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Amanda on March 24 at 12:04AM

Diagram Question

I'm having a bit trouble diagraming the information, I was trying to do the missing premises drills and I think I understand the core concept but I also feel that I'm missing something to fully get the answers right.

7 Replies

Amanda on March 24 at 12:24AM

Also, I'm trying to understand S&N before I move any further, just because I think that was mainly what I have been missing in the previous studying I have done. Not sure if I'm doing the right thing.

Amanda on March 24 at 12:24AM

Also, I'm trying to understand S&N before I move any further, just because I think that was mainly what I have been missing in the previous studying I have done. Not sure if I'm doing the right thing.

Shunhe on March 24 at 12:03PM

Hi @Amanda_r01,

Thanks for the question! Do you have any more specific questions about the missing premises drills or S&N? IT’s hard for me to help you unless you ask more specific questions, but I can try to do this much at least.

Basically, for missing premises, we might have a logical chain that tells us something like:

A —> B
B —> C

And then we’re asked how we can conclude C. Well, if we know that A, then B, and therefore, C. So knowing A would be one way to do this. Similarly, if we know that

A
A —> B
Therefore, C

And we’re asked to fill in a missing premise, then it has to be one either directly linking A to C (A —> C) or linking B to C (B —> C) since that’s how we need to sort of fit the pieces of the puzzle together to get from A to C.

For S&N, just know that

S —> N

Since if “S”, is true, then “N” is true (meaning that S is sufficient for N). On the other hand, if N is false, then S is false (because of the contrapositive), and so N is necessary for S.

if X then Y = X —> Y
only (if) Y then X = X —> Y
Y unless X= ~X —> Y

These are the main things you need to know for each of these topics. Like I said, if you have more specific questions, feel free to ask them! Hope this helps.

Amanda on March 24 at 03:01PM

-How do we identify when to use the contrapositive ( C+ ) to connect the logical chain?

-What is a good way yo pick the set up for the questions diagram using the information given. I get kind of lost when using all the initials fro the setup.

Shunhe on March 24 at 08:27PM

Hey @Amanda_r01,

Great follow-up questions. Sometimes, we’ll notice that we are given a conditional statement, and the negation of the necessary part of that statement. For example: If it rains today, I will stay in. But I did not stay in. We can diagram this as

Rains —> Stay in
~Stay in

Now note that we have the same “stay in” condition in a premise and in the necessary part of the conditional, but negated. This is when we might use a contrapositive:

~Stay in —> ~Rains
~Stay in

And using this, we can conclude that it did not rain. We might also use it to connect two conditionals to make a longer one, also when we notice that the same term appears in both but negated. For example: if it rains, I will stay in. If I go to the restaurant, I did not stay in. We diagram this as:

rains —> stay in
restaurant —> ~stay in

and then we see that “stay in” is again the same in the two, so we can take the contrapositive of either one, but the second one will make more sense here:

rains —> stay in
stay in —> ~restaurant

And now we can make the chain

rains —> ~restaurant

I’m not sure exactly what you mean by “the set up.” If you mean knowing what to diagram, then that will follow from key indicator words like “if,” “only (if),” “unless,” “all,” and etcetera. If you mean picking the initials, that’s whatever works for you. Let me know if you have further questions.

Amanda on March 26 at 09:48PM

Can you please explain the argument completion drills? Those are giving e trouble in all the sections I have doe so far.

Shunhe on March 28 at 03:27PM

Hi @Amanda_r01,

Sure thing. Let me know if there’s any specific drills you want help on. I’ll walk through the first one as an example, so you can see the kind of thing we need to do. We’re told that cultures advance only when independence replaces dependence, or when imposition by outsiders is replaced by initiatives from within. The second sentence basically rephrases the first, and the third sentence just provides evidence supporting the first sentence. We can diagram the first sentence as:

Cultures advance —> Independence replaces dependence

Now, we’re asked to apply this argument to a new scenario. We’re told to consider individual schools as separate cultures, and then asked for the key to educational progress. Well, based on the statement we have above, we know that a necessary condition for cultures advancing is that independence replaces dependence. And we know that we’re considering individual schools as separate cultures. So for a school to advance, independence must replace dependence as well. And this is what (A) tells us: that individual schools must be independent of outside imposition.

Hope this helps! For argument completion questions, it’s important to diagram the argument you’re given carefully, and see how it applies to a new situation, or to see what logical consequences come as a result of putting the premises together. Let me know if there are other questions you have, or questions about argument completion generally.