Why E is incorrect?

Started by Margaret22 · started 2019-10-06 12:44 · last activity 2021-01-21 19:49 · 2 replies

The argument of C and E seems very similar to me, both looks right. Please explain:)

Replies

  1. Irina · 2019-10-07 01:30

    Let's look at the structure of the argument. Any popular television series (P) that is groundbreaking (Q) is critically acclaimed (R) P ^ Q -> R Contrapositive of this statement is : ~R -> ~P v ~ Q If a show is not critically acclaimed, it is either not popular or not groundbreaking. But not all popular television series are critically acclaimed. This statement tells us that P is true but R is false - popular but not acclaimed. We can see from the first premise, that if R is false, then either P or Q must be false: ~ R -> ~P v ~ Q Since we know that P is true, we can conclude that Q is false (not all shows are groundbreaking) Therefore, ~Q. Let's look at the pattern of reasoning in (C) & (E): (C) If biography is unbiased (P), it contains embarrassing facts (Q) about the subject. P -> Q The contrapositive of this premise is: ~Q -> ~P Since not all biographies contain embarrassing facts (~Q), then not all biographies are unbiased. ~Q Therefore, ~ P This is a valid argument, per premise (1), we can conclude that if ~Q is true, then ~P is true. Let's compare it to (E): If a book is worth reading (P), it is worth buying (Q) P -> Q Since not all books are worth reading, not all books are worth buying ~P Therefore, ~Q This is in an invalid argument as it commits a logical fallacy of mistaken reversal. We can only conclude that ~Q -> ~P (a proper contrapositive of the first premise), we cannot conclude ~Q when ~P is true. Let me know if this makes sense and if you have any further questions. ~
  2. eishamaqbool · 2021-01-21 19:49

    I am still not understanding why is E is incorrect?

Sign in to reply.