Another Pattern of Reasoning problem Forum

[gweng]

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

[autarkh]

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]

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

[autarkh]

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

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