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Diagramming Unless, Except issue

dlstudy1dlstudy1 Alum Member
in Logical Reasoning 76 karma

Can someone help diagram the question below? I'm having a lot of trouble wrapping my head around it.

Manuscripts written by the first time authors generally do not get serious attention by publishers except when these authors happen to be celebrities. My manuscript is unlikely to be taken seriously by the publishers for I am a first time author who is not a celeb.

I diagrammed "except" the same way I would diagram "unless".

not CELEB --> FIRST TIME AU OR not SERIOUS ATTN

When I looked this up, the CORRECT diagram was:

not CELEB --> not FIRST TIME AU OR not SERIOUS ATTN

My first question, Why is it: not FIRST TIME AU?

Second, I'm having trouble diagramming the parallel argument below for the same reasons:

"Fruit salad that contains bananas is ordinarily a boring dish unless it contains two or more exotic fruits. This fruit salad has bands in it, and the only exotic fruit is a guava."

I diagrammed this as follows:

not TWO OR MORE --> contains bananas OR boring

But the correct way to diagram it is:

not TWO OR MORE --> not contains bananas OR boring

Why?

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Comments

  • taschasptaschasp Alum Member Sage ⭐
    796 karma

    I think the way you tried to diagram it is misleading. We are talking about a category of first time authors (FA) here. So, for all FA:

    /C -> /SA

    If you want to include FA into the conditional, you'd have to say,

    /C -> /SA OR /FA

    Why? Well, let's think about it.

    If I said, if someone is patient, then if they have to wait in line they will not get angry. So for all P, WIL -> /A. But There might be some impatient people who wait in line and do get angry. According to our principle, though, if anyone waits in line and gets angry, they aren't patient. So WIL -> /A OR /P. Because if you wait in line and get angry, then you must be impatient. So if you wait in line, logically, either you don't get angry or you are impatient. It's not exclusive, so you could be both, but you can't be neither of them. If you remember truth tables, that's the point of an OR statement -- it's excluding the possibility that, given someone is waiting in line, they could be both angry and patient.

    More abstractly, if I told you, for all A, B -> C. You can conclude "B -> C or /A": that if something is B, then it has to be at least one of either C or /A. Because something that is B logically can't be both /C and A, as that would be a contradiction.

    So let's go back to our original question. We're doing the same thing here, it's just that our translation rule uses unless. For all FA, /C -> /SA. So we can conclude that if someone isn't a celebrity, then either they aren't getting serious attention or they aren't a first time author. Because we are excluding the possibility that someone who is a celebrity could be both a first time author and get serious attention (which would clearly contradict what the stimulus states!).

    Same with "Fruit salad that contains bananas is ordinarily a boring dish unless it contains two or more exotic fruits." We're talking about fruit salads that contain bananas here, and saying that /2+F -> B. So, in the same vain, /2+F -> B OR /FS

    I will say, I don't think it's necessary to actually diagram the question this way to answer it. We have "categories" like this a lot in the LSAT, where we say--"for a moment let's talk about fruit salads, and here's a condition relationship that has to do with fruit salads". You usually don't have to include the fruit salads in the diagramming. You can just put a little note to remind yourself you're talking about fruit salads. And, quite simply, if something isn't a fruit salad then the conditional relationships won't matter (which is, effectively, what that little "OR" part is expressing--either the conditional relationship holds, or we aren't talking about fruit salads).

    Hope this helps!

  • LSATLSAT-3LSATLSAT-3 Core Member
    edited March 2020 419 karma

  • paul-a-spaul-a-s Member
    7 karma

    Thanks @taschasp! I diagrammed the conditional the same as you. But I think JY diagrams it differently, and I'd love to know if I'm missing something here. (Video: https://7sage.com/lesson/first-time-authors-pm-question)

    JY writes:
    (1st and /C) → /S.
    But I think it should be:
    (1st and S) → C.

    I normally wouldn’t question JY on a logic diagram, but he acknowledges that he’s just doing this by intuition and not following any rule.

    He says we don’t have a rule for diagramming “except when”, but isn’t it the same as “except if” or “except”, and aren’t those all the same as “unless”, “until”, and “without”? i.e. Group 3 (negate the sufficient)? We have 3 terms here instead of 2, which makes it more complicated. But I think if we break it down, it’s just a Group 3 statement.

    (In our stimulus we’re dealing with probabilities (“generally”) but since JY ignores that and just translates this into conditional logic, I’ll do the same here.)

    Let’s start with a simple form:
    A except when B (which, again, seems the same as “A unless B”)
    Translated to lawgic: /A→B.

    Now assume A is itself a conditional statement X→Y. Then we have (X→Y) except when B.
    Translated to lawgic: /(X→Y)→B
    Which is the same as (X and /Y)→B.

    In our stimulus, we have:
    (Manuscripts by 1st-time authors→/Serious attention) except when Celebrity.
    or (1st→/S) except when C
    Now use the Group 3 and negate the sufficient:
    /(1st →/S) → C
    (1st and S) → C.

    JY’s version feels right as well, so I can see why he would diagram it that way. But it doesn’t feel as right to me, and I can’t see any reason not to treat this as a Group 3 statement.

    I’d love to hear other thoughts.

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