- PowerScore Staff
- Posts: 1787
- Joined: Dec 06, 2013
- Fri May 21, 2021 5:28 pm
#87254
This is it entirely. If A is sufficient for B, then adding more conditions to A can't possibly make it doubtful whether B is true.
I'll illustrate.
Let's say we have a supposed conditional like the following: "Anyone who gets an A on the final will pass the class." Let's say I cut every class session before the final, take the final, and get an A. The professor responds: "Well, if you get an A on the final but cut every class, I'm not going to pass you." This just entirely contradicts the original conditional - if the original statement was true, it wouldn't matter if I was a felon who got an A on the final, assaulted the professor and got an A on the final, or, as I did, cut every class and got an A on the final. According to the original conditional, I should have passed. So the professor is NOT saying something compatible with the original conditional. If adding conditions (with "and") to the sufficient condition makes the necessary sometimes false, then we've seriously mislabeled the original statement. If something is sufficient for something else, by the definition of "sufficient", any situation where that something is true should make the something else true.
This is actually closely related to a concept in symbolic logic called "monotonicity". If a certain set of premises suffices to make a conclusion follow, supplementing those premises with more, without dropping any of the original premises, MUST still make the conclusion follow. A valid argument is not made invalid by strictly adding premises.
Robert Carroll
cornflakes wrote: ↑Fri Apr 02, 2021 3:09 pm The only way I can square my confusion here is an inherent truth about sufficient conditions altogether that I haven't grasped - if something is sufficient, then it does not matter what else it is paired with, so long as that condition exists, the necessary will always follow (due to the inherent truth of something being "sufficient").corn,
Is this a correct way of thinking about this problem? How do you deal with the possibility that conditions with unknown outcomes (they could be sufficient for negating the necessary condition) could be paired with sufficient conditions that bring about the necessary condition?
Thanks
This is it entirely. If A is sufficient for B, then adding more conditions to A can't possibly make it doubtful whether B is true.
I'll illustrate.
Let's say we have a supposed conditional like the following: "Anyone who gets an A on the final will pass the class." Let's say I cut every class session before the final, take the final, and get an A. The professor responds: "Well, if you get an A on the final but cut every class, I'm not going to pass you." This just entirely contradicts the original conditional - if the original statement was true, it wouldn't matter if I was a felon who got an A on the final, assaulted the professor and got an A on the final, or, as I did, cut every class and got an A on the final. According to the original conditional, I should have passed. So the professor is NOT saying something compatible with the original conditional. If adding conditions (with "and") to the sufficient condition makes the necessary sometimes false, then we've seriously mislabeled the original statement. If something is sufficient for something else, by the definition of "sufficient", any situation where that something is true should make the something else true.
This is actually closely related to a concept in symbolic logic called "monotonicity". If a certain set of premises suffices to make a conclusion follow, supplementing those premises with more, without dropping any of the original premises, MUST still make the conclusion follow. A valid argument is not made invalid by strictly adding premises.
Robert Carroll