I STILL don't understand necessary vs sufficient assumptions

laww
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I STILL don't understand necessary vs sufficient assumptions

Postby laww » Mon Jun 10, 2013 7:13 pm

Can someone make this easier for me?

I'm following the MLSAT and I'm getting more questions wrong now... I like the book but its way too wordy.

Can someone please give me some tips?

I'm about ready to give up... :/

Nicolena.
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Re: I STILL don't understand necessary vs sufficient assumptions

Postby Nicolena. » Mon Jun 10, 2013 8:47 pm

laww wrote:Can someone make this easier for me?

I'm following the MLSAT and I'm getting more questions wrong now... I like the book but its way too wordy.

Can someone please give me some tips?

I'm about ready to give up... :/



I went over the assumption chapters about three times. What I noticed is this

Necessary (what's required - partial)
- in the stem: required, depends on/ relies on, necessary
- this can fluctuate between partial and barely a lot of info, but the info must be true.
- with the answer: if negation destroys it, then it is necessary.

Sufficient (enough/ perfect - whole)
- in the stem: follows logically, allows
- usually more info than needed/ should be 100% or more to fill the gap.

I hope this helps.

laww
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Re: I STILL don't understand necessary vs sufficient assumptions

Postby laww » Mon Jun 10, 2013 10:11 pm

Thank you.

That was indeed helpful. I'm writing a "cheat sheet" for each type of question and taping it to my wall so whenever I'm bored I can go over each question type :P I will add what you provided to it!

I just did some questions as Dr. Dre suggested and I got 8/9 assumption questions correct. Just gotta work at it :P

Nicolena.
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Re: I STILL don't understand necessary vs sufficient assumptions

Postby Nicolena. » Mon Jun 10, 2013 10:29 pm

laww wrote:Thank you.

That was indeed helpful. I'm writing a "cheat sheet" for each type of question and taping it to my wall so whenever I'm bored I can go over each question type :P I will add what you provided to it!

I just did some questions as Dr. Dre suggested and I got 8/9 assumption questions correct. Just gotta work at it :P


I like this cheat sheet idea. In plain view so when your mind wanders, it's still surrounding you. Thanks for the tip. Glad I could help. :)

westtech
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Re: I STILL don't understand necessary vs sufficient assumptions

Postby westtech » Tue Jun 11, 2013 9:05 pm

The thing that I did that helped me understand necessary and sufficient conditions was incorporating them into my day. Whenever I was listening to people talk i.e. (on a phone call that I didn't particularly care for, or small talk that you didn't really ask for) I would listen for conditional language. If someone said "if I go out this weekend, I'm going to get wasted" or anything similar I would run through the inverse, the converse and the contrapositive in my head. Doing that got me to where I don't HAVE to diagram a conditional stimulus in LR, although I do sometimes anyway if I notice a transitive argument. Hope this helps.

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steel_shot
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Re: I STILL don't understand necessary vs sufficient assumptions

Postby steel_shot » Tue Jun 11, 2013 10:01 pm

I think MLSAT explains it the best:

Sufficient guarantees the conclusion 100%:

P:All As are Bs
P:All Cs are Ds
C: All As are Ds

What would you need to guarantee the conclusion? Something that connects the argument, so all Bs are Cs would 100% guarantee that this conclusion is true. I find I can usually prephrase these fairly easily.

Now necessary just means it's required for the conclusion to be true, same argument:

P:All As are Bs
P:All Cs are Ds
C: All As are Ds

There's too many to list here, but what about the fact that not all Bs are Fs? If you negate that, to find that all Bs are Fs, that would completely ruin the argument that all As are Ds. Same could be said about not most Bs are Zs, or any other combination.

Does this help? I realize using letters oversimplifies it, but really almost every assumption question falls into this sort of pattern.

kaiser
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Re: I STILL don't understand necessary vs sufficient assumptions

Postby kaiser » Tue Jun 11, 2013 10:19 pm

I like to analogize it as follows. A necessary assumption is like the lifejacket that simply serves to keep the argument from going under. Without the necessary assumption, the argument is shot, since the conclusion cannot possibly follow without the necessary assumption. So think of it as something that is keeping the argument ever so slightly afloat.

On the contrary, a sufficient condition is a surefire rescue. It takes your premise and GUARANTEES with complete certainly that the conclusion MUST follow. It leaves you with no other choice. Thus, if you have that assumption, combined with the given premise, it is a one way ticket straight to the conclusion. It must fully "bridge the gap" or else it is not truly sufficient.

I know it seems confusing and tough at first, but once the concept sinks it, it becomes completely intuitive.

laww
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Re: I STILL don't understand necessary vs sufficient assumptions

Postby laww » Tue Jun 11, 2013 10:41 pm

Do you guys know any good courses for LR that won't break the bank (about 400 dollars or less please)?

Nicolena.
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Re: I STILL don't understand necessary vs sufficient assumptions

Postby Nicolena. » Wed Jun 12, 2013 1:12 am

laww wrote:Do you guys know any good courses for LR that won't break the bank (about 400 dollars or less please)?


I would try the books first and once you understand the foundations and basic concepts (like identifying LR types/ what to look for) I would suggest finding a tutor. I've take two prep courses and they've helped, but with the money I've spent, I wish I would have tried training myself first with MLSAT and PTs and them find a tutor for my weaknesses. This is just my advice.

KingofSplitters55
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Re: I STILL don't understand necessary vs sufficient assumptions

Postby KingofSplitters55 » Wed Jun 12, 2013 1:17 am

westtech wrote:The thing that I did that helped me understand necessary and sufficient conditions was incorporating them into my day. Whenever I was listening to people talk i.e. (on a phone call that I didn't particularly care for, or small talk that you didn't really ask for) I would listen for conditional language. If someone said "if I go out this weekend, I'm going to get wasted" or anything similar I would run through the inverse, the converse and the contrapositive in my head. Doing that got me to where I don't HAVE to diagram a conditional stimulus in LR, although I do sometimes anyway if I notice a transitive argument. Hope this helps.


I totally second this method. I find that incorporating "LSAT-style thinking" into your daily life not only makes the concepts seem less daunting/abstract but also provides a solid stream of repetition. Then (hopefully) when one walks in on game day and tackles those LR's they'll seem just like more of the same.

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John_rizzy_rawls
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Re: I STILL don't understand necessary vs sufficient assumptions

Postby John_rizzy_rawls » Wed Jun 12, 2013 4:17 am

How can something be sufficient but not necessary?

Seems pretty sound to reason that anything that completely ensures the conclusion of an argument is also enough to "barely hold the argument afloat" and then some.

The phrase "sufficient but not necessary" makes little logical sense to me.

Unless the LSAT is asking us to specifically point out premises that must be true in order for the conclusion to follow while not completely ensuring it, when asking for something necessary. Which makes sense.

But when MLSAT LR uses the phrase "sufficient but not necessary" that just doesn't make sense.

jrd93
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Re: I STILL don't understand necessary vs sufficient assumptions

Postby jrd93 » Wed Jun 12, 2013 4:42 am

The perfect example from the MLSAT guide would be the following.

The shirt costs $20----> John has enough money to buy the shirt.

1.Sufficient and Necessary: John has $20.
2.Sufficient but not necessary: John has $300.
3.Necessary but not sufficient: John has at least $15.

The reason 2 would be sufficient but not necessary is that if you negate it, it doesn't destroy the argument. He could still have $299 for all we know.

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John_rizzy_rawls
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Re: I STILL don't understand necessary vs sufficient assumptions

Postby John_rizzy_rawls » Wed Jun 12, 2013 4:51 am

So the distinction there is that something that can be negated but still ensures the conclusion to be true is sufficient but not necessary. Got it.

I didn't realize inability to negated was a necessary condition of being "necessary" lol

That actually makes perfect sense. Thanks.

jrd93
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Re: I STILL don't understand necessary vs sufficient assumptions

Postby jrd93 » Wed Jun 12, 2013 5:27 am

You have it to a certain degree....
If it is sufficient then it, without a doubt, justifies the argument 100%.

In the previous example, a sufficient answer choice would state something along the lines of John has $300.
So if we insert this into the argument core....

The shirt costs $20 (John has $300)---->John has enough money to buy the shirt.

This would be sufficient but is it necessary? Absolutely not! If you negate it "John doesn't have $300" it doesn't destroy the argument. He could have $250, $100, or $21.

So, having $300 is sufficient but not necessary.

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Dr. Dre
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Re: I STILL don't understand necessary vs sufficient assumptions

Postby Dr. Dre » Wed Jun 12, 2013 6:37 am

laww wrote:I just did some questions as Dr. Dre suggested and I got 8/9 assumption questions correct. Just gotta work at it :P



Great job man!

You just gotta be at it all day every day.

If you feel like quittin' just think this to yourself: "Fuk dat, I won't be a little bitch"

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ScottRiqui
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Re: I STILL don't understand necessary vs sufficient assumptions

Postby ScottRiqui » Wed Jun 12, 2013 8:08 am

John_rizzy_rawls wrote:So the distinction there is that something that can be negated but still ensures the conclusion to be true is sufficient but not necessary. Got it.

I didn't realize inability to negated was a necessary condition of being "necessary" lol

That actually makes perfect sense. Thanks.


I just equate "sufficient but not necessary" to "overkill".

Like the shirt example above, $300 will get me the shirt (sufficient), but I don't need all of it to do so (not necessary). Likewise, a chainsaw is "sufficient" for cutting butter, but it's not "necessary".

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vuthy
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Re: I STILL don't understand necessary vs sufficient assumptions

Postby vuthy » Wed Jun 12, 2013 9:01 am

I think what gets me confused is the difference between sufficient/necessary conditions, and sufficient/necessary assumptions? Am I wrong in thinking there is some difference? In conditional logic, the sufficient condition is the "if," and the necessary condition is the "then." (That, on its own, is hard enough for me to get my head around, because the word "necessary" really means "the thing that is going to happen.") But then for S and N assumptions, the whole "if/then" trigger drops out, right?

I think like a lot of people I can get all the LSAT questions right. But at a conceptual level, I'm struggling to understand what the relationship is between N and S conditions and N and S assumptions.

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Re: I STILL don't understand necessary vs sufficient assumptions

Postby Reframe » Wed Jun 12, 2013 9:27 am

vuthy wrote:I think what gets me confused is the difference between sufficient/necessary conditions, and sufficient/necessary assumptions? Am I wrong in thinking there is some difference? In conditional logic, the sufficient condition is the "if," and the necessary condition is the "then." (That, on its own, is hard enough for me to get my head around, because the word "necessary" really means "the thing that is going to happen.") But then for S and N assumptions, the whole "if/then" trigger drops out, right?

I think like a lot of people I can get all the LSAT questions right. But at a conceptual level, I'm struggling to understand what the relationship is between N and S conditions and N and S assumptions.


Hi vuthy!

The relationship between a sufficient condition and a necessary condition is the same as the relationship between a sufficient assumption answer and the conclusion in the prompt, once we take all the other premises to be true. The relationship between a necessary condition and a sufficient condition is the same as the relationship between an inference question answer and the information in its prompt taken as a whole, once we take it all to be true. The necessary assumption question is a special kind of inference question because what "must be true" given that the prompt is true presents itself to us not as a logical deduction but as an assumption-style gap in the argument, or as a defense against a possible counterargument (like you would get in a strengthen question).

Let me know if that's unclear or if you need an example of any of it.

Edit: This structural similarity is what enables us to use the "negation test" or "denial test" (or whatever you want to call it) above. The test for a necessary assumption answer is just a special case of the contrapositive: for the answer to be right, we need to be able to construct a conditional statement that says, roughly, If Prompt, then Answer; this would be logically equivalent to constructing a conditional statement (the contrapositive) that says, roughly, If not-Answer, then not-Prompt. Technically, we could do this in other inference questions as well, but it would be very inefficient given what those answer choices normally look like.

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Pneumonia
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Re: I STILL don't understand necessary vs sufficient assumptions

Postby Pneumonia » Wed Jun 12, 2013 9:48 am

sufficient:
if "x" then "y"

necessary:
only if "x" then "y"

necessary/sufficient:
if and only if "x" then "y"

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BruinRex
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Re: I STILL don't understand necessary vs sufficient assumptions

Postby BruinRex » Wed Jun 12, 2013 9:59 am

Maybe this will help.

Beheading is sufficient to bring about death. If you are beheaded, then you are necessarily dead.

If something is necessary, then whatever event occurred could not have been otherwise. IE- Something happened and nothing else could have possibly happened. Sufficient is what it sounds like, that it is enough to bring about an outcome, but isn't the only way that outcome could have been accomplished.

If you are dead, have you necessarily been beheaded? No, you could have been beheaded, been hanged, had a piano fall on your skull, etc. All of these things are sufficient to bring about death, and if any one of them happened, death is the necessary outcome.

For the LSAT, like someone mentioned before, if the necessary assumption in an argument is negated (in this case - death), then the whole argument falls apart. If you are not dead (i.e.- you are alive), then you were not beheaded, you were not hanged, and a piano did not fall on your head. A sufficient assumption is one that is 'enough' and 'will always' bring about a necessary event. A necessary assumption is one that, if it were not the case, destroys the whole argument. If an assumption is negated and the argument survives, then you know that it was not a necessary assumption.

Reframe
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Re: I STILL don't understand necessary vs sufficient assumptions

Postby Reframe » Wed Jun 12, 2013 4:36 pm

The Venn diagram approach helps some people, so try it out: http://i.imgur.com/SdNfftf.jpg

The top example is BruinRex's. You see that there's a bunch of different events that are sufficient for death, and that this means that death is necessary for all of them. What this means it that, if we locate any event inside the diagram, that event being in the "Pianos" circle, for example, means that it's also in the "Deaths" circle.

For assumption questions, we just extend this logic to "situations": For the sufficient assumption, any situation where the right answer is true is a situation where the prompt is "true" (i.e., a good argument with a true conclusion), which we can see graphically; for the necessary assumption, any situation where the prompt is "true" is a situation where the right answer is true.

If you're more of a visual thinker, just keeping the Venn approach in mind can be helpful.

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vuthy
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Re: I STILL don't understand necessary vs sufficient assumptions

Postby vuthy » Wed Jun 12, 2013 8:50 pm

The Venn is really helpful actually. Thanks.

I guess the only part I'm still trying to get my head around is this:

Reframe wrote: For the sufficient assumption, any situation where the right answer is true is a situation where the prompt is "true" (i.e., a good argument with a true conclusion), which we can see graphically; for the necessary assumption, any situation where the prompt is "true" is a situation where the right answer is true.


I went and re-read a bunch of easy N and easy S questions with this idea in mind. But for some reason, I'm not seeing the distinction. It seems as though in all situations, it is the right answer choice that makes the prompt "true." Can't somehow see it in reverse. Can you point me to an example of a real question that could help drive this home?

Thanks again.

Reframe
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Re: I STILL don't understand necessary vs sufficient assumptions

Postby Reframe » Wed Jun 12, 2013 8:54 pm

vuthy wrote:The Venn is really helpful actually. Thanks.

I guess the only part I'm still trying to get my head around is this:

Reframe wrote: For the sufficient assumption, any situation where the right answer is true is a situation where the prompt is "true" (i.e., a good argument with a true conclusion), which we can see graphically; for the necessary assumption, any situation where the prompt is "true" is a situation where the right answer is true.


I went and re-read a bunch of easy N and easy S questions with this idea in mind. But for some reason, I'm not seeing the distinction. It seems as though in all situations, it is the right answer choice that makes the prompt "true." Can't somehow see it in reverse. Can you point me to an example of a real question that could help drive this home?

Thanks again.


Here's a really stark example which illustrates the characteristic "tentative" or "hesitant" feel of necessary assumptions (often existential statements) as opposed to the "broad" feel of sufficient assumptions (often universal statements):

Prompt: The sky is a thing. Therefore, the sky is blue.

Sufficient assumption: All things are blue.
You can probably see why fairly clearly; if not, just think of the Venn diagram, and remember we'll have "Things" inside "Blue" here, and the sky will be a dot inside "Things".

Necessary assumption: Some thing is blue.
Well, imagine no things were blue. The sky is a thing. So that would mean it couldn't be blue. That's the opposite of our conclusion. So something's gotta be blue if the conclusion is right.

Reframe
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Re: I STILL don't understand necessary vs sufficient assumptions

Postby Reframe » Wed Jun 12, 2013 9:24 pm

A great real-test example for necessary assumptions is PT39, section 4, #19. #25 in that section is okay too. You can see that both of these have "tentative" words in the answer that render them insufficient to generate the conclusion, but completely necessary for it. Remember that the negation of a very tentative claim is a very broad claim, and vice versa.

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vuthy
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Re: I STILL don't understand necessary vs sufficient assumptions

Postby vuthy » Wed Jun 12, 2013 10:06 pm

Interesting. So would it be fair to think (at least for now as I get my footing) of necessary as something like "bare minimum," or sine qua non? In other words, a necessary assumption is a kind of minimum threshold thing -- something without which the conclusion can't be true. Take it away and it doesn't matter what else is out there in the world -- the conclusion can't happen. Keep it in, and the conclusion has at least a fighting chance of being true.

If this is roughly right, I feel better about it -- although I do go back to the fact that much of the confusion comes from the word "necessary," which we tend to associate with being a strong descriptive (e.g., "by any means necessary"). Whereas in conditional logic, it's almost another meaning of necessary that prevails -- something like I described above.




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