## PT 61, Section 4, Q25

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fruitoftheloom

Posts: 391
Joined: Sat Mar 31, 2012 10:38 pm

### PT 61, Section 4, Q25

Okay - so I'm not really good at the formal logic questions. If I can intuit the answer, I do better than actually trying to write out the symbols. On question 25, my writing looked like Good Life -> Social Integrity -> Individual Freedom -> Rule of Law. (I tried applying the "not rule"). I chose answer C - you can't have the good life without rule of law. I don't understand why that's incorrect and instead it's B - you can't have social integrity w/o the rule of law.

Help?

bp shinners

Posts: 3086
Joined: Wed Mar 16, 2011 7:05 pm

### Re: PT 61, Section 4, Q25

Alright, let's take a look at the formal logic here:

First thing I notice is a 'without' in the first clause of a sufficient assumption question - that tells me I'm going to be diagramming. Second thing I notice is that the clause after the comma starts with 'for' which is a clear indicator that what follows is a premise supporting what I just said; ergo, that first clause is my conclusion.

To diagram 'without', I change it to 'if not'. So the first clause/conclusion becomes:
If not Rule of Law, then no Individual Freedom
or
~RL -> ~IF

Then, I move to my premises, both using 'without' so I change them both to 'if not'.
If not Social Integrity, then no Individual Freedom (~SI -> ~IF)
If not Social Integrity, then Pursuing Good Life not Possible (~SI -> ~PGLP)

And, overall, it looks like:
~SI -> ~IF
~SI -> ~PGLP
_______________
~RL -> ~IF

I notice a few things. First, RL never shows up in my premises, so I need that to be in my answer choice. Second, both of my premises share a sufficient condition, so I can't combine them (well, I can, but it gives me ~SI -> ~IF and ~PGLP, which is nothing new).

So in an answer, I need ~RL to be in the sufficient condition to match my conclusion (or RL to be in the necessary condition, which is the contrapositive). And I need to attach it to something that guarantees me ~IF in the necessary condition (since that's how I get to my premise). I notice ~IF is necessary to my first premise, so I'm going to attach my new term (~RL) to that premise. It gives me:
~RL -> ~SI
which, put together with my first premise, means:
~RL -> ~SI -> ~IF
and my conclusion is valid.

So I go to the answers looking for ~RL -> ~SI, or SI -> RL. That's B.

Let's look at C now. If I diagram C, I get:
~RL -> ~PGLP
If I put that back into my argument, I get:
~SI -> ~IF
~SI -> ~PGLP
~RL -> ~PGLP
_______________
~RL -> ~IF

Well, ~PGLP is the necessary condition of my second premise and answer choice. I can't combine those two premises, so it doesn't get me my conclusion. It's not sufficient, because not being able to pursue the good life doesn't help me get to whether or not we have individual freedom.

BlaqBella

Posts: 868
Joined: Fri Jan 28, 2011 9:41 am

### Re: PT 61, Section 4, Q25

OP, just to add, we know that the conclusion here is in the first sentence and the two premises follow. My set up looks as follows (all contrapositives):

Keys
IF - Individual Freedom
SI - Social Integrity
PGL - Pursuing Good Life
RL - Rule of Law

Premise 1: IF --> SI
Premise 2: PGL --> SI
____________________
Conclusion: IF --> RL

OR in simpler terms:

Premise 1: A --> B
Premise 2: C--->B
____________________
Conclusion: A--->D

In my class, we are taught to look for similar sufficients in our conditionals to make deductions. In this case, Premise 1 starts with the same sufficient (A) as the conclusion, and as such, we can then use to find the missing premise.

So if A--->B how can we then conclude A--->D? By connecting the necessary statements in these conditionals, (B) and (D):

B--->D (our missing premise which in this case is SI-->RL).

****************

ETA: Answer choice (B) is the contrapositive to SI-->RL

Remember,"without" introduces the sufficient. Like "unless", you can introduce the words "IF NOT" when seeing these indicator words.

fruitoftheloom

Posts: 391
Joined: Sat Mar 31, 2012 10:38 pm

Thanks guys!!