Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 6

An argument is rationally unpersuasive if there is no good reason to accept a premise, even though the argument is deductively valid and sound. An argument is defeated if a person reasonably believes the premises, but, nevertheless, reasonably rejects the conclusion. An argument is rationally persuasive for a person if the argument is either deductively valid or inductively forceful (1), the person reasonably believes the premises (2) and the argument is not defeated for that person (3).

There are several points considering rational persuasiveness:

1. It is not possible for the conclusion of a deductively valid argument to be defeated by a person’s total evidence. It is only possible for inductively forceful arguments.
2. An argument does not have to be sound in order to be rationally persuasive.
3. Rational persuasiveness is a matter of degree
4. Rationally persuasive does not merely mean persuasive or convincing. A rationally persuasive argument may fail to persuade anyone.
5. Judgements about the rational persuasiveness very frequently depends on estimates of the legitimacy oft eh authority behind certain propositions.
6. A rationally persuasive argument does not mean that the premises of this argument will and have to be used in further conclusions.

There are three ways in which someone can be mistaken about the rational persuasiveness of an argument:

1. People can mistakes concerning whether or not an argument is valid or inductively forceful
2. People can think they have a good reason to accept a premise when they don’t or the other way around.
3. People can be mistaken about whether or not an argument is defeated for them

LOGICAL ASSESMENT
If an argument is not valid, the question should always be asked whether the argument is inductively forceful. When assessing conditionals, we should always assume the antecedent is true in order to see whether the consequent is true and the argument is thus deductively valid.

Conditional proof refers to determining whether ‘if A then B’ follows from some premises. In order to do so, we should ask ourselves whether B follows from those premises together with A.

One way of assessing the validity of an argument is to suppose the premises are true but the conclusion is false. If this is impossible, then the argument must be valid.

REFUTATION BY COUNTEREXAMPLE
A counterexample, especially using the same reasoning as the original argument, can illustrate why an argument is invalid or not inductively forceful.