If an assumption is sufficient, is therefore also necessary?

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nothingtosee
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If an assumption is sufficient, is therefore also necessary?

Postby nothingtosee » Sun Jul 14, 2013 5:45 pm

Assumption questions give me fits, and I'm not sure I'm improving that much on them. One question I have: If an assumption is sufficient, is therefore also necessary?

Could someone give me a plain English example of this being true/false?

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ScottRiqui
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Re: If an assumption is sufficient, is therefore also necessary?

Postby ScottRiqui » Sun Jul 14, 2013 5:56 pm

No, sufficiency does not also mean necessity.

"If you do well on your test, I'll take you for ice cream." Doing well on your test is the sufficient condition, me taking you for ice cream is the necessary condition. DW --> IC

But doing well on your test isn't the ONLY way to get me to take you for ice cream. Maybe you cleaned up the house real well, maybe you washed the car, or maybe I just like ice cream and you talked me into it.

So while doing well on your test is enough to get me to take you for ice cream (sufficient), it's not required (necessary) for you to do well in order to get ice cream from me.

kaiser
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Re: If an assumption is sufficient, is therefore also necessary?

Postby kaiser » Sun Jul 14, 2013 6:00 pm

nothingtosee wrote:Assumption questions give me fits, and I'm not sure I'm improving that much on them. One question I have: If an assumption is sufficient, is therefore also necessary?

Could someone give me a plain English example of this being true/false?


Another example:

If you steal the answer key, you will do well on the test

Stealing the answer key is sufficient for me to conclude that you will do well on the test. It becomes a matter of deductive logic. You stole the answer key? Ok, well you will do well on the test. It is necessary that this conclusion follow from the sufficient condition. That is what a sufficient condition is: an occurrence/phenomenon that guarantees the occurrence of another phenomenon.

Of course, there are other sufficient ways to reach the same necessary conclusion. If you successfully bribe the teacher, you will do well on the test. But do you see how the necessary condition does not in itself guarantee anything? If all I said was "I did well on the test", you couldn't possibly know what led to that (i.e. did I bribe the teacher, steal the answer key, study hard, etc.?)

kiyoku
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Re: If an assumption is sufficient, is therefore also necessary?

Postby kiyoku » Sun Jul 14, 2013 10:16 pm

Pair of shoes costs 100 bucks. I can buy the shoes.

What would be an example of a sufficient assumption that helps this argument?
"I have at least $120 in my pocket"
Why? Because having 120 bucks or more guarantees and is enough to buy the 100 bucks shoes.

Let's think about this same assumption again:
"I have at least $120 in my pocket"

Can we say that this assumption is also a necessary assumption?
In this case, no. We don't necessarily need 120 or more to buy the shoes. We only need 100.

There's an example

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jk148706
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Re: If an assumption is sufficient, is therefore also necessary?

Postby jk148706 » Sun Jul 14, 2013 10:55 pm

No

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nothingtosee
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Re: If an assumption is sufficient, is therefore also necessary?

Postby nothingtosee » Sun Jul 14, 2013 11:55 pm

Thank you for the helpful illustrations. Are there any "tests"/questions you can ask yourself for assumption questions?

e.g.

Which one of the following is an assumption required by the columnist’s argument? [I try to ask, "Which one of these would knock out the argument if it proved false.]
vs.
The conclusion drawn in the argument above follows logically if which one of the following is assumed? [Which one of these fills in a missing link or disarms a potential objection]

I'm getting into that frustrating part of studying where I feel I have the 101 fundamentals, but am still missing something.

kiyoku
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Joined: Sat May 11, 2013 2:25 am

Re: If an assumption is sufficient, is therefore also necessary?

Postby kiyoku » Mon Jul 15, 2013 9:22 am

nothingtosee wrote:Thank you for the helpful illustrations. Are there any "tests"/questions you can ask yourself for assumption questions?

e.g.

Which one of the following is an assumption required by the columnist’s argument? [I try to ask, "Which one of these would knock out the argument if it proved false.]
vs.
The conclusion drawn in the argument above follows logically if which one of the following is assumed? [Which one of these fills in a missing link or disarms a potential objection]

I'm getting into that frustrating part of studying where I feel I have the 101 fundamentals, but am still missing something.


i agree with negation for your necessary assumptions, as a test.

For Sufficient assumption, the assumption must make the argument "logically follow." Thus, it must make the argument airtight. After you apply the sufficient argument, if the argument can still have possibilities of it being wrong, then the assumption was not a sufficient assumption in the first place. My question I ask myself when looking for a sufficient assumption is, "Does this assumption make the argument air-tight? Does it make the logical argument completely work?" (Of course, looking at the support and conclusion is most important to figuring out exactly where the logical missteps are in the argument, but I also find that in some more subtle questions there's important information in the background of the stimulus.)




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