People who are red/green color-blind cannot distinguish between green and brown. Gerald cannot distinguish between gr...

wparham3 August 6, 2019

Represent red green color blindness as RGCB; represent cannot distinguish green from brown as ~GB

General Principle: RGCB => ~GB,
Then contrapositive is GB => ~RGCB

The premise is ~GB, ie, it is given that ~GB. The question is whether you can infer RGCB.

Symbolically, the question is: is it true that ~GB => RGCB?

Note that the statement in question (~GB => RGCB) is a reversal of the positive statement, above, (RGCB => ~GB). Recall that one can never just reverse, which is what the statement in question does - it reverses.
So the statement in question, ~GB => RGCB is flawed, because it reverse the positive statement, which, without also negating, is illegal, ie., flawed.

Abstractly, If carrots are not hamburgers, and x is not hamburger, then you cannot conclude that x is a carrot. It might be a potato.

Hope this helps

Ravi August 6, 2019

@Lauren,

Great question.

Here's how we diagram the stimulus:

RGCB - >can't distinguish between green and brown

Gerald can't distinguish between green and brown (satisfies the
necessary condition of the above statement)

Conclusion: Gerald is RGCB (the sufficient condition of the above statement)

The problem with this argument is that it's invoking the necessary
condition to conclude the sufficient condition. This is improper
logic. If the necessary condition is satisfied, the sufficient
condition may or may not be true.

If, on the other hand, this argument had said that Gerald CAN
distinguish between green and brown (that is, he fails the necessary
condition), then we could conclude that Gerald is not RGCB (the
sufficient condition is failed).

Think about this example argument:

All girls in the WNBA play basketball. Alexa plays basketball.
Therefore, Alexis is in the WNBA.

Do you see how this matches the flaw of the argument in the stimulus?

WNBA - >basketball

Alexa plays basketball

Therefore, Alexa is in the WNBA

See how that doesn't make any sense? The necessary condition is being
invoked to conclude the sufficient condition.

This is precisely the flaw we see in (B).

Sinusitis - >lose sense of smell

Mary has lost sense of smell (satisfies necessary condition)

Conclusion: Mary has sinusitis (sufficient condition is triggered)

Just as seen in the stimulus and our sample argument, (B) is
incorrectly invoking the necessary condition to conclude the
sufficient condition.

Does this make sense? Let us know if you have any other questions!