Another Pattern of Reasoning problem

gweng
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Joined: Tue Feb 09, 2010 9:31 pm

Another Pattern of Reasoning problem

Postby gweng » Sat Mar 13, 2010 8:00 pm

Prep Test 25, June 1998
Part 2, Problem 22.
Can someone explain the answer?

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autarkh
Posts: 314
Joined: Sat Sep 26, 2009 9:05 pm

Re: Another Pattern of Reasoning problem

Postby autarkh » Sat Mar 13, 2010 8:47 pm

I'll take a stab.

There are two layers to this problem:

The first, and the one we should be most concerned about, is the argument's structure: we're given a conditional claim, followed by its contrapositive.

The second layer is the argument's main point: on the basis of the contrapositive violating common sense, we should conclude that the original statement is absurd.

Let's look at a diagram:
GS = Government Subsidy
ACA = Allowed to Create Art

Original claim:
not GS --> not ACA (Author claims this is absurd because...)
Contrapositive:
ACA --> not not GS, which is equivalent to: ACA --> GS (...it would imply this, which violates common sense)

We get this in answer choice A:
A = Arrested
BL = Break Law
! = not

!A-->!BL (Author claims this is absurd because it would imply...)
BL-->A (...which violates common sense)

All of the other answer choices do not have the same structure.

Let's look at B:
!A-->!B
A-->B (fallacy of the inverse)

C is also wrong:
SSG = Scientist Supported by Grant
S = Successful

SSG-->S
S-->SSG (fallacy of the converse)

As is D:
SSG-->S
!SSG-->!S (fallacy of the inverse)

And E:
AR = Allowed to do Research

SSG->S
AR --> !!SSG : AR --> SSG (equivocation between success and being allowed to do research)

gweng
Posts: 27
Joined: Tue Feb 09, 2010 9:31 pm

Re: Another Pattern of Reasoning problem

Postby gweng » Sun Mar 14, 2010 12:12 am

Nice! Thanks a bunch.
So the double negative "no one...without" = if...then.

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autarkh
Posts: 314
Joined: Sat Sep 26, 2009 9:05 pm

Re: Another Pattern of Reasoning problem

Postby autarkh » Sun Mar 14, 2010 12:41 am

gweng wrote:Nice! Thanks a bunch.
So the double negative "no one...without" = if...then.


Yep. None/no...without == if...then.




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