Necessary and Sufficient Flaw

CinnamonTea

Hello all,

I'm having a bit of trouble understanding the difference between a necessary and sufficient "switch" in a flaw question (i.e., a conditional reasoning logical fallacy.) In the LSAT trainer it mentions on pg. 101 that a flaw that mistakes sufficient for necessary is one type of flaw (I.e., it mistakes one way for the only way.) I understand this.

It then goes on to state, however, that "You may notice that this is the 'mirror flaw' of mistaking necessary for sufficient, which we discussed in the last lesson."

I guess my question is: What exactly is the difference between mistaking and mistaking ? Any examples would be helpful.

inactive

Bumping this!

Wind-Up Bird

The difference between a sufficient and necessary assumption is incredibly subtle, and distinguishing them requires a fair bit of practice. However, mastering this distinction is the key to answering "necessary assumption" type questions on the LSAT.

A necessary assumption is a condition that the argument absolutely requires in order to be valid. If you take away this condition, the entire argument falls apart. The tricky thing is that necessary assumptions are super subtle. You might not even be aware that an assumption was necessary until you apply the "negation test" that J.Y. discussed in the core curriculum.

On the other hand, a sufficient assumption is a condition that may make an argument valid, but it's not necessarily a condition that the argument needs in order to work. Unlike a necessary assumption, if you take away a sufficient assumption, the argument doesn't fall apart. For example, there might be other sufficient assumptions that support the argument just fine.

In addition to the basketball player example that J.Y. used in his lessons, here's another example that might help...

Argument: I'm the best figure skater in the world.
Sufficient assumptions: I'm more graceful than Patrick Chan, one of the world's best figure skaters.
Necessary assumptions: I'm not a paraplegic.

An easy way to pick out the necessary assumption answer on the LSAT involves using the "negation test", which involves logically negating each answer choice. In the above example...

a) It's not the case that I'm more graceful than Patrick Chan, one of the world's best figure skaters

Okay, so I might be less graceful or as graceful as Patrick Chan. What if I'm more graceful than Ashley Wagner, or if I have some quality other than gracefulness that makes me the best figure skater in the world? As you can see, negating this assumption doesn't completely wreck the argument. Now, if you negate the necessary answer choice...

b) It's not the case that I'm not a paraplegic (i.e. I'm a paraplegic).

See what happens when you take away/negate the necessary assumption? If I'm a paraplegic, how can I even skate to begin with? Like I said, necessary assumptions are incredibly subtle, but they're necessary in order for an argument to hold up.

If you have any more questions, feel free to ask. Cheers, and best of luck on your studies.

Alex

@"Wind-Up Bird" said:

If you have any more questions, feel free to ask. Cheers, and best of luck on your studies.

Great explanation @"Wind-Up Bird" !

CinnamonTea

Hello; thank you for your explanation but I think you misunderstood my question.

My question was NOT: How can I tell the difference between a necessary and sufficient assumption?

My question was: What is the difference between a FLAW that mistakes sufficient for necessary, versus a FLAW that mistakes necessary for sufficient?

Thanks in advance.

CinnamonTea

Also, Dillon, what does "bumping this" mean? (Sorry I'm a 7sage beginner)

Stevie C

@CinnamonTea said:
My question was NOT: How can I tell the difference between a necessary and sufficient assumption?

My question was: What is the difference between a FLAW that mistakes sufficient for necessary, versus a FLAW that mistakes necessary for sufficient?

Bumping is internet-slang for replying to a topic for the express purpose of raising it to the top of a forum. It's intended to help generate more substantive replies by others

My understanding is: when they say "mistake sufficient for necessary" they mean calling something necessary when it's actually sufficient. Likewise, "mistake necessary for sufficient" means calling something sufficient when it's necessary.

Example of argument that mistakes necessary for sufficient: "For someone to be elected President of the USA, they must be at least 35 years old. I am 36 years old. Therefore, I will be elected President of the USA."

Example of argument that mistakes sufficient for necessary: "Anyone who wins the lottery will become rich. Little Timmy didn't win the lottery, so he won't become rich."

desire2learn

@"Stevie C" with a great explanation!

CinnamonTea

Thanks for your examples! I think I get it; could you clarify both with an explanation? I know mistaking sufficient for necessary is thinking that one way is the only way for the necessary to occur. Could you explain in words what is going on in each of your examples, and the distinction between them?

Thanks a lot in advance!

Cant Get Right

Okay, this is going to go way more indepth than you need, lol, but I'll get to the point eventually! So, this is often called a mistaken reversal. Structurally, it looks like so:

A --> B
B
therefore
A

This is the underlying logical structure of the above examples.

To elaborate further, with any argument taking the A --> B form, there are two things we can do to draw an inference. We can satisfy the sufficient which forces the necessary (A therefore , or we can deny the necessary which in turn denies the sufficient (/B therefore /A). We can also deny the sufficient or satisfy the necessary, but by doing either of these, the other term is unaffected. By denying the sufficient, the necessary is free to be satisfied or not. Conversely, by satisfying the necessary, the sufficient term can do whatever it wants.

Let's consider all of those abstract forms concretely with a concise example we know to be true.

If it's a dog, then it's a mammal.
It is a dog.
Can we conclude anything?
Yes. If it's a dog, it MUST be a mammal. No exceptions ever.

It's not a mammal
Can we conclude anything?
Yes. If it's not a mammal, it just can't be a dog. No way.

It's not a dog.
Can we conclude anything?
Nope. It could still be a jellyfish or a kangaroo or anything but a dog. All we know is that it's not a dog.

It's a mammal
Can we conclude anything?
Of course not. Same thing with the last one. There's tons of things it could be other than a dog. It's free to be a dog, or it could be a mouse or a bear or something.

So necessary/sufficiency switch is when an argument tries to draw a conclusion by either denying the sufficient or satisfying the necessary:

It's not a dog therefore it's not a mammal
or
It's a mammal therefore it's a dog.

Because this is such a simple and common sense example, it's very clear that these two statements are wrong, given our original argument. What's cool about conditional logic is that however abstract, complex, or unfamiliar the topic, these rules are always just as absolute.

CinnamonTea

Thanks so much @Cant Get Right! All clear now.