Critical thinking
Chapter 5
The practice of argument-reconstruction

Extraneous material

The first step in reconstructing an argument is to make a list of the argument’s premises and conclusion as concisely and clearly as possible.
Making such a list is only the first step towards a complete reconstruction.

Defusing the rhetoric

Expressive epithet: terms used to refer to some person, group or other entity but that characterize the entity referred to for rhetorical purposes.

Logical streamlining

When reconstructing arguments we should strive to display the logical relationships in an argument in the simplest, clearest and most familiar ways possible.

• Where appropriate, rewrite sentences as either conditional or disjunctive sentences of one of the following forms:
  • If A then B
  • If not-A then B
  • A or B
  • Not-A, or B
  • .If not-A then not-B
  • If A then not-B
  • A or not-B
  • Not-A, or not-B
• Rewrite generalizations in one of the following forms, where the blank ‘_’ is filled by a quantifier such as ‘all’, ‘some’, ‘most’, ‘not’, ‘almost all’, ect
  • _F are G
  • _ are not-G

This is not always possible, and doing it will sometimes distract us from other points we are trying to make.

Implicit and explicit

Not only do actual statements of arguments typically include a lot of material that is inessential to the argument, they often exclude some of what is essential to the argument.

• Some essential propositions are left implicit.

Our task is to make the argument fully explicit.

A proposition is implicit: the proposition is part of the argument intended by the arguer but it has not actually been stated by the arguer.
To make a proposition explicit: to state it.

Connecting premises

Connecting premise: the premise which you have to make explicit in order to make an argument valid.

Usually, when people give arguments, the premises they give explicitly will be only those which pertain to the particular facts or subject matter they are talking about.
Arguers very often leave implicit the more general assumptions they make.

We cannot assume that whenever an argument, as explicitly given, is neither valid nor inductively forceful, the intended argument is valid or inductively forceful.
It is not always the case that the arguer is implicitly relying on an appropriate connecting premise.
In other cases, the implicit connecting premise is just not true, in which case the argument is unsound.

Covering generalizations

Connecting premises are usually generalisations.

Covering generalisations need not be hard generalisations.
In such a case the inference from generalisation to instance is inductive rather than deductive.

Generalisations of the ‘All A are B’ sort are themselves conditionals, except they are generalised. The same goes for ‘No A are B’ form.

Very often, when people assert conditionals, they do so on the basis of some covering generalisation.

Connecting premises are almost always necessary, but they can fail to be sufficient to bring out the real basis of an argument.

Relevance

When a proposition stated by the arguer is irrelevant to the reasoning that delivers the conclusion, that proposition should not be included in a reconstruction of the argument.

Why not include irrelevant material?

• It is distracting
• If the irrelevant material is not true, it can make the argument unsound.

The truth-values of the premises actually advanced by an arguer can be more or less relevant to the soundness of the argument. Sometimes is is highly relevant that a given premise is false, sometimes is its much less so. It depends upon the nature of the mistake, and upon the role played in the argument by the premise.

• The degree of relevance must be taken into account in the process of reconstruction.

Ambiguity and vagueness

Ambiguity

In reconstructing arguments, we have to eliminate any ambiguities in the original statement of the argument.

• If the original statement contains an ambiguous sentence, we have to decide which of the possible interpretations was most likely intended by the arguer.
• In our reconstruction of the argument, we have to rewrite the sentence, choosing a form of words that conveys the intended meaning unambiguously.

A primary purpose of reconstruction is to represent the propositions that constitute an argument in the clearest way.

• We should have no qualms about changing the language used to express those propositions. In changing it, we are only trying to gain a better grasp of what the arguer was thinking.

There is not guarantee that we will not change or distort the arguer’s thinking, but there is no point in allowing ambiguous language to remain unchanged. We can simply not evaluate an argument if we do not know exactly what argument we are evaluating.

If we cannot decide between two interpretations of an ambiguity, we must give both interpretations of the argument, and evaluate the two arguments independently.

Vagueness

Important for critical reasoning are words whose meanings are vague.
We often have the feeling that these things are bad, or that they are good, without any precise idea of what they mean.
What they signify is typically a whole group or cluster of things that are not unified in any exact way.
(Like liberal or love).

In reconstructing arguments, the best thing to do with vague words is simply to eliminate them.

Many of the most rhetorically highly charged words in public discourse are vague. Eliminating them four our argument-reconstructions achieves two things:

• it clarifies the argument
• it enables us to focus without distraction upon the logic of the argument.

The best thing to do with ambiguous or vague language is to replace it with language that is not vague or ambiguous.
The aim is to employ language that will express the intended propositions without ambiguity or vagueness.
But, this is not always possible.

• In an ambiguous case we can assess each of the possible versions of the argument, but we may have to confess that we cannot tell which version the arguer intended.
• If the language used is vague, we have to admit that the arguer’s thinking may simply have been vague or confused.

More on generalisations

Soft generalisations are very often expressed without any quantifier at all.

Since there is often confusion over the difference between hard and soft generalisations, we should, when constructing arguments, always make clear whether a generalisation is hard or soft. (The one exception to this is the case of statements about cause and effect).

• If an intended quantifier is merely implicit, there is room for misinterpretation. It is a kind of ambiguity.

The way to eliminate the ambiguity is to add an explicit quantifier.

The scope of generalisation

Subjects of generalisations: what the generalisations are about.

The scope of generalisations: how big the subject is.
It can be wider and narrower.
(For example: all cows or all black cows).

We can compare generalisation scopes only when the subject of one is a subset of the subject of the other.

It can sometimes be important to adjust the scope of a generalisation, making it either narrower or wider.
Usually, in reconstructing arguments, we have to narrow them.
By narrowing the generalisation, the issue is defined more exactly.

When reconstructing arguments, we should take care not to employ a hard generalisation that is wider in scope than we need if there is anything doubtful about the wider one that could be eliminated by employing a narrower one.
If a narrower (but hard) generalisation will suffice for constructing an argument for the desired conclusion, when we should employ the narrower one.
This is not to say we should always choose narrow generalisations whenever possible!

In some cases there is not natural word or phrase for the class of cases we wish to generalise about. In such cases we have to reduce the scope of a generalisation by explicitly accepting a certain class of what would otherwise be counterexamples.

Practical reasoning

Practical conclusions: a conclusion that enjoins or commends a particular action.
What the argument says is that doing one thing in necessary if a certain desirable outcome or end is to be achieved.

Practical reasoning: means-end reasoning.
Based upon two sorts of considerations:

• an outcome is specified as being either desirable or undesirable.
• There is a proposition put forwards that says either:
  • if such-and-such action is performed, the outcome will result
  • if the action is performed, the outcome will not result
  • .if the action is not performed the outcome will not come about
  • if the action is not performed the outcome will not come about

But:

• We need to know that the cost of the proposed action does not outweigh the benefit of the outcome.
• We need to know that there is not some other means that would bring about the same benefit but at lower costs. We need to know that the proposed action is the most efficient or economical way to bring about the desired outcome.

In reconstructing arguments, we need to incorporate both of the points above as premises.

Balancing costs, benefits and probabilities

Practical reasoning involves a weighing of one value (the value of the desired result) against another value (the negative value of the cost of the envisaged means of bringing about the desired result).
Almost any action could, in principle, be rationalised by practical reason.

In cases when the argument must be represented as inductive, we have to juggle three factors

• Cost
• Benefit
• Probability.

There are only rough estimates. No one assumes that anyone can specify exactly how bad or how good outcomes would be relative to each other.

Expected value: for each possible outcome of the action, you multiply the probability of the outcome by its value (its cost or benefit, as the case may be). Then you add these figures together.

When given a range of possible actions, one should do whatever maximises expected value.

There is a certain limit to the application of expected value calculations: the expected value of a proposed action tells us whether or not it would be rational to do something, unless it is overridden by the existence of rights or moral rules.

Explanations as conclusions

In an explanation, the truth-value of that proposition is not in question.

Use the word ‘cause’ or ‘because’ in the conclusion.

Abduction

The generalisations appealed to in arguments of this kind are often soft rather than hard, and more generally the arguments can be inductive rather than deductive.

Abductive argument: an inductive explanation.
The best and most likely explanation.

Causal generalisations

Causal statements often appear as generalisations about types of events or states of affairs.

The word ‘cause’ does not always, or even typically, indicate hard generalisation of this kind.

In order to infer a causal relationship from a correlation between X and Y, we need to know that the correlation holds, or would hold, even when other possible causes of Y are absent or were present.

A short cut

Where an argument contains a conditional among its premises, we have, in order to infer the consequent of the conditional, to write down its antecedent as a separate premise.

If P2 is a conditional whose antecedent is P1, instead of rewriting P1 out in full, we may abbreviate its simply as ‘P1’.