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The value of each outcome must be assigned a number, but the purpose of the numbers is only to indicate the comparative values of the possible outcomes. For example if one outcome is judged to be twice as good as a second, we could assign them any two numbers so long as the first is assigned a number that is twice that assigned to the second. Expected value is the central concept of cost/benefit analysis. The idea is that, given a range of possible actions, one should perform the action with the highest expected value.

Explanations We give an argument for something when we seek to persuade an audience that that proposition is true. By contrast, when we give an explanation of something, we know, or assume, that the audience already accepts that the proposition to be explained is true. Our aim is not to give reasons for believing that proposition, but to specify, for example, the causes of the event that it mentions. Both arguments and explanations can be described as answering 'why?' questions, but there is a crucial difference: whereas the question in the case of explanation is 'why is it so?', or 'why did it happen?', the question in the case of argument is 'why should I believe it?'.

Potentially confusing is that in order to establish that an explanation is the correct one - e.g. that it specifies the actual cause of an event - we often have to give reasons why it should be believed, i.e. an argument. That is, we sometimes have to argue for an explanation.

Extended arguments An extended argument for a proposition is one containing more than one inference: a conclusion is used as a premise for a further argument, the conclusion of which may be used as a premise for a further argument, and so on. Conclusions used as premises for further inferences in an extended argument are called intermediate conclusions.

Extension The extension of a general term such as 'cat' or 'red car' is the set or group of things designated by the term.

Factual assessment The stage in the assessment of an argument in which we determine whether or not the argument's premises are true. If the argument is either valid or inductively forceful, then the argument is sound if and only if all its premises are true.

Fallacies The term 'fallacy' encompasses certain commonly encountered failures of argumentation; it is partly because they are often effective as rhetorical ploys that they are commonly encountered. Formal fallacies are simply logical mistakes; that is, arguments that fail to be valid or inductively forceful in certain characteristic ways. Substantive fallacies are arguments that implicitly assume some quite general premise of a kind which, when more closely and explicitly considered, can readily be seen to be false. Some other common defects in argumentation fit neither classification; but since they involve fooling the audience in the context of argument they can be appropriately classified as fallacies.

Generalisations A generalisation is a proposition concerning a class of things, either explicitly or implicitly involving a quantifier such as 'all', 'every', 'no', 'some', 'most', 'twelve', 'at least twelve', and so on. For example, whereas 'That dog is black' is not a generalisation, replacing 'that dog' by 'every dog', 'no dog', 'at least one dog', and so on, yields a generalisation. Sometimes the verb must be changed to the plural form, and likewise the predicate if it involves a noun rather than an adjective.

Gettier cases Gettier cases are cases in which someone satisfies the conditions for knowing a proposition that are set down by the tripartite account of knowledge, yet fails to know it. This is usually because the person is only accidentally justified in believing a true proposition.

Good reasons For someone to have good reasons for believing a proposition is for that person to possess an argument for that proposition that is rationally persuasive for them.

Hard generalisation A hard generalisation is one that is correctly conveyed by using a quantifier such as 'all', 'every', 'each', and 'no'. Unlike soft generalisations, such generalisations are true only if there are no counter-examples.

Implicit A premise is implicit in an argument if it has been assumed but not actually stated by the arguer. Conclusions may also be implicit, though this is less common. Whether or not, as a matter of psychological fact, a given premise has been assumed by an arguer is often beside the point. In general, implicit propositions are those not stated by the arguer that would be included in a reconstruction produced in accordance with the Principle of Charity.

Implicit relativity A statement is implicitly relative when the type of fact it expresses involves a relation to something that is not explicitly mentioned in the statement. For example 'John is tall' is implicitly relative because what it really means is 'John is taller than the average man' (if John is a man). The relation to the average man is not explicit in the original statement.

Implicit speaker-relativity An implicitly speaker-relative statement is one that is implicitly relative, where the implicit term of the relation is the person making the statement. Thus the statement is speaker-relative, but only implicitly so. For example 'Chocolate ice cream tastes better than strawberry ice cream' is implicitly speaker-relative because what it really means is 'Chocolate ice cream tastes better to me than strawberry ice cream does'. (Some might say that the implicit term here should not be 'me' but something like 'most people').

Inductive force The inductive force of an argument is the conditional probability of its conclusion relative to its premises.

Inductive inference To draw an inductive inference is to conclude, on the basis that a certain proportion of a sample of a population possesses a certain feature, that the same proportion of the whole population possesses that feature. The inference is inductively forceful to the degree that the sample is representative of the population.

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