PHL111 Valid Reasoning, Past Assignments
Reading: Read chapter 1 of CIL.
Practice: Hand in at the beginning of class your answers
to problems 1-5 at the end of chapter 1. Each of these problems
asks you to come up with 5 examples; to make the homework
shorter, for each problem just come up with 2 examples.
Handwritten is acceptable (for many of our later homeworks there
are special symbols or tables and it is too much work to try to
Reading: Read chapter 2 of the book.
Practice: Complete problems 5 and 6 at the end of chapter 2.
(I've been asked about how to do this. For each problem (that, is
for 5 and then for 6) make one translation key,
showing what each atomic sentence letter means in English. Each
atomic sentence in your key should correspond to an atomic sentence
in English. So, look through the problems in 5 (a-j), identify all
the atomic sentences, write them down, and tell me which letter
corresponds to each sentence. Your key will look like:
Then, after having done that, and using your key, translate all
those sentences. Do the same again for 6.)
P: Josie is a cat.
Q: Josie is a mammal.
R: Josie is a fish
Philosophy club meets at 4:30pm in MCC 211.
The meeting will be a showing of the 2017 movie Annihilation.
Read chapter 3 of our textbook.
Homework listed below! Two quick points.
* A reminder: we have a no-phones, no computers policy in class. I
know that's hard! We are all used to checking snapchat or scores
or whatever every ten seconds. But psychologists have proven that
no one is good at multi-tasking--you will inevitably miss out if
you cruise the web during class, and the people around you will be
distracted too. I don't grade for attendance, so you can skip
class without penalty if you need to text or watch some video or
whatever. My goal is to create a place and time where we all try
to be focussed, that's all. Thanks!
* I defined "argument" in a very thin way: as an ordered list of
sentences, one of which we call the conclusion, and the others
which we call premises. Then, we distinguish good from bad
arguments by saying the valid arguments are the good ones; all
arguments that are not valid are bad. But sometimes in colloquial
English people use "argument" to mean an argument that is valid or
that at least has some other good feature. Here is a famous
example (at 2:15)!
Homework: Since our last translations didn't go so well,
let's try again.
Translate the following sentences from English into our logical
language, the Propositional Logic. Provide one key for the entire
assignment that shows to which (hopefully atomic) English
sentences your propositional logic sentence letters correspond.
Always try to show as much as you can about the structure of the
sentence in our logic (that is, don't translate them all as a
single letter, like P). Hand in your answers and translation key
at the beginning of class. Write your homework neatly, since I
might want to show yours on the overhead as an example.
For these problems: The last one is hard! It nests
"if... then..."s. Try it. Also, think hard about "material" and
"immaterial" -- can you show their relation using our logic (using
one idea standing for "material")? It would be best if you could.
Number 9 is tricky. Remember our discussion of "only if."
What do we mean by
"translation key"? We mean a translation from English to
our logical language. Suppose instead one of
our sentences was....
- The mind is brain activity.
- The mind is material.
- The mind is immaterial.
- If the mind is immaterial, then the mind is not
- If mind is brain activity, then the mind is material.
- Provided the mind is not immaterial,
then the mind is brain activity.
- Alzheimers is a disease of the mind.
- If the mind is brain activity,
then Alzheimers is a disease of the brain.
- The mind is brain activity only if the mind is material.
- If the mind is brain activity,
then Alzheimers is a disease of the mind
only if Alzheimers is a disease of the brain.
8. Spongebob pays no property taxes, if Spongebob lives in
You identify the atomic sentences inside that complex sentence,
and then make a key. There are two atomic sentences in this
sentence, so your key would include the following:
English ..................................... Propositional Logic
Note that we took out the negation. We want to handle negations
with our "¬" symbol. And then if you translated the sentence:
Spongebob lives in Bikini Bottom........... P
Spongebob pays property taxes........... Q
8. (P → ¬ Q)
Someone would be able to use your key to determine
how to translate your logical sentence back into an
equivalent English sentence.
So, for this homework, you'll write instead one key (put it at
the top of the page), which will have a column of atomic
English sentences, and beside it a column of atomic logic
sentences (P, Q, R....). Then, and only then, write up the
Reading: chapter 4 of our text.
Homework: Complete problems 1a-c, 2a-c, 3, and 4 at the end
of chapter 3. Hand them in at the beginning of class.
Note revised due date! Complete the problems at the end of
I apologize, it appears the numbering is disappearing there, but
there are 4 problems. Problem 1 includes a-h. The problems 2 and
3 are: make an argument. Problem 4 is like what we did in class:
translate and prove the verbal argument.
Sorry we haven't gone over the problems from the last homework
yet. But for making your own argument, be sure you have a
complete separate sentence for each premise, and a complete
separate sentence for your conclusion. Don't write a long long
single sentence. (Here's a hint. Take one of the arguments you
know how to prove, like: Premises: (P → Q), P. Conclusion:
Q. And then just come up with a complete English sentence for P
and another complete English sentence for Q. That's your key.
Now your argument is something like: "If P then Q. And indeed it
is true that P. Therefore I conclude in conclusion, Q." Where of
course you fill in the Ps and Qs with your English sentences from
I am always eager to see you, but I know that sometimes people
like to talk also with a peer. Senior Josh Reiss, who is
finishing a minor in logic and is very good at it, will be helping
out. He will offer tutoring this semester MWF, 12:30-1:30 and
3:00-6:00. You must make an appointment via the tutoring center
website. ("What?" you just shouted. "There's a logic minor?"
Yes, your dreams have been answered. You can learn more here.)
Homework: Read chapter 5. Answer questions 1, 2, and 3 at
the end of the chapter. Problem 4 would be good to do--let's
call it extra credit if you do it also.
Quiz 1. Valid and sound arguments. Semantic definition of the
connectives. Translations. Semantic checks of arguments via
truth tables. Syntactic proofs. Symbolizing complex sentences.
I was asked for some practice problems. Here are three.
Here are answers.
- Premises: (¬¬P → S), P. Show: ¬¬S.
- Premises: (¬P → V), ¬V, (P → Q). Show: Q.
- Premises: (¬(P → S) → V), ((P → S) → Q), ¬Q. Show: V.
Read chapter 6.
Here is a printable version of chapter
10. Print it and keep it handy.
The average for quiz 1 was 75. The high score was 97, the low was
8. I have more data to share in class.
Do chapter 6 problems 1a, b, c and 2a, b, c.
Read chapter 7.
Let's review a bit, before we start a new topic. These are
problems from all the earlier chapters. My hope is that some
review will give all of us a chance to catch up. If any of this
is unclear, come see me! We want to be sure that everyone knows
how to solve these kinds of problems, before we move on.
Homework: Complete the following problems.
A reminder: my office is MCC212A. I can see people MWF mornings
between my other classes if you email me and we coordinate.
Otherwise, I am available most days after class (some Wednesdays
and some Mondays I have another meeting at 3:15, but I'll let you
know when that happens). Come see me any time or email me to set
up a time, and I can help you if you want to cover anything from
- Chapter 3, problem 1 d
- Chapter 3, problem 2 d
- Chapter 5, problem 7
- Chapter 6, problem 1 d
- Chapter 6, problem 1 e
- Chapter 6, problem 1 f
- Chapter 6, problem 2 d
- Chapter 6, problem 2 e
- Chapter 6, problem 3 a
- Chapter 6, problem 3 c
- Chapter 7, problem 1
- Chapter 7, problem 2
Read chapter 8.
You may be interested to know that we have a new major on
campus: Philosophy, Politics, and Economics. PP&E is perfect
for those of you interested in policy and politics, or otherwise
aiming to take over the world. A flier is here.
talk, "Climate Justice and Carbon Renewal" in MCC room 132
from 4-5 pm. Extra-credit if you come to the talk and identify
one of the lecturer's arguments and try to evaluate it using our
logical tools. There will be a sign-up sheet in the very back.
Then you can write your thoughts on a single page and drop it off
on Friday before class. (He handed out an argument--but note it
lacks a few premises that are implied but not stated. Can you
make the argument valid by filling those in?)
From chapter 7, do problem 3 (all parts a-e); then, from
chapter 8, do problems 1a, 1b, 1c, 2c and 2d.
Read chapter 9.
From chapter 9, do problem 1 and problem 2f.
Read chapter 11.
Read chapter 12.
Homework: From chapter 11, do problems 1, 2, and 3.
Now is a good time to think about thinking and studying, since you
got your midterm grades, and we still have much to learn. You
should watch the following videos, and reflect on them:
- First, you need the growth mindset: there is no such
thing as being "smart", there is only working harder: watch this
video by the psychologist Carol Dweck.
- Second, watch the five videos staring Dr. Chew
From chapter 12, do problems 2 and 3.
(I know that's two homeworks in a row on two class days,
but I wanted you to get in practice before quiz 2!)
Quiz 2. It will be very similar to the first quiz. Included will
be truth tables for all connectives. Truth tables to tell when a
complex sentence is true or false. Proofs using all connectives.
Conditional and indirect proofs. Translating using predicates and
names. Concepts like: arity, equivalence, theorems, tautology.
Read chapter 13.
Read chapter 14.
Complete problems 1, 2, and 3 from chapter 13. This is 13 proofs!
So get started early! This is our penultimate homework, so let's
go out with a bang.
A few of these are hard! But note that 2c and 3a require
some very similar moves. Review how we proved one of DeMorgan's
theorems in chapter 9 (where DeMorgan's Theorems are called T3 and
T4). (Note: you can just use theorem T3 or T4 if you find that
helpful, and are comfortable using theorems. Read section 9.7 if
you want to know more about that.)
homework: Do problem 1 in chapter 14. Hand in at the beginning
Read section 15.2 of chapter 15.
If you are a logic hero,
read the whole chapter. It's scintillating!
In class, we
will go over the last homework.
I will be in my office from 9-12 and 1-4. If I can help in
any way, stop in and see me.
Extra credit homework: do problem 2 of chapter 15.
(You can hand these in during class.)
In class, we will discuss:
seven shocking and strange things that advanced logic has
Practice/Review session! In our classroom from 11:00-12:00.
We can review the practice problems from Friday, which I will
return to anyone who has done them. Then we can review anything
you would like. Bring questions! Sorry if you have a test during
that time-- I couldn't find another free slot between our last
class and our test.
Practice you can try before our review:
(Do these problems on your own, I'll post answers or
review them in our review session.)
Here are practice
problems for translation. Try translating these using the given
key. Here are some answers.
Here are some hints. For the first theorem, which is an instance
of DeMorgans, we actually prove it in chapter 9 (though there is a
typo in line 24 of the proof--sorry!). So you can look there to
check your proof. For the second theorem: that's pretty easy.
Show each direction (that is, show (∀x(Fx → ¬Gx)
→ ¬∃x(Fx ∧ Gx)) and (¬∃x(Fx ∧
Gx) → ∀x(Fx → ¬Gx))) and use the bicondition
rule. Inside each of your two conditional derivations, you'll
need an indirect proof at some point; for the first conditional,
to prove ¬∃x(Fx ∧ Gx); for the other conditional
to prove ¬Gx'.
If you want some practice proof problems, try proving:
- Prove the theorem (¬(P ∧ Q) ↔ (¬P v ¬Q)).
- Prove the theorem (∀x(Fx → ¬Gx) ↔ ¬∃x(Fx ∧ Gx)).
Final exam 2:00-4:00 PM in our classroom.