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Philosophy
120A Autumn 2007 Introduction to Logic |
| Extra Credit Problems
Some students have requested the opportunity to do some additional problems for extra credit. So here are ten such problems. They are entirely optional. Your grade will not be reduced if you decide not to do these problems, even if many students choose to do them. If a grading curve needs to be imposed to increase the median grade, that will be done before points earned on these problems are taken into account. These problems are designed for those students who want to do some extra work to make up for previous exercises not completed, or who want some way to improve their grades. Each problem will be worth two points. Since there are ten problems, the maximum amount of extra credit possible is twenty points. You may submit as many or as few of these problems as you like, but only one submission is permitted (as in a regular homework assignment). What effect will this extra credit have on your grade? I estimate that an additional twenty points of extra credit will increase one’s grade by between .2 and .3 grade points. For those who choose to do the extra credit problems, they are due on Friday, December 7. Electronic submissions must be submitted to the Grade Grinder by noon; all extra-credit exercises submitted to the GG must be part of a single submission, labeled EC. Paper (or email) submissions must also reach your TA’s mailbox by noon (but paper submissions will also be accepted in class). List of extra credit problems: 9.20 Some Hints on extra credit problems:
Please read these hints if you are going to attempt these problems.
11.22: Be sure to consult Table 1.2 on p. 30. You will not be able to solve this problem satisfactorily if you fail to do this. Remember, you are being asked to translate into colloquial English. This means that you should avoid using expressions like “2:00 pm,” or “1:55 pm,” and instead use expressions like “now,” “5 minutes ago,” and “within the last 5 minutes” (or even just the present tense), where appropriate. For example, you should translate Fed(max, carl, 1:55) as “Max fed Carl 5 minutes ago,” and Fed(max, carl, 2:00) as “Max is feeding Carl now.” Please note that these instructions do not apply to Exercise 9.20, for in that problem you are not told that the sentences are being uttered at 2:00 pm on 1/2/2001. 11.25: Be sure that sentence (1) in your file is the one that is true in Reichenbach’s World 1, and that sentence (2) in your file is the one that is true in Reichenbach’s World 2. You will find that your sentences will involve long conjunctions with many conjuncts, and there will be many existential quantifiers. Since you are limited in the blocks language in the number of variables you can use, you will have to reuse two variables. Be careful to avoid any conflict of bound variables. 13.58: Pay attention to the instructions in parentheses at the end of the problem about what you may assume. In particular, you may not assume that in general (outside of the blocks language) Medium(a) and Medium(b) logically imply SameSize(a, b). That is, you may not assume that all medium objects are exactly the same size; you must allow for the possibility that one medium sized object may be larger than another. 14.2: Just give your translations. You do not need to explain your answers.
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