Sufficient Condition Modifiers

hrhyoo

Hey guys,

Are "depends only on" and "all that is needed" sufficient condition modifiers? If yes then why? Please help!

H

taschasp

DEPENDS ONLY ON

You could either look at this as a logical indicator, or as an indicator of a correlation.

Take this example: weight loss depends only on having a large enough caloric deficit

You could interpret that as: Weight loss -> Large Enough Caloric deficit.
Because if you have lost weight, then you must have had a caloric deficit, since weight loss DEPENDS on having a caloric deficit means.

But you could also conceivably say a Large Enough Caloric Deficit -> Weight Loss, since weight loss depends ONLY on the caloric deficit. If that's all weight loss is dependent on, then conceivably, if you have a large enough caloric deficit that should result in weight loss (since there are no other things that would, according to the logical statement, be needed or relevant in determining whether or not weight loss would happen). So In effect, Weight loss <-> Large Enough Caloric Deficit

If the 'large enough' part wasn't there, though, and we just said "weight loss depends only on having a caloric deficit', you might not know how much of a caloric deficit we actually need to get weight loss, so we'd probably need to assume the "large enough" part to turn it into a biconditional. But I'd say its better to just think of that as a strict correlation.

ALL THAT IS NEEDED

A hammer is all that is needed for John to be able to fix your broken sink.
That means that a hammer is sufficient for John to be able to fix your sink, so hammer -> John can fix your sink

hrhyoo

Thank you so much!