot of people struggle with at some time or another. It's also closely related to how we negate words like "always" and "never". Negating conditionals is weird, and, as you probably realize now, does *not* work the way you listed it before.

Think for a moment about what a conditional really is: it's a rule. It's no different than saying ALWAYS about something. So, imagine I told you that I always wear high heels. Now, you want to negate that, or call me a liar. How do you do it?

You don't need to go so far as to say that I NEVER wear high heels. All you need to call me a liar is show that sometimes I don't wear them. Thus, the negation of "I always wear high heels" is "Sometimes I don't wear high heels."

The same thing happens with conditionals. Because a conditional is saying "this result always occurs", we want to negate it by saying "no, sometimes it doesn't". In other words, once the trigger occurs, it's not always true that the result occurs.

For the conditional A-->B, the negation would simply be that sometimes A and ~B can happen at the same time. This might be phrased as:

• It is not true that B must always follow A, or
  Sometimes when A occurs, B does not happen, or
  It's possible to have A and ~B happen simultaneously, etc

So the negation of a conditional is a fuzzy kind of statement that will say that it's possible to have the sufficient of the conditional and yet not have the necessary clause of the conditional.

Does that help at all?

[thevuch]

This is a great question, actually, because it's something that a lot of people struggle with at some time or another. It's also closely related to how we negate words like "always" and "never". Negating conditionals is weird, and, as you probably realize now, does *not* work the way you listed it before.

Think for a moment about what a conditional really is: it's a rule. It's no different than saying ALWAYS about something. So, imagine I told you that I always wear high heels. Now, you want to negate that, or call me a liar. How do you do it?

You don't need to go so far as to say that I NEVER wear high heels. All you need to call me a liar is show that sometimes I don't wear them. Thus, the negation of "I always wear high heels" is "Sometimes I don't wear high heels."

The same thing happens with conditionals. Because a conditional is saying "this result always occurs", we want to negate it by saying "no, sometimes it doesn't". In other words, once the trigger occurs, it's not always true that the result occurs.

For the conditional A-->B, the negation would simply be that sometimes A and ~B can happen at the same time. This might be phrased as:

• It is not true that B must always follow A, or
  Sometimes when A occurs, B does not happen, or
  It's possible to have A and ~B happen simultaneously, etc

So the negation of a conditional is a fuzzy kind of statement that will say that it's possible to have the sufficient of the conditional and yet not have the necessary clause of the conditional.

Does that help at all?

gaul you should listen to this person. manhattan taught me everything i know about LR

[GAUL]

This is a great question, actually, because it's something that a lot of people struggle with at some time or another. It's also closely related to how we negate words like "always" and "never". Negating conditionals is weird, and, as you probably realize now, does *not* work the way you listed it before.

Think for a moment about what a conditional really is: it's a rule. It's no different than saying ALWAYS about something. So, imagine I told you that I always wear high heels. Now, you want to negate that, or call me a liar. How do you do it?

You don't need to go so far as to say that I NEVER wear high heels. All you need to call me a liar is show that sometimes I don't wear them. Thus, the negation of "I always wear high heels" is "Sometimes I don't wear high heels."

The same thing happens with conditionals. Because a conditional is saying "this result always occurs", we want to negate it by saying "no, sometimes it doesn't". In other words, once the trigger occurs, it's not always true that the result occurs.

For the conditional A-->B, the negation would simply be that sometimes A and ~B can happen at the same time. This might be phrased as:

• It is not true that B must always follow A, or
  Sometimes when A occurs, B does not happen, or
  It's possible to have A and ~B happen simultaneously, etc

So the negation of a conditional is a fuzzy kind of statement that will say that it's possible to have the sufficient of the conditional and yet not have the necessary clause of the conditional.

Does that help at all?

Yes, thanks, that helps. And there's something other, since you are here

I always regard the suffient/necessary assumption question as, essentially, that asks for the antecedent/consequent in a condtional argument, is it right? Since thevuch said to him/her conditional logic never came to such question, and I did meet some problems when I saw the question in that way, I wonder whether there's something wrong with it.

Thanks.

[GAUL]

This is a great question, actually, because it's something that a lot of people struggle with at some time or another. It's also closely related to how we negate words like "always" and "never". Negating conditionals is weird, and, as you probably realize now, does *not* work the way you listed it before.

Think for a moment about what a conditional really is: it's a rule. It's no different than saying ALWAYS about something. So, imagine I told you that I always wear high heels. Now, you want to negate that, or call me a liar. How do you do it?

You don't need to go so far as to say that I NEVER wear high heels. All you need to call me a liar is show that sometimes I don't wear them. Thus, the negation of "I always wear high heels" is "Sometimes I don't wear high heels."

The same thing happens with conditionals. Because a conditional is saying "this result always occurs", we want to negate it by saying "no, sometimes it doesn't". In other words, once the trigger occurs, it's not always true that the result occurs.

For the conditional A-->B, the negation would simply be that sometimes A and ~B can happen at the same time. This might be phrased as:

• It is not true that B must always follow A, or
  Sometimes when A occurs, B does not happen, or
  It's possible to have A and ~B happen simultaneously, etc

So the negation of a conditional is a fuzzy kind of statement that will say that it's possible to have the sufficient of the conditional and yet not have the necessary clause of the conditional.

Does that help at all?

Here is the thing:

From the perspective of conditional logic, B->A is of course an illegal reversal of the original argument A->B, hence we cannot get [A->B] -> [B->A]
While on the other hand, the contrapositive of the negation of B->A (that is B->Not A), is A->NOT B, which is the negation of the original argument, and hence it could be true that [A->B] ->[B->A].

or shall I just negate every choices and stop thinking too much?

[Clearly]

This is a great question, actually, because it's something that a lot of people struggle with at some time or another. It's also closely related to how we negate words like "always" and "never". Negating conditionals is weird, and, as you probably realize now, does *not* work the way you listed it before.

Think for a moment about what a conditional really is: it's a rule. It's no different than saying ALWAYS about something. So, imagine I told you that I always wear high heels. Now, you want to negate that, or call me a liar. How do you do it?

You don't need to go so far as to say that I NEVER wear high heels. All you need to call me a liar is show that sometimes I don't wear them. Thus, the negation of "I always wear high heels" is "Sometimes I don't wear high heels."

The same thing happens with conditionals. Because a conditional is saying "this result always occurs", we want to negate it by saying "no, sometimes it doesn't". In other words, once the trigger occurs, it's not always true that the result occurs.

For the conditional A-->B, the negation would simply be that sometimes A and ~B can happen at the same time. This might be phrased as:

• It is not true that B must always follow A, or
  Sometimes when A occurs, B does not happen, or
  It's possible to have A and ~B happen simultaneously, etc

So the negation of a conditional is a fuzzy kind of statement that will say that it's possible to have the sufficient of the conditional and yet not have the necessary clause of the conditional.

Does that help at all?

Here is the thing:

From the perspective of conditional logic, B->A is of course an illegal reversal of the original argument A->B, hence we cannot get [A->B] -> [B->A]
While on the other hand, the contrapositive of the negation of B->A (that is B->Not A), is A->NOT B, which is the negation of the original argument, and hence it could be true that [A->B] ->[B->A].

or shall I just negate every choices and stop thinking too much?

Def stop over thinking it. Two wrongs don't make a right, multiple negations don't net inferences. In any conditional situation look at the rule, and the contrapositive as the only valid inferences you can make, everything else either could possibly be true, or might be entirely false, but none of that matters.

Also, try looking at assumption questions from a different perspective, 80% of them are just asking you to plug a gap between two terms.

[Christine (MLSAT)]

This is a great question, actually, because it's something that a lot of people struggle with at some time or another. It's also closely related to how we negate words like "always" and "never". Negating conditionals is weird, and, as you probably realize now, does *not* work the way you listed it before.

Think for a moment about what a conditional really is: it's a rule. It's no different than saying ALWAYS about something. So, imagine I told you that I always wear high heels. Now, you want to negate that, or call me a liar. How do you do it?

You don't need to go so far as to say that I NEVER wear high heels. All you need to call me a liar is show that sometimes I don't wear them. Thus, the negation of "I always wear high heels" is "Sometimes I don't wear high heels."

The same thing happens with conditionals. Because a conditional is saying "this result always occurs", we want to negate it by saying "no, sometimes it doesn't". In other words, once the trigger occurs, it's not always true that the result occurs.

For the conditional A-->B, the negation would simply be that sometimes A and ~B can happen at the same time. This might be phrased as:

• It is not true that B must always follow A, or
  Sometimes when A occurs, B does not happen, or
  It's possible to have A and ~B happen simultaneously, etc

So the negation of a conditional is a fuzzy kind of statement that will say that it's possible to have the sufficient of the conditional and yet not have the necessary clause of the conditional.

Does that help at all?

Here is the thing:

From the perspective of conditional logic, B->A is of course an illegal reversal of the original argument A->B, hence we cannot get [A->B] -> [B->A]
While on the other hand, the contrapositive of the negation of B->A (that is B->Not A), is A->NOT B, which is the negation of the original argument, and hence it could be true that [A->B] ->[B->A].

or shall I just negate every choices and stop thinking too much?

No! Stop, stop, stop!

Okay, we need to clear up some terminology issues stat.

For the conditional A-->B

• "Illegal reversal" - refers to the illegal inference B-->A. It's possible this statement is true, but we cannot infer it from the original conditional alone.
  
  "Illegal negation" - refers to the illegal inference NOT A --> NOT B. It's possible this statement is true, but we cannot infer it from the original conditional alone.
  
  "Negation" - this refers to the standard negation of answer choices in order to test them in the "negation test", which is used to determine if something is a necessary assumption. The negation of the above conditional is "sometimes A is not followed by B". Negations of conditionals are not themselves conditional statements.

Please note that "illegal negation" is not the same thing at all as "negation for the negation test". Also, note that illegal negation of a conditional negates both sides of the conditional, not just the necessary-result. Lastly, note that the contrapositive of the illegal negation is the illegal reversal. That's not a coincidence.

Also, you need to realize that the illegal negation and the illegal reversal are bad things - things that you never want to do. The standard negation for the negation test, however, is a tool that you want to use to see if the negated assumption destroys the argument.

Neither the standard negation (for the negation test), nor the "illegal negation" would ever net a statement "A --> NOT B".

Thoughts?

[Christine (MLSAT)]

Yes, thanks, that helps. And there's something other, since you are here

I always regard the suffient/necessary assumption question as, essentially, that asks for the antecedent/consequent in a condtional argument, is it right? Since thevuch said to him/her conditional logic never came to such question, and I did meet some problems when I saw the question in that way, I wonder whether there's something wrong with it.

Thanks.

I'm not entirely sure what you mean by that, could you explain a little more?

A necessary assumption question is asking for the assumption the argument needs in order to be valid. So, you could think of it as the necessary-result of the statement:

• If the argument is valid --> the assumption is true

So, the contrapositive would be:

• if the assumption is not true --> the argument is not valid

This is the essential foundation for the negation test. Negating the necessary assumption should produce a situation where the argument is not valid.

Similarly, a sufficient assumption question is asking for the assumption that would guarantee the argument's validity. So, you could think of it as the sufficient-trigger of the statement:

• If the assumption is true --> the argument is valid

If that's what you mean, then yes, that's an accurate way of looking at the questions. However, the thing that is assumed (in either case) may or may not be a conditional statement itself. I personally tend to just think of the assumptions this way:

• Necessary assumptions - like oxygen - without it, the argument dies (think negatively to see result)
  
  Sufficient assumptions - Tim Gunn assumptions - they make it work! (think positively to see result)

If you're coming from this type of viewpoint, unless the answer choice is itself a conditional, you wouldn't really think much about conditional logic.

Does this make sense?

[GAUL]

Yes, thanks, that helps. And there's something other, since you are here

I always regard the suffient/necessary assumption question as, essentially, that asks for the antecedent/consequent in a condtional argument, is it right? Since thevuch said to him/her conditional logic never came to such question, and I did meet some problems when I saw the question in that way, I wonder whether there's something wrong with it.

Thanks.

I'm not entirely sure what you mean by that, could you explain a little more?

A necessary assumption question is asking for the assumption the argument needs in order to be valid. So, you could think of it as the necessary-result of the statement:

• If the argument is valid --> the assumption is true

So, the contrapositive would be:

• if the assumption is not true --> the argument is not valid

This is the essential foundation for the negation test. Negating the necessary assumption should produce a situation where the argument is not valid.

Similarly, a sufficient assumption question is asking for the assumption that would guarantee the argument's validity. So, you could think of it as the sufficient-trigger of the statement:

• If the assumption is true --> the argument is valid

If that's what you mean, then yes, that's an accurate way of looking at the questions. However, the thing that is assumed (in either case) may or may not be a conditional statement itself. I personally tend to just think of the assumptions this way:

• Necessary assumptions - like oxygen - without it, the argument dies (think negatively to see result)
  
  Sufficient assumptions - Tim Gunn assumptions - they make it work! (think positively to see result)

If you're coming from this type of viewpoint, unless the answer choice is itself a conditional, you wouldn't really think much about conditional logic.

Does this make sense?

Clearly I've confused the two concepts. Yes, a thousand thanks, you really help a lot.

[GAUL]

This is a great question, actually, because it's something that a lot of people struggle with at some time or another. It's also closely related to how we negate words like "always" and "never". Negating conditionals is weird, and, as you probably realize now, does *not* work the way you listed it before.

Think for a moment about what a conditional really is: it's a rule. It's no different than saying ALWAYS about something. So, imagine I told you that I always wear high heels. Now, you want to negate that, or call me a liar. How do you do it?

You don't need to go so far as to say that I NEVER wear high heels. All you need to call me a liar is show that sometimes I don't wear them. Thus, the negation of "I always wear high heels" is "Sometimes I don't wear high heels."

The same thing happens with conditionals. Because a conditional is saying "this result always occurs", we want to negate it by saying "no, sometimes it doesn't". In other words, once the trigger occurs, it's not always true that the result occurs.

For the conditional A-->B, the negation would simply be that sometimes A and ~B can happen at the same time. This might be phrased as:

• It is not true that B must always follow A, or
  Sometimes when A occurs, B does not happen, or
  It's possible to have A and ~B happen simultaneously, etc

So the negation of a conditional is a fuzzy kind of statement that will say that it's possible to have the sufficient of the conditional and yet not have the necessary clause of the conditional.

Does that help at all?

gaul you should listen to this person. manhattan taught me everything i know about LR

yes, you are right, manhattan knows things.