Q21 - If a mechanical aerator is installed...

[Carlystern]

MA --> PPA
~MA --> ~PPA
~PPA --> ~FT
------------------
~FT

Is my setup correct?

[Carlystern]

Tryin again....

A --> B
~A --> ~B
~A --> ~C
--------------
~C


Answer (A):

A --> B
~A --> ~B
~B --> ~C
--------------
~C

Out of all the answers, this one is the closest....but it STILL doesn't look right. :/

[Carlystern]

Is it the question set up:

A --> B
~A --> ~B
~B --> ~C
--------------
~C

Which is also seen in answer (A).....

the prior post, I had the third row incorrectly notated.

Ugh, trying hard, here!

[patrice.antoine]

Is it the question set up:

A --> B
~A --> ~B
~B --> ~C
--------------
~C

Which is also seen in answer (A).....

the prior post, I had the third row incorrectly notated.

Ugh, trying hard, here!

Yes, this is what I have.

[WaltGrace1983]

Thought I'd do a full breakdown of this one. I really like it! There are two arguments within the same stimulus so that would probably be a source of confusion for some. The first time I did this, I just assumed that both arguments were flawed but that is actually not the case.

MA → PA
~MA
⊢ ~PA

So we know that if MA, then PA is possible. John has ~MA and the argument is concluding that ~PA. This is false negation. There could be 100 different ways that the water can be properly aerated! Sure, a mechanical aerator is one way but does that mean it is the only way? Absolutely not! What if John uses an analog aerator? What if aerates the water himself? (by the way, I have absolutely no knowledge of anything related to aeration so I apologize if none of that made sense to all you people with fish ponds ). Because of all this, we have to be looking for a false negation in our answer choices.

MA → PA
~MA
⊢ ~PA

~PA → ~T
⊢ ~T

I added the second argument in there. We don't really know if this argument is valid or not because it hinges on whether or not John's pool actually is properly aerated (PA). If it isn't PA, then we know that argument #2 is not flawed. If it is PA, then argument #2 is actually out of scope/inconsequential/irrelevant because if the sufficient condition (~PA) isn't satisfied, we still know nothing.

All this leads me to believe that we are looking for an argument with a false negation on one side, and another conditional argument stemming from the conclusion of that false negation on the other. Let's go!

(A)

#1: A → R, ~A, ⊢ ~R
#2: ~R → ~C ⊢ ~C


This is the exact same argument told in the exact same fashion! The only tricky part about this argument is that it uses the word "unless" rather than "not." Otherwise, it is identical! Let's look at the other ones just to be sure though.

(B)

P → G, ~P → ~G


The first argument starts okay, not perfect. The reason is that, while it does give us a false negation, it does so in the form of giving us two premises in which each is a false negation of the other. This is very much unlike the original argument that gives us a conditional premise (A→B), gives us another premise (~A), and then concludes (~B) for a false negation. The difference is subtle - but the difference is crucial.

Yet one might look past that and not fully realize it. I know I didn't completely realize it when doing this timed! Either way, we can safely eliminate (B) because it gives us a prescriptive claim, telling one what he or she "should" do. This is drastically different from the original conclusion. Eliminate.

(C)

P & ~E → ~S, B → ~E ⊢ (P & B) → ~E (which means (P & ~E)), ~S


This argument is actually valid. However, we probably could have eliminated this due to the wildly different language. It brings up different kinds of conditional reasoning and is ultimately a very different type of argument. I didn't give this one too much thought and quickly eliminated it.

(D)

M → G
~M → ~FD
M ⊢
G


This one is interesting. It had all the signs of being right initially by giving us a conditional and then giving us a negated sufficient condition. However, it led to different reasoning. This would have been right if you changed things up a bit, like the following:


M → G
~G → ~FD
~M ⊢
~G


That would actually have been the same logic. However, the tell-tale sign that this argument is different from the original is that it starts off with the premise (M → G), gives us (M), and concludes (G). We would actually want it to give us ~(M) and conclude ~(G).

(E)

~DP → sometimes S → can I
~DP
⊢ could be I


There are a lot of weird things going on here ("can," "sometimes," etc.) that makes me believe this is not truly conditional language. I actually don't even know if this is flawed or not (I feel like it is) but either way it is pretty different from the original reasoning so we can eliminate.