4: Conditionals, Conditions and Conceptual Analysis

Question 1

What are the variables S and P in classical logic?

Answer 1

• variables for terms in order to express the four forms of general statements

Question 2

In sentential logic what are the variables p, q, r, s, and t?

Answer 2

• placeholders for statements
• statements are substitutions instances of statement forms (not the other way around)
  
  • the variables are statement forms

Question 3

What do you add when you wish to deny a statement in sentential logic?

Answer 3

• a tilda
• ~
  
  • S = Sophie is a cat
  • ~ S = it is false that Sophie is a cat

Question 4

What do you add to signify “and” in sentential logic?

Answer 4

• a bold dot “•”
  
  • S • G = Sophie is a cat and God exists
  • ~S • G = it is false that Sophie is a cat and God exists
  • ~(S•G) = it is false that Sophie is a cat and it is false that God exists

Question 5

What is the symbol for “or” in sentential logic?

Answer 5

• “v”
• S v G
  
  • Sophie is a cat or God exists

Question 6

What is the symbol for “if… then” in sentential logic?

Answer 6

• the hook “⊃”
• S ⊃ G
  
  • If Sophie is a cat then God exists

Question 7

What is the symbol for “if and only if” in sentential logic?

Answer 7

• the three bar symbol “≡”
• S ≡ G
  
  • Sophie is a cat if and only if God exists

Question 8

In what level are you reasoning in a conceptual analysis?

Answer 8

To do conceptual analysis is to reason at the level of a single statement.

Question 9

What are the three types of conditions?

Answer 9

1. Sufficient Condition
2. Necessary Condition
3. Necessary and Sufficient Condition

Question 10

What is a Sufficient Condition?

Answer 10

• a good enough condition
• “p if q” expresses a sufficient condition
  
  • if q then p (equivalent)
• Something is a ___ if it is ___ .
  • Brandy is a doctor if she has Ph.D. (conditional statement)
  • Anyone is a doctor if she has Ph.D. (general statement)

Question 11

What are Necessary Conditions?

Answer 11

• MUST be the case
• “p only if q” expresses a necessary condition
  
  • if p then q (equivalent)
• Something is a ___ only if it is ___
  • Someone is a doctor of philosophy only if he has a Ph.D.

Question 12

What is a Necessary and Sufficient condition?

Answer 12

• the strongest condition
• “p if and only if q”
• Something is a ___ if and only if it is ___ .
  
  • Brandy will get an A on the exam if and only if she earns 89.5 or more points.

Question 13

What are some questions that we ask that motivates us to construct conceptual analysis?

Answer 13

• What conditions must be met for x to be true?
• What must be assumed to prove that x is true?
• What conditions must be met for something to be an x?

Question 14

Why do we want to do a conceptual analysis?

Answer 14

To analyze a concept (claim, belief, theory) is to identify all the necessary simpler ideas (conditions or assumptions) that compose it, then to evaluate them.

Question 15

What is the anatomy of a conceptual analysis?

Answer 15

Question 16

What are the four requirements for a successful conceptual analysis?

Answer 16

1. The analysandum and its analysans must be alike in both meaning and truth-value.
2. The analysans must be clearer than the analysandum.
3. All and only the necessary conditions must be identified (so they are jointly sufficient).
4. The analysis must not admit of a counterexample to any necessary condition or to their joint sufficiency.

Question 17

What is a counterexample to a necessary condition?

Answer 17

• identify something that is an x but that does NOT have the feature asserted to be necessary

Question 18

What is a counterexample to the sufficiency of the analysans?

Answer 18

• identify something that is NOT an x but would be if the analysans remain the way they are