Conditional Logic Help!!

notwilliamwallace

Hey Everyone,

Needed some help with this conditional statement.

"Deep empathy is required for full understanding of an individual's actions. Internal empathy will grant partial understanding, but only if the individual is open minded towards the process."

I have: Full Understanding ---> Deep Empathy ; (Internal Empathy --> Partial Understanding) --> Open Minded.

The question asks: Dina has acquired both deep and internal empathy of Barry, who is not open minded towards anything. Relative to Barry, Dina will gain: _________

So I know that it is unknown whether Dina will gain full understanding as she satisfies a necessary condition. But, will she also not gain partial understanding since the necessary condition is deinied (Barry is not open minded)??

How do we translate this statement and it's contrapositive: "Internal empathy will grant partial understanding, but only if the individual is open minded towards the process".

Any help would be great. Thanks for your time.

DumbHollywoodActor

This question seems fishy. I can’t make any inferences about Dina RELATIVE to Barry with the given information. Where is this question from?

DumbHollywoodActor

@notwilliamwallace said:
How do we translate this statement and it's contrapositive: "Internal empathy will grant partial understanding, but only if the individual is open minded towards the process".

To answer this question, I’d translate that sentence as "Internal empathy + open mind --> partial understanding” because the open mind is necessary for internal empathy to guarantee partial understanding.

CoolPrez

I could be wrong, but my answer for the question is that Dina gains more understanding. Barry is not open so he does not have partial understanding. Dina has internal empathy so she does have partial understanding. Like DumbHollywoodActor said above, this question is strange in that it asks about relativity and it asks what she "gains" as a result of Bary's unopeness. I am curious what others think about this and I would love further elaboration and analysis.

CoolPrez

I just realized something that may help, but I don't know what to do with it. Is it possible that the stimulus saying "partial understanding" actually means "not full understanding"? Which would mean it would be internal empathy--> /fullunderstanding? This would make a lot of sense because if something is not full understanding, then it is partial, some, or no understanding.

notwilliamwallace

Thanks for answering @DumbHollywoodActor and @CoolPrez ... this was from a course book my friend was using. He asked me for help but I was kinda confused as well.

@CoolPrez said:
Is it possible that the stimulus saying "partial understanding" actually means "not full understanding"?

I think that makes sense. I will ask him to ask his instructor as well. Thanks again guys.

Cant Get Right

I'm not sure we can equate partial empathy with /deep empathy. /deep empathy would encompass no empathy which would exclude partial empathy. They certainly overlap, but to equate logically, they have to be equivalent.

For the original question, I don't think Dina will gain anything.

hlsat180

@DumbHollywoodActor said:
@notwilliamwallace said:
How do we translate this statement and it's contrapositive: "Internal empathy will grant partial understanding, but only if the individual is open minded towards the process".

To answer this question, I’d translate that sentence as "Internal empathy + open mind --> partial understanding” because the open mind is necessary for internal empathy to guarantee partial understanding.


This statement is not intuitive to diagram (any philosophy major, please weigh in) but I think this version better represents the argument* (and more consistent with your explanation) to make short work of the answer:

Partial Understanding --> Internal Empathy + Open Minded

To answer the OP, since Dina fails a necessary condition (i.e., not Open Minded) she does not gain Partial Understanding.

-----

*To test the diagram, substitute a parallel argument: A [Vaccine] will grant [Immunity] but only if the individual is [Already Healthy]:

Immunity --> Vaccine + Already Healthy

notwilliamwallace

@DumbHollywoodActor said:
Internal empathy + open mind --> partial understanding

This is it. My friend confirmed with his instructor that this is the right way to do it. Internal Empathy AND Open Mindedness together are sufficient to guarantee Partial Understanding.

What confused was the "only if" that was mentioned before open mindedness. This definitely was not easy for me to grasp, but now it makes sense.

hlsat180

@notwilliamwallace said:
Internal Empathy AND Open Mindedness together are sufficient to guarantee Partial Understanding

This seems to mix conditional logic and causation. I rather read the argument as "Internal Empathy AND Open Minded(ness) are both necessary for Partial Understanding."

@notwilliamwallace said:
What confused was the "only if" that was mentioned before open mindedness. This definitely was not easy for me to grasp, but now it makes sense.

I'm also/still confused by this confirmation because [Open Minded] ought to be a necessary condition for the reason you stated.

Could someone (JY Ping, Jonathan Wang, quinnxzhang) definitively explain how to construct this argument?

notwilliamwallace

A way to think about this is this: If you have internal empathy, what is definitely guaranteed? It is that you will have partial understanding. Thus, partial understanding is the necessary condition for internal empathy. But then, the author says, "wait a minute, not just internal empathy, in addition to that, the other person needs to be open minded". So he is saying that these two things together are sufficient.

Although, I would appreciate further clarifications as well. This, indeed, is hella confusing. @quinnxzhang ... any help, please and thank you?

DumbHollywoodActor

@hlsat180 said:
To test the diagram, substitute a parallel argument: A [Vaccine] will grant [Immunity] but only if the individual is [Already Healthy]:

Immunity --> Vaccine + Already Healthy

To explain the flaw in your logic, I’ll use your parallel example. There are people in the world who are immune to diseases but haven’t necessarily been given vaccines. Maybe the immunities were passed from the mother in breast milk or they were genetically passed to the offspring. So, immunity is not a sufficient condition to getting a vaccine.

Cant Get Right

@notwilliamwallace said:
Deep empathy is required for full understanding of an individual's actions. Internal empathy will grant partial understanding, but only if the individual is open minded towards the process."

I have: Full Understanding ---> Deep Empathy ; (Internal Empathy --> Partial Understanding) --> Open Minded.

This is what I’ve got @notwilliamwallace .

I read: Only if open minded will internal empathy lead to understanding. If not open minded, then this says, to me, that the relationship between empathy and understanding does not hold. So my contrapositive here would be something like:

~Open minded —> ~(Internal empathy —> Partial Understanding)

hlsat180

@DumbHollywoodActor said:
@hlsat180 said:
To test the diagram, substitute a parallel argument: A [Vaccine] will grant [Immunity] but only if the individual is [Already Healthy]:

Immunity --> Vaccine + Already Healthy

To explain the flaw in your logic, I’ll use your parallel example. There are people in the world who are immune to diseases but haven’t necessarily been given vaccines. Maybe the immunities were passed from the mother in breast milk or they were genetically passed to the offspring. So, immunity is not a sufficient condition to getting a vaccine.


What you say is true in the "real world" but irrelevant to LSAT LR. If the LSAT said, "All clowns are blue but only if they are short" then you could argue the argument is flawed (more precisely: unsound) because in the real world there exist tall, blue clowns. But LSAT LR doesn't care.

The purpose of this "test" (substituting in simpler terms) is to help distill the underlying conditional logic from an argument obfuscated by strange terminology (e.g., internal empathy, partial understanding, etc.). In other words, the purpose is to help understand an argument's validity rather than its "real world" soundness - which LSAT LR never "tests."

So our problem still remains: What is the valid diagram for the OP's statement (below) and how is it determined?

@notwilliamwallace said:
Internal empathy will grant partial understanding, but only if the individual is open minded towards the process.

DumbHollywoodActor

@hlsat180 said:
What you say is true in the "real world" but irrelevant to LSAT LR.

(Forehead smack!) Of course! I’m almost embarrassed to make that error.

I just sort of did this in my head, but I looked back at the curriculum. I’m no longer 100% certain anymore with my logic. I’m calling in @c.janson35 to figure this out.

hlsat180

@DumbHollywoodActor said:
I’m no longer 100% certain anymore with my logic.

Yet that critical mindset is necessary for attacking the LSAT. I empathize: anyone who's been prepping hard for the LSAT tends to mentally attack every argument on auto-pilot. That said, in the interest of maintaining relationships (especially with my wife) I personally refrain from always verbalizing such thoughts...:)

@"Cant Get Right" said:
(Internal Empathy --> Partial Understanding) --> Open Minded

EDIT: After further thought and testing, I too agree with this diagram:

"X grants Y but only if Z" translates to "( X -> Y ) -> Z"

Therefore, the answer to the question is no effect because, via the contrapositive, NOT Z (Barry is NOT Open Minded) means X does NOT trigger Y:

NOT Z --> NOT ( X -> Y )

This all disagrees with the OP's friend/his instructor's diagram and so I still remain interested in how they arrived at their solution. @notwilliamwallace could you find out?

notwilliamwallace

@"Cant Get Right" said:
~Open minded —> ~(Internal empathy —> Partial Understanding)

Yup, that was the only thing that made sense to me. Ah, this statement is not fun at all.

Daniel.Sieradzki

That is a very strange conditional statement. I agree with @"Cant Get Right"'s diagram.

The word "grants" tells us that Internal Empathy is sufficient for partial understanding. However, it is not really sufficient in that this technique of using internal empathy to get partial understanding requires being open minded as a necessary condition.

Thus we get (Internal Empathy *technique* -> Partial Understanding *result of technique*) -> Open Minded *necessary for technique to work*.

Because of this relationship, one could say that being open minded is a necessary and sufficient condition for using the technique of internal empathy to derive partial understanding. Thus, I do believe that the teacher's use of Internal Empathy + Open Minded -> Partial Understanding does hold up.

@"Cant Get Right"'s contrapositive of ~Open minded —> ~(Internal empathy —> Partial Understanding) makes a lot of sense. If the person is not open minded, the technique of using internal empathy to derive partial understanding will NOT work.

The super important thing to realize is that being open minded is NOT a necessary condition for Partial Understanding. It is only a necessary condition for the particular technique of using internal empathy to derive partial understanding. For all we know, there is another technique that can be used to derive partial understanding without needing anyone to be open minded.

On the LSAT, the sufficient term is usually a singular item. In this case, we are dealing with a set of sufficient conditions. This leads to a lot of difficult and confusing logic. Thankfully, I don't remember seeing this type of issue coming up to much on the LSAT (LG is the only place that comes to mind). It is still a great mental workout.

hlsat180

@Daniel.Sieradzki : awesome explanation! Especially how you reconciled both the instructor's and @"Cant Get Right" 's diagrams by explaining how Open Minded functions as both a necessary and sufficient condition. Brilliant.

DumbHollywoodActor

Awesome explanation, @Daniel.Sieradzki . Or should I say Sage Daniel.

Jonathan Wang

(IE -> PU) -> OM is right and would be how I'd represent it. Pretty standard embedded conditional statement.

I'm on the fence about whether the IE + OM -> PU interpretation is correct, but I lean toward no. If the word 'but' wasn't present then this interpretation would be wrong for sure: "Internal empathy grants partial understanding only if the subject is open-minded" definitely doesn't imply that open-mindedness is the only necessary condition. The word 'but', in this case, looks to me like it just functions as a conjunction, so my instinct is that it has no logical force. But I haven't thought deeply enough about it to say that with 100% certainty. I can certainly see how it changes the reading.

Anyway, since it's not required for the question in this case, it's a moot point in this context. If it mattered for the question, I'm betting that the rule would be expressed more unambiguously.