Q10 - All material bodies are divisible

[peg_city]

Even though mapping this one was easy, I still couldn't get the conclusion.

MB-->DIP-->I
MB-->I
S--->MB(~)

The answer is S--->I(~)

But is that really necessary for the conclusion to be drawn? Can't it still be I(~)-->S. That still fits in
I(~)-->S-->DIP(~)-->MB


Thanks Again

[bbirdwell]

It's not necessary, no. This question is not asking for a necessary assumption -- it's asking for a sufficient assumption.

So you're right:
MB-->DIP-->I
MB-->I
S--->~MB

On these question-types, once you get this far you're home-free. Just find the part that's new to the conclusion and "hook it in."

Here, S is the new element. So, using the evidence above the line, how can we get from S to ~MB? Well, the only way to arrive at ~MB is via the contrapositive of the your second line above: ~I --> ~MB.

Therefore, we want S --> ~I so that we get our conclusion S-->~MB.

That's almost always how these questions work, so use your great up-front analysis to predict the correct answer and get through these efficiently!

[jasonxu89]

Hi, I have read a lot of your explanations and thanks so much!
You've mentioned sufficient and necessary assumptions several times and can you elaborate on their differences a little bit more? I would really appreciate that!

It's not necessary, no. This question is not asking for a necessary assumption -- it's asking for a sufficient assumption.

So you're right:
MB-->DIP-->I
MB-->I
S--->~MB

On these question-types, once you get this far you're home-free. Just find the part that's new to the conclusion and "hook it in."

Here, S is the new element. So, using the evidence above the line, how can we get from S to ~MB? Well, the only way to arrive at ~MB is via the contrapositive of the your second line above: ~I --> ~MB.

Therefore, we want S --> ~I so that we get our conclusion S-->~MB.

That's almost always how these questions work, so use your great up-front analysis to predict the correct answer and get through these efficiently!

[bbirdwell]

Necessary conditions appear on the right side of conditional statements, sufficient conditions on the left.

A --> B

This tells me that A is SUFFICIENT to guarantee B. No matter what else I have (C, Z, $%jk8), if there's an A, that's enough to guarantee me a B.

B is NECESSARY to A. This means the same as above, just from a sort of reverse angle. No matter what, if I ever have an A, B MUST come with it -- it's necessary. I can never have an A without a B.

Those are the basic elements of necessary/sufficient. It's a broad and deep topic that is essential to mastery of this test as well as to success in understanding the law.

[jasonxu89]

Thanks for your reply! I understand sufficient and necessary conditions, for sure. But how are they related to finding assumptions. Can you give me an example of sufficient assumption and an example of necessary assumption in an argument? Still a little bit confused.

And,
I have practiced about 20 tests now and found several assumptions follow the same pattern. Can you take a look at my inferences below and make sure I am right? Thanks!
Example 1
Premise: A-->B
Conlusion: A-->C
assumption in the right answer choice: B-->C

Example 2

Premise: B-->A
Conlusion: C-->A
assumption in the right answer choice: C-->B

Necessary conditions appear on the right side of conditional statements, sufficient conditions on the left.

A --> B

This tells me that A is SUFFICIENT to guarantee B. No matter what else I have (C, Z, $%jk8), if there's an A, that's enough to guarantee me a B.

B is NECESSARY to A. This means the same as above, just from a sort of reverse angle. No matter what, if I ever have an A, B MUST come with it -- it's necessary. I can never have an A without a B.

Those are the basic elements of necessary/sufficient. It's a broad and deep topic that is essential to mastery of this test as well as to success in understanding the law.

[peg_city]

It's not necessary, no. This question is not asking for a necessary assumption -- it's asking for a sufficient assumption.

How did you know we were looking for a sufficient assumption? It seems that we could work in 'I~' in two places.

S -> I~ ->MB~
or
I~ -> S -> MB~

In which case 'the spirit is perfect' would be backwards.

Thanks

Also, why is E wrong?

[bbirdwell]

The question itself indicates that we want a sufficient assumption: "IF assumed."

Not sure what you mean about "working ~I in." That's not our goal.

If the argument looks like this;
MB-->DIP-->I
MB-->I
S--->~MB

Then our goal is to work S into the evidence. At this point, the inclusion of S in the conclusion is totally unsupported. We want to take the pieces of our evidence (above the line) and add in "S" in such a way that our conclusion is validated.

We know that ~I --> ~MB (contrapositive), and we WANT S --> ~MB. If it were true that S --> ~I, we'd automatically get S --> ~MB. So that's what we want.

If we had ~I --> S, as you suggested, we would simply get this:
~I --> S & ~MB. This is no good, as we need S to be on the left, as it is in the conclusion, directly leading to ~MB.

(E) is wrong for the simple reason that it doesn't lead us to the conclusion we want. Adding (E) to the evidence we already have, we now have this:
MB-->DIP-->I
MB-->I
S --> ~DIP or I

Putting all of these together in any way possible, we will never arrive at S --> ~MB. Try it.

A --> B --> C
A --> C
D --> ~B or C

You can't get D --> ~A out of that, and that's what we have to do.

[WaltGrace1983]

Here is what I got on this problem:

Material body --> Divisible --> Imperfect

Therefore...

Spirit --> ~Material body

Whooaaaaa, where did THAT come from? Well the first thing I am going to do here is recognize that I know nothing about being ~material body up front. Thus, I have to take the contrapositive of the premise. This will lead me to the following:

Perfect --> Indivisible --> ~Material body

*Note: I could have just as easily said "~imperfect" but because not being imperfect means being perfect, I figure that in this case I wanted to take the extra two seconds and actually rewrite it in such a way that is intuitive to my understanding.

So now I look back at "Spirit --> ~Material body" and see that I can absolutely make this connection if "Spirit --> Perfect" OR "Spirit --> Indivisible." I can have either/or because they will BOTH lead me to to the conclusion that "Spirit --> ~Material Body"

Knowing this, I look at my answer choices:

(A) I know that all material bodies are divisible (the premise states that) but I don't really know anything else. Plus, this doesn't tell me where spirit falls into all of this and it is 100% necessary to link up the word that is stated in the conclusion but never stated in the premise (i.e. "spirit")

(B) I know that Divisible --> Imperfect (this is also from the premises) but for the same reasons as (A) I can eliminate this one quickly.

(C) Close! If the spirit is divisible I know that it is imperfect; this still doesn't tell me anything though.

(E) Very tempting! This is tempting because I know that being indivisible leads to being a ~Material Body. HOWEVER, being imperfect does not lead me to any conclusions about being or not being a material body. Why is this wrong then? After all, it COULD BE that the spirit is indivisible and then this would conclude that the spirit is ~material body. This is wrong simply because it gives us the possibility for the spirit to be imperfect, something that we cannot make any deductions from. If I said "I will give you either A or B" does it absolutely 100% following that I will give you A? B? No. I will give you one or the other. Because sufficient assumptions are all about 100% guarantees, this doesn't really get us anywhere.

(D) is correct. If the spirit is perfect, it must be ~MB

[mcho91]

So if answer choice E said the spirit is indivisible, would that make this the correct answer?