Critical thinking
Chapter 6
Issues in argument assessment

Rational persuasiveness

The role of an argument is to give us reasons for accepting its conclusion as true.
The aim is to give an argument by which the intended audience is ought to be persuaded.

We cannot always tell whether or not the argument is sound.
Sound arguments must have true premises.

• An deductively sound argument is one that has true premises and which is deductively valid.
• An inductively sound argument is one with true premises that is inductively forceful.

Since we do not always know which propositions are true and which false, we cannot always tell whether an argument is sound or not.

To say that an inductively forceful argument is defeated for a person: the person reasonably believes the premises, but, nevertheless, reasonably rejects the conclusion.
(They have, for example, extra information).

An inductively forceful argument whose premises you have reason to accept is rationally persuasive only if your total evidence does not defeat the argument for you.

To say that an argument is rationally persuasive for a person:

• the argument is either deductively or inductively forceful
• the person reasonably believes the argument’s premises (at the time)
• it is not an inductively forceful argument that is defeated for that person (at that time).

Rationally unpersuasive argument: an argument that is deductively sound and valid, but gets you no closer to knowing the truth-value of the conclusion.

Rational persuasiveness is doubly relative.

• An argument is or is not rationally persuasive for a person at a particular time.

Since people are in different states of information at different times, an argument may be rationally persuasive for one person, but not for another.

Seven points to bear in mind as regards rational persuasiveness:

1 It  is not possible for the conclusion of a deductively valid argument to be defeated by a person’s total evidence. This is only possible for inductively forceful arguments.

• If you accept with good reason the premises of an argument that you recognize to be deductively valid, you must accept the conclusion as well.
• The adverb ‘probably’ (or a similar term) before the conclusion of an inductively forceful argument allows the possibility that the premises are true and the conclusion is false.

2 Rational persuasiveness is not part of the definition that the argument be sound (either deductively or inductively).

• The notion of rational persuasiveness is intended to capture what it is about an argument that constitutes its rational claim on a person.
  (For example: an argument can have a false premise, hence be unsound, but still be rationally persuasive for a person).
  So there is such a thing as a reasonable mistake.

3 An attempt at persuasion by argument is an attempt at rational persuasion, as opposed to other kinds of persuasion, which do not appeal to your reason.

4 Rational persuasiveness is a matter of degree, it is not all-or-nothing.

• The reasonability with which one hold beliefs is a matter of degree.
• Inductive force is a matter of degree.

5 ‘Rationally persuasive’ does not mean merely ‘persuasive’ or ‘convincing’. A rationally persuasive argument may fail to persuade anyone. Whether or not an argument is rationally persuasive for you does not depend upon whether you think it is.
An argument may be rationally persuasive for you even though you are not persuaded by it. There are cases you ought to be persuaded by an argument, but you are not.
Likewise, there are cases where you are persuaded or convinced by an argument, but where you should not be, because the argument is not rationally persuasive for you.

• Rational persuasiveness and soundness are properties that arguments can have independently of whether an individual or group actually finds them persuasive.
  There are three ways in which one can be mistaken about the rational persuasiveness of an argument:
• We can make mistakes concerning whether or not an argument is valid or inductively forceful.
• We can think we have a good reason to accept a premise when we don’t, or vice versa.
• You can be mistaken about whether or not an argument is defeated for you.

6 Judgments about rational persuasiveness very frequently depend on estimates of the legitimacy of the authority behind certain propositions.

7 In saying that an argument is rationally persuasive for a person only if the person reasonably believes the premises, we are not requiring that the person have at his or her disposal further arguments with those premises as conclusions.
What we are requiring is that the person be justified in accepting the premises.
Justification is a wider concept than rational persuasiveness: if one has a rationally persuasive argument for a proposition then one is justified in accepting it, but one may be justified in accepting it by means other than argument.

Some strategies for logical assessment

If you can think of ways in which the premises would be true but the conclusion false, then you must determine to what degree, if any, the argument is inductively forceful.
What you do here is to imagine various situations in which all the premises are true.
Of these situations, which are more likely? The ones in which the conclusion is true, or the ones in which it is false?
If the situations in which the conclusion is true would be more likely than those in which it is false, then the argument is inductively forceful, if not, it is not.
If it is forceful, it remains only to specify the degree to which it is so.

Whenever we find that an argument is not valid, we should always ask whether there are premises that:

• the arguer could reasonably expected to know, or which we know to be true
• those premises would make the arguer inductively forceful, if added.

Arguments with conditionals or generalisations as conclusions, conditional proof

What a conditional asserts, roughly, is a certain relation between the antecedent and the consequent. That if the antecedent is true, then so the consequent is.
The question:
If the premises of the argument were true, then would this purported relationship hold?

To answer that question, we suppose not only that the premises of the argument are true, but that the antecedent of the argument’s conclusion is also true.
Then we want to know whether, under all these suppositions, the consequent of the argument’s conclusion would also have to be true.
If that is so, then that conditional proposition does follow from the premises.

In order to determine P → Q follows from some premises, we ask whether Q follows from those premises together with P.
This is conditional proof.
It provides a simplified means of proving a conditional.

Supposing the conclusion is false

Another way to assess the validity of an argument is to suppose the premises are true but the conclusion is false. If we can see that this is impossible, then, according to the definition of validity, the argument is valid. If we can see that this is possible, then we know that the argument is invalid.
This method can be used on any argument.

Refutation by counterexample

You can give a counterexample for an argument by giving another argument in the same form.
And make everything explicit.

If an argument is unsound due to an implicitly assumed but false generalisation, first make explicit the assumed generalisation in such a way that the argument becomes deductively valid (or inductively forceful). Then find a true premise and false conclusion that are suitably analogous to the premise and conclusion of the original argument, and substitute them.

Engaging with the argument I: avoiding the ‘who is to say?’ criticism

Sometimes an argument will contain a premise that no one would say can be known with certainty.

Where an argument is inductively forceful, the person who says ‘who is to say’ that the conclusion is true is either repeating what nobody doubts (that the argument is not deductively valid) or expressing a seemingly unreasonable scepticism, like a person who refuses to believe that past observation supports the hypothesis that spring will follow winter.

In order effectively to criticise an argument, in order to engage with it, one must either:

• show that the argument is neither valid nor inductively forceful
• show or argue that there is no reason to believe one or more of the premises, or that one or more of them is false
• show, if it is an inductive argument, that is is defeated by some other argument.

Merely pointing out that a term occurring in the argument is vague or value-laden is not sufficient.
Certainly remarking the presence of vagueness is not sufficient.

Engaging with the argument II: don’t merely label the position

Argument commentary

Argument analysis: a two-stage process, comprising first the reconstruction, then the assessment of the argument.

When the analysis of an argument is undertaken, you may sometimes want to produce a piece of written work that summarises the analysis you have made.
This should consists of:

• The argument (or arguments) as originally expressed
• The argument(s) expressed in the standard form.
• A commentary on the argument(s), written in ordinary prose.

He commentary is simply a written piece of work that covers the following points (either all of them, or as many as seems relevant in the particular case):

1 A general discussion of the argument, explaining, as appropriate:

• the context in which the argument is given.
• if needed, some discussion of the structure of what the arguer has written or said.

2 A discussion of how and why the standard-form reconstruction was derived as it was, focusing especially on any problems encountered in the process. In particular:

• The exclusion of extraneous material should be explained
• Any rhetorical ploys should be pointed out, explained, and eliminated
• If any implicit premises (or any implicit conclusions) have been added, it should be explained why
• If the conclusion or any premises have been re-worded, it should be explained why
• It may also be useful to explain meanings of important words that appear in the reconstruction

In general, this section should ideally include everything necessary to justify the given reconstruction.

3 A discussion of the validity or degree of inductive force of the argument.

• You have first to pronounce whether or not the argument is deductively valid. If it is not, you should explain why it is not.
• And if it is not, you should pronounce and explain to what degree, if any, the argument is inductively forceful. If the argument commits a fallacy, then you may identify it at this point, especially if the fallacy is a formal one.

4 If the argument is either valid or inductively forceful, a discussion and verdict concerning the truth-values of the premises. This will amount to a verdict regarding the soundness of the argument. It should be explained in detail which premises are most debatable and why.

• Except where it more or less obvious, these explanations must be substantive; actual reasons for accepting or doubting particular premises must be given.
• If the arguments commits a substantive fallacy, then you would explain why.

5 In the case of an inductively sound argument, you should say whether or not the argument is defeated for you.