Chapter 6

Question 0

Propositional Logic (Branch of formal logic) definition:

Answer 0

Study of argument that focuses on relations between propositions and connectives that join them

Question 1

Formal Logic Definition:

Answer 1

Study of argument that focuses on relations that hold solely in virtue of the form of an argument

Question 2

Primary relation that interests us in propositional logic is:

Answer 2

Validity

Question 3

In a propositional logic, Validity concerns:

Answer 3

Form of an argument

Question 4

Validity:

Answer 4

If the premises are true, then conclusion must be true.

Question 5

Multiple arguments can in instantiate the…

Answer 5

same form:
If one instance of a form is valid, then all instances are valid.
So: the two following arguments instantiate the same form

Question 6

Modus ponens is when:

Answer 6

2 of of the arguments instantiate the same form, where each proposition can be replaced with a placeholder.

Question 7

Propositions and Connectives contain:

Answer 7

Propositions and Truth Functional Connective ( TFC ).

Question 8

Propositions definition:

Answer 8

The content of a belief (T or F)

Each proposition is either true or false but not both (only 2 truth values).

Question 9

Truth Functional Connective (TFC) Definition:

Answer 9

Something that connects two simple propositions.

Question 10

Truth Functional Connective (3):

Answer 10

1. Propositions is simple if doesn’t feature a connective
2. Has compound Propositions (Conjunction, disjunction, Negation, Biconditional).
3. Main connectives identifies what kind of compound proposition it is : Main connective is the TFC that governs the whole proposition.

Question 11

Compound Propositions:

Answer 11

Simple propositions connected by truth functional connective.

Question 12

Truth value rule: What are the conditions that make the connective true or false?

Answer 12

Each connective has its own distinct truth value rule.

Question 13

Formalization

Answer 13

• Use lower case letters to represent propositional variables ( for argument forms)
  P v Q, P, Q
  -Form is valid, not just an individual argument (No invalid substitution instances).

Question 14

Scope are Parentheses, (), brackets and braces, they are to:

Answer 14

• Break propositions and make well formed arguments and indicate order of operations.
• They also work from the inside out and finish with the main connective.

Question 15

Formalization (4)

Answer 15

1. Use lower case letters to rep propositional variables (for argument forms)
2. Contains scope
3. Order of premises do not matter for valid propositional argument forms
4. Expression for connective can be different (use judgement to distinguish).

Question 16

Negation definition:

Answer 16

Standardly expressed by “not” symbolized by tilde ~

Question 17

Truth value rule for Negation:

Answer 17

True when proposition it negates is false and false when proposition it negates is true. Because it is the only connective that can affect a single proposition.

Question 18

Negation, negates what _______ follows the tilde (Simple or compound). P (negation applies to _____ ); (P & Q) ( negation applies to _____ conjunction: P & Q (Negation applies only to _____)

Answer 18

immediately, “P”, Whole, “P”

Question 19

Double negation logically equivalent to un-negated propositions: P = P

Answer 19

~ P ~ P = P

Question 20

Conjunction definition:

Answer 20

Standardly expressed by “and”, symbolized by the “&”.

Question 21

Conjunction Truth Value Rule (TVR):

Answer 21

True when both of the conjuncts are true, otherwise false.
-Conjuncts can be simple or compound.
Ex. p & q, (p v q) & (r & s)

Question 22

Commutative Definition for conjuncts:

Answer 22

Order of the two conjuncts does not affect truth value of the proposition.
P & Q is truth functionally equivalent to or can be substituted with Q & P.

Question 23

Disjunction definition:

Answer 23

Standardly expressed by “or”, symbolized by the wedge (“v”).

Question 24

Disjunction Truth Value Rule (TVR):

Answer 24

False only when both of the disjuncts are false, otherwise true. "v" is always located between the two disjuncts (P v Q) -Disjuncts can be simple or compound. Ex. p v q, (p v q) v (r & s)

Question 25

Commutative rule for disjuncts:

Answer 25

Order of the two disjuncts does not affect the truth value of the proposition. P v P is truth functionally equivalent to or can be substituted with Q v P.

Question 26

Inclusive sense of disjunction:

Answer 26

Either one disjunct or the other disjunct can be true, or both can be true together (only kind of disjunction that the "v" represents).

Question 27

Exclusive disjunctions are:

Answer 27

where either one or the other disjunct is true but not both.

Question 28

Conditional definition:

Answer 28

Standardly expressed by: "if... then..." symbolized by horseshoe."

Question 29

Conditional Truth Value Rule:

Answer 29

False if antecedent true, and consequent false. Otherwise true. Write antecedent first, then horseshoe then consequent. Ex) P ) Q