Philosophy 101 (Bentley College)

Mid-term scoring table and
answers to logic questions

I. Scoring table

The following table explains the correspondence between numerical scores and letter grades that I used on the mid-term examination:

LETTER GRADE	NUMERICAL SCORE FOR ONE QUESTION	NUMERICAL SCORE FOR WHOLE EXAM
A+	20	96–100
A	18	88–95
A-	17	79–87
B+	15	71–78
B	13	63–70
B-	12	54–62
C+	10	46–53
C	8	38–45
C-	7	29–37
D+	5	21–28
D	3	13–20
D-	2	4–12
F	0	0–3

How this works: The exam contained two parts, one consisting of four essay questions, each counting for 20 possible points, and the other consisting of questions on logic, counting for 20 possible points all together, so that the total possible number of points on the exam was 100. The essay questions were marked with letter grades, which were then converted to numerical scores on a 20-point scale according to the second column of the table. Logic questions were scored numerically, so that their total could simply be added to that of the numerical scores for the essay questions. This resulted in a numerical total which was then converted to a letter grade according to the third column. Thus, the second column was used only for converting letters to numbers on individual essay questions, the third column for converting numbers to letters for the whole examination.

In the second column, only one figure is included instead of a range because where two numbers were possible for a given letter grade, I always used the higher figure. For example, a B- would, in principle, correspond to a range of 11 to 12, but was always converted to 12, never to 11; for this reason, no "11" appears in this column of the table.

II. Answers to logic questions


(1)	1.	If there is less than a quarter-tank of gas in the car, we need to stop at a gas station.	If P then Q
	2.	We do not need to stop at a gas station.	Not Q
	.: 3.	Therefore, there is not less than a quarter-tank of gas in the car.	Not P From 1 and 2, by DC Valid

(2)	1.	You can use the pool if you’ve paid your dues.	P if Q = If Q then P
	2.	You haven’t paid your dues.	Not Q
	.: 3.	So you can’t use the pool.	Not P From 1 and 2, by DA Invalid

(3)	1.	If my father is a wrongdoer, then it is pious to prosecute him.	If P then Q
	2.	My father is a wrongdoer if he has killed a man who did not threaten him.	P if R = If R then P
	3.	My father has killed a man who did not threaten him.	R
	4.	Therefore, my father is a wrongdoer.	P From 2 and 3, by AA
	.: 5.	Therefore, it is pious to prosecute him.	Q From 1 and 4, by AA Valid

(4)	1.	If it is raining, a dripping noise will be audible.	If P then Q
	2.	If it is not raining, birds will be singing.	If not P then R
	3.	No dripping noise is audible.	Not Q
	4.	Therefore, it is not raining.	Not P From 1 and 3, by DC
	.: 5.	Therefore, birds will be singing.	R From 2 and 4, by AA Valid

In scoring answers to these questions, I made two liberal allowances: (i) In answers to question 3, where respondents wrote "by AA" without saying whether this referred to the conclusion in step 3 or the conclusion in step 5, I took it to apply to both conclusions (both of which are drawn by AA), so that such a response got two points. (ii) In answers to questions 3 and 4, where respondents used only two letters instead of the requisite three to stand for the three component propositions in the argument, I accepted these answers provided that the analyses could be made consistent with the original argument by distinguishing between, say, P₁ and P₂ where the respondent had used "P" to stand for two different propositions.