REASONING 2: INDUCTIVE REASONING

Deductive Arguments

Arguments intended to provide definitive support for a conclusion.

Inductive Arguments

Arguments intended to provide probable support for or increase the likelihood of a conclusion.

Strength

The condition in which an inductive argument makes a conclusion likely or probable if the premises were true. Strength comes in degrees and an inductive argument can be more or less strong depending on the level of support the premises give, but it is always possible for the premises to be true and yet the conclusion false due to the ampliativity of inductive arguments.

Cogency

The condition in which an inductively strong argument has true premises along with a true conclusion.

Ampliativity

The condition in which an argument’s conclusions go beyond the information provided in the premises and as a result, the truth of the premises does not guarantee the truth of the conclusion. It is a feature of inductive reasoning, unlike for deductive reasoning, where the conclusion is implicitly contained in the premises.

Generalization

A type of inductive reasoning that involves drawing out conclusions about a whole class of things on the basis of premises about a sample of that class (concluding that all antlered animals are herbivores based on looking at samples of antlered animals (deer, moose, etc.)). Generalizations can even establish causal connections among things and their properties.

Hasty Generalization

An informal fallacy where a conclusion is drawn about a whole class of things on the basis of an insufficiently large or varied sample of that class and therefore the argument moves too quickly from the premises to the conclusion.

How can a hasty generalization be avoided?

Ensuring a sufficiently numerous and various sample size, looking for disconfirming instances as well as confirming instances of the generalization, and considering whether the generalization is plausible given any other knowledge present.

Mill’s Methods

Methods of testing for causal connections through generalizations devised by 19th century British philosopher John Stuart Mill. They include the method of agreement, method of difference, joint method, method of concomitant variations, and method of residues.

Method of Agreement

One of Mill’s methods of testing causality where a common factor, a, is present in all cases where an effect, E, occurs, and therefore a causes E. In this method, factor a is proven as a sufficient condition for E.

Method of Difference

One of Mill’s methods of testing causality where an effect, E, does not occur when a common factor, a, is absent, and therefore a causes E through holding all other factors constant in all cases. In this method, factor a is proven as a necessary condition for E.

What is the negative use of the method of agreement?

The negative use consists in showing that E does not occur in one or more cases when a is present and therefore a does not cause E.

What is the negative use of the method of difference?

The negative use consists in showing that E occurs in one or more cases when a is absent and therefore a does not cause E.

Joint Method

One of Mill’s methods of testing causality where the methods of agreement and difference are utilized together. It demonstrates that the common factor, a, is the only factor common in two or more cases in which the effect, E, occurs, E does not occur in one or more of those cases if a is removed while holding the other factors constant, and therefore a is the cause of E. In this method, factor a is proven as a sufficient and necessary condition for E.

Method of Concomitant Variations

One of Mill’s methods of testing causality where quantitative changes in a common factor, a, are systematically related to quantitative changes in the effect, E, and therefore a causes E. This methods allows for the observation of the precise quantitative relation between a and E. It can be used when it isn’t possible to eliminate a certain factor altogether.

Method of Residues

One of Mill’s methods of testing causality where certain factors (b, c, d, etc.) are known to potentially cause a certain effect, E, and therefore any remaining antecedent factor, a, must be the cause of any remaining effect.

Analogical Reasoning

A type of inductive reasoning that involves analogies, which compare different things to bring out a point of similarities. It argues that a source analogue and a target analogue have similar properties, and therefore a property, P, of the source analogue is assumed to also be a property of the target analogue.

Arguments of analogy are composed of what 4 parts?

A source analogue, a target analogue, shared properties between both analogues, and the observation of a further property, P, of the source analogue that is inferred to be a property of the target analogue as well.

Source Analogue

The analogue in an argument of analogy that is the base of comparison with the target analogue.

Target Analogue

The analogue in an argument of analogy in which the source argument is compared to and about which a conclusion is drawn.

What are the four criteria for evaluating arguments of analogy?

The number of shared properties, the number and variety of source analogues, the number of relevant differences, or disanalogies, between analogues, and the number and variety of counter-analogues.

How does the number of shared properties play a role in the evaluation of arguments of analogy?

The more relevant similarities both analogues share in terms of their properties, the likelier the conclusion and the stronger the argument.

How does the number and variety of source analogues play a role in the evaluation of arguments of analogy?

Additional source analogues can strengthen the connection between the shared properties and the further property, P. The more, and the greater the variety of, confirming cases, specifically source analogues sharing properties with the target analogue, the stronger the argument.

Differences/Disanalogies

Differences shared between both the analogues in an argument of analogy. They mainly serve to weaken the argument. If a high number of those differences are found between the analogues, or if the differences are relevant enough, the likelihood of the conclusion and the strength of the argument will decrease.

Counteranalogues

Cases in arguments of analogy where either the shared properties between analogies are present but the further property, P, is not or P is present while the shared properties are not. They call into question the link between the shared properties and P, therefore weakening the argument.