Q4 - Only if the electorate is moral

[samuelfbaron]

Hi,

I got this questions right, but I was wondering if someone could provide some background on the formal logic.

I diagrammed it as follows:

Only if X then Y

Not Y therefore Not X.

How come answer (A) can't be inferred?

Is it simply that fulfilling the sufficient condition does not permit us to infer that the necessary condition will follow?

[fmuirhea]

You have your logic a bit turned around; "only" indicates a necessary condition, so your conditional diagram would be:

democracy functions well --> electorate is moral & electorate is intelligent

The valid contrapositive is represented by the credited response, (C):

~electorate is moral / ~electorate is intelligent --> ~democracy functions well

(A) is a mistaken reversal.

[ohthatpatrick]

Great response.

You may have noticed that (A) looks almost exactly like the original sentence. On LSAT, that often means that we need to be suspicious.

Are these two statements the same?

Only if you have skis can you go skiing.

If you have skis, you can go skiing.

They're not the same. The first sentence describes a requirement of skiing.

We could rephrase the first sentence as its contrapositive:
If you don't have skis, you can't go skiing.

But that's not the same as saying "if you have skis, you can go skiing." You need more than skis to go skiing. Snow is helpful.

This question is just testing our knowledge of conditional logic.

We can represent "If X, then Y" as
X --> Y

The ONLY thing we can otherwise infer from that rule is the contrapositive, in which we negate both ideas and flip their order.

~Y --> ~X
(you read '~Y' as 'not Y')

One extra layer of complexity is that if you have an AND or an OR on either side of the arrow, you switch it when you write the contrapositive.

Have Driver's License --> Passed Written AND Passed Driving Test

contrapositive:
~Pass Written OR ~Pass Driving --> ~Have Driver's License

Similarly,
Dem. Functions Well --> Moral AND Intelligent

contrapositive:
~Moral OR ~Intelligent --> ~Dem. Functions Well

== other answers ==
(A) an illegal reversal of the original statement (going from X--> Y to Y --> X)
(B) no reason to be that pessimistic. It could be true that a democracy DOES function well and the electorate IS moral and intelligent.
(C) correct contrapositive
(D) illegal negation (going from X --> Y to ~X --> ~Y)
(E) this is also assuming the illegal reversal of the original (it assumes that if Y is true, then X must be true)

Hope this helps.