5. The Counterexample Method

Question 1

Show an Argument Invalid (3)

Answer 1

1) Possible Invalid Situation (Apply Principle of Invalidity)
2) No Possible Derivation
3) Come up with Counterexample

Question 2

Invalid by Definition (2)

Answer 2

A) Apply Principle of Invalidity, show a possible situation where the premises are true yet the conclusion is false
B) If you haven’t found a situation it can be because of a fault of imagination (not looked hard enough).

Question 3

Invalid by No Possible Derivation (2)

Answer 3

A) Show that there does not exist a derivation that starts with the premises and ends with the conclusion
B) If you haven’t found a situation it can be because of a fault of imagination (not looked hard enough).

Question 4

Invalid by Counterexamples (5)

Answer 4

A) Find another argument having the same pattern of inference which is uncontroversially invalid (True premises and false Conclusion).
B) Advantage: Clear murky example w/ new instantiation
C) Disadvantage: Counterexamples require imagination
D) Disadvantage: Diff argument forms can instantiate one arg, so one can use Counterexamples for another form by accident
E) Use binaries for counterexamples (Man, Woman)

Question 5

Summary of Invalidity (2)

Answer 5

A) Principle of Invalidity
Actual Situation → Other (Invalid) Situation
B) Counterexample
Actual words in arg. → Other words in Arg
The argument with other words still needs to be proven invalid so it relies on A)

Question 6

Practicality of Counterexample

Answer 6

Counterexample is a demonstration and clarification tool rather than a validation tool