FORMAL LOGIC

[Bruin96]

Hello,

I am going through the Formal Logic Test Preparation that is located in the 8th lesson and came across the Logic Ladder and had a question. On page 12, at the bottom, in the example of all Doctors are Lawyers. I saw that through the logical ladder it could be deduced that

[*]Doctors ---> Lawyers
[*]Doctors ---M--> Lawyers
[*]Doctors --S--> Lawyers.

Later in the explanation, it states that because in the last example of Some Doctors are Lawyers it can also be assumed that Some Lawyers are Doctors. I wanted to know if this would apply to all logical reasoning that contained the word (all). I have never noticed that this was possible and it is so great to know. Because in the lesson we are taught that (some statements) are the ONLY reversible relationship.

Also, how would this apply if instead of all it said No/None?

Is there a logical ladder for None?

[Bruin96]

I have continued with the lesson and found the negative logical ladder.

Although, I find myself a bit confused on page 19. So in the diagram, we are given it is

A<---some--->B<---NOT--->C.

From the diagram, I took away that
-Some A's are B's
-Some B's are A's
Next,

All B's are not C's or No B's are C's (Is that logically correct to state?)
Inferences from this were
-Some B's are not C's, Some C's are not B's
Therefore, there could be no link between A to C.

I see that the paper states otherwise and I wanted to know the difference between my lack of connection and the statement that Some A's are not C's.

[Adam Tyson]

That logic ladder is pretty great, isn't it? Looks like you got the hang of it, up to a point, Bruin96. However, in the last step you made you forgot the original relationships.

If we started at the bottom of the ladder, where we know that some A's are B's and some B's are not C's, we could not make any inferences about a relationship between A and C. But in this case, we got to the bottom of the ladder by starting higher up. We can infer the stuff at the bottom because of the relationships higher on the ladder - all A's are Bs and no B's are Cs. THAT relationship allows us to make a connection between A and C - it must be true that no As are Cs.

To help visualize it, let's put real world terms on it:

A = people who attend UCLA
B = go to school in Westwood
C = were raised by wolves

All As are Bs - all people who attend UCLA go to school in Westwood.

No Bs are Cs - nobody who goes to school in Westwood was raised by wolves.

Therefore, it must be true that nobody who attends UCLA was raised by wolves!

The "some"relationships don't allow us to make that connection, but the "all" relationships still do. If we only knew that some people who attend UCLA go to school in Westwood, we could not prove that nobody who attends UCLA was raised by wolves. We have to look at all the relationships up and down the ladder to see what we can and cannot prove.

We can do a reversal at the bottom of the ladder and say that some people who were not raised by wolves attend UCLA.

Make sense? Good on you for working through that material! Formal logic is not one of the biggest players on the LSAT, but it pops up enough that it's a good idea to get very adept at it. I love it, and love to apply numbers when I encounter it. For example, if I read "most employees at XYZ Corp have health insurance," in my mind there are instantly 100 employees and at least 51 have health insurance. Maybe more, maybe not, but 51 for sure.

Keep at it, and have fun!