## Symbolic Logic Operators

This is just like computer science!

## Operators

(~) Negation operator

(&) (And) Conjunct operator

(v) Disjunct operator

(->) (if then) Conditional operator

(<->) (if and only if) Biconditional operator

## For All X: Chapter 1 Reading Response

#### Response

1. What is Philosophy? What is the role of Logic in Philosophy?

Philosophy is the love of wisdom. According to the book, “Logic is the business of evaluating arguments, sorting good ones from bad ones. ” I see logic as the tool that allows us to carefully examine the validity of claims and the cogency of arguments. For me, philosophy (especially logic and ethics) is an extension of empathy, allowing us to examine and more deeply understand one another’s perspectives and experiences of power and injustice; hopefully leading to compelling deontological claims about our responsibilities toward correcting those injustices and improving one an other’s experience of life.

2. What are the two types of logic and which will this class focus upon? Define each.

-SL, which stands for sentential logic. “The smallest units are
sentences themselves. Simple sentences are represented as letters and connected
with logical connectives like ‘and’ and ‘not’ to make more complex sentences.”

-QL, which stands for quantified logic. “In QL, the basic units are
objects, properties of objects, and relations between objects.”

3. What is the value of Philosophy?

From What Is Philosophy, “You don’t have to accept something on someone else’s authority or because it seems obvious or because you can see it, but because you have reflected about it and scrutinized it in the most rigorous possible philosophic way.”

4. What are the two ways that an argument can go wrong? (You should become familiar with these as we move through the course. Every argument makes two claims—these are the two ways an argument can go wrong. If an argument does not meet both of its claims, then the argument is a bad one; it is not to be trusted.

-Sufficient, true premises

-Valid argument form

5. You’ll be doing more work on these three terms: contingent, tautology and contradiction. What do these terms mean?

A contingent argument depends on another argument. For example, an appeal to authority depends on the validity of the authority.

A tautology is a claim which is always true in all possible universes. For example, the desk is either black or it is not black.

A contradiction is a claim which is never true in any possible universe. For example, the cup is both blue and not blue.

6. When are two statements logically equivalent? Consistent?

An equivalent set of statements is a set of statements that are either true together or false together. For example,

-I fed the cat before I went to Starbucks.

-I went to Starbucks after I fed the cat.

Consistent statements are statements that do not disagree with one another. For example

-I fed the cat.

-I went to Starbucks.

#### Homework

Part A: Which of the following are ‘sentences’ in the logical sense?

1. England is smaller than China. Yes
2. Greenland is south of Jerusalem. Yes
3. Is New Jersey east of Wisconsin? No
4. The atomic number of helium is 2. Yes
5. The atomic number of helium is π. Yes
6. I hate overcooked noodles. Yes
7. Blech! Overcooked noodles! No
8. Overcooked noodles are disgusting. Yes
10. This is the last question. Yes

Part B: For each of the following: Is it a tautology, a contradiction, or a
contingent sentence?

1. Caesar crossed the Rubicon. Contingent
2. Someone once crossed the Rubicon. Contingent
3. No one has ever crossed the Rubicon. Contingent
4. If Caesar crossed the Rubicon, then someone has. Tautology
5. Even though Caesar crossed the Rubicon, no one has ever crossed the
6. If anyone has ever crossed the Rubicon, it was Caesar. Contingent

Part C: Look back at the sentences G1–G4 on p. 11, and consider each of the
following sets of sentences. Which are consistent? Which are inconsistent?

G1 There are at least four giraffes at the wild animal park.
G2 There are exactly seven gorillas at the wild animal park.
G3 There are not more than two martians at the wild animal park.
G4 Every giraffe at the wild animal park is a martian.

1. G2, G3, and G4. Consistent
2. G1, G3, and G4. G3 or G4 are inconsistent with the others. To remove either of these would make the rest consistent.
3. G1, G2, and G4. Consistent
4. G1, G2, and G3. Consistent