Negation - necessary assumption

[amazagri]

okay, so obviously necessary assumptions are either a supporter or a defender. My main focus on here is defenders. So every argument is assuming that it has no weakness/flaw, and anything that does weaken it in negation would be a necessary assumption. My question though is to what extent does it have to weaken it. I have seen examples where you can say it makes the argument seem less likely to happen - although it doesnt completely destroy the argument.

I guess from my experience i have noticed two things - either the negation has to completely destroy the conclusion, or it has to weaken the logical force of the premise used.

Example, bob goes to stanford. Therefore, bob is smart.

NA = people who go to stanford are smart. The negation of this statement clearly destroys the conclusion. However, people who go to standord are smart is equal in meaning to "all people who go to stanford are smart." the negation of this statement "not all people who go to stanford are smart" doesnt destroy the conclusion, but it does weak the first premise that is used; I guess my question is when they say that the negation doesnt have to disproof the conclusion, but weaken the logical force of the premise, what do they mean by that? does the example i wrote out an example of such a thing?

[Dave Killoran]

The negation just has to weaken the argument. If it destroys it, then great! But it doesn't have to do that.

Example, bob goes to stanford. Therefore, bob is smart.

NA = people who go to stanford are smart. The negation of this statement clearly destroys the conclusion.

It actually doesn't destroy the conclusion. Bob could still be smart; we just don't know from the information given that it is for sure that Bob is definitely smart. Hence, the conclusion is weakened.

However, people who go to standord are smart is equal in meaning to "all people who go to stanford are smart." the negation of this statement "not all people who go to stanford are smart" doesnt destroy the conclusion,

Exactly, which is in line with what I said above.

but it does weak the first premise that is used;

It actually doesn't weaken the premise; Bob is still going to Stanford. It instead weakens the absolute nature of the conclusion. We simply don't know for sure that Bob is smart now; he may be, but it's just not certain. This is the essence of weakening: it just means to introduce doubt. To weaken an argument is ultimately the process of making it less certain to be true. If we can make it less certain by utterly destroying it, then that would be great. But that can be very difficult to achieve given the short form of LR, and hence the bar to cross is to simply to undermine it in some way

Thanks!