PHL309 Logic, Language, and Thought Professor: Craig DeLancey

Office: Marano 212A

Email: craig.delancey@oswego.edu

Past Assignments29 AugustTwo readings, and a quick assignment.

Reading 1:Read the Allegory of the Cave section of Plato'sRepublic. You can read this by reading the first half of book 7, which is available for free here. Or, I have a trimmed version here.

Reading 2:read the short dialogueThe Menoby Plato. If you are pressed for time, just read the part where Socrates talks to the slave boy. You can find this part by searching for "Boy." and you'll find where he first interacts with the child. (From: the line "Men. Certainly. Come hither, boy. " to the line: "Men. Yes, they were all his own."). (Typo! "right feet" should be "eight feet"!)

Assignment:what is it that Socrates ends up drawing in the dirt with the boy? Can you reconstruct in drawings the steps of his proof? Try to do so on a piece of paper, along with a brief explanation of the steps and what they show. Hand this in at the beginning of class. Imagine you are trying to explain to someone you know: what Socrates does in his discussion with the boy.

If you feel you need a resource for reviewing logic, at any time during the semester, you can use my book, which is free.31 AugustPlease read Book 1 ofEuclid's Elements. You are reading just to familiarize yourself with how Euclid thought and argued. You'll find you know everything he says; just note how he arrives at his conclusions. An online version can be found here.

Come to class prepared to answer these questions.

- Is Euclid a Platonist? That is, how do you think that he believes he knows the things he claims to know?
- Consider postulate 5. As we'll see this semester, this is a very important postulate. Do you agree with it? That is, in your view, is it true? If you believe it is true, how do you think you know that it is true? If you doubt it, why would you doubt it?
5 SeptemberReading. Read the selection from Galileo'sTwo New Sciences: First Day, from pages 11 [49] to 28 [67].

I'll email you the prefered translation. If you don't get that email let me know.

Also, a fair translation is freely available here.

Short reading question: A brief question for you to answer in a single page. Galileo considers a reason why some things may hold together. He uses the two slabs of marble example to illustrate the idea. What is his reason? Do we consider it today sufficient explanation of why things hold together? Write up your answer and bring it to class.

Fun to see: scan of the original "Sidereus Nuncius".

7 SeptemberReading. Read from Galileo'sTwo New Sciences: First Day, from pages 28 [67] to 35 [73].

Philosophy club meets at 4:30pm in MCC 211. The meeting will be a showing of the 2017 movie Annihilation.12 SeptemberRead pages 35 [73] to 42 [80] of our Galileo selection. I think there are at least five arguments in these few pages meant to prove that we cannot reason about infinity or infinitesimals. This is the important part! Read it closely!

Homework:Identify and describe two (2) of Galileo's arguments that we cannot have or reason about infinity or infinitesimals. Each is a reductio ad absurdum argument. Describe it is such, identifying the contradiction that he identifies. Write your answers up to be handed in.

14 SeptemberConsider, and have an opinion about the following question: What is Galileo's solution to his paradoxes about infinity?

We'll consider that question as we continue reviewing Galileo's arguments, talk about how lots of people worried about infinitesimals, and then begin our discussion of Kant!

17 SeptemberWe begin our discussion of Kant!21 SeptemberPractice/homework!:Due at the beginning of class: A quick homework. This will require you to hand in 7 sentences. Give an example of a sentence for each of Kant's four kinds, and also an example of a sentence for each of the cross-category kinds. Each sentence example must be your own (no credit for an example we used in class or in the class notes!). So, you must provide an example of your own of a sentence that is:If you disagree with Kant's notions, consider yourself as trying to find examples that he would accept.

- a priori,
- a posteriori,
- synthetic,
- analytic,
- analytic a proiri,
- synthetic a posteriori,
- synthetic a priori.

Remember from our discussion:Look at the first two pages of our Lecture Notes on Kant for examples.

- "Analytic" means that you can tell if the sentence is true or false based on the meaning of the parts of the sentence.
- "Synthetic" means the sentence combines (synthesizes) new things, so that you cannot tell if the sentence is true or false based on the meaning of the parts of the sentence.
- "A priori" means that you can know whether the sentence is true or false before having to check experience.
- "A posteriori" means that you can know whether the sentence is true or false only after having checked experience.
24 SeptemberWe will continue our discussion of Kant.

Someone just pointed out to me this fun video series covering some of the stuff we're discussing:

- This one discusses postulate 5.
- This one discusses Bolyai on non-Euclidean geometry. It uses the word "true" in a problematic way (we'll discuss this) but it's funnish.
3 OctoberHomework! Working on your own, write up your answers to the following questions, and hand them in at the beginning of class.One of you was kind enough to send the following video. If you feel like jumping into a different perspective....

- For each claim, identify if it is true or false.
a. 2 ∈ {1, 2, 3}

b. {c} ∈ {{a}, {b}, {c}}

c. 1 ∈ {{1}, {2}, {3}}

d. {a} ∈ {a, b, c}

e. {} ∈ {a, b, c}

- For each claim, identify if it is true or false.
a. 2 ⊆ {1, 2, 3}

b. {c} ⊆ {{a}, {b}, {c}}

c. 1 ⊆ {{1}, {2}, {3}}

d. {a} ⊆ {a, b, c}

e. {} ⊆ {a, b, c}

- For each of these pairs: are they identical? (You can answer "yes" or "no".)
a. {1} and {{1}}

b. {2, 3, 1} and {1, 2, 3}

c. {7} ∩ {9} and {7, 9}

d. {7} ∪ {9} and {9, 7}

e. {} ∪ {9, 7} and {9, 7}

- Give an example of a
propersubset of each of the following sets.a. {1, 2, 3}

b. {a, b}

c. {{1}, {2}, {3}}

d. {1}

e. {1, 2, 3, 4, 5, ....}- For each of the following sets, what is its Powerset? (Remember also our rule, if a set has n things in it, then it has 2
^{n}subsets.)a. {a}

b. {a, b}

b. {a, b, c}

c. {}

d. {{}}

- Assume these sets continue in the simplest way as listed. For problems a and b, can you give an example of a function that relates the first set to the second set in a 1-to-1 correspondence (an on and onto function that would also be a function if it went backwards)? For problem c, can you find a function that is on the first set and onto the second set, even if it is not 1-to-1? (You can answer these using some basic arithmetic -- no need to get fancy; for example, the function relating the naturals to the even numbers would look like: f(x) = 2x.)
a. {2, 4, 6, 8, 10....} and {200, 400, 600, 800, 1000....}(Note that for c, the second set contains only one element, namely the number one.)

b. {1, 2, 3, 4, 5....} and {1, 3, 5, 7, 9, ....}

c. {1, 2, 3, 4, 5....} and {1}

In class, we'll organize your table and see if that helps us with our next topic: Cantor's theorem.5 OctoberWe'll review the homework, the Diagonal Argument, and then Cantor's Theorem. What are the consequences of Cantor's theorem?

10 OctoberWe will continue to discuss Cantor's antinomy and Frege!

Things you should know:Remember we have extensive class notes.

- Basic facts about functions and sets
- Cantor's definition of cardinality
- Cantor's Claim
- The Diagonal Argument
- Cantor's Theorem
- Cantor's Antinomy

If you purchased the optionalLogicomix, it covers the period we are discussing now. Read it! (If anyone wants to borrow my copy, let me know.)

Also, here is our set notes handout.

12 OctoberWe agreed some more practice would help. So here is a brief homework for you to hand in at the beginning of class.Some folks have asked me for logic resources. My book is free and can be read here. The last chapter includes a brief overview of set theory.

- Write out on a single page the following sets (where P(A) means the power set of A):

- P({1})
- P({2,3})
- P(P({}))
- P({{1, 2}}) (this is a trick question! Pay attention to what the set is, and what its member(s) are/is.)
- Intersection and union.

- What is {a, b} ∩ {b, c}?
- What is {a, b} ∩ {}?
- What is {a, b} ∪ {b, c}?
- What is {a, b} ∪ {}?
- General questions

- If x ∈ A, then is the following true? x ∈ A ∩ {} (Explain your answer.)
- If x ∈ A, then is the following true? x ∈ A ∪ {} (Explain your answer.)
- Infinite sets can have proper subsets of the same cardinality. Name a proper subset of the natural numbers that we have not discussed in class as an example, that has the same cardinality as the natural numbers. Describe the function that shows that it is the same cardinality as the Naturals.