2.4 Analyzing

Topic 15: Assumption
Topic 16: Rabbit Principle
Topic 17: Holding Hands Principle
Topic 18: Inference Objection
Topic 19: Argument Pattern
Topic 20: Deductive Argument
Topic 21: Inductive Argument
Topic 22: Abductive Argument

Topic 15: Assumption

The notion of an assumption is a familiar one, which for current purposes we define as follows:

An assumption is a proposition which somebody takes to be true without having provided or considered evidence in relation to it.

Acknowledged, Stated and Unstated (Hidden) Assumptions
Assumptions vary in the degree to which we are aware of them and recognize them for what they are.

‘I’m not going to have chemotherapy,’ said Holly Hopeful. ‘You’ve got to believe that you’re one of the lucky ones. Besides, my herbalist, Dr. Wu, is giving me natural medicines. Dr. Wu is an excellent doctor.’

Here Holly is fully aware that her belief that she will be one of the lucky ones is an assumption. This is an acknowledged assumption, one that is recognized for what it is.

Holly says, explicitly, that Dr. Wu is an excellent doctor. However she does not seem to realize that she has not considered, or provided, any evidence for this. The assumption is stated, though not acknowledged as such.

Holly has not said this, but she apparently believes, without any basis, that Dr. Wu’s medical expertise extends to cancer and its treatment. This assumption is not even explicitly stated, let alone acknowledged. Assumptions like this are unstated. Such assumptions are sometimes described as hidden, though this term is often misleading in suggesting that the assumption was actively or deliberately concealed.

Where Assumptions are Found
As illustrated above, assumptions occur frequently in reasoning, and play a variety of roles. It is important to understand where they occur, because assumptions, by their nature, are potential points of vulnerability. More often than not, when an argument has a crucial weakness, it is one of the assumptions which turns out to be the problem. Places where assumptions are often found include:

• Basic premises. Recall that a basic premise is one where the arguments ‘bottom out,’ i.e., one that has no further reasons or objections bearing upon it. Basic premises (at least, those with no basis) are classic cases of assumptions.
• Unstated co-premises. A co-premise which has not been stated, has not, almost by definition, been provided with any evidence; as far as the audience is concerned, it is an unstated assumption.
• Bases. Any given basis is generally surrounded by a cluster of assumptions, usually unstated. For example, Holly Hopeful’s basis for taking natural medicines is Dr. Wu’s (supposed) expert opinion that such medicines would help her heal. In doing so she is assuming that Dr Wu’s expertise is relevant to cancer and its treatment.

Identifying Assumptions
Identifying the assumptions in a piece of reasoning is one of the most important and yet difficult tasks in reasoning. It requires practice, experience, and lots of imagination to uncover all the significant assumptions, while also avoiding the mistake of attributing assumptions which are not in fact required.

In case of unstated co-premises, knowledge of the basic structure of reasons and objections can greatly assist in pinning down, in succinct form, exactly what assumptions are being made.

See also: Topics Proposition and Basis

Topic 16: Rabbit Principle

The so-called Rabbit Principle is one of the simplest, and yet most profound and useful of all rules of good reasoning. Informally, it is:

Rabbit Principle: contentions should contain no magic rabbits.

More prosaically:

Every significant term or phrase appearing in the conclusion of a simple argument should also appear in a premise of that argument.

Figure 2.12

For example, consider the VitaChaff argument above. Note that the contention contains the following significant terms or phrases:

• VitaChaff
• is good for you

Notice also that each of these appears somewhere in the premises; indeed, in this case each one appears in a distinct premise. This argument observes the Rabbit Principle.

Figure 2.13

This argument is much more typical of peoples’ ordinary reasoning. The contention contains the following terms or phrases:

• Humanity
• faces
• a period
• unprecedented
• turmoil

Not a single one of these appears in the premise as provided. The terms are magic rabbits; they suddenly appear ‘out of nowhere’ in the contention. In this argument there is a big gap, or ‘leap of logic’, between the premise and the contention.

Why ‘Rabbit’?
The name Rabbit Principle alludes, of course, to that most clichéd of all magician’s tricks, pulling a rabbit out of a hat. However things appear on stage, we all know that if a rabbit is pulled out of a hat, it must have already been in the hat; rabbits do not appear ‘by magic’. Similarly, if you want to prove something about Humanity, then you will have to say something about it in your premises.

Why Care about Rabbit Principle Violations?
Observing the Rabbit Principle has a number of salutary effects on our reasoning, including:

• helping us articulate fully the premises needed to establish the contention,
• helping us tighten the connection between premises and contention.

In short, observing the principle makes reasoning more explicit and rigorous.

The Rabbit Challenge
The Rabbit Principle is a very simple concept, but observing it fully can be surprisingly challenging. First, it is much easier than you might think to miss a magic rabbit; the eye glides over the text, often failing to notice the sudden irruption of new ideas.

Second, telling what is, and what is not, a violation of the principle often requires subtle judgment. Is ‘Humanity’ the same thing as, say, ‘billions of people’? Is the word ‘is’ significant here, for the purposes of the principle? Third, making the right adjustments in the contention, or the premises, to fix Rabbit violations can present quite a puzzle.

Fortunately, as with most skills, one gets better – and faster – with practice.

Topic 17: Holding Hands Principle

The Holding Hands Principle is an aid to good reasoning, helping us make arguments more explicit and rigorous. Like its sister the Rabbit Principle, Holding Hands is a simple idea, yet profound and very useful.

The basic idea is that in a simple argument (a reason or objection), premises should ‘hold hands’ with each other and the contention by overlapping in the terms they contain. More formally,

Every significant term or phrase appearing in a premise of a simple argument should also appear in either the contention or one of the other premises.

Figure 2.14

For example, consider the VitaChaff argument above. Note that the first premise contains the following significant terms or phrases:

• VitaChaff
• contains
• wheat germ

‘VitaChaff ’ appears in the contention, and so the first premise ‘holds hands’ with the contention. Similarly, ‘wheat germ’ appears in the second premise, and so the premises hold hands with each other. Figure 2.15

However, the Holding Hands Principle is not fully satisfied, since ‘contains’ does not appear elsewhere. The argument must be modified somewhere to remove the violation.

One approach is illustrated above. Now, every significant term or phrase appearing anywhere in the premises appears somewhere else too.

Observing the Holding Hands Principle in this case has a number of effects:

• It has helped ensure that no significant term or phrase is not properly bound in the overall structure of reasoning.
• It has strengthened the connection between claims, by increasing the degree to which they have terms or phrases in common.
• It has forced the unstated assumption VitaChaff is food into the open. (This may sound trivial, but VitaChaff might have been, say, horse feed.)

Such benefits are the reward which commonly flows from the painstaking work involved in ensuring that the Holding Hands Principle is fully satisfied.

Strategies for Removing Violations
When refining an argument to remove violations of the Holding Hands and Rabbit Principles, the following strategies can be applied:

• Use exactly the same term or phrase for a concept, wherever it appears.
• Strip out terms or phrases which, on reflection, are not crucial to the argument, and can be dispensed with.
• Add another co-premise if necessary, but be very careful that in doing so you do not introduce additional Holding Hands problems.

Topic 18: Inference Objection

Generally, objections are directed upon claims; they provide evidence that the claim is false. Sometimes those claims are themselves premises of other arguments. In such cases the objection says, effectively, ‘that argument is no good, because a premise is not true.’ In other cases, objections appear to be targeted not at any premise, but at the move from the premise(s) to the main contention. Consider:

Radichio: Things are terrible! The economy is going to pieces. It must be President Artfulwaffle’s fault. Things were fine last year before he was elected. Fennel: Why blame Artfulwaffle? Lots of other things could have caused the economy to go bad.

Fennel is not objecting to Radichio’s premise that the economy was fine before Artfulwaffle was elected. Rather, she thinks that the premise (though perhaps true) does not show that President Artfulwaffle is ruining the economy.

An inference objection is an objection to the evidential link between the premises and the contention of a simple argument.

Figure 2.16 A standard objection

Figure 2.17 A premise objection

Figure 2.18 An inference objection

Converting to Premise Objections

Figure 2.19

How can we reconcile the general definition of an objection as a reason to think a claim is false, with the notion of an inference objection as an objection to an evidential link (i.e., not a claim)? By realizing that every inference objection is equivalent to an objection to an as-yet-unstated premise. If we properly articulate all the premises of the first argument, we will find that the inference objection finds a natural place objecting to one of those added premises.

In the example above, Radichio’s argument has the unstated assumption that Artfulwaffle must have caused the change in the economy. Fennel’s objection is targeted on this assumption.

Genuine Inference Objections
A genuine inference objection must do more than assert that the conclusion does not follow from the premises. It must give some reason to believe that the conclusion does not follow.

Argument: Soccer must be the best sport – more people around the world play soccer than any other sport. Objection: The best sport does not have to be the one played the most.

In this example, the objection turns out to be merely denying the unstated co-premise that the best sport is the one played by most people around the world. A genuine objection would provide some substantial evidence – e.g., that ‘Historical and cultural factors, rather than just the quality of the sport, strongly influence the number of people who play it.’

See also: Topic Objection

Topic 19: Argument Pattern

The range and number of arguments that have been made, or could be made, is practically infinite. As you would expect, however, within this vast range there are important similarities and differences between arguments, and so we can sort arguments into various types. Some of these types crop up quite often:

An argument pattern is a common, distinctive structure of reasoning.

Argument patterns can be very helpful in reasoning and critical thinking:

• Understanding. Recognizing familiar argument patterns helps us follow reasoning more easily, particularly when it gets complicated.
• Constructing. We can assemble arguments more effectively when building them out of familiar components.
• Evaluating. We can use our knowledge of the strengths and weaknesses typically found in arguments of a certain pattern to help us rapidly appreciate the quality of a new instance of that pattern.

Example

People very frequently reason along the following lines:

If the volcano was going to erupt soon, then we’d be detecting earth tremors. There aren’t any tremors, so we are safe for the while at least.

This is an instance of a pattern which is so common and useful it has a Latin name – modus tollens. Using symbols, we can represent the pattern as follows:

If P were true, then Q would also be true. Q is not true. Therefore, P is not true.

Where P is the claim ‘The volcano will erupt soon,’ and Q is ‘We are detecting earth tremors.’

Arguments fitting the modus tollens pattern have the rather nice feature that they are valid. This means that the premises, if true, guarantee that the contention will be true. Now, suppose you are interested in evaluating the argument, i.e., determining how strong it is. If you have correctly identified the argument as an instance of modus tollens, you know right away that you can put all your efforts into investigating whether or not the premises are in fact true.

Varieties of Argument Patterns
There are dozens, perhaps hundreds, of argument patterns. These include

• Simple deductive argument forms, such as modus tollens.
• Inductive argument patterns, such as the kind of statistical generalization used in political polling.
• Argument patterns that are characteristic of particular domains, such as legal argument.
• Fallacies – commonly occurring arguments that are generally poor reasoning. And many others…

Know Thy Patterns
Developing conscious familiarity with a wide range of argument patterns is a key part of acquiring advanced skills in reasoning and critical thinking. There is a direct analogy here with the development of expertise in many other fields. A jazz musician, for example, has, through years of listening and practice, acquired deep familiarity with an extensive collection of melodies, chord sequences, rhythms, etc., enabling her to perform with apparently effortless fluidity on the night. Similarly with reasoning; argument patterns are like the riffs or musical motifs of critical thinking.

See also:

• Topics Deductive Argument, Inductive Argument, Abductive Argument and Fallacy
• Rationale Wiki on www.reasoninglab.com

Topic 20: Deductive Argument

In some arguments there appears to be a kind of irresistible logical force at work. In such cases, the contention follows inexorably from the premises; accept the latter and it seems you are rationally compelled to accept the former. Consider for example:

Figure 2.20

If you accept that every Scot is a devotee of Robert Burns, and you accept that Dougal McDowell is a Scot, you must also accept that Dougal McDowell is a devotee of Robert Burns.

Or, put another way – it is impossible for Douglas McDowell not to be a devotee of Robert Burns, if indeed he is a Scot, and all Scots are devotees of Robert Burns. This relationship between premises and contention is known as validity – technically, an argument is valid if it is impossible for the contention to be false if the premises are true.

Notice another thing about our example – it works just as well for Tania McTaggart as it does for Dougal McDowell. Indeed, we can abstract away entirely from Scots, and Robert Burns, and see that the real work is being done by the logical structure of the argument, rather than the meanings of the terms:

Figure 2.21

Figure 2.22

The original argument seemed utterly compelling, even though you probably do not know Dougal McDowell, because its logical form seemed to guarantee that the contention would follow.

A deductive argument is one which purports to be valid by virtue of its logical form.

Put another way, such a deductive argument tries to force you from its premises to its (main) contention by virtue of the way it is constructed. Perhaps it is constructed correctly, and you should in fact accept its contention if you accept its premises. But it might be poorly constructed, in which case the argument, though deductive, is invalid.

Deductive arguments are enormously important in logic, and in related fields such as mathematics and computer science. A large and often very technical sub-field of logic, known as formal logic, is devoted to the study of deductive arguments.

In ordinary or ‘everyday’ reasoning, we do often encounter deductive arguments, though generally these arguments belong to a limited number of simple types. More commonly, everyday arguments are not deductive. To determine whether or to what extent they guarantee their contentions, we must look at more than just the logical form; we need to know what the terms mean, and something about the domain those terms are describing.

Indeed, most everyday arguments do not even purport to be valid; they purport to increase the acceptability of their contentions, rather than guarantee them. There are many kinds of non-deductive arguments, but they are usually contrasted with inductive arguments (those involving some kind of extrapolation or generalization) and abductive arguments (those concerned with explaining some range of evidence).

See also:

• Topics Inductive Argument, Abductive Argument, Argument Pattern and Fallacy
• Rationale Wiki on www.reasoninglab.com

Topic 21: Inductive Argument

Of the three major kinds of arguments commonly distinguished by logicians – the deductive*, inductive and abductive – inductive arguments are probably the most common and useful.

An inductive argument is an argument in which there is some kind of extension or generalization from a situation (a ‘source’) to some wider or related situation (a ‘target’).

For example, suppose you have been given a box of chocolates, each wrapped in the same brown shiny foil. You open and eat two of them, and find that they both have a caramel syrup filling. If you conclude that all chocolates in the box have caramel filling, then you would have made an inductive inference, generalizing from the sampled chocolates to the whole ‘population’ of chocolates in the box.

Inductive Generalizations
Inductive arguments of this kind (from samples to whole populations) are known as inductive generalizations. You will be familiar with them because they get reported in the news all the time. When you hear that 87% of US citizens do not know the difference between a Sunni and a Shiite, you are hearing an inductive generalization from a sample of maybe 300 folks in places like Iowa and Ohio to their 300 million compatriots.

Inductive arguments rely on there being detectable patterns in the world. In making an inductive inference you are hoping that a new situation will be a continuation of the pattern you have seen already. If you are lucky or wise, you have identified a pattern that really does hold up.

Statistical Syllogism
An inductive argument can be driven in the other direction, from the general to the particular. Suppose you have succumbed to temptation and eaten 10 chocolates from the box; they have all had caramel fillings. You reach out for another, telling yourself that this chocolate will definitely be the last one. If you are expecting caramel again, you are expecting this particular final chocolate to continue the pattern of the previous 10. This kind of inductive inference from a more general claim to a particular case is known as a statistical syllogism.

Analogy
A third common kind of inductive argument is the use of analogy. An analogical argument picks up on the similarity between two particular situations, and extends knowledge from one to the other. For example, suppose you have eaten one chocolate with a brown silvery foil and it had a caramel filling. You pick up another, and before unwrapping it, you think

‘This chocolate seems just like the one I just ate. It probably has a caramel filling too.’ Probably unwittingly, you would have made an analogical inference.

Arguments by analogy can, of course, be much more serious. The similarities between the US interventions in Vietnam and Iraq have often been noted. One might argue that, since the Vietnam war ended in a humiliating US withdrawal, and the Iraq war is just like the Vietnam war, the US will make a humiliating withdrawal from Iraq too. Figure 2.23

Inductive arguments, like any other arguments, can be laid out in an argument diagram or map. When these arguments are made fully explicit, there will always be a premise of some kind asserting the similarity between the source situation and the target situation.

Inductive arguments are always at risk of misfiring. This happens when reality fails to conform to the pattern we think we have identified. For centuries, Europeans believed that all swans were white, making a reasonable inductive generalization from the swans in their experience. As they later found out, when black swans were found in Australia, their generalization had been confounded by nature, whose real patterns are endlessly subtle and diverse.

How can you tell how strong an inductive argument is? There is no general answer to this, but there is, fortunately, a sophisticated science of inductive reasoning. You can begin to learn this science by studying disciplines such as probability, statistics, and scientific method.

See also:

• Topics Deductive Argument, Abductive Argument, Argument Pattern and Fallacy
• Rationale Wiki on www.reasoninglab.com

Topic 22: Abductive Argument

You are walking in the park and come across a newborn chick on the ground. You look up and see a nest with a large bird glowering warily down. You can also hear chirping from the direction of the nest. You conclude, naturally, that the newborn chick had fallen from the nest.

This is abductive reasoning. In essence, it is reasoning from a body of evidence to some situation or ‘hypothesis’ that would explain the evidence. In the current example, you did not actually see the chick fall out of the nest, but you infer it probably did, because that would explain why there is a vulnerable newborn chick on the ground underneath a nest containing a mother bird and other chicks. Figure 2.24

Abductive reasoning is inferring that some hypothesis is true because it would causally explain some body of evidence.

The term ‘abductive’ is derived from the Latin ab (from) and duco (lead), conveying the idea that abductive reasoning works ‘back’ or away from some phenomenon to something prior which was responsible for it.

In its simplest form, abductive reasoning considers just one hypothesis, and assumes that the hypothesis either does or does not explain the evidence. Sometimes, multiple hypotheses are entertained (e.g., chick fell out of nest; chick was thrown out of nest; chick was placed on the ground by a researcher; etc.) and the most plausible of these hypotheses is taken to be true. In this more elaborate form, abductive reasoning is also known as ‘inference to the best explanation’.

Abductive reasoning is very common. It is the dominant form of reasoning in areas such as:

• Medical diagnosis, in which a doctor tries to identify the source of the various symptoms displayed by a patient.
• Science, which has a major goal describing the causal structure of the world, and in which scientists are constantly inferring to the truth of causal propositions (e.g., that AIDS is caused by HIV infection).
• Problem solving, in which we attempt to determine the underlying cause of some problem, such as a car failing to start.

Abductive reasoning has a striking similarity, in basic shape, to the argument pattern known as ‘Affirming the Consequent’. This has the structure ‘ If P then Q; Q therefore P’; for example, if it is raining, then it is wet outside; it is wet outside; therefore it is raining. Affirming the Consequent is a well-known fallacy of deductive logic; it has the superficial appearance of a deductively valid argument, but the premises do not in fact guarantee the contention (e.g., it may be wet outside due to melting snow).

However, abductive reasoning is not intrinsically fallacious. Abductive arguments are intended not to ‘guarantee’ their contentions, but to render them more probable. The degree to which they do this – i.e., their strength – depends on the reliability of the evidence, the plausibility of the hypothesis as an explanation of the evidence, and the relative plausibility of alternative hypotheses. Conclusions are drawn tentatively or provisionally, since it is always possible that the body of evidence may change or another, more plausible hypothesis may arise.

See also:

• Topics Deductive Argument, Inductive Argument, Argument Pattern and Fallacy
• Rationale Wiki on www.reasoninglab.com