1. Truth Tables – Logic (Continued)
Philosophical Methods

3. Here’s some Vocabulary we will be talking about in this PowerPoint.
Atomic Sentences: Statements which express one proposition
Connectives: These are used to make more complex statements. Connectives connect statements together, i.e..: “and”
Conjunction: A conjunction connects two sentences by saying that they are both “true.”
Disjunction: (inclusive) – A disjunction connects two sentences that at least one of the statements are true, if not both.
Disjunction: (exclusive) – A disjunction where one of the two statements are true, not both.
Negation: A negation in English denotes in by using the word “not” or more formally “it’s not the case that.” It is a strange connective that operates in only one atomic sentence.
Material Conditional: This is a stylistic variant that contains an antecedent and a consequent, i.e.: “If…then.”
Material Biconditional: This is a variant that contains the same truth value for both conditions, i.e.: “if and only if.”

5. Atomic Sentences Today is Thursday.
Not Atomic Sentences
Today is Thursday.
The atomic number of hydrogen is 1.
It is raining outside right now.
The atomic number for hydrogen is 1 and the atomic number for helium is 2.
Are you hungry?
Tomorrow is not a weekday.
We can symbolize atomic sentences by using a capital letter. Traditionally, logicians like to start with the letter P and go on alphabetically from there. Some use a symbol representing the sentence, such as: H for The atomic number of hydrogen is 1.

7. :
Conjunction: P: The atomic number of hydrogen is one. “and” Q: The atomic number of helium is two.
Conjunction
Symbol: 
Example: P  Q
Stylistic variants: and, but, although, in addition to
The truth table for conjunction is the following: P Q
P  Q T F

9. Disjunction: (Inclusive)…Logic uses inclusive even when an argument is obviously exclusive like the one below. When doing so, they are giving the author Philosophical Charity. P: I will roll a 7 on this roll. “or” Q: I will roll an 11 on this roll.
Disjunction
Symbol: 
Stylistic variants: or, either or, unless
Example : P  Q
Inclusive disjunction (also called “or”) is a Logic operation. It normally takes two inputs. It is false when both inputs are false. Otherwise it is true.
The truth table for an inclusive disjunction is the following: P Q
P  Q T F

11. Negation: P: The sky is blue. P: It is not the case the sky is blue
Symbol: 
Stylistic variants: it is not the case that, not, un-, non-
Example: P
The truth table for negation is the following: P P T F
Example using a negation:
(P  Q)  (P  Q).
Translating back to English, that says “P or Q, but not both P and Q.”

13. Material Conditional: P: x > 4 Q: x > 2
Symbol: 
Stylistic variants: if…then, given that, only if
Example: P  Q
**Take note of lines 3 and 4**
The truth table for material conditional is the following: P Q
P  Q T F

15. Material Conditional - Continued Reflection
1. X = 5
Then both the antecedent and the consequent are true.
2. X = 3
Then the antecedent is false but the consequent is true.
3. X = 1
Then both the antecedent and the consequent are true….
Notice that we can’t find a value for x that makes the antecedent true but the consequent false. In other words, rows three and four of the truth table should be true!
If x > 4 then x > 2 -or-
symbolically, (x > 4)  (x > 2)
Is this true?
(Yes)
Is it always true or just sometimes true?
(Hmm??? Let’s see…) P Q
P  Q T F

17. Material Biconditional P: The lightbulb will go on
Material Biconditional P: The lightbulb will go on. “iif” Q: The light switch is turned on
Material Biconditional
Symbol: 
Stylistic variants: if and only if, just in the case that
Example: P  Q
**Take note of line 4**
The truth table for the material biconditional is the following: P Q
P  Q T F
Intuitively, P if and only if Q means that P and Q should always possess the same truth value, which is reflected in the truth table.

18. Time for a little Laugh Therapy!
YAY!!!!!! We made it through!
Time for a little Laugh Therapy!