4: Conditionals, Conditions and Conceptual Analysis Flashcards Preview

Introduction to Logic (UNO) > 4: Conditionals, Conditions and Conceptual Analysis > Flashcards

Flashcards in 4: Conditionals, Conditions and Conceptual Analysis Deck (18)
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1

What are the variables S and P in classical logic?

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

2

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

3

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

4

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

5

What is the symbol for "or" in sentential logic?

  • "v"
  • S v G
    • Sophie is a cat or God exists

6

What is the symbol for "if... then" in sentential logic?

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

7

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

8

In what level are you reasoning in a conceptual analysis?

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

9

What are the three types of conditions?

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

10

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)

11

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.

12

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.

13

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?

14

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.

15

What is the anatomy of a conceptual analysis?

16

What are the four requirements for a successful conceptual analysis?

  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.

17

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

18

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