What are the variables S and P in classical logic?
 variables for terms in order to express the four forms of general statements
In sentential logic what are the variables p, q, r, s, and t?
 placeholders for statements
 statements are substitutions instances of statement forms (not the other way around)
 the variables are statement forms
 the variables are statement forms
What do you add when you wish to deny a statement in sentential logic?
 a tilda
 ~
 S = Sophie is a cat
 ~ S = it is false that Sophie is a cat
 S = Sophie is a cat
 ~ S = it is false that Sophie is a cat
What do you add to signify "and" in sentential logic?
 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
 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
What is the symbol for "or" in sentential logic?
 "v"
 S v G
 Sophie is a cat or God exists
 Sophie is a cat or God exists
What is the symbol for "if... then" in sentential logic?
 the hook "⊃"
 S ⊃ G
 If Sophie is a cat then God exists
 If Sophie is a cat then God exists
What is the symbol for "if and only if" in sentential logic?
 the three bar symbol "≡"
 S ≡ G
 Sophie is a cat if and only if God exists
 Sophie is a cat if and only if God exists
In what level are you reasoning in a conceptual analysis?
To do conceptual analysis is to reason at the level of a single statement.
What are the three types of conditions?
 Sufficient Condition
 Necessary Condition
 Necessary and Sufficient Condition
What is a Sufficient Condition?
 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)
 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)
What are Necessary Conditions?
 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.
 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.
What is a Necessary and Sufficient condition?
 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.
"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.
What are some questions that we ask that motivates us to construct conceptual analysis?

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?
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?
Why do we want to do a conceptual analysis?
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.
What is the anatomy of a conceptual analysis?
What are the four requirements for a successful conceptual analysis?

The analysandum and its analysans must be alike in both meaning and truthvalue.

The analysans must be clearer than the analysandum.

All and only the necessary conditions must be identified (so they are jointly sufficient).

The analysis must not admit of a counterexample to any necessary condition or to their joint sufficiency.
The analysandum and its analysans must be alike in both meaning and truthvalue.
The analysans must be clearer than the analysandum.
All and only the necessary conditions must be identified (so they are jointly sufficient).
The analysis must not admit of a counterexample to any necessary condition or to their joint sufficiency.
What is a counterexample to a necessary condition?

identify something that is an x but that does NOT have the feature asserted to be necessary
identify something that is an x but that does NOT have the feature asserted to be necessary
What is a counterexample to the sufficiency of the analysans?

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