Relates to LR Strategy Guide(No New Post in that folder)

[EricL659]

Error about Necessary Assumption Definition

For argument

it’s raining. → it’s cold outside.

, the assumption is

If it’s raining, then it’s cold outside

. It is said the assumption is both sufficient and necessary. Later in the book the necessary assumption is defined as

Without it, the conclusion may be true, but the argument doesn’t make sense. For instance, if it isn’t necessarily cold outside when it’s raining, why are we drawing the conclusion that it is cold?

Actually, if without it, the argument can still hold true, it is a gold standard to say it is not necessary.

Consider “if it is raining, then it is sometimes cold outside.” This is a weaker version of the given assumption. The negation would be “if it is raining, then it is not cold outside.” This combines with the premise can lead to the conclusion must be false.

Compare the two assumptions:
If it’s raining, then it’s (must) cold outside.
if it’s raining, then it’s sometimes cold outside.

The second is a weaker inference and fits perfectly as a necessary assumption, which means the first stronger one is not necessary.

I would like to point out that definition for the necessary assumption should be that without it, the conclusion is definitely not true.