Problem Set 02

This Problem Set requires both an essay and a series of truth tables. The truth tables may be handwritten, but the essay portion must be typed. The entire problem set is due Tuesday, 9/11. I do not mind students working on the problem sets in groups--it is, in fact, encouraged--but your answers must be your own. Be sure that each answer is as complete, well-expressed, clear, and precise as you can make it. The value of each problem in a problem set is given in parentheses after the question. If you have any question, puzzle, or require clarification, please do not hesitate to contact me (; 3976, 944-2756 mobile--texts strongly preferred). Finally, the following maximums and minimums must be scrupulously observed for the essay portion of the Problem Set:

  • No less than 10pt font.
  • No less than 1.5 line spacing.
  • No less than 1 inch margins on all sides.
  • No more than 1 side of 1 page for this problem set.
  • A header line which has "Problem Set 02", the date, and your name at the very top of the page.

Note that these are maximums and minimums only. You may, for instance, write less than one page or use greater than a 10pt font.

In light of these admittedly serious constraints on the space available for answers, it is extremely important that you excise any and all extraneous or redundant material. For example, the phrases "It can be argued that", "I claim that", "I think that", or their kin preceding a sentence add absolutely nothing to the sentence, take up valuable space, and are in fact wholly redundant. Of course it can be argued that, claimed that, or thought that, or you would never have written it!

Every word must count for answering the question. Philosophical writing is thus austere, but terribly precise. Such is its virtue. That said, writing philosophy can be jarring at first, especially for those who have labored and suffered under the delusional five-paragraph essay regime.

For additional advice on writing philosophy, I encourage you to study some of the advice linked from the resources page. Not all of the advice applies directly to these problem sets, as even in philosophy they are atypical. Nevertheless, there is much sound and helpful advice to be had about writing in general and writing philosophy in particular.

1. Essay Question

Suppose you are chatting with a friend not in the class who asks, innocently enough, "What is validity?" Use your own examples--that is, not examples we've given in class--to explain the concept of validity to your friend. Be sure that your explanation is clear, concise, in your own words, and pitched in such a way as to make the concept clear to someone who isn't in the class and doesn't have access to the notes or handouts. (40pts)

2. Truth Tables

Using the standard method of filling out truth tables I gave in class today, give truth tables for the following WFF's of PC. (5pts ea.)

a. (P → (P → Q))

b. (∼(P ∨ Q) ↔ (∼P ∧ ∼Q))

c. (P ∧ Q) ∨ (∼P ∧ ∼Q)

d. ((P ∨ Q) → ∼R)

e. ((P ∨ R) → (Q ∨ S))

f. ((∼P ↔ ∼Q) → (P → Q))

g. (P ∧ (Q ∨ R)) ↔ ((P ∧ Q) ∨ (P ∧ R))