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How do you apply the Assumption Test to a conditional?

Moreover, how do you apply it to a sentence that has phrases like "less likely," "more likely," etc.?

To negate a conditional: the conditional is false.
So if original is a->b, the negation is a and not b. For example, original: if I'm tall, then I'm good looking. Negation is: I'm tall and not good looking.

For less likely, the negation is not less likely. This includes equally likely and more likely.

For more likely, it's not more likely. This includes equally likely and less likely.

Toss in that good ol' "not" or "no."

Examples:

"I will purchase the car if I save up enough."
Negated, it becomes "I will NOT purchase the car if I save up enough."

Suppose the stimulus says something like "I'd have a sweet ride by the end of the week when I get my paycheck,"
then, because of the negation, the argument makes no sense.

"If provoked, at least one of my dogs will bark."
Negated, we get "if provoked, NO dogs of mine will bark (alternatively, NONE of them do)."

If the conclusion states "some of my dogs roar like lions towards aggressors," the argument falls apart.

Deardevil wrote:
"some of my dogs roar like lions towards aggressors,"

My corgis do this, actual problem.

Giro423 wrote:

Deardevil wrote:
"some of my dogs roar like lions towards aggressors,"

My corgis do this, actual problem.

Corgis being too cute is the real problem.

Thanks for the input.

Can the Test be applied to Sufficient Assumption questions too?

WeightliftingThinker wrote:Thanks for the input.

Can the Test be applied to Sufficient Assumption questions too?

Nope. Only necessary.

For SA, the correct AC need not be true to justify the conclusion; it just has to.
Therefore, negating something you otherwise do not already need is counter-intuitive.

WeightliftingThinker wrote:How do you apply the Assumption Test to a conditional?

Moreover, how do you apply it to a sentence that has phrases like "less likely," "more likely," etc.?

When negating for necessary assumptions, you're trying to find the relative opposite, not the polar opposite.

e.g. "I always go to the club when I get my paycheck"

Relative opposite: "I don't always go to the club when I get my paycheck"
Polar opposite: "I never go to the club when I get my paycheck"

Like someone else mentioned, I think adding a "no" or "not" is the easiest way to think about this. So 'less likely' just becomes "not less likely," and so on.

This only works for necessary assumption questions. If you negate one and it breaks the argument, then it must be a required assumption to allow for that conclusion. Sufficient assumptions guarantee the conclusion, but their absence doesn't necessarily break the argument, so this won't work there.

e.g.:
Premise: Pizza is delicious. When I eat delicious things, I am happy.
Conclusion: I am happy.

Sufficient assumption: I am eating pizza.

If we negate this, it becomes "I am not eating pizza." But that doesn't necessarily mean that I am not happy - we never established that eating delicious things was the only way for me to be happy, so this doesn't break the argument. It is sufficient, but not necessary.

Now let's take a necessary assumption. There are many possible ones, but let's look at the following: "I am capable of feeling emotions."

If we negate this, it becomes "I am not capable of feeling emotions." If this were true, then there's no way I'd be able to be happy, so as obvious as this statement sounds, it is a necessary assumption.

Hope that helps!