Question about Lawgic

notwilliamwallace

Hey All,

Had a question that I was confused about. Statement is, "People who aren't handsome are happy". Isn't the logical indicator "not" here, meaning it is in group 4 (Negate Necessary). Translated into lawgic, shouldn't this be, "Happy -> /Handsome ; Handsome -> /Happy". However, in the lessons, I found it to be " /Handsome -> Happy ; /Happy -> Handsome".

Any help would be appreciated. Thank you for reading this.

legal_name

To be honest, I might just add to the confusion. I find this a really good question. What I tried to do was to re-work the sentence so that it technically meant the same thing but incorporated a group 1 indicator.

"People who are not handsome are happy" became "Anyone who is not handsome is happy".

/Handsome -> Happy; /Happy -> Handsome

I believe the "not" in this instance is treated as negation rather than an indicator. Indicators in group 4 are generally: "no, none, not both, never, and cannot". I would love some clarification on this question as well in case I've misunderstood.

Cant Get Right

"People who" is your indicator here. Group 1. "Not" is only functioning as a negation of handsome. There may be some exception I'm not aware of, but I don't think "not" by itself can function as an indicator. Just a negation.

Accounts Playable

@"Cant Get Right" I don't think this is quite it.

"People" is the subject and the "who" (besides being a very good rock band) modifies "people." So, the "People who..." is just indicating a very specific set of people that is the subject of the sentence.

Instead, there is an implicit "All" to start the sentence. "[All] people who aren't handsome are happy" is a version of the "All As are Bs" structure, and "All" introduces the sufficient condition.

notwilliamwallace

Thanks guys. So in the statements where they have "aren't" just signifies a negation, not group 4? Also, can "not" be ignored completely as something that is not part of group 4 (ex, "people who take too many sick days will not get time off during Christmas" = Too many sick days --> /Time Off)?

J_Clarkson

people (subject) who aren't handsome (modifier) are happy (predicate).
in other words, people -- all people? -- no just those who aren't handsome -- okay what about them? -- they're happy.
So if you're a /PH then we know you're H. Don't let yourself live and die by mechanical translation methods. Hope that helps!

Cant Get Right

@"Accounts Playable" . I'm not sure there's an instance where "people who" doesn't carry the implied "all," but you're definitely correct to make the distinction. It's the unstated "all" that actually makes this work as a group 1, not the stated "people who."

And yeah, Who is the greatest rock band of all time, and I'll stand on Mick Jagger's coffee table and say that.

quinnxzhang

I have some serious qualms with how "lawgic" is generally taught on the LSAT (not just specific to 7sage), and I think this results in a lot of confusions on complicated translations. But that's beside the point here. I think the answers you received are as good as they're going to get, barring some minor confusions.

@notwilliamwallace, On the off chance you're interested in a more formal explanation, it's because the negation isn't taking wide-scope. The scope of the negation is within the antecedent of the conditional, as opposed to outside of the conditional -- that is to say, the "main" connective is the conditional, not the negation. There's a difference between ~(P→Q) and (~P)→Q, and this sentence belongs to the latter category. I'm guessing the former, wide-scope negation, is what 7sage calls "group 4"?

Wide-scope negation propositions usually begin with something like "it's not the case that..." or have some indication of negated quantification ("there are no...", "none of the...", etc.). However, you should only treat these expressions as rules of thumb. You're going to have some serious problems if you memorize your so-called "indicator" phrases and apply them blindly. For example, "if it's not the case that people who aren't handsome are happy, then I am happy" is not a so-called "group 4" sentence, but rather a standard conditional sentence with an embedded negated conditional in the antecedent.

Regarding the discussion between @"Accounts Playable" and @"Cant Get Right", I think you're right to assume there's always an implicit "all" for LSAT purposes, since this is one of the many places where the LSAT simplifies a complex academic debate. But this isn't something that should be assumed outside of the LSAT. In linguistics and philosophy of language, these kinds of sentences are called "generics" (e.g. "people are evil", "cats climb trees", "babies cry a lot"), and there's substantial controversy over what the proper logical form of generics is. If you're interested, here are a few papers on the topic:

http://web.mit.edu/~shaslang/www/resch/LiebesmanSG.pdf

http://www.princeton.edu/~sjleslie/RoutledgeHandbookEntryGenerics.pdf

https://www.princeton.edu/~sjleslie/Generics Oversimplified SUBMITTED 10-22-12.pdf

stepharizona

@notwilliamwallace said:
"People who aren't handsome are happy".

I always try to phrase these into the "if" so If you are not handsome then you are happy /Handsome -> Happy /Happy-->Handsome

Jonathan Wang

@quinnxzhang said:
You're going to have some serious problems if you memorize your so-called "indicator" phrases and apply them blindly. For example, "if it's not the case that people who aren't handsome are happy, then I am happy" is not a so-called "group 4" sentence, but rather a standard conditional sentence with an embedded negated conditional in the antecedent.

This is the heart of it right here. It feels to me like people think they're learning formal logic because it allows them to shortcut around parsing out a sentence, where in reality formal logic is only useful if you use it as a tool to actually parse out the sentences in question and understand what they mean. If you take the mechanics but leave the intuition behind those mechanics, you are doing yourself active harm. I expanded about this in "Why Formal Logic" in the Sage Advice section if anyone's interested, and quinnxzhang's example here is a good example of why you need to go beyond just blindly applying mechanics when learning this stuff.

Not to hijack the thread further, but take another example: "I cannot utilize the word unless without thinking about the word until." How many conditional indicators are in that sentence, 1 or 4? Your answer to that question says a lot about where you are with conditionals.