Q20 - Scientist: Some critics of public

[linzru86]

I can see why E is correct but it seems as if B could also be correct. Wouldn't B have to be right in order for E to even come into play?

[giladedelman]

Thanks for bringing this up -- it's a tough question!

Let's try to break down the scientist's statements. First he points out that critics have said that continued funding is justified only if public benefit can be indicated. Then he says that if this were true, we wouldn't see the public support that we're seeing.

The question asks us what else must be true on the basis of these statements, so we know we're being asked to make an inference. Well, what can we infer? If the critics' position were true, we wouldn't be seeing the public support -- but we are seeing the public support, so the critics' position is not true!

Notice that the position in question is a conditional statement that doesn't weigh in on the facts of the situation. The wrong answers will test our understanding of that distinction.

(E) is correct. It makes our inference explicit. If the indication of public benefit is not a requirement, i.e., a necessary condition, for continued funding, then the critics' position is false.

(A) is incorrect. For one, we're talking about whether benefits can be indicated, not just whether they exist; second, although we can infer that it's not a requirement, to say that it's "irrelevant" is to go too far.

(B) is tempting, but we can't conclude anything about whether funding is justified! The only thing we can infer about is whether the indication of public benefits is necessary to justify the funding. And no, to answer your question: whether funding is in fact justified has no bearing on whether the indication of public benefits is a necessary condition.

(C) is out of scope, for starters: the scientist doesn't say anything about the relationship between public support and the justification of funding. Also, "surest" indication? That should raise an alarm.

(D) is incorrect. It causally connects two elements from the scientist's statements that we have absolutely no basis to connect.

Please let me know if that cleared things up for you!

[mcrittell]

Is E correct because "pub benefit" isn't a requirement/necessary condition, but rather, a sufficient one?

[timmydoeslsat]

The critics' position is this:

Continued public funding justified for project ---> Indicated how public can benefit from project


However, the scientist states that if the critics were right about that, then there would be not be the tremendous support that actually exist.

In other words,

[Continued public funding justified for project ---> Indicated how public can benefit from project] ---> ~Tremendous public support


However, there is tremendous public support!

So that means that our conditional is not true.

How do you show that a conditional statement is not true?

You show that sufficient condition DOES NOT NEED THE NECESSARY CONDITION.

Continued public funding justified for project ---> ~Indicated how public can benefit from project


Thus, E is correct that the necessary condition of public benefit does not have to be fulfilled.

[Shiggins]

Timmy, I understand how you formed the logic down, but I am having trouble on how there "is support". Is that based off of the last line of the critics giving support or is there some other sentence that I missed or didn't interpret right. I see how if there is tremendous support the condition in parenthesis is wrong by making the sufficient term of justification not lead to the necessary of public benefit.

[timmydoeslsat]

Hey Shiggins,

I concluded that there was public support from the last line. You are correct.

I will quote the last line.

"If the critics were right about this, then there would not be the tremendous public support for the project that even its critics acknowledge."

Critics right ---> ~Tremendous Public Support


"Critics right" refers to this conditional statement that they posited in the stimulus:

Continued public funding justified ---> Indicated how public will benefit


However, the last part in the last line of the stimulus is so crucial. "...then there would not be the tremendous public support that even its critics acknowledge." That is saying that the critics agree that there is tremendous public support.

That would invoke the contrapositive. That would let us conclude that the critics would not be right about their conditional statement.

We show the sufficient without the necessary, which is choice (E): That indication is not a necessary condition of justifiable continued public funding.

[gilad.bendheim]

So at the end of the day, does this 'public support' that the scientist invokes actually matter, or is it just the logical framework that is set up? As far as I can understand from these posts, the argument would work just as well if it ended with 'If the critics were rights about this, then there wouldn't be the giant red cat that just crossed the street, which even the critics acknowledged.'

If not, im still struggling to understand how 'public support' matters at all, because there remains a logical gap either 'between public support' and 'public benefit' or 'public support' and 'justification of the project'

Thanks.

[mcrittell]

Can someone re-explain the interpretation of the last sentence in the stim so that one can negate the already-negated "tremendous" bit? I'm unsure how to handle that....

[ManhattanPrepLSAT1]

This argument has two statements essentially. The first sentence is not something the author is claiming to be true, so we should not really express it as true. The second sentence is clever, elegant, and tough to deconstruct. Essentially you get two ideas that structurally look like:

A ---> B
~B

From this we could infer ~A.

In this case A = (FJ ---> IBP) and B = PS

Notation Key: FJ - continued funding is justified, IBP - indicate how the public will benefit, PS - tremendous public support

So the stimulus actually says

1. (FJ ----> IBP) ---> ~PS
2. PS

The tough part I think is seeing that it is implied there is tremendous public support; "that its critics acknowledge."

Using contrapositive argument structure we can infer

~(FJ ---> IBP)

or in English, "it's not the case that continued funding being justified is sufficient to infer that we've indicated how the public will benefit, nor is indicating how the public will benefit a requirement of continued funding being justified - best expressed in answer choice (E).

(A) is too strong. It's not that there is no relationship between indicating how the public will benefit and continued funding being justified, but rather that there isn't the one specific relationship advocated by the critics.
(B) cannot be inferred. We cannot know for certain whether continued funding is or is not justified.
(C) is not supported. We are not using the public support to address whether the funding is justified but whether funding being justified would imply that we've indicated how the public will benefit.
(D) is out of scope. We do not know why there is tremendous public support, just that it's there.

Hope that helps! And let me know if that doesn't answer your question.

[mcrittell]

I'm still not seeing how we get "2. PS" Where/how does the arg imply that?

[timmydoeslsat]

The Public Support premise is indeed the last sentence.

So we know that the first part of the stimulus established:

Continued public funding justified ---> Indicated how public will benefit

That is the conditional some critics believe.

The last sentence tells us that if the critics' conditional were true [Funding Justified ---> Indic. Pub. Benefit] then there would not be public support for the project that even the critics admit exist.

So we have established this new conditional:

Critics conditional true ---> ~PS

And the last sentence indicates that there is indeed PS.

We can now use the contrapositive to get to the idea that the critics conditional is not true.

To say a conditional is not true is to say that the the necessary condition is not actually necessary. That is what E states.

[BackoftheEnvelope]

Why can't we do the following:

1. PFJ-->IPB
2. CR-->~PS
3. PS
4. ~CR
5. ~(PFJ-->IPB)
6. ~(~PFJ v IPB)
7. ~~PFJ ^ ~IPB
9. ~~PFJ
10. PFJ
10. ~IPB

where

PFJ: public funding justified
IPB: indicated public benefit
CR: critics right
PS: public support

The bolded is where my solution diverges from the one provided. If the critics aren't right, that means it is not the case that continued public funding is justified only if it can be indicated how the public will benefit from the project (i.e., public funding is justified and there is no indicated public benefit).

[BackoftheEnvelope]

Using contrapositive argument structure we can infer

~(FJ ---> IBP)

Hey Matt,

Could you please let me know what your thoughts are on my process above. ~(FJ ---> IBP) allows us to infer FJ and ~IPB.

Thanks

[BackoftheEnvelope]

I've just taken a fresh look at the question and read it more carefully this time around (when two ACs seem very appealing it's usually a function of a poor read on my part). Here's how I read the second sentence this time around: "If the critics were right about this [IPB being necessary to PFJ], then there would not be the tremendous public support for the project that even its critics acknowledge [but there is PS; so IPB is not necessary to PFJ]."

Instead of reading it as the "critics are wrong" (as I previously did), I now read it more carefully as "the critics are wrong about an indicated public benefit being necessary to continued public funding," which makes a world of difference. The former ("the critics are wrong") led me to infer ~(PFJ-->IPB), which allows both PFJ and ~IPB as tautological consequences -- additionally satisfying AC (B).

[ohthatpatrick]

I think you just gave us a logical proof for why we never recommend negating conditional statements.

It looks like you have some symbolic logic in your background, because you were using symbols I vaguely recognize from Philosophy classes a decade or two ago.

You never need that on LSAT, and it might actually be an inferior approach to engaging your conceptual understanding more (as you saw with your re-read).

I don't actually think you have an accurate idea there with how to negate a conditional.
(I also don't think you're using 'tautology' right -- isn't that a self-justifying truth, like "This sentence is in English"?)

You're making it seem like
~(A --> B)
gives us certain ideas such as ~A and/or ~B.

It wouldn't give us anything like that.

Negating a conditional should look more like this in your mind:
A ---/---> B

This doesn't mean A must lead to ~B.
It means that there is NOT some inflexible connection between A and B (at least in that direction).

It's easier to negate a conditional when you say it as a sentence, rather than when you symbolize it.

For example, here's a conditional:
All moms like chocolate.

If I negate that conditional .. i.e. if I say "the dude who said that is wrong", we have a couple choices

~(M --> LC)

M ---/---> LC

If you're a Mom, maybe you DO like chocolate, maybe not.

Or negate the original sentence "all moms like chocolate" and get
"not all moms like chocolate" = "at least one mom doesn't like chocolate"

In this case, our conditional wasn't triggered by a UNIVERSAL like "all", it was triggered by a REQUIREMENT, "only if".

Justifying public funding REQUIRES that you've indicated the public benefit.

If someone was wrong to say ^ that ^, then just negate that sentence.

Justifying public funding DOES NOT REQUIRE that you've indicated the public benefit.

That puts us in a much better position to like (E).

If you want another example of an annoying conditional logic Inference question, try PT59, S3, #19. It's no accident that the trap answer to these questions always appears higher in the stack of choices than the real answer.

Hope this helps.

[BackoftheEnvelope]

You're making it seem like
~(A --> B)
gives us certain ideas such as ~A and/or ~B.

It wouldn't give us anything like that.

Could you please refer to where I said ~(A-->B) would allow us to infer ~A and/or ~B? It would allow us to infer A and/or ~B. Here's a quick demonstration: A-->B is equivalent to ~A v B, so ~(~A v B) is A ^ ~B, which allows us to separately infer A and ~B.

(I also don't think you're using 'tautology' right -- isn't that a self-justifying truth, like "This sentence is in English"?)

I did not use tautology. I'd be grateful if you could refer to where I said it in my posts.

Three things I want to address more generally:

(1) Negating conditionals

A conditional of the form (P-->Q) allows us to infer (~P v Q). Check the truth table below to verify:

P | Q || P-->Q | ~P v Q
T | T || T T T | F T T T
T | F || T F F | F T F F
F | T || F T T | T F T T
F | F || F T F | T F T F

Replacing P with PFJ and Q with IPB, here's how it looks:

PFJ | IPB || PFJ-->IPB | ~PFJ v IPB
T | T || T T T | F T T T
T | F || T F F | F T F F
F | T || F T T | T F T T
F | F || F T F | T F T F

The truth values of PFJ-->IPB and ~PFJ v IPB are identical under their main connectives (bolded), meaning they are both (a) equivalent to each other and (b) consequences of one another (i.e., there is no row in which PFJ-->IPB is true and ~PFJ v IPB false). This will allow us to infer PFJ and/or ~IPB from ~(PFJ-->IPB) as I demonstrate formally below.

(2) Proof

We want to prove that ~(PFJ-->IPB) allows us to infer PFJ and ~IPB. Let's use the formal deductive system Fitch.

We are given:
1. ~(PFJ-->IPB)
We want to prove PFJ and/or ~IPB can be inferred:
2. ~(~PFJ v IPB) ; tautological consequence: line 1 (see truth table above)
3. ~~PFJ ^ ~IPB ; application of DeMorgan's law: line 2
4. ~~PFJ ; conjunction elimination: line 3
5. PFJ ; negation elimination: line 4
6. ~IPB ; conjunction elimination: line 3

So, ~(PFJ-->IPB) does indeed allow us to infer PFJ and ~IPB. The important step here is that PFJ-->IPB can be transformed to ~PFJ v IPB; or A-->B can be transformed to ~A v B.

(3) Tautological consequence

I use tautological consequence the way it is traditionally used in formal logic: demonstrating consequence by virtue of truth-functional connectives. I did not use tautology (as I previously mentioned).

Using your example of moms and chocolate, let's now describe a language where:

the unary predicate Mom denotes "x is a mom"
the binary predicate Likes denotes "x likes y"
the individual constant "c" denotes chocolate
Ax denotes the universal quantifier
Ex denotes the existential quantifier
<--> denotes logical equivalence

We want to express "not all moms like chocolate". We can do so in one of two ways in our language:
~Ax(Mom(x)-->Likes(x, c)) <--> to Ex(Mom(x) ^ ~Likes(x, c))

Proof below
1. ~Ax(Mom(x)-->Likes(x, c))
2. Ex~(Mom(x)-->Likes(x, c)) ; first-order consequence: line 1
3. Ex~(~Mom(x) v Likes(x, c)) ; tautological consequence: line 2
4. Ex(~~Mom(x) ^ ~Likes(x, c)) ; DeMorgan's: line 3
5. Ex(Mom(x) ^ ~Likes(x, c)) ; negation elimination: line 4

Further information on the justification of each step follows:
2: "Not everything" is the same as "something isn't" (more formally, "It is not the case that for every object x in our domain..." is the same as "There exists an object x in our domain such that it is not...")
3: P-->Q is equivalent to ~P v Q; see truth table above
4: DeMogan's Laws: ~(P v Q) <--> ~P ^ ~Q ; ~(P ^ Q) <--> ~P v ~Q
5: ~~P <--> P

Now, let's check if they're equivalent simply by virtue of their truth-functional connectives. Using the truth-functional algorithm for our language we get: ~Ax(Mom(x)-->Likes(x, c)) or (~P); and Ex(Mom(x) ^ ~Likes(x, c)) (or Q). But ~P <--> Q does not hold. These sentences are, thus, logically equivalent but not equivalent by virtue of their truth-functional connectives.

With ~(PFJ-->IPB) we don't rely on quantifiers or the meaning of predicates to demonstrate consequence (that we can infer PFJ and/or ~IPB). I wanted to specifically demonstrate that PFJ and ~IPB are both a consequence of ~(PFJ-->IPB) simply by virtue of their truth-functional connectives -- the strictest form of consequence -- which I why I used the term.

--

Apologies in advance for the volume of information. I definitely was not planning on responding at length. I did feel compelled to respond, however, after the strong language in your post. Hope this clarifies any confusion!

[ohthatpatrick]

Yikes! Fascinating logical stuff there, but obviously insane for this forum, so I'm going to end up deleting our whole conversation after I respond (since it would really be of no benefit to anyone using this forum for LSAT help).

I was being unclear if not wrong when I said negating "A --> B" did not allow us to conclude ~A and/or ~B. It specifically allows us to infer "something is A and ~B".

I thought I saw you doing the common student error of distributing the negative,
going from
~(A-->B)
to
~A

In reality, you were doing some intermediary step I didn't understand (and don't use) in which you had
~(~A ...

I just couldn't follow your proof because, as said before, I haven't taken a symbolic logic class in two decades and we don't need to know any of that for LSAT.

When we say
~ (PFJ --> IPB)
then we can definitely say that
there is at least one example of something that is PFJ, but NOT IPB.

The whole idea of negating a conditional is something that meets the Suff, fails the Nec.

The problem with your original proof, I think, is just that it hides the important feature of "at least one" example of SUFF, ~NEC.

You wanted to assume that THIS RESEARCH PROJECT is the example of the SUFF, ~NEC, but we don't know that.

Consider this analogy:
In discussing whether or not his mom likes chocolate, Tony said that all moms like chocolate.
If Tony were right about this, then mother's day would be sponsored by Hershey, though it definitely is not.

We can infer that "not all moms like chocolate".

We cannot infer that "Tony's mom doesn't like chocolate".

I'm glad you were using tautological correctly. I was just checking whether it meant what I thought it meant.

[mengluwu1986]

Could someone help me with the grammar, especially the last part of the last sentence? I am confused about what was omitted after "acknowledge" and why it refers back to the main sentence "acknowledging that there is tremendous public support"?

I do get the logic part of this question after I accept the grammar part.

Thanks in advance!