LR Bible page 223 number 4 (conditional linkage)

[fmihalic1477]

Hi all,

I peeked at the S&N conditions chapter of the bible for the first time today. I haven't look at it before in my preparations before because I have studied logic formally in school and thought that it wasn't an urgent priority. Needless to say, I've been humbled on multiple levels.

To the question , "If there are any inspired musical performances in the concert, the audience will be treated to a good show. But there will not be a good show unless there are sophisticated listeners in the audience, and to be a sophisticated listener one must understand one's musical roots."

I diagrammed " IMP -- GS -- SL -- UMR "

However. I could not figure out how to write the contrapositive of this. The correct answer ultimately was something that would have been right in front of my face with the contrapositive.
In addition, how exactly do the antecedents and the consequents works with conditional linkage? Are the rules in accordance with "regular" conditional statements? How do I write ones that are longer?

For example, just because there are people in the audience who understand their musical roots does not guarantee that the show was good. That would a form of affirming the consequent. So with this particular question, B is an example and denying the antecedent and C, D, and E are examples of affirming the consequent.

Lastly, it appears that I've learned to make "unless" into a conditional statement a bit different from the main method shown t=in the bible.

I typically would write "It will be a good show unless there isn't a single inspired musical performance." like this:

"If there's at least one inspired musical performance, then the show will be good." This is perfectly acceptable, correct?

Contrapositive: Is the show hasn't been good, then there has;t been at least one inspired musical performance.

Thank you in advance!

Frank

[Francis O'Rourke]

Hi Frank,

A lot of your questions are explained earlier in this chapter of the Logical Reasoning Bible, so I would recommend that you read through it at your earliest convenience.

The contrapositive of a chained conditional statement such as If A, then B, and if B, then C would simply be If Not C, then not B, and if not B then not C

A B
B C

THUS

A B C

THEREFORE

C B A

In case you cannot see that clearly, there are strikes through the letters in the last chain, which we use to indicate "Not"

If a necessary condition (consequent) fails or is negated, then the sufficient condition (antecedent) fails. Since, when we link A, B, and C as we did above C becomes a necessary condition for A, when C does not exist, A does not exist. This is true for single linkages (I'm assuming that is what you mean when you say 'regular') or multiple, chained links.

If this isn't clear to you, then imagine a real world example:

• If I buy Apples,I must buy Blueberries. If I buy Blueberries, I must buy Cherries.

According to this statement, whenever I buy Apples, I must buy Cherries, so whenever I fail to buy Cherries, I must not buy Apples.


What you refer to as denying the antecedent, and affirming the consequent, our book will refer to as the Mistaken Negation, and Mistaken Reversal, respectively. You can read pages 165-170 for more information about these on the LSAT, but it looks like you are correct about answers (B) through (E)!


Lastly, what you produced as the diagram for the unless statement is correct. In fact, that is simply the contrapositive of the way that we will diagram unless statements in the Logical Reasoning Bible. Since contrapositives are logically identical to the conditional statement, there is no universally agreed upon better way to form a unless statement. For example, the phrase "It will be hot, unless it rains" can be diagrammed as either of the following ways:

1. It will be hot, unless it rains
2. hot rain
3. rain hot

In this example both statements tell you the exact same information; they are logically equivalent. The reason that we recommend you initially diagram "unless" statements like the first diagram is that it often yields immediately helpful inferences on this exam.

[fmihalic1477]

Hi Francis,

Thank you very much for the reply. I realized after posting this that maybe what I needed was a second or third look through the chapter. So that's what I did. In particular I spent a ton of time with the chain linkage and double arrows/ not arrows. Now I understand much, much better. Unless it's a chain linkage must be true problem, I can do it in my head.

On a side note, I strongly prefer the unless formula to the formula that I was using. It is very simple and usually can be done mentally with minimal effort.