Confuses a necessary condition with sufficient & viceversa

[jklink94]

Hello! I have been having trouble describing both Mistaken Negation and Mistaken Reversal in abstract terms, specifically both “confuses a necessary condition with a sufficient condition” and “confuses and necessary condition with sufficient condition” I know what both flaw look like when diagrammed for example.

A B

Mistaken Reversal: B A

Mistaken Negations (not)A (not)B

I have always thought that a mistaken reversal is to confused the necessary for a sufficient condition and for a mistaken negation it is to confuse a sufficient for necessary condition. Upon taking a practice test (PT 75 sec.3 #16) the correct answer was A. I dismissed this because it did not describe the flaw (mistaken negation) to what I thought was correct. Can anyone help me to clarify when and how these abstract descriptions are properly used? I’ve already read the explanation and it says that a mistaken negation can also be described as confusing the N for the S. So now I’m confused thinking that there are instances where each these two conditional flaw can be described by both abstractions. Please help, thanks!

[Malila Robinson]

Hi jklink94,
This is a classic type of LSAT question. The key is in recognizing that an original statement A B and its Contra Positve Not B Not A, mean the same thing.

In this question the argument is saying

(If) capable of planned locomotion (CPL) (Then) Able to form internal representation of environment (FIRE) & able to send message to muscles to control movement (MMCM) Central nervous system (CNS)

(If) Not CPL (Then) Not CNS

So it seems clear that the answer is that the flaw is a Mistaken Negation.

BUT what is the Contra Positive of that second diagram? (If) CNS (Then) CPL

And there it is. If we look at that statement, which means the exact same thing as the last sentence in the stimulus, then Answer A is clearly correct. It did in fact confuse and necessary condition with a sufficient condition. The Contra Positive of the last sentence made the necessary condition (CNS) a sufficient condition. And that is why a Mistaken Reversal answer works for a flaw question that appears to clearly be a Mistaken Negation.
Hope that helps!
-Malila

[lathlee]

Hi. I have an intersting dilemma rrelated to this topic.

How does The only Requirement(precondition) works?

This random Scenario popped in my head as I was studying last night:

The only requirement(precondition) to to get in to this play is to be a ticket-holder and Not being drunk.

The only is a necessary condition introduce but technically functions as the term that follows as a sufficient conditioner.

So THIS Particular phrase appears, THE ONLY Requirement , would that functions as "if and only if" in this case?

THE precondition to get into this play is a ticket-holder and Not being drunk.
Tom is an sweet boy with a ticker in his hand and not being drunk.

in this case, WE know TOM met the necessary condition WHICH he may or may not get in to a play.

Following sentence: the only precondition to get into this play is a ticket-holder and Not being drunk; Tom is an sweet boy with a ticker in his hand and not being drunk.

I have two Questions in this scenario:

1) Is this correct way to diagram to following scenario: In this case,


Ticker holder + Not being drunk Get into Play



2) can tom get into play as of 100%, like A-----> B Since Tom is a A, Therefore, B shall be achieved. As we all know In a double arrow situation when one condition is met, the other one is met.

[lathlee]

Merry Christmas

[Dave Killoran]

Hi Lathlee,

"The only" typically precedes some type of indicator that modifies another part of the sentence, making "the only" act as a sort of sufficient condition indicator in terms of proximity. Consider this example:


The only way to the top of the mountain is the switchback trail


"Way" modifies "trail," and thus the diagram is:


Top of mountain switchback trail


So, if you see someone on top of the mountain, then according to the author they took the switchback trail. On the other hand, if someone took the switchback trail, does that mean they got to the top of the mountain? No, so switchback trail is not a sufficient condition.

But, consider "the only" as it operates above. you could say it is sufficient for "top of the mountain," ignore the "way" portion and still have the same diagram. Two different ways to get to the same conclusion as it were

My colleague Nikki put it similarly:

• This may sound unorthodox, but I've always considered "the only" to be a sufficient condition indicator, because it's always directly proximate to the sufficient condition:
  
  The only people who drink are those who smoke:
  
  Drink Smoke
  
  The only way to succeed is to work hard:
  
  Succeed Work hard
  
  The only place to get a good slice of pizza is Luzzo's.
  
  Good pizza Luzzo's
  
  And so on. It's imperative to make a distinction between "the only," "only," and "only if." The last two directly precede a necessary condition, whereas "the only" directly precedes a sufficient condition. Technically, they are all necessary condition indicators because in the case of "the only," the actual referent is elsewhere in the sentence. But it's easier to think of it as a sufficient indicator for the reasons mentioned above.

Now, in your example I wouldn't say it's a double-arrow; it would still be a single arrow because people with a ticket and not drunk don't have to then go to the play, they could go elsewhere instead.

Sound good? Let me know. Thanks and Happy Holidays!

[T.B.Justin]

I hope you all don't mind me jumping in

The only people who drink are those who smoke:

Drink Smoke

The only way to succeed is to work hard:

Succeed Work hard

The only place to get a good slice of pizza is Luzzo's.

Good pizza Luzzo's

I was wondering on maintaining the validity of these statements with "only if"

Those people drink only if they smoke:

Drink Smoke

Not smoke Not drink

Some people drink only if they smoke:

Some drink Smoke

(What is the CP?)

[lathlee]

Hey Bro,

the Example you gave to us :

Some people drink only if they smoke:

Some drink Smoke

(What is the CP?)

---------------------------------------------------------------------------------------

The word some indicates the quantity of some (1-100%)

So .... It is Drink people Smoke

CP, i think you meant contrapositive, we can infer it is following : Smoke Drink people

Let me put it this way:
You and I both know; Some stuff that grown on the Solid ground are trees ,

Stuff grown on the Solid Ground Trees

So by now, we at least knows Some Trees (1-100% of all trees) are grown on the solid ground. right ?
We both know, Not all tree grow from solid ground; There are a tree kind that grows on the swamp and from other trees.
(Aka: in Philosophy example, Karl Popper's famaous (Black Swan Example)
Contrapositives in this case would be trees grown on the solid ground.


Btw Dave, the above example by T.B. reminded me of one question i have been meaning to ask:

EX: No boy is left behind; we know no works as negation of the other side indicator this case (but not all the time)

so diagram it would be Boy - Left behind.

But What is the correct way to interpret

No money, No girlfriend ?

is it - Money - Girlfriend ?

[T.B.Justin]

Hey lath,

Thanks for the reminder!

I am going to add another chain to this:

Some people drink only if they smoke, most people that smoke if only they drive

Drive Smoke Drink

Where we have some people that drink, smoke and most people who drive, smoke but we know nothing about if the people who drink, drive or if the people who drive, drink.

[lathlee]

Hey Bro, I know where your question is coming from , i am happy to help ...


Every yearr, Most USA Basketball college players make to the NBA player, some NBA players make to NBA Hall of fame.

USA B.College NBA Hall of NBA Hall of Fame

well in this case, we don't really have any information how many of some NBA players is consist of B.college with addition how much percentage who make to hall of fame right?

as in let's say, there are 150 players NBA players , usually 100 goes to NBA, and among 500 NBA Players only 1-2 % make to Hall of fame. We don't really have any information to determine there is any college players.

but the logic train only works if <all> or NONE as 100% vs 0 %.

Same example,

Every year, Most USA basketball college players make to the NBA player, all NBA Players are athletic geniuses.

USA B.College players NBA athletic geniueses.

then we can make an inference Most USA basketball players who made to NBA are athletic genius

[T.B.Justin]

Right, cannot go All to Most or Most to Some or Some to None or All to Some etcetera.

Thanks!