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Allen goes to the park everyday except on days when Chris goes to the park.
NotMyName
Alum Member Sage ⭐
https://7sage.com/lesson/except/
JY says this conditional statement is a biconditional which is equivalent to "Allen is in the park if and only if Chris is not in the park". But I see more complexity in the statement than that due to the fact that "everyday" introduces frequency. I believe that we can clearly say "/C --> A" or "If Chris is not in the park, then Allen is in the park every day", therefore if Chris is not in the park on a given day then Allen is definitely in the park that day.
However, it gets messy when Chris does go to the park. JY says that when Chris is in the park "we can definitely say that Allen doesn't go". But I don't think that that's the proper translation because it ignores the frequency aspect of the original sentence. Rather, I think it translates to "If Chris goes to the park, then Allen is not in the park everyday" or "Allen is not necessarily in the park". Which means, we don't know whether Allen is in the park or not and therefore this is not a biconditional at all in fact.
TLDR
We can say "/C --> A" "If Chris isn't in the park, then Allen is in the park"
We cannot say "C --> /A" "If Chris is in the park, then Allen is not in the park that day"
We can't say this because "everyday" negates to "at most 364 days of the year". We can't forget about "everyday" when we translate.
Comments
I like that you're making me really process this statement, but I do think that JY has it correct. Parsing a bit...
Allen goes to the park every day
Lawgic: A
(Allen goes to the park)
... except on days when Chris goes to the park
C --> /A
(If Chris goes to the park, then Allen does not)
Contrapositive of that...
A --> /C
If Allen goes to the park, then Chris does not.
There's really only 2 acceptable solutions here. Either Allen is at the park (because he goes there every day) or Chris is at the park and Allen is not (... every day except the days that Chris goes to the park). If all we know is that Chris is at the park, we know that Allen is not there because per the original statement, he doesn't go on the days that Chris is at the park.
So we have ultimately either
A --> /C
or
C --> /A
But we know it does have to be one or the other. One of them is always at the park. There's no scenario in the first sentence where neither of them is at the park. This makes it a bi-conditional. There will always be one of them at the park and not the other. That makes it a "forever apart" bi-conditional of A <--> /C.
@"Leah M B"
I think this is where my issue lies. Where does the original statement stipulate that Allen and Chris cannot both be in the park? We only know that when the exception is met (Chris goes to the park), then Allen is not there every day. But if in a given week, Chris goes to the park Monday and Friday, why can't Allen be there for only one of those days? That doesn't seem to contradict the logic to me.
The frequency is key to my understanding of this sentence.
The sentence doesn't say this though. It says "Allen doesn't go every day"
I think our intuitive understanding of this sentence is not air tight enough to translate into a biconditional. It's PSA strength but not SA strength.
"Except on days" implies the same day.
So A can go Monday Tuesday Wednesday;
But if C goes on Thursday A can no longer go because it is on a day in which C went.
Allen goes to the park everyday unless Chris goes to the park that day.
You replace the unless with an arrow and negate the sufficient term?
/A -> C
In the case that Allen does not go to the park, Chris must have gone to the park BECAUSE Allen goes to the park everyday otherwise.
Do we get the biconditional by the presence of a necessary condition indicator, "except," and a sufficient condition indicator, "when"?
@LSATcantwin
Yes it implies the same day but what is implied for that day? As I read it, what is implied is that we cannot reliably say that Allen will be there but we know he cannot always be there. I don't actually see anything that explicitly precludes any days on which C and A are both there.
"Babe hits home runs every game except during games when Clemens pitches". Why can't Babe hit a home run during a game when Clemens pitches? Why can't we say he just hits less home runs when Clemens pitches?
The word "except" makes it so that he can't hit home-runs when Clemens pitches.
If I order a sandwich and say; "I want everything except peppers" do I want peppers on my sandwich? No I'm telling them to exclude them.
Babe hits home runs every game excluding the games when Clemens pitches
^^
That is identical to
Babe hits home-runs every game except during games when Clemens pitches.
What is happening is that we are being forced to put A down every single day. Then we are further told, except on a day when C goes.
A A A A (C /A) A A
m t w th f s s
So A is always going until C goes, then A no longer goes.
And if A goes C can't go because A can't go when C does.
@LSATcantwin I don't think that sandwich example is an equivalent use of "except" because you are omitting the critical term "every". Introducing frequency means that these things can overlap but they can't overlap every time.
As I read that Babe/Clemens sentence, I don't think it says "Babe never hits a home run when Clemens pitches". Swapping out "except" for "exclude" also doesn't change my understanding but what is being excluded is that Babe will definitely hit a home run.
We could also replace "except" with "unless", in which case I think the meaning is held intact and supports my understanding of the text.
This is the original statement:
Allen goes to the park everyday except on days when Chris goes to the park.
I guess what you are saying is that: On days when Chris does not go to the park, Allen doesn't go every day.
That is a confusing statement, is it not? Because you can't go "every day" or "not every day" in a single day. And this is referencing a single day that Chris goes to the park. It doesn't really work to say, "Chris goes to the park on Tuesday, and Allen goes to the park not every day on Tuesday." What the second clause in that sentence is negating is not the "every day" but which day Allen goes. He goes on all of them, except the days that Chris goes.
Other ways to say it:
I go to the mall every day, except the days that I go to the post office. (So if I go to the post office, then I don't go to the mall that day.)
I buy an apple every day, except the days that I buy a banana. (That means I am either buying a banana or an apple every day.)
All Jedis use the force, except the Jedis that own droids. (If a Jedi owns a droid, then s/he doesn't use the force. So a Jedi would always either own a droid or use the force. Never both, never neither one.)
Treat it as two different rules.
Allen goes to the park every day.
Allen does not go to the park on days when Chris does.
How do you handle it now?
Or
I'm ordering 10 sandwiches.
On every sandwich I want everything except peppers.
Hey I lost you somewhere in the frequency argument, but the logic of it being equivalent to "Allen is in the park if and only if Chris is not in the park" pretty much makes sense to me with the caveat that it really should be "Allen is in the park on any given day if and only if Chris is not in the park on that day".
Our intial statement is:
Allen goes to the park everyday except on days when Chris goes to the park.
Say for simplicity there was only one day in existance. We will all this day Day A.
First we have to translate the universal sentence from every day to our individual day. We get something like "Allen goes to the park on Day A except if Chris goes to the park on Day A."
We could split the world into two possibilities Chris is in the park at some point on Day A or he is not.
If Chris is in the park on this day, then we apply our rule know Allen is not. This is because of the except portion of the rule.
If Chris is not in the park the exception does not occur and instead we apply the Allen goes to the park on Day A portion of the rule.
We can do the same thing with any number of days. The point is we always end up with either Chris or Allen, but not both.
C<-->¬A or A<-->¬C could both represent the rule equally well.
I think you are forgetting to get rid of the universal quantifier. It is a step we often do pretty quick because it is fairly easy. But, if you forget to do it you get nonsensical statements when you try to flip rules, apply Demorgan's law, and translate into lawgic. This is because the every should already be gone by the time you apply the rule to a single day.
I'm actually really curious about this, and I'm not sure I have an answer so much as a question. How does the plurality of "home runs" affect the logic of this? Could Babe hit a single home run when Clemens pitches? Negating the plural just means "not home runs" and I'd think that hitting a single home run would fall outside the scope of "home runs." I think this is largely semantic and really just depends on what we really mean by hitting home runs, but I'd never though about how negating a plural would work.
If we wanted to be strictly logical we would probably have to say that Babe could hit a single home run when Clemens pitches. In fact he might have to since 0 is also technically plural. Babe might not be allowed to hit zero "home runs" on a day where Clemens pitches. Of course this would be ridiculous and we would probably want to go to the intent of the writer and either assume Babe hits zero home runs on days where Clemens pitches or possibly zero or one home runs on days where Clemens pitches.
The reason you have not had to think about it is that English has these sorts of ambiguities and poorly phrased statements, but Lawgic doesn't. C<-->¬B is beyond misinterpretation as long as you understand what C and B are. The LSAT also tries its best to avoid ambiguity because they want there to always be one correct answer to every question.
I know that's not really a fully satisfying answer either...
@"Leah M B"
LOL yes it's definitely a confusing statement. We agree about the fact that it is referring to a specific day, but we disagree about what is known for that day. In the original statement, we know that any given day of the year is included in the set of "every day" so if chris is not there on a given day, we know Allen is since whatever day that is is included in "every day". But when Chris is there, I still don't see any semantics which prevent Allen from also being there since "not every day" just means "we have almost no idea".
Each of those examples you provide mirror the original statement well. But I challenge the meaning you extract from them. For example if we were to augment the original statement to
"Allen goes to the park everyday except on days when Chris goes to the park; on those days, Allen only goes to the park if it is raining"
Have I altered the meaning of the sentence or have I only increased its specificity? I argue for the latter.
@LSATcantwin
A perfect biconditional!! lol
"Allen does not go to the park on days when Chris does".... by including this sentence you have eliminated the ambiguity that prevents me from drawing the inference C --> /A
I do agree that if someone were to tell me that they go to the park every day except for the days when I am there, I would understand them to be saying "I love the park but I don't go when you're there". However, that informal understanding is not all that is allowed for in the semantics of our original statement. This is a terribly hair-splitting issue but I do believe it's supported. Especially if you consider what I shared with Leah
@"Seeking Perfection"
LOL yeah I don't think the "frequency" aspect is necessary. I was reasoning off the cuff and wound up down a hole in that line of thought. But I understand why "Allen is in the park on any given day if and only if Chris is not in the park on that day" results in a clear cut biconditional. My issue is with how to treat exception criteria in logical statements.
I agree with what you said to CantGetRight
It falls in line with what I said to LsatCantWin
Which brings me my fundamental issue: We do A except in cases of B. Excluding "every day" for simplicity, I believe this is the structure we are working with in the original sentence. However, I don't think this leaves us with a clear course of action unless we augment it to "We do A except in cases of B, in which cases we do C".
An example of this would be "Allen is always in the park except when Chris is there; during which time Allen is only there if it is raining". I offered this to LeahMB above. It highlights my understanding of the original statement well in that we know very little about the conditions governing Allen when Chris is in the park. It could be that our intuitive understanding is correct and Allen is never in the park, but I don't believe, as it is written, that other scenarios which do allow for them both to be present are excluded. As I said above, this would be PSA vs SA strength.
I wasn't able to check 7Sage at all yesterday and I found myself thinking about this. My understanding hasn't changed. What am I missing? If those other scenarios, such as Allen and Chris can be there together so long as it's raining, are in fact excluded by the original statement, how is that so?
What I said to @"Cant Get Right" was about the plural rather than the except. Although it applies here in that once we get an accurate translation to lawgic we don't have to worry.
I think the except is still clear and clearly rules out the two being in the park at the same time.
After that I start to lose you again. I think it is because you keep adding in more needless complexity. In my experience it is easier to understand things when they are simpler and harder when we add complexity. So let's simplify further.
Instead of "Allen goes to the park everyday except on days when Chris goes to the park."
Let us use "Allen goes to the park everyday except on Saturdays."
I would say Allen is in the park Sunday through Friday and not on Saturday.
If I'm understanding our disagreement right, you would say Allen is in the park Sunday through Friday, but we don't know whether he is in the park on Saturday or not.
If this is the core of our disagreement, I would say natural languages are imprecise and I would normally be inclined to agree to disagree. However, for the sake of the LSAT you should probably agree to feign agreement with me because I'm pretty sure they use except to mean what I think it means.