CONDITIONAL LINKAGE

[Marce]

ON Pgs. 2-50 and 51 IN the LSAT coursebook, concerning question 4, why can't the chain be: AS->GI->PCE (with a slash through it)? ... instead of what the book says IT IS AS, PCE->AS->GI.

[Jonathan Evans]

Hi, Marce,

Great question. First, let's parse out the stimulus to identify the conditional reasoning elements. When we encounter language that makes us think, "Hey, that looks conditional!", let's stop and evaluate.

First sentence is kind of a cool fact, but not doing much for me so far.

Next sentence we see something! That word "only." Okay, pause. Let's make sure we get this straight. What is required here for something else? The Moon's gravity is required to keep the orbit stable. Now we know what's necessary: Moon's gravity. From that we know the thing it's necessary for must be sufficient.

• Stable Angle Moon's Gravity

Move on to the next sentence. This looks conditional too! We're on to something! "Without" gives it away. Ask ourselves again, what is the requirement here? What makes something else possible? Okay, so the stable angle is a requirement for supporting life. Again, here we know what's necessary: stable angle. What's it necessary for? Supporting life.

• Supporting Life Stable Angle

The abbreviations/variables are arbitrary, but the analysis is the same. Now I'm going to adopt the book's convention for consistency:

• Moon's Gravity = GI
  Stable Angle = AS
  Supporting Life = PCE

Here's each conditional:

• AS GI
  PCE AS

Put it all together:

• PCE AS GI

I hope this helps!

[Marce]

Hi Jonathan,
Thank you, I've outlined my specific issues with this question:

Sent. 2) AS GI
Sent. 3) PCE AS - This sentence "Without such a stable and moderate AXIS TILT, A PLANET'S CLIMATE IS TOO EXTREME AND UNSTABLE TO SUPPORT LIFE. Shouldn't the necessary cdtn be the axis tilt, not the angle?
----------------------
3)PCE AS GI :Here's my other issue with this linkage, the final linkage has PCE first instead of AS, whereas in prior examples of conditional linkage, it flows in the same order as given, for example on pg: 2-49 (see below):
1) KS-->AUC
2) AUC-->WEWP
3) KS-->AUC-->WEWP, This linkage makes complete sense;and flows in order, 1 +2 =3. The linkage above is out of order, it goes from sent 3 to sent. 2 then the final conditional linkage

Please advise thanks!

[Jonathan Evans]

Hi, Marce,

Thanks so much for following up and for taking the time to engage with this in detail. Conditional statements are indeed challenging, and your question highlights one of the particular difficulties of multiple conditionals. That is, when you have multiple conditionals that share elements in common, the LSAC likes to change the language slightly without changing the meaning of the terms.

Let's look at that issue here. You are correct, the necessary condition is the Axis Tilt. However, here's the tricky thing: The Axis Tilt is the Angle! The "stable and moderate axis tilt" is synonymous with "axis tilted...at an angle of roughly 23 degrees...kept stable."

In the first conditional statement from the second sentence, we could write it out long form in a couple ways:

• Angle of axis tilt kept stable at roughly 23 degrees gravitational influence of the moon

• OR

• Stable and moderate axis tilt gravitational influence of the moon

So here's where you have to be careful. When you have more than one conditional, you have to see whether there are terms in common. Often there are; sometimes there aren't. You have to ask yourself what might sync up between multiple conditionals. (For another example of the necessity of linking terms together and making connections, take another look at problem 4 from the lesson on page 2-12).

Your next question addresses another important aspect of conditionals (and arguments in general!): the order of the statements in a stimulus need not correspond to the way the argument is organized.

Let's return to the other example you mention to illustrate this concept.

What would happen if we were to swap the two sentences from problem 3 on 2-48? In that case, we would have the conditionals in the following order:

• AUC WEWP

• and then

• KS AUC

So that kinda muddles it up a bit! However, the connection still follows in the same way:

• KS AUC WEWP

In the same way, let me rephrase the stimulus on 2-50 to conform to the order in which it ends up when linked together. It would read something like this:

If a planet doesn't have an extreme environment, it must have an axis tilted at a stable angle. If a planet is to have such a stable axis tilt, it must have the gravitational influence of a large, nearby moon.

Notice that this way that I have reworded the stimulus in no way changes the underlying structure of the argument. I have kept all the conditionals the same; I've just changed the syntax and order of the statements in an attempt to make the argument clearer.

Does this explanation help to address your questions? Please follow up if I may be of further assistance.

[Marce]

Hi Jonathan!
I UNDERSTAND everything, except:

Based on what you wrote regarding the conditional linkage on pg. 2-49:
"AUC WEWP
and then
KS AUC
So that kinda muddles it up a bit! However, the connection still follows in the same way:
KS AUC WEWP"

Does this mean the chain on pg. 2-51 can also be:
Sentence 2: AS-->GI
Sentence 3: PCE (SLASH through it) -->AS
Chain: AS-->GI-->PCE (SLASH through it) [What I previously asked, but not quite answered]
.... as well as the book's version of PCE (slash over it) -->AS-->GI
Are these 2 stmts, AS-->GI-->PCE (SLASH through it) AND PCE(slash through it) --> AS-->GI equivalent?

[Jonathan Evans]

Hi, Marce,

Thanks for following up! No, the link does not work that way. When you see these arrows you must keep the direction of the arrows consistent.

For instance, let's discuss the statements on 2-51. To recap:

(2) AS GI
(3) PCE AS

Notice that in (2) the arrow next to AS points at GI. This means AS is a sufficient condition for GI. What does that mean exactly? It means that the Angle Stable relies on the Gravitational Influence. If we know we've got an Angle Stable, we know for sure that we have a Gravitational Influence.

Now here's the thing though. Just having a Gravitational Influence is not by itself enough to know that we have an Angle Stable. We could have Gravitational Influence but with an Unstable Angle. The GI makes it possible to have an Angle Stable. Like, cool, we've got that GI. Now it's possible to have an Angle Stable, but we don't have to have an Angle Stable. It could go either way. That's what it means for something to be a necessary condition (but not a sufficient condition). GI is a necessary condition for AS but not a sufficient condition for AS.

This is why the arrow points away from AS (sufficient) towards GI (necessary). This could be read as "If AS is true, then GI also is true."

Remember the Mistaken Reversal™ error: "If GI is true, then AS is true."

This is a fallacious statement.

The arrow always points away from the sufficient condition towards the necessary condition.

sufficient necessary

However, in (3) the arrow points away from PCE and towards AS.

This is a brand new conditional statement, with its own sufficient and necessary conditions. In this statement PCE is the new sufficient condition and AS is the new necessary condition.

This is where the magic happens. Which element do statements (2) and (3) have in common? AS appears in both (once at the sufficient condition, and once as the necessary condition). It can serve both these roles independently, but you can do cool stuff by putting the statements together!

AS is the glue that holds these two conditionals together because in one statement (2) it is the sufficient condition, and in the other statement (3) it is the necessary condition. There are two arrows connected to AS. These arrows cannot change directions. Let's look only at AS and the arrows that connect to it:

AS

The left arrow points towards AS as the necessary condition. The right arrow points away from AS as the sufficient condition.

Refer back to our two statements. AS is the necessary condition for PCE. Therefore as far as PCE and AS are concerned, the arrow must remain consistent, pointing away from PCE and towards AS. This remains true whether the conditionals are linked together or written by themselves. Thus we know:

PCE AS

and

PCE AS

Well we have only one more element to connect, GI. AS is the sufficient condition for GI, so the arrow must point away from AS and towards GI, whether written separately or in a chain conditional. Thus:

AS GI

and

AS GI

Now we can put it all together:

PCE AS GI

There is no connection between GI and PCE except through AS. There's no other way to link PCE and GI.

Because they all connect together in this one way, we can read the chain backwards and forwards:

PCE is sufficient for AS, which is in turn sufficient for GI.

Because every time you have PCE you must have AS, and every time you have AS you must have GI, you can infer that PCE is also sufficient for GI. In other words, PCE is the starting point, the starting sufficient condition, that leads you to its necessary condition, AS, which then leads you to its necessary condition, GI. Start at PCE and go all the way to GI.

PCE GI

Now remember that since GI is necessary for AS, and AS is necessary for PCE, you can form the contrapositive as well by flipping each arrow and negating each element. This leads you to:

GI AS PCE

In the same way as we just cut out the middleman above, you can do the same thing here:

GI PCE

Start with no Gravitational Influence, end up with no Angle Stable, and finish with a Planet Conditions Extreme!

I hope this helps! Please let me know how I can be of further assistance.

[Marce]

Hi Jonathan

Thank you!