Q24 - No mathematical proposition can be

[peg_city]

How do I map this?

MPT(~) -> BO
IK -> MPT

MPT - Mathematical proposition can be proven true
BO - By observation
IK - Impossible to know

If this is right, then all I have to do is match the two single items together

'Impossible to know' and 'by observation' with one of them negated.

I decided on C. BO -> IK(~)

The answer is E. IK (~) -> BO

So basically I had it backwards. How am I supposed to know the direction of the conditional reasoning?

Thanks ahead of time.

[ManhattanPrepLSAT1]

Here's how I'd map this one out...

MP --> ~PTO

----------------
MP ---> ~KT

Notation Key: MP = mathematical proposition, PTO = proven true by observation, KT = known to be true

it follows that the gap is:

~PTO ---> ~KT

Taking the contrapositive: KT ---> PTO

Here's what the answer choices look like..

(A) KT ---> PT
close... but not quite. It should be proven true by observation, not just proven true.
(B) is garbage... sorry if you picked this one!
(C) PTO ---> KT
close... but represents a reversal of the logic.
(D) ~KT ---> ~PTO
close, but represents a negation of the logic.
(E) KT ---> PTO
ahhh. Just right!

I think as you get more practice notating conditional logic, you'll eventually be able to avoid reversals. If your notation had given you a clearer picture of the gap, I think you wouldn't be so tempted with answer choices that represent either a reversal or a negation of the logic. Use key words such as "if, only, unless, etc." to organize your notation, so that your conditional statements or properly organized and be careful that your terms represent the terms as closely as possible.

Good luck, and let me know if you still have questions on this one!

[peg_city]

Wow, I was a little off

A few question:

1. Why did you negate 'proven to be true by observational' when the beginning of the question says 'no mathematical proposition?' Shouldn't Mathematical proposition be negated?

2. For the conclusion, why did you map it that way and not
KT (~)---->MP?

Thanks very much ahead of time.

[ManhattanPrepLSAT1]

It's all about the words!

"No" introduces the sufficient condition and implies the negation of the necessary condition.

A statement that reads, "No A's are B's", would be diagrammed:

A ---> ~B

As far as the conclusion is concerned. Notice the word "any." It introduces the sufficient condition, so the statement is organized backward of how it sounds!

MP ---> ~KT

Also, I try to stay away from diagramming "impossible" as "I". It's safer to incorporate that as a negative term. So "irreversible" would be diagrammed "~R" and "impossible" would be diagrammed "~P".

Great questions!

[geverett]

It's interesting to note here that a cursory glance could lead one to believe that answer choice A would qualify as a sufficient assumption because of the broad use of "propositions that can be proven true". While the use of a broader term is normal in many sufficient assumption questions, in this case it actually could weaken the argument.

The reason being is the author has drawn an argument around a specific type of proposition - one which can be proven true by "observation". If answer choice A were true and the kind of proposition was broadened to any that "can be proven true" then this would serve to weaken the stimulus because it would allow for propositions to be proven true by more ways than "observation". Make sense? yes? no?

It is somewhat odd, but let me know if these points need any further clarification.

[ManhattanPrepLSAT1]

I would suggest that rather than weakening the argument it strengthen the argument, because it does at least provide part of the missing link. The problem is that it doesn't bridge the gap entirely to the desired destination.

So for example, suppose you were in New York and you were going on a trip to Paris. If you were catching a flight to France, that would definitely help support your trip, but would it guarantee the exact outcome you were looking for, no.

So saying that the proposition cannot be proven true, would get you closer to the idea that it cannot be proven true by observation, but it wouldn't get you all the way there.

One more thing here, had the broader generality been in the trigger rather than in the outcome, it would have been okay.

Take the argument that whoever has a doctorate has had many years of education. Therefore, every professor of biology has a has had many years of education. The assumption being that every professor of biology has a doctorate. But if an answer choice said, "every professor has a doctorate," the gap would be bridged and the conclusion would be ensured.

So, we have to be flexible and know when we can widen our scope and when to be very picky! Make sense?

[geverett]

Matt, I'm freakin' out over this:

One more thing here, had the broader generality been in the trigger rather than in the outcome, it would have been okay.

Seriously unbelievable. #mindblown

What an incredible explanation, and I feel like I've just had one more secret on my quest for LSAT perfection revealed to me. Really killer. I don't know if you guys have written that into the LR guide, but if not it definitely deserves a mention in the next version you guys do.

[ManhattanPrepLSAT1]

Glad we can help! That's why we're here...

[WaltGrace1983]

So just making sure I understand what was just said...

One more thing here, had the broader generality been in the trigger rather than in the outcome, it would have been okay.

Take the argument that whoever has a doctorate has had many years of education. Therefore, every professor of biology has a has had many years of education. The assumption being that every professor of biology has a doctorate. But if an answer choice said, "every professor has a doctorate," the gap would be bridged and the conclusion would be ensured.

P: Doctorate --> Many Years of Education

C: Professor of Biology --> Many Years of Education

We need: Professor of Biology --> Doctorate

Yet if we said Professor-->Doctorate this would undoubtedly make sense even though it widens the scope of the trigger. However, we cannot widen the scope of the consequent because this could entail something like:

Professor of Biology --> Advanced Degree?

Thus, it could be that Advanced Degree --> Many Years of Education but we don't necessarily know that and, thus, it would fail to be sufficient. Right?

[tommywallach]

Yep! Looks great!

-t

[WaltGrace1983]

But if we contrapose (A), we get ~(Proven True) → ~(Known to be True).

Wouldn't ~(Proven True) be the broader version of ~(Proven True by Observation)? If something is NOT proven true, then it must be the case that it is NOT proven true by observation.

Is contraposing this an illegal logical move?

[christine.defenbaugh]

Hey WaltGrace1983!

So, you're playing with some potentially very confusing concepts here. It's good stuff, but I find that sometimes it's just easier to find the formal disconnect.

CONCLUSION: (Math Prop) ----------------------------> ~(KnowTrue)
PREMISE:.....(Math Prop) ----> ~(ProveTrueObs)

If I add in the missing link ~(ProveTrueObs) --> ~(KnowTrue) I can build the whole bridge.

CONCLUSION: (Math Prop) ----------------------------> ~(KnowTrue)
PREMISE:.....(Math Prop) ----> ~(ProveTrueObs)----->~(KnowTrue)


You've got to be careful in how you think about narrow vs. broad here. The concept of 'proving true' is a broader concept than 'proving true by observation'. Let's take a look at how that relationship works:

If you DO prove something true by observation, then it would be a correct thing to say that you have indeed proved it true. Affirming the narrow guarantees that the broad category has been fulfilled.

However, if you DON'T prove something true by observation, does that necessarily mean that it can't be proven true AT ALL? Of course not! Maybe we could prove it true some other way! Denying the narrow doesn't tell me anything about whether the broader category has been fulfilled.

If we're going to add in answer choice (A), it needs to tell me something about mathematical propositions. All I know about them from the premise is that they are NOT proven true by observation. Can I use the contrapositive of (A) to now tell me anything more about them? No! I don't know that these math propositions can't be proven true at all, I just know they can't be proven true by observation.

Notice your own wording here, also:

If something is NOT proven true, then it must be the case that it is NOT proven true by observation.

What you're doing here is saying "what if I ALREADY KNEW that the trigger in this answer choice was fulfilled (not proven true) - then wouldn't that tell me the premise is correct (not proven by obs)?" That's not the direction you need to be thinking.

You should be "If I already know that the premise is correct (not proven by observation), then would that fulfill the sufficient-trigger in this conditional (not proven true)?" And the answer to THAT question is no!

Please let me know if this helps clear up a few things!

[WaltGrace1983]

Thanks! But I am still a bit confused. I think I am understanding what you are saying but maybe I am not being clear. Here is my thought process from top to bottom:

MP --> ~PTO
========
MP --> ~KT

The assumption here is obvious: ~PTO --> ~KT. The argument is assuming that NOT being able to prove it true by observation is sufficient to say that it CANNOT be known to be true.

Now I know that my answer choice is going to include the new term: knowing to be true. So I eliminate (B) because it deals with "proving," not knowing.

Here is how I map out the rest of the answer choices:

(A) KT --> PT
(C) PTO --> KT The negation of what I need. Eliminate.
(D) ~KT --> ~PTO same logical structure as (C)! Eliminate
(E) KT --> PTO

So I am down to (A) and (E). I am not going to get them how I want unless I contrapose. (Maybe this is where I am going wrong?)

(A) ~PT --> ~KT
(E) ~PTO --> ~KT

(E) looks perfect. This is an exact match.

However, (A) also looks good to me because IF we cannot prove it true, period, than we definitely cannot prove it true by observation. Thus, wouldn't the sufficient condition by satisfied because the sufficient condition ~(PT) is broader than than the sufficient condition of the assumption ~(PTO).

I think right here is where my thinking is going wrong but I guess I am still just confused on why it is wrong.

[Mab6q]

I think the difference A and E are very hard to understand. Christine could you elaborate some more on why the negation of A doesn't give us our assumption??

Thanks.

[wxpttbh]

Here's how I'd map this one out...

MP --> ~PTO

----------------
MP ---> ~KT

Notation Key: MP = mathematical proposition, PTO = proven true by observation, KT = known to be true

it follows that the gap is:

~PTO ---> ~KT

Taking the contrapositive: KT ---> PTO

Here's what the answer choices look like..

(A) KT ---> PT
close... but not quite. It should be proven true by observation, not just proven true.
(B) is garbage... sorry if you picked this one!
(C) PTO ---> KT
close... but represents a reversal of the logic.
(D) ~KT ---> ~PTO
close, but represents a negation of the logic.
(E) KT ---> PTO
ahhh. Just right!

I think as you get more practice notating conditional logic, you'll eventually be able to avoid reversals. If your notation had given you a clearer picture of the gap, I think you wouldn't be so tempted with answer choices that represent either a reversal or a negation of the logic. Use key words such as "if, only, unless, etc." to organize your notation, so that your conditional statements or properly organized and be careful that your terms represent the terms as closely as possible.

Good luck, and let me know if you still have questions on this one!

Excellent!!