Use deductive arguments when you intend to create a valid argument with true premises and a true conclusion. Sometimes, however, you can’t make a valid argument that proves your point, so you must use inductive arguments to win your audience.

Suppose, for example, you want to argue that the sun will rise tomorrow. Can you create a valid argument, a sound argument, or a proof to support your conclusion? To answer the question, let’s review a few definition.

An argument is

validif and only if the conclusion is necessarily true, given that the premises are true. Similarly, an argument isvalidif and only if the conclusion cannot be fals while the premises are true. Finally, and argument isvalidif and only if the conclusion would have to be true, were the premises to be true.An argument is only

soundif and only if it is valid and has all true premises.An argument is a proof if it is known to be sound. In other words, a proof is an argument that is known to be sound and known to have all true premises.

Let’s try to argue deductively in favor of tomorrow’s sunrise:

In the past, the sun has risen every day.

∴ The sun will rise tomorrow.

Here, the premise is true, but the conclusion is *not necessarily* true. The fact that the sun has, so far, risen every day has no bearing on whether it will rise tomorrow. The conclusion is *reasonable*, but it is *not necessarily true*. The above argument is, therefore, an *inductive argument*.

## Inductive Arguments: Making your point despite invalidity

### Identifying inductive arguments

#### Language

Deductive arguments use words such as: “Necessary,” “certainly,” “Has to be,” or “conclusively.”Inductive arguments use words such as: “Most likely,” “Probably,” “likely,” or “it is reasonable to believe”

#### Structure

Structure – valid arguments are ipso facto deductive. Invalid arguments come in a variety of forms including:

Polls and samples.

Predictions about the future.

Arguments to establish causal conclusions (such as analogies and arguments from authority).

#### General or particular

Discern whether a statement begins with the general vs. particular. Deductive arguments usually begin with general statements and lead to particular ones.

For example:

P1: All dogs are mammals.

P2: Hucleberry Hound is a dog.

∴ Huckleberry Hound is a mammal.

Inductive arguments begin with particulars and end with generalizations.

For example:

P1: Most people I’ve seen are shorter than seven feet tall.

∴ Most people are shorter than seven feet tall.

#### The “add a premise” test

Deductive arguments are complete. Also, they are either valid or invalid. Adding a premise to a deductive argument cannot improve it. Inductive arguments, on the other hand, can increasingly be strengthened by adding information to them.

Consider the following argument:

P1: I’ve eaten four pizza’s from Columbo’s Pizza. They were all fantastic.

∴ All pizzas from Columbo’s Pizza are fantastic.

The above argument can be improved by eating more pizzas from Columbo’s Pizza.

#### Consider the discipline

You’ll find that disciplines that aim to prove conclusions such as mathematics, law, ethics, religion and philosophy. Inductive arguments emerge from disciplines that depend on experiments for their conclusions (biology, sociology, psychology, etc.).

## Five Types of Inductive Reasoning (Arguments)

Inductive arguments depend on premises that cannot absolutely support their conclusion. Good and bad inductive arguments exist. Formulating an inductive argument requires you to invoke premises that strongly support your conclusion.

The strength of your premises directly affects the success of your argument.

With an inductive argument, you always have an invalid structure (You can have true premises and a false conclusion).

**1. Enumerative Induction**

An *enumerative induction* takes the following form:

All observed P have F.

∴ All P have F.

An argument that assumes that a sample of a population represents the entire population. Consider the following examples:

P: All observed swans are white.

∴ All swans are right.

P: All observed emeralds are green.

∴ All emeralds are green.

**Conditions of Strength**

**2. Statistical Generalization**

An inductive argument that takes the following form uses *statistical generalization* as its basis:

P: R% of observed P have F.

∴ Roughly R% of P have F.

You can use a percentage or use terms such as “most”, “almost all”, and “many”. Consider the following examples:

P: Most people I know like pizza

∴ Most people like pizza

-Conditions of strength: the number of observed P is sufficiently large and varied; the margin of error is small enough to support the conclusion

#### Conditions of Strength

### 3. Statistical Syllogism

A syllogism is a construct that draws a conclusion from two stated or implied premises having a term in common with the conclusion and a common term not present in the conclusion. A statistical syllogism is one that uses statistics in its first premise. Consider the following form:

P1: R% of P have F.

P2: m is a P.

∴ m has F.

P1: 98% of Republicans are conservative

P2: Mike Huckabee is a Republican.

∴ Mike Huckabee is a conservative.

#### Conditions of Strength

A statistical syllogism is strong when m is a typical P and R% is greater than 50%.

### 4. Argument from Analogy

P1: A is like B.

P2: B has F.

∴ A has F.

P1: This Toyota Corolla is like other Corollas

P2: Toyota Corollas are durable.

∴ This Toyota Corolla is durable.

#### Conditions of Strength

An argument from analogy is strong when the number of B is sufficiently large and varied and A is like B in all relevant respects.

**5. Argument from Authority**

X says “A.”

∴A

Prof. Jones says table salt is NaCl.

∴Table salt is NaCl.

#### Conditions of Strength

The following conditions indicate strong inductive arguments from authority:

- X is an expert on A.
- No other experts disagree with X.
- X is honest.

## Criticizing Inductive Arguments

When criticizing deductive arguments, you must attack the premises to persuade your audience that one or more of them are false. Such a process involves the use of a *counterexample*. You can also create a counter argument to prove the invalidity of a conclusion. Argument B is a counterargument to Argument A if (and only if) they both have the same form and both have true premises and a false conclusion. Inductive arguments are different.

An inductive argument is one where the premises are intended to offer good, but inconclusive, support for a conclusion.

The lack of a definitive conclusion complicates your effort to criticize an inductive argument. Still, you *can* do it.

## Criticizing inductive arguments

### 1. show a premise to be false.

**P1:** 40% of respondents to the poll will vote for Donald Trump to be President.

**∴** About 40% of all voters will choose Donald Trump.

Here, you can question the honesty of the respondents. Some people were planning to vote for Trump, but would not *says* so. Also, as Wikileaks proved during the 2016 election, you should also question the honesty of the pollster. Either way, you could show that the conclusion is false.

### 2. Showing that an argument violates a condition of strength:

#### i. demonstrate unwise statistical generalization

Prove that the sample used in the experiment did not accurately represent the overall population. Sample size can directly impact the *margin of error* of a poll. For example, a survey might require 4,000 samples to get a plus or minus two percent error.

#### ii. prove an invalid comparison

Suppose someone argued:

Life is unpredictable like a box of chocolates – or – life is like a baseball game.

You could argue that a box of chocolates is predictable when it has a map identifying the various candies. A baseball game a finite set of well-defined rules by which everyone plays. Life has many undefined rules, and many people do not recognize the same rules that you follow.

#### iii. arguing from authority

You can often defeat an inductive argument by attacking the authority of the arguer. For example, someone who has no experience or education in nuclear science might Successfully argue about the nature of radiation. You can also discredit the honesty of the arguer or show that she is arguing based on her financial prosperity, not on an objective review of the evidence (ad hominem abusive).

#### iv. Statistical Syllogism

The percentage of a sample must be greater than 50. The sample must be typical. Is a sample the same as the group?

### 3. Criticize the conclusion

Explain that the conclusion does not follow the stated premises.

## Three supports for inductive arguments

Let’s take a look at three common types of support for inductive arguments: Correlation to cause, controlled experiments and natural experiments.

### Causal Reasoning

P1: C is correlated with D.∴ C causes D.

*correlation does not prove causation*.

**Using experiments**

### Controlled Experiments

#### Conditions of strength

- The control group and experimental groups must be similar in every relevant respect.
- Both groups must be sufficiently large and varied.

Of course, you should always remember that exposing flaws in the conditions of strength can negate the potential of a controlled experiment. Suppose:

### Natural Experiments

*controlled*experiment, you can allow the forces of nature and natural circumstances form the basis for an inductive argument.

*not*exposed to radiation. You’d have trouble performing such an experiment in a controlled environment because of the moral and ethical issues involved. However, natural forces set the stage, so you have an experiment that might support your inductive argument that, for example, exposure to radiation negatively impacts cognition.

*prospective study*that looks forward based on a given cause, or a retrospective study that tries to determine if an effect has already occurred.

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