Extra credit assignments FLO 125 Due on the Last Class Day 1. Identifying Fallacies and Biases (worth half a quiz grade) Your first project had you identify two examples of fallacies/biases in some form of major print media from the past year. Find a third example. (See that assignment for further instructions.) 2. Challenging Proofs (each question worth a quarter of a quiz, with no partial credit) Construct proofs of the following arguments. a. A ? (B ? F) B ? (D & E) F ? G ~G & A D & (~E ? ~A) b. [(A ? C) ? D) & (D ? B) ~C ? (D & ~B) (~B ? A) & ~D ~A ? D c. (C ? D) & (~A ? B) D ? (C & E) (~E ? B) ? [P ? (Q & R)] (~A ? E) & (E ? D) (P ? Q) & (E ? C) d. T ? (~P & Q) (~T ? P) & (P ? ~T) R ? (S & P) (R ? ~T) ? S
3. Indirect Proofs (each question worth half a quiz, with no partial credit) Indirect Proof is a method of indirect reasoning that is common both in formal logic and in everyday thinking. The basic idea is that we suppose that something is the case, show that such a supposition is, in fact, impossible, in the sense that it is logically inconsistent, and thus conclude that the supposition is false. This gives us a new basic argument form (Indirect Proof, or IP) that operates in a slightly different proof technique, in which we propose a hypothetical world, within the proof, with additional premises. Consider, for instance, the following proof: 1. ~(K & L) 2. K ? L ~K |3. K Assumption |4. L MP 2, 3 |5. K & L Conj. 3, 4 |6. (K & L) & ~(K & L) Conj. 1, 6 7. ~K IP 3-6 What has happened here is that we have assumed an additional premise, K, and have use it with the original premises, within a hypothetical situation indicated by the vertical lines, to show that something impossible has occurred – in line six, we have a conjunction of the form (P & ~P), which is logically impossible, since we cannot have a single proposition that is both true an false at the same time. Since this is impossible, our assumption must have been false, and so we can state that in line 7,…