Additive Inference Drill #3

[cgschotten]

I disagree with a couple of the inferences made, and want to know it I just misunderstood the instruction from Chpt 11, or if the two inferences in question are incorrect.

Diagram: E F G H

Inferences:
G /E (by working ALL backward from G to F to get G F combined with if no Fs are Es - I agree with this inference)

I don't understand the next two:
F H (How can All Fs be Hs without us know that all Gs are Fs? For instance, there may be 5 Fs that are all Gs, but since we do not know that all Gs are Fs perhaps there are 10 Gs that are all Hs. This just doesn't seem to work.)

Based on that inference an additional inference is made that H /E, but how can this be if working ALL backward would produce two some arrows which does not yield any inferences?

[Dave Killoran]

Hi CG,

Thanks for the question. Those inferences are correct, so let's take a look at each.

1. F H

This inference results from the straight linkage of F G H. If all Fs are Gs, and all Gs are Hs, then all Fs are Hs. The number of Gs in the example you cite isn't relevant, because they tell us that all Gs are Hs; once we have that info, any H that is a G will also then be an H.

2. Remember, inference are like bridges--if you can build it in one direction, the link is made and is secure. It doesn't have to "look" right from the other side to be valid. The inference here is made in the same fashion as the first inference you understood, so the logic is seamless. This point is critical, and may well have contributed to the issue you had in the inference above. If you look at F G H, coming from F we can travel down the arrows and get to H, creating the F H inference. But, if "start" at H, all you get is two going towards F, so it "looks" like you can't make the inference (and which is why and H F inference does NOT exist).

Ultimately, to make this inference, we use the inference from 1 above to create the following chain:

E F H

That yields E H, which is our inference (and which is identical in form to the inference that you agreed with in your original post

Please let me know if that helps. Thanks!

[cgschotten]

Thank you for the clarification. After working on some of the actual LSAT sample formal logic questions, these types of additional inferences make a lot more sense.

[Dave Killoran]

Excellent, I'm glad to hear that! Please let us know if you have any other questions.

Thanks!

[yihannah90]

Hi!

I have a quick question about diagramming "No E's are F's" from Q. 3 on page 334.

I understand that it can be diagrammed as E F. But isn't it also possible to diagram it as "X ~Y"? (~ means negation here) I think the Powerscore book confirms this idea on page 306 under the C. The Double-Not Arrow section.

If this is the case, the diagram can also look like: E ~F G H

Then, shouldn't I be able to infer E ~G and also E H?

When I first tried this problem, I immediately came up with those two inferences but was a little surprised to see that the drill answer key didn't list them. Where did I go wrong?

Thank you so much in advance!

Best,
Hannah

[Dave Killoran]

Hi Hannah,

Thanks for the question! Let's take a closer look at this, because while you are correct about the first part, the way you tried to apply it in the second part doesn't work.

Looking at "No E's are F's," the full diagram is indeed E F. And, as you note, all double-not arrows results from the basic statement:

E F

and its contrapositive:

F E


Those two statements are the subcomponents (and, really, the generators) of any double-not arrow where both conditions are positive.

Moving on to where you ran into a problem, let's take a closer look at that first diagram: E F. Note that the necessary condition is "not F." The next statement on that list is diagrammed F G, and the sufficient condition here is simply F. The difference between those two conditions is the key to the issue.

When you created the diagram of E ~F G, you chained together two statements as if they both involved F, when only one involves that term. That doesn't work, and that's why those inferences can't be drawn.

Please let me know if that helps. Thanks!

[yihannah90]

Dear Dave,

AHHH I see it now! Thank you so much for your prompt reply! It really helped

Hannah

[Dave Killoran]

Great, glad I could help! Please let me know if you run into any other problems.

Thanks!

[Jerrymakehabit]

Can someone please help me with my question below?

From E F G H, I can get E F G. If it is E then it is not F, most of F are G. Can I say E G?

Thanks
Jerry

[Brook Miscoski]

Jerry, I am not sure what edition you are using, so I cannot be sure that my answer helps you. If it does not, please provide edition information so that someone can follow up.

The short answer to your question is that the conclusion does not follow in the logic that you mapped out. Think of it this way. If you have F, then you don't have E, and you do have G. However, what do you know if you don't have F? You don't know anything at all, since the failure of a sufficient condition doesn't allow you to move forward. Thus, you cannot conclude that E and G are dissociated. But that leaves the question of what you're trying to interpret.

I think you are trying to diagram a LR method of reasoning question--argument part-- that features a psychologist.You do not need to diagram the stimulus to determine that the requested information is a conclusion.