Mistaking Necessary vs. Sufficient Conditions

[nadianyc]

Hi everyone,

I am new to the forums here, so I hope I am posting this question in the right place, (if not, please let me know!)

I have been having a lot of trouble understanding the differences between necessary and sufficient conditions during my time studying for the LSAT, in fact, I think it may be my main deterrent. I understand conditional statements and formal logic for the most part, but I always get stuck with "Mistaking Necessary and Sufficient Conditions."

An example of what I am confused about is:
“In order to build a shelf, the only materials a person needs are wood, a saw, nails, and a hammer. I have all of those things, so I should be able to build a shelf.” - The flaw here is that the author mistakes necessary characteristics for sufficient ones, and fails to consider other factors necessary or potentially important to the conclusion.

Is the necessary condition having "all of those things," while the sufficient condition being "able to build a shelf?" In other words, would “In order to build a shelf, the only materials a person needs are wood, a saw, nails, and a hammer. I should be able to build a shelf, because I have all of those things." correct the flaw at hand (not including the fails to consider other factors flaw, of course)

Another example:
“Successful business must have three characteristics: consistent revenue, low costs, and adequate capital reserves. Since our business has those three characteristics, it must be false that our business is unsuccessful.” which is also mistaking necessary for sufficient, if it stated “Successful business must have three characteristics: consistent revenue, low costs, and adequate capital reserves. It must be false that our business is unsuccessful, because our business has those three characteristics.” would that be correct, not considering the other flaws in the argument?

I am fairly good at Necessary/Sufficient Assumption questions, thanks to the Powerscore books, however, I have been stuck on this topic for months, even after reading numerous threads and textbooks.

Any help, advice, or tips are greatly, greatly appreciated!

[Dave Killoran]

Hi Nadia,

Thanks for the message! I'm in the middle of the July LSAT-Flex administration, but I saw your thread and thought I might share some helpful articles/threads to review when you have time:

• Avoid Real World Interpretations and Follow the Language: http://forum.powerscore.com/lsat/viewto ... p=216#p216
  
  One More Look on what Sufficient and Necessary Means (this is key so that when indicators aren't present, we know what we're doing): http://forum.powerscore.com/lsat/viewto ... 6166#p6166
  
  LSAT Conditional Reasoning: When To Diagram: http://blog.powerscore.com/lsat/bid/333 ... To-Diagram
  
  The PowerScore LSAT Blog, Conditional Reasoning articles - https://blog.powerscore.com/lsat/catego ... reasoning/. We write often about this concept, and there are over 20 articles here discussions all sorts of interesting conditional language and arrow relationships.
  
  My posts on this Forum, all searchable: lsat/search.php?author_id=63&sr=posts

As for your two bolded statements, there are some indicators in those that you should look for, including in order to and must.

That's a start and we'll try to come back and finish this up after these tests pass.

Thanks!

[Jeremy Press]

Hi Nadia,

I'm circling back to this post to address your specific examples and try to clear up some confusion I see. In your first example, you've correctly identified the necessary condition ("all of those things," i.e. the saw, nails, and hammer) and you've also correctly identified the sufficient condition ("build a shelf").

The change you propose to the argument doesn't change it from a logical perspective, and here's why: the necessary condition ("all of those things") is the given premise in both of the ways you've phrased the argument. It's the premise (preceding the word "so") in the first version of the argument, but it's also the premise (following the word "because") in the second version of the argument. This is mistaken reasoning in both instances, because it's trying to use the necessary condition in a way the necessary condition can't be used: as a guarantee that the sufficient condition happens. Remember this: a necessary condition (or conditions) can always occur with or without the sufficient condition. So when I know a necessary condition has happened, it doesn't tell me for sure that its sufficient condition occurred.

Here are two changes you could make to that argument, to make it logically sound:

1. We have built a shelf, therefore we must have had a saw, hammer, and nails. (Knowing a sufficient condition occurred, as the premise states here, tells me with certainty that the necessary condition was present as well.)

2. We don't have all the materials (we don't have nails or a hammer or a saw), therefore we cannot build a shelf. (Knowing a necessary condition does NOT occur tells me with certainty the sufficient condition CANNOT occur.)

You ran into the same problem in your rephrasing of the second argument. You made the necessary condition (the three characteristics) the premise (flagged by the word "because"), and you inferred the occurrence of the sufficient condition from it.

Here are two changes you could make to the second argument, to make it logically sound:

1. Since our business has been successful, therefore we know our business has had consistent revenue, low costs, and adequate capital reserves. (Again, knowing a sufficient condition has occurred, as the premise states here, allows me to conclude with certainty that the necessary condition also occurred.)

2. Since our business does not have the three characteristics (its revenue has been INconsistent, or it has had HIGH costs, or it has INadequate capital reserves), it follows that our business cannot succeed.(Again, knowing a necessary condition does NOT occur, as the premise states here, tells me that I can conclude validly that the sufficient condition CANNOT occur.)

Let us know if this clears things up!

Jeremy