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Related Discussions
"Until" as a logical indicator
JeckaSaysWhyNot
Alum Member
Hi all, I'm not through the CC yet (obviously). When learning logical indicators, I'm trying to reason my way through them, because I know I will forget rote memorization. I understand why all the translation rules apply so far, except for "until."
If you tell me to "add pennies to the jar until Bob tells you to stop," my brain translates that as "when/if Bob tells you to stop, stop adding pennies to the jar." I cannot see how this is logically wrong. Bob telling me to stop is sufficient for me to stop. And yet according to the translation rules, the correct translation is the converse--"if Bob doesn't tell you to stop, add pennies to the jar." Which of course also sounds true. Any help here?
And if there's a better place to post this, let me know. Wasn't sure about using this category.
Comments
I think I have trouble specifically with commands for some reason. "Until" is the same as "unless" and "without" in that it indicates a necessary condition, but not a sufficient one. It's necessary for Bob to tell me to stop, but maybe something else has to happen too in order for me to stop. That's how I'm thinking of it.
This is my stab at an explanation (I'm sure someone else will do better). I think there is some causation going on here that is confusing the issue. There is a difference between things that logically trigger and things that physically trigger. There is a whole section on causation in the CC ( https://7sage.com/lesson/causation/ )
Below I believe is the correct translation of your statement. I would agree with your second statement. I think this is why it is useful to drill on some flash cards with these then it all feels like second nature.
Do you think your first statement is the contrapositive of your second statement?
/(add pennies) --> bob said stop
/(bob said stop) --> add pennies
Example of normal causation reasoning mixing with logic.
If I have not seen the movie Black Panther then I have never seen any movie.
/(BP) --> /(seen any movie)
(seen a movie) --> (BP)
This is technically the logical translation of my statement, but maybe as a "true" statement it does not make sense, as I could have seen another movie. Sometimes the english ideas of things don't mix with the "logic" inherent in how we structure the statement.
Another example would be a giberish statement linked together with logic such as:
If I understand logic in the future then I will never understand logic. This statement can be logically translated but does it have meaning?
Another fun logic defying statement is "this statement is false." If the statement is true then it is not false, and if it false then it is not true (aka it logically makes no sense).
Moral of the story is abstract the two ideas and stick to the logic rules. I don't think the LSAT mixes false casual reasoning with logical statements to give illogical outcomes (other than maybe a few old LR questions that are contradictory).
"Until Bob tells you to stop, put pennies in the jar."
So you're there, putting pennies in the jar per your instructions. According to the statement, the only way that ever changes is if Bob tells you to stop. You're obligated to keep on sticking pennies in the jar until Bob opens his mouth.
Well, what if he just keeps his mouth shut forever? Then you're stuck putting pennies in the jar from now until eternity. Bob never told you to stop, so your only 'out' is gone and you're doomed to be Sisyphus rolling the boulder up a hill, except with pennies. That's a stone (haha) cold guarantee. So, the translation "~Bob says stop -> put pennies in jar" is 100% set here.
Now, Bob eventually wanders over and tells you to stop. What does that actually do for us here? Where's the instruction that says "When Bob tells you to stop, stop"?
We can certainly concede that one option here would be to gratefully follow his instructions and stop. But is it a guarantee that we'll stop? What if the full instruction set looked like this:
"Put pennies in the jar until Bob tells you to stop. And then, ignore him and keep putting pennies in the jar, making sure to stare him in the eye as you do it, because Bob is a jerk and we want to make him angry and putting pennies in his jars completely unhinges him."
Is that a completely nonsensical set of instructions, internally inconsistent and unfollowable? Or is that a legit state of the world that could come into being upon Bob telling you to stop? Maybe you like putting pennies in jars. Maybe you don't want to stop. Absent a specific rule that forces you to stop, you can't say for sure that you're stopping just because Bob gives the word. All you know is that if he DOESN'T say anything, you're obligated to keep on doing it.
Conditional statements are guarantees. A->B means if A happens, B is DEFINITELY happening, no debate. You can't get that out of an unless/until/without statement in the way that you're thinking about it. To the extent that our colloquial English usage contradicts that, our colloquial English usage is wrong. (See also: "either or" vs. "not both", colloquial vs logically precise usage)
More practically speaking, if the LSAT wants to establish the converse you're proposing, it will do so explicitly and separately from the initial statement. They always use their words in a technically correct manner. I'd actually be interested in seeing how they did it, though my personal favorite upon cursory thought would have to be "until, and only until...", just for the teeth-gnashing such a phrasing would inevitably generate...
This is interesting!
I get what you are saying, and your translation seems natural (at least to me). I think (I may be wrong) "add pennies to the jar until Bob tells you to stop" is more like:
Stop adding pennies only when Bob tells you to stop.
/(add pennies) ---> Bob tells you stop
So unless specifically told to stop by Bob, you have to keep adding pennies. You have to keep adding until Bob says "Stop!"
This means that when you stop adding pennies, it has to be the case that Bob said "Stop!"
This is consistent with the Group 3 translation of "add pennies to the jar until Bob tells you to stop"
/(Bob tells you stop) ---> add pennies
/(add pennies) ---> Bob tells you stop
But I do see your point. Bob telling you to stop seems sufficient for you to stop adding pennies in this particular case. So I think there could be a bi-conditional relationship, but we don't actually know from the statement itself.
Maybe this example in Quiz - Group 3 Translations 1 w/ Answers can make it clear:
Farmers know income → tax returns are calculated and submitted the following April.
Do we know if tax returns are calculated and submitted, farmers must know their income? No. We don't know if tax returns being calculated & submitted is sufficient for them to know their income. There could be other conditions necessary for farmers to know their income.
Instead of complicating things I prefer replacing unless without or untill with 'if not'
It just simplifies things.
If Bob doesnt tell you to stop you gotta add those pennies.
This specific sentence on the other hand creates certain confusion because it is an order. If Bob tells you to stop you gotta stop.
According to group 3 way of translation on the other hand it does give you trouble.
If you stopped adding these pennies then necessarily Bob had told you to stop.
On the other hand it is also true vice versa. If Bob had told you to stop then also necessarily you should have stopped adding these pennies.
In a sense it becomes a bi conditional statement and it does so because of the nature of imperative.
I was gonna cite categorical imperative as an example but realized that is simply too much.
Sometimes thinking about conditional statement strictly in a technical way gives you headache.
Here is an example of hypothetical imperative.
If you wish to be a great piano player, you must practice.
Now what would be the contrapositive? Commonsensically speaking it is something like if you dont practive you cannot be a great piano player. And normally that is gow we would interpret that statement.
But technically that is not a contrapositove. It yields something like if you dont practice then you dont wish to become a great piano player.
And that is clearly a weird statement though it is exactly what it says. An 'opinion' or 'order' likewise is not exactly a great object for conditional analysis.
--
This is super interesting. I did not get into this in the CC but I should have. When I update the CC in the year 2030 I will include it.
The short answer is that there are two versions of "until" and "unless", a strong one and a weak one. On the LSAT, you generally are not penalized for interpreting "until" and "unless" as weak. That's the one I teach in the CC in Group 3 when I say "negate, sufficient." Weak until = inclusive or = weak or. Strong until = exclusive or = strong or. How do you know which version? Context and common sense.
weak (unidirectional, disjunctive) until
(S) No action should be taken until the issue has been examined.
(1) accurate translation:
action should be taken → issue has been examined
(2) inaccurate translation:
issue has been examined → action should be taken
(2) is just not what (S) is saying. There might be other things you also have to do before you take action. (S) is simply stating one road block you have to clear before taking action.
strong (bidirectional, biconditional) until
Mother says to child: (S) I'm not getting you a puppy until you make honor roll this term.
(1) obviously accurate translation:
get puppy → made honor roll
(2) perhaps less obvious but also accurate translation:
made honor roll → get puppy
This has to be. Otherwise you have a liar for a mom. Imagine if your mother said "well, when you satisfy the necessary condition of a conditional..." No, shut up. I got straight A's where's my puppy?
(S) is just a promise to get you puppy if and only if you make honor roll.
(3) complete and accurate translation:
get puppy ↔ made honor roll
Now onto @JeckaSaysWhyNot's statement
(S) Add pennies to the jar until Bob tells you to stop.
(1) obviously accurate translation:
[not] add pennies to jar → Bob tells (has told) you to stop
(2) perhaps less obvious but also accurate translation:
Bob tells (has told) you to stop → [not] add pennies to jar
Why is (2) accurate? Because common sense. You're given instructions: Add pennies to the jar until Bob tells you to stop. Then, Bob tells you to stop. What do you do? If you're following instructions, you stop. That's it. (S) is biconditional.
(3) complete and accurate translation:
Bob tells (has told) you to stop ↔ [not] add pennies to jar
I do not recall seeing a correct answer on the LSAT trade on your being able to distinguish a strong v. a weak "until" or "unless". As far as I recall, if you interpret until as weak, you do not get penalized, even if the strong interpretation is more reasonable. In the future, they could think it fair game for us to utilize context to figure out the more reasonable interpretation. Or maybe they already have and it has just slipped my notice.
In summary, just translate "until" using Group 3 rules. If you see a sentence that does not conform to that translation (even in quizzes that I made up), ignore because it's not like that on the LSAT.
Related: This lesson talks about inclusive/weak "or" v. exclusive/strong "or".
I'll donate some money in 2030 because 7Sage will be my alma mater.
https://media.giphy.com/media/lA0pONycTezZK/giphy.gif
@akistotle found a strong until in PT13.S2.Q02 and indeed it does not trade on your being able to distinguish a strong v. weak until, though it looks very much like the LSAT used a strong until.
I can't type the question up here (copyright) so I'll do an analogy instead.
Premise: My dog walker usually walks my dog at 1pm each day and he's incredibly consistent. However, this coming Tuesday will be a national holiday and on national holidays, he is supposed to walk my dog two hours later than usual.
Conclusion:
(S) Therefore, my dog will probably not be walked until 3pm this coming Tuesday.
(1) obviously accurate translation (weak until):
[not] 3pm → my dog will probably not be walked
my dog will probably be walked → 3pm
(2) perhaps less obvious but also accurate translation:
3pm → my dog will probably be walked
(3) complete and accurate translation (strong until):
3pm ↔ my dog will probably be walked
How do we know (2) and (3) are right? Because the premises pretty much guarantee it. That's why it feels natural to interpret (S) as strong until.
Now, say you interpret as weak until. No big deal. The answers don't penalize you for having drawn an accurate but incomplete conclusion.
Thanks everyone, I've got it now!
I really apologize for beating a dead horse, but I wanted some clarification on this issue. The idea of a "strong" until and except seems plausible, but do you have any sources on this issue? I ask only because some of your examples don't intuitively make sense to me, and Jonathan Wang's take on this issue earlier does seem persuasive, although it is seems counter to the idea of a "strong" until and except.
In particular, the statement "I'm not giving you a puppy until you make honor roll this term." You write that this creates a biconditional, but I don't see why it wouldn't have the strictly logical meaning of honor roll being a necessary condition for a puppy. It may not be the only necessary condition. Maybe the mom is also thinking "and another requirement is to quit doing marijuana", but she just did not express that requirement in the statement she chose to make. To get a biconditional, we have to accept the potentially unwarranted assumption that the mom was being as helpful as possible in her expression and was stating the only requirement for getting a puppy.
Jonathan Wang's explanation of how "add coins to the jar until bob tells you to stop" could be consistent with a world in which the next instruction is "and then continue doing so but stare into his eyes as you do it" makes sense to me -- and it is suggesting to me that the statement does not have to imply that if bob tells you to stop, you should definitely stop. I'm reading it as "if bob tells you stop, then we don't necessarily know whether you should still add coins"
So far, it seems like, it's never wrong to read until/except as introducing only a necessary condition and not also a sufficient. Which suggests to me that it's because that's what those words actually mean...
Things would be so much clearer if there were a problem that did depend on an "until" or "except" creating a biconditional, which would prove that the words sometimes do in fact have that meaning. Until (heh, until) we find one, I will be a little bit confused.
I will note that in the sentence I just wrote -- "Until we find an example, I will be a little bit confused," it feels natural to read that as creating a biconditional, such that "If we find an example --> I won't be confused anymore". However, I wonder if that meaning does not come from that sentence alone, but rather from the prior sentence that "things would be so much clearer if there were a problem that did depend..." It seems the biconditional aspect of until/except may stem from surrounding sentences and assumptions about the situation in which the statement was made, but not strictly from the literal language itself?? Maybe that is the reason these words are confusing?
I'm a confused as to why in the Group 3 flashcards answers we had:
1. [not] add pennies → I tell you to stop
2. [not] I tell you to stop → add pennies
but JY's #2 above is different (T→/A vs the flashcard's /T→A). Does the order matter? Does which side we choose to negate matter?
I'm glad you got it! I literally just memorized that "W", "U", and "U" are "negate sufficient".
"Add pennies to the jar until Bob tells you to stop" means that if Bob does not tell you to stop, keep adding pennies to the jar. If you get stuck in the moment, thing about it in standard English. Did Bob tell you to stop yet? If not, keep going! If Bob told you to stop, then stop.