Conditional Logic, valid & invalid arguments

2ndTimestheCharm

Even though conditional logic seemed easy when I went through the CC, it continues to trip me up on harder questions, so I'm reviewing some basics:

1. To have a valid conditional statement, the SOME or MOST statement must come first followed by the ALL statement. (You can't conclude ANYTHING if the ALL statement comes before a SOME or MOST statement.) So A some B->C, therefore A some C is valid. Also A most B->C, therefore A most C is valid.

2. In a valid argument, the conclusion must be true. Basic valid argument examples include affirming the sufficient (A->B, A, therefore B ) ; denying the necessary (A->B, /B, therefore /A); transitive property (A->B->C, therefore A->C).

3. Other valid arguments show us instances where one thing (A) arrows out to two other things and there's therefore overlap between those two other things:
   If A->B and A->C, then B some C.
   If A->B and A some C, then B some C.
   If A->B and A most C, then B some C.
   If A most B and A most C, then B some C.

4. Invalid arguments mean the conclusion doesn't have to be true. Examples include affirming the necessary (A->B, B, therefore A); denying the sufficient (A->B, /A, therefore /B), and putting the ALL statement before the MOST or SOME statement (A->B some C, therefore A some C OR A->B most C, therefore A most C).

5. Other invalid arguments show us that we can't conclude anything from 2 some SOME statements:
   A some B some C, therefore A some C (transitive property does NOT apply to SOME statements)
   A most B most C, therefore A most C (transitive property does NOT apply to MOST statements)
   A some B, A some C, therefore B some C.

6. You cannot take a contrapositive of a SOME or MOST statement.

7. Quantifiers have specific meanings on the LSAT that are often counterintuitive. Some is the trickiest one because it means at least one, but could be limited to one, and could go up to all. Be suspicious 😒 of ACs that use any variation of some, such as sometimes and somewhat. Always ask, “just one??” Many sucks too because is the same as some; it is not MOST. Few means some are, most are not. In most cases, we're talking about 3 or 4, but we can think of the range as up to 50 because more than that is MOST.