## PHL111 Valid Reasoning, Past Assignments

Past Assignments

29 AugustReading:Read chapter 1 of CIL.

31 AugustPractice: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 type them).5 SeptemberReading:Read chapter 2 of the book.7 SeptemberPractice: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.)KEY

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.12 SeptemberRead chapter 3 of our textbook.14 SeptemberHomework 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 brain activity.
- 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 Bikini Bottom.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:Note that we took out the negation. We want to handle negations with our "¬" symbol. And then if you translated the sentence:.....................................EnglishPropositional Logic

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 homework.17 SeptemberReading:chapter 4 of our text.21 SeptemberHomework:Complete problems 1a-c, 2a-c, 3, and 4 at the end of chapter 3. Hand them in at the beginning of class.26 SeptemberNote revised due date!Complete the problems at the end of chapter 4.

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 your key.)

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.)3 OctoberHomework: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.8 OctoberQuiz 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.
10 OctoberRead 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.12 OctoberDo chapter 6 problems 1a, b, c and 2a, b, c.15 OctoberRead chapter 7.22 OctoberLet'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 the course.

- 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
24 OctoberRead 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.25 OctoberSteinkraus 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?)

29 OctoberFrom chapter 7, do problem 3 (all parts a-e); then, from chapter 8, do problems 1a, 1b, 1c, 2c and 2d.31 OctoberRead chapter 9.5 NovemberFrom chapter 9, do problem 1 and problem 2f.7 NovemberRead chapter 11.9 NovemberReadchapter 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:12 NovemberFrom 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!)16 NovemberQuiz 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.19 NovemberRead chapter 13.26 NovemberRead chapter 14.28 NovemberComplete 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.)3 Decemberhomework:Do problem 1 in chapter 14. Hand in at the beginning of class.5 DecemberRead 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.6 DecemberI will be in my office from 9-12 and 1-4. If I can help in any way, stop in and see me.7 DecemberExtra 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 discovered.10 DecemberPractice/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 exam2:00-4:00 PM in our classroom.