## Counterexample i A counterexample to a generalisation is a

particular statement - a statement that is not a generalisation - that is the negation of an instance of the generalisation. For example 'Darcy Bussell is a great ballerina who is tall' is a counter-example to 'No great ballerinas are tall', (ii) A counter-example to an argument is an argument of the same form or pattern as the first argument that is clearly invalid or inductively non-forceful. It is used as an illustration to make it clear that the first argument is invalid or inductively non-forceful.

Covering generalisation Often, where a premise of an argument is a conditional proposition of the form 'If Mary is a doctor, then Mary has a university degree', it is implicitly inferred from a generalisation of which it is an instance - in this case, 'All doctors have university degrees'. This relation is made more conspicuous if we express the generalisation in the form 'For any given person, if that person is a doctor, then that person has a university degree'.

Credibility The degree to which someone's having said something constitutes a reason to think it true. While critical reasoning requires us to focus on an argument and not on the person putting it forward, a person's character and actions are certainly relevant to their credibility.

Deductive validity Validity can be defined according to either of the following, equivalent formulations: (1) An argument is valid if and only if it would be impossible for its premises to be true but its conclusion false. (2) An argument is valid if and only if necessarily, if its premises are true, then its conclusion is true.

Defeated argument An inductively forceful argument, whose premises a person reasonably believes, is defeated for that person if he or she has good reasons to think the conclusion false.

Expected value The expected value of a given action depends on the values and probabilities of the possible outcomes. In particular, if ov on, .. . and so on are the possible outcomes of an action, V(o) is the value of a given outcome, and P(o) is the probability of a given outcome, then the expected value of the action is

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