Concept
7 readings
Counterexample
Concept · 7 readings
A counterexample is a possible case that tests an inference or a general claim. Showing that support fails is not the same as proving the opposite conclusion.
A place to begin
A counterexample workshop · Lesson 1 of 1
Testing a claim with a counterexample
A counterexample can test a general claim, or test an inference by describing a case in which its premises are true and its conclusion false. The workshop practices both, then asks what a fair repair of an argument should preserve.
All readings
7 readings · Title A–Z
Inference under challenge · Lesson 2 of 2
Dharmakīrti: a reason that establishes its conclusion
For Dharmakīrti, a reason must belong to its subject and be inseparable from what it establishes, and the connection must be known. The lesson compares his account with Nyāya’s, keeping apart what follows, what is known and what a countercase defeats.
Guided course · Module 3 · Lesson 9
How can we tell whether we know?
Nyāya counts perception, inference and testimony among the ways of coming to know, and sets out an inference in five steps. How can inquiry check its own instruments without demanding certainty in advance?
Guided course · Module 11 · Lesson 62
Logic, meaning and a new ideal of clarity
Frege distinguishes an expression’s sense from its reference to explain how an identity can be informative. The lesson also shows why substituting one name for another can change what a belief report says.
Inference under challenge · Lesson 1 of 2
Nyāya: what warrants an inference?
Setting out a Nyāya inference in five parts does not establish its warrant: the sign must be connected to what it proves, in the right direction. A countercase can expose an additional condition without showing that the conclusion is false.
A counterexample workshop · Lesson 1 of 1
Testing a claim with a counterexample
A counterexample can test a general claim, or test an inference by describing a case in which its premises are true and its conclusion false. The workshop practices both, then asks what a fair repair of an argument should preserve.
Guided course · Module 1 · Lesson 2
What does a reason actually support?
Whether a conclusion follows is one question, and whether the premises are true is another; imagining true premises with a false conclusion tests whether it follows. Reasons can still support a conclusion they do not guarantee.
Guided course · Module 7 · Lesson 34
What does experience tell us about the world?
Vasubandhu uses dreams to ask what appearances establish, and store consciousness to explain continuity without a permanent owner. Rival interpretations of representation and external objects stay open.
Study this in sequence
A counterexample workshop
Test how far a claim reaches by finding a case in which it fails, and practice on general statements, inferences and fair repairs to an argument.
Inference under challenge
What makes a sign a reason to believe something we cannot see? Follow selected Nyāya accounts and Dharmakīrti’s argument to examine the connection a sign needs, our grounds for relying on it and what a countercase can show.