Could anyone help me with this conditional conundrum?

Comments

• EveryCookCanGovern Alum Member

  October 2019 edited October 2019 401 karma

  No, I don't think that latter flaw choice would be correct. Because even if it is true, the mistake is still confusing sufficiency and necessity. For example, assuming other things are necessary to A: A --> A, B, C. Therefore: B --> A. The mistake is still the same.
• Jerry Alum Member

  October 2019 edited October 2019 176 karma

  When discussing an answer choice about the converse being wrong, I feel like I more commonly see something like, "Confuses something that is necessary with something that is sufficient." Or something like, "Mistakes something that is needed for a result with something that would guarantee a result."

  If we fill in your template with an example, the stimulus would say something wrong, like:
  "If you're required to join the army, you're a man. Therefore, if you're a man, you're required to join the army."
  Army --> Man
  Man --> Army

  And the answer choice says something like:
  "Takes for granted men are the only ones who are required to join the army."
  Army ---> Man

  That answer choice would just be a restatement of one of premises, instead of attacking the relationship between the premise and the conclusion. Therefore, it wouldn't be correct.
• T.Burton Alum Member

  October 2019 37 karma

  While it would be very, very rare to see an AC like this, I believe it could be correct (though you should ask a philosophy professor or logician).

  The crux of the problem is whether a set of all NCs is equal to a SC. In your example AC, the "author takes for granted that only B is required for A.” If B is the only NC, it is equal to the set of all NCs.

  It seems to me that if we meet all NCs, we have a SC. For example,

  For a plant to grow, there are 3 NCs: sunlight, water, and nutrients. If we have these 3 NCs, can we correctly infer the plant will grow? No. These are three NCs, but they are not the entire set of NCs. For example, if a plant is infected it will not grow, if it is chopped down it will not grow, etc.

  However, what if we have two groups of NCs. Group 1 (G1) = all things contributing to growth. Group 2 (G2) = all things inhibiting growth. Assuming none of these NCs are by themselves a SC (as that would defeat the point), would this not mean that if we meet all G1 NCs and the opposite of all G2 NCs (e.g. no infections), we would have a SC? I’m not sure, but it seems reasonable to me that if we have all NCs, that set of NCs is equal to an SC.

  To return to your question, if B is the only NC, I think it is equal to a SC.

  ———
  LSATscrub’s explanation misses the fact that your author states “only B is required” when LSATscrub states “assuming other things are necessary.”

  Jerry’s lawgic translation is not entirely correct. I think a more accurate translation would be:

  Required to join Army (RA) —> Man (M)
  M —> RA

  "Takes for granted that solely being a man is necessary for being required to join the army.”

  =

  Assumes that: only M is a NC for RA

  Which is the original conundrum.
• 1 Like

  Jerry Alum Member

  October 2019 edited October 2019 176 karma

  Required to join Army (RA) —> Man (M)
  M —> RA

  "Takes for granted that solely being a man is necessary for being required to join the army.”

  =

  Assumes that: only M is a NC for RA

  Which is the original conundrum.

  Hmm, if B is the only necessary condition for A, then does that make B a sufficient condition that would guarantee A happening?

  I'm not sure. After reading @T.Burton's explanation, I thought it might make sense. But now I think it's just another way of restating something we already know.

  If being a man is the only necessary condition for being required to join the army, that would mean that:

  Necessary condition to being required to join the army --> Man

  I feel like this would just serve as an extra emphasis on what the necessary condition is, but we already know that you're only required to join the army if you're a man. So, I feel like this answer choice still doesn't add anything new to the argument.

  "The only thing you need to do to take the LSAT is pay $200."
  "Paying $200 is the only thing you need to do in order to take the LSAT."
  "If you want to take the LSAT, the only necessary condition is that you pay $200."

  Three ways of phrasing the same thing — that there's ONLY ONE requirement. Put another way, I'm just stressing the fact that you should pay $200 if you want to take the LSAT, because otherwise you're definitely not going to be taking the test. But even if you do end up paying $200, meaning you fulfilled all of the requirements (the only requirement) for taking the test, does that mean you're now a shoo-in to take the LSAT no matter what? I don't think so.

  If something is the only necessary condition, and you fulfill that requirement, I don't think that's any guarantee that the original sufficient condition must now occur. It's just an extension of something we already know, which is that even if you fulfill all the necessary components of a conditional relationship, there's still no guarantee that the sufficient condition will actually occur.

  If being a man is the only requirement for being conscripted, that doesn't mean that mean that every single man is now required to join the army. It just means you don't have much say in the matter if you're a man and they end up picking you.

  If paying $200 is the only thing you need to do to take the LSAT, that doesn't mean that after submitting your payment, you're now guaranteed to take the test. Even if you fulfill your end of the bargain, there's still the possibility of inclement weather, or you getting in an accident, or the LSAT going bankrupt.

  TLDR: When someone says there's only one necessary condition, it's just another way of emphasizing what the necessary condition is.
• T.Burton Alum Member

  October 2019 37 karma

  @Jerry Thanks for the great reply.

  Disclaimer: I’m not a logician; I’m sure this quandary has been answered somewhere in a philosophy textbook or journal article.

  I completely empathize with your $200 LSAT argument, but I think it falls into an important trap.

  In the real world, the $200 fee can be commonly accepted as the only requirement to take the LSAT. However, in the “world of logic,” $200 is NOT the only NC. It is also necessary to be alive, to register online, etc. There are a million other NCs. In your own words “ there's still the possibility of inclement weather, or you getting in an accident, or the LSAT going bankrupt.” Are these not also a kind of NC? It is necessary that none of these conditions (which are by themselves necessary) occur.

  Thus, $200 is either not the only NC OR the other conditions you mentioned are not NCs.

  I would imagine that we can only identify all the NCs in the world of logic.

  This is why I’m quite confident that you would never see the phrase “the only NC” in LG and very, very rarely in LR (maybe in older PTs). Though, it would be great if someone could find an example.

  TLDR: If you state there’s only one NC, you cannot include any new NCs.
• josie.buchwald Alum Member

  October 2019 21 karma

  If the NC is the only NC of the SC then it's a bi-conditional.
• 1 Like

  Jerry Alum Member

  October 2019 edited October 2019 176 karma

  @T.Burton Yeah, I think you're right that there's a discrepancy between how the real world uses the phrase "only requirement" versus how it would play out in a logically consistent world.

  In real life, some parents say to their kids, "The only thing you need to do in order to make me happy is get good grades." And, yet, when children fulfill their end of the bargain by bringing home all A's, the parents still act disappointed for some reason. So, I guess getting good grades wasn't the only necessary condition after all.

  And if the LSAC says, "To take the LSAT, you only have to pay $200," there is indeed a slew of other implicit necessary conditions that must also take place in order for you to take the test. But if you do actually end up fulfilling all of the infinite necessary conditions to ever be in existence (being alive, having a car, waking up on time, not getting lost, you still wanting to do this, the LSAC still being in business, the world still existing, etc.) then I guess there truly is no conceivable force in the universe that could prevent you from sitting down for the LSAT. You would, in other words, be absolutely fated to do so.

  Anyways, I guess what @josie.buchwald said is correct about there being a bi-conditional relationship when you only have one necessary condition. In which case, picking that answer choice would be correct if you saw that the argument's conclusion was the converse of the premise.

  Sufficient Condition <—> All Necessary Conditions

  In the real world, the way we use "only requirement" turns out to not be logically sound, because we have the tendency to add more necessary conditions after the fact. I guess humans just can't possibly conceive what all the requirements are. ¯\_(ツ)_/¯