Symbolic Logic 4/20/2001

Outline

·  The Four Aristotelian Forms (5.7)

·  Hand back exam 3

·  Go over exam 3

·  Discussion of Exam grades

·  SRTE’s

The first day of this class, I mentioned the Aristotelian syllogism. The example of a syllogism I gave was:

All men are mortal.

Socrates is a man.

Therefore, Socrates is mortal.

The syllogism is made up of 4 kinds of statements:

The universal Affirmative (A form):

All P’s are Q’s.

The universal nEgative (E form):

No P’s are Q’s.

The particular affIrmative (I form):

Some P’s are Q’s.

The particular negatiOn (O form):

Some P’s are not Q’s.


These forms correspond to the following FOL statements

All P’s are Q’s:

"x (Px ® Qx)

Note that this statement says something about every P, but not about every Q. That is, we know something about all P’s (that they’re all Q’s, but we don’t know anything about all Q’s).

No P’s are Q’s:

"x (Px ® ØQx)

Note that this statement says something about every P and every Q. We know that for every P it cannot be a Q. We also know that anything that is a Q cannot be a P. Thus, this statement says something about all members of both classes.

Some P’s are Q’s:

$x (Px Ù Qx)

Note that some may be tempted to translate this sentence as:

$x (Px ® Qx) [ wrong!]

This is incorrect, however, as we can see when we note that it is equivalent to this statement:

$x (ØPx Ú Qx)

which does not say that some P’s are Q’s.

Some P’s are not Q’s:

$x (Px Ù ØQx)


Hand back & go over Exam 3


Exam Grades

The average for the 1st exam was ~80.

The average for the 2nd exam was ~63.

The average for the 3rd exam was ~73.

An average of 75 seems reasonable for each exam of this difficult so, in order to achieve this, I’m going to add 12 points to exam 2 and 2 points to exam 3 (+3 because the key was wrong for #2 = +5 for exam 3).

Note that this is still not enough to save some of you who are in danger of failing this course.

So, in order to enable you to help yourselves, I’ll make the following deal:

Anyone who gets a B (scores at least 80) on the final exam will receive a grade no lower than a D for the course.

The rationale for this is that because the exams are cumulative, a demonstration of reasonable mastery of the material on the final exam is tantamount to a demonstration of reasonable mastery of the material for the entire course.

No-Homework Option / Homework Option

Exam 1 15%

Exam 2 25%
Exam 3 25%

Final 35%

Total 100% / Homework 30%
Exam 1 15%
Exam 2 15%
Exam 3 15%
Final Exam 25%
Total 100%