11. Inductive reasoning II

What do analogy-based arguments look like?

An argument based on analogy is an argument that says that something has a certain property, because an equal thing has the same property. For instance:

• Bill loves fishing.
• That's why his brother Sam loves fishing.

The analogues in the example above are Bill and Sam. The conclusion analogue (Sam) is attributed a certain characteristic (to love to fish), because the premise analogue (Bill) loves to fish.

What guidelines for critical thinking about an argument based on analogy are there?

Here are a few guidelines for evaluating arguments based on analogy.

• The more similarities there are between the premise analogue and the conclusion analogue, the stronger the argument.
• The fewer similarities between the premise analogue and the conclusion analogue, the weaker the argument.
• If there is more than one premise analogue, the argument becomes stronger.
• If there is more than one premise analogue and there are not very many opposing premise analogues (a premise analogue that does not have the particular characteristic), the stronger the argument.

When it is proven that an argument based on analogy is wrong, there is "the attack of an analogy". A weak analogy (also called false analogy) is a weak argument based on unimportant similarities between two or more things.

When are you generalizing based of a sample?

You generalize from a sample when you attribute a certain trait to members of a certain population, because this is proven in a small(er) group that belongs to that population.

The most important principles for evaluating such arguments are:

• The more a-typical the sample is, the weaker the generalization. If you have a sample with primary school children, but you do this at a school for super smart children, the generalization will be weak.
• The less varied the sample, the weaker the generalization. If you do a sample that is based around racism and you only interview white people, your results will be very monotonous.
• Generalizations based on samples that are too small to mirror the entire population are weak. Three people are not very representative of a world of seven billion, for instance.

The "sampling frame" is a definition of the population and the attribute. It helps us to determine whether an individual belongs to the population and whether they have the attribute. It is therefore a part of the population (or: a sample) that we were able to determine to study. However, we do not know for certain whether the values ​​resulting from the sample are exactly the same in the population. Which party people vote for, for example, also depends on gender, age, religion and income. A sample represents a population if the variables linked to the attribute are present in the same proportion in the sample as in the population.

A sample is biased when the variable is not present in the sample in the same proportion as in the population.

The spread that is calculated differs from sample to sample, in other words: a random (or random) variation is created. This is also referred to as the error margin. The error margin can be calculated on the basis of (1) the sample size and (2) the confidence level. The confidence level shows the probability that the proportion found in a sample falls within the margin of error. A sample can be increased to reduce an error margin. In colloquial language we use informal terms to indicate the likelihood that a conclusion is true, for example by using terms such as "likely" and "it is almost certain that ...".

A random sample is therefore not completely free of biases, because the variables are still vulnerable to random variation.

Statistical syllogisms

If you want to reason from general to specific, it has the following form:

• "Most X’s are Y’s."
• "This is an X".
• Conclusion: "That is why this is (also) a Y".

Example:

• "Most teachers (X) are SP voters (Y)".
• "This is a teacher"
• Conclusion: "That is why he / she is an SP voter".

In the example you find above is an inductive syllogism (also called statistical syllogism). The power of an inductive syllogism depends on the general statement, namely "Most X’s are Y’s". If this is not correct, then the conclusions that result from this statement are not correct either. The more often most X’s and Y’s are (for example, the more often teachers appear to vote for the SP), the stronger the argument is that someone who is a teacher should be an SP voter.

What are causal statements?

A causal statement describes the cause of a certain event. A causal hypothesis is a statement describing that X causes another variable (Y). It is important that a certain causal pattern is not incorrectly described. Three principles apply:

1. When something unusual happens, this does not necessarily have to be the cause of what follows. It is therefore important to look at whether something else unusual happened at the same time that could also be an explanation. This is called the paired unusual events principle.
2. Common variable principle: a variable that is common to multiple appearances of something can be related to causality. As; "20 men went out to eat yesterday and now 5 of those have abdominal pain. These 5 all ordered the chicken yesterday. The chicken is therefore the common variable here.
3. Covariation principle: when a variable in one phenomenon is accompanied by the variation in another phenomenon, there is covariation or correlation. There is then no direct causality. For example: it is assumed that X → Y. However, there is a third variable (the covariate) that causes X to lead to Y. This is noted as: X → Z → Y.

Methods to confirm causal statements

In a randomized experiment, subjects are randomly assigned to one of the conditions: the experimental condition or the control condition.

Observational studies are not experiments. The researcher does not manipulate the allocation of people to a certain group. The groups are merely observed. A distinction is made here between a prospective (something that has yet to take place) and a retrospective (something that has already taken place is being investigated) design.

Calculating statistical opportunities

If we want to calculate the probability that two independent events occur together (X and Y), then we need to multiply the probability of X and the probability of Y with each other. Many people go wrong and add up the chances. However, if we want to calculate the probability that one of these two events occurs (X or Y), then we add the probabilities of X and Y together.

The estimated value is the result of how much you expect to win combined with the amount that you can win. If the estimated value is greater than 0, it makes sense to take the gamble.

Practice questions

1. What is a proposition? What is the difference between a single and compound proposition? What is the role of conjunctions in this?
2. What is fallacy? Why is verification also called "fallacy of the consequences"? Explain this on the basis of the reasoning scheme (syllogism) of verification and the accompanying truth table.
3. What are physical causal explanations? What are behavioural causal explanations? This question is based on the 10th edition of the book
4. What is meant by the Best Diagnosis Method? What is this method used for? What is the role of background knowledge in this? This question is based on the 10th edition of the book
5. a What is an argument based on analogy?

b. Which parts does such an argument consist of?

6. When is there generalization?
7. Which three principles apply to a causal statement?
8. What methods are there that can be implemented to confirm or deny a causal statement?

Answers

1. A proposition is a statement that can be true or false, it cannot be further simplified (Paul is at home -> true or false). A single proposition is a single proposition. A compound proposition consists of 2 propositions that can be connected to each other in various ways by joining (eg A and B).
2. A fallacy is a proposition that cannot be verified on the basis of an argument, because this argument is missing, or because the argument does not apply to the proposition.

Suppose: "If P then Q" = 1 and Q = 1 then P can be both 1 and 0. You can see this in the first and second to last line of the truth table. Verification therefore provides no certainty and is also referred to as the fallacy of the consequence (fallacy of the consequent). Verification is used in testing and accepting hypotheses, but according to the proposition logic therefore gives no certainty. The hypothesis is correct with regard to the observation, but can also be caused by something completely different.

3. Statements and arguments are different things, but they can have something in common. Declarations can be used as an argument, namely as a premise and as a conclusion. There are many kinds of explanations. Two of these are: (1) physical causal statements and (2) behavioural causal statements.

• 1. Physical causal explanations

With a physical causal explanation, a causal explanation is requested for an event in terms of the physical background. The physical background is about the general conditions in which an event has occurred. Examples of these general conditions are temperature or humidity. Often these conditions are not specifically highlighted because we already know them. When the conditions are not expected, it is often necessary to specifically highlight them. The physical background of an event is also about the direct cause of an event. However, in reality, multiple causes contribute to an event. Our interests and knowledge determine which link in a causal chain we identify as the cause of the event. Examples of questions that deal with physical causal explanations are: "How come my tape is empty?", "How come I have high blood pressure?", "Why are some species extinct?" “How does global warming come to be?'

• 2. Behavioural causal statements
• When we ask ourselves what the cause of a behaviour is, a behavioural causal explanation is sought. This happens in terms of reasons and motives. Just as with physical causal explanations, behavioural causal explanations often also contain relevant background information and an attempt to determine the cause of the behaviour. The causal background is often about political, social, economic and psychological factors. It is important to distinguish between a reason for doing something and a specific reason for a person doing something. There may be a specific reason why someone helps a homeless person, but the same reason may not be the basis of other people's helping behaviour. With a "reason" for doing something we give an argument why someone does something and with a "specific reason for doing something" we explain why someone does something. Examples of behavioural causal statements are: "Why did the board not approve the contract?", "Why was Emma opposed to the idea?", "Why do people fight?" And "Why do butlers get paid more when they have an English accent?”

4. The "Best Diagnosis Method" is different from the Method of Difference or the Method of Conformity. It is about the best explanation of various symptoms when diagnosing a disease. However, this method can also be used in other non-medical situations. When a murder is committed, the clues can serve as "symptoms," while the murder can be called "disease." In this case, the best possible explanation of the murder is called the "Best Diagnosis Method."
5. a. An argument based on analogy is an argument that something has a certain property, because an equal thing has the same property.

b. Such an argument consists of two analogues: a premise analogue and a conclusion analogue.

6. You generalize from a sample when you attribute a certain trait to members of a certain population, because this is proven in a small group.
7. Three principles apply here: the "paired unusual events principle", the "common variable principle" and the covariate principle.
8. These methods are (1) a randomized experiment, (2) prospective observational study, and (3) retrospective observational study.