Critical Thinking Skills TEST

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Thomas Francis University • Course G120 • Segment 2

DEDUCTIVE VS. INDUCTIVE REASONING

—Douglas R. Kelley, PhD, CH, CSL

Updated: October 11, 2021

Upon Completion of this Segment, You Will Know:

• The nature of deductive reasoning.

• The nature of inductive reasoning.

• Formal vs. informal reasoning.

• The meaning of “inference” vs. “implied.”

It is the mark of an educated mind to be able to entertain a thought without accepting it.

— Aristotle

will be the first to admit that trying to understand the differences between deductive and

inductive reasoning can be quite daunting—especially if one conducts research online. Most of

the explanations are either hopelessly ambiguous or they are outdated. Some describe deduc-

tive and inductive reasoning as opposites, which is not entirely true. Either way, one wonders if

anyone with an IQ below 4,000,000 truly comprehends the differences in all of their various forms.

To make things worse, some dictionaries define “deductive reasoning” as going from the general

to specific, and “inductive reasoning” as going from the specific to the general. However, these

definitions are rather outdated because the opposites can also be true.1 Furthermore, these diction-

ary definitions are difficult to understand in practical terms. Fortunately, there are better and easier-

to-understand definitions available that actually make sense.

Some ways to remember the difference between deductive and inductive thinking are:

1. With deductive thinking, if the premises are true, the conclusion is guaranteed to also

be true. If you change the premise(s), you also change the conclusion.

2. With inductive thinking, if the premises are true, the conclusion is likely to also be

true. If you change the premise(s), you may or may not also change the conclusion.

3. Deductive thinking deals with the “what” whereas inductive thinking deals with the

“why and how.”

1 The Internet Encyclopedia of Philosophy, http://www.iep.utm.edu/ded-ind/.

Segment 2: Deductive vs. Inductive Reasoning

4. And my favorite is how Jessica G., one of my students, described it on her final exam

for this course: “Deductive reasoning deals with facts. Inductive reasoning deals with

possibilities.”

Deductive Reasoning

A valid deductive argument is one that, if the premises are true, the conclusion is guaranteed to

also be true. Therefore, the conclusion naturally and necessarily follows the premises. For example:

1. All men have minds. (true premise)

2. DaVinci was a man. (true premise)

3. DaVinci had a mind. (true conclusion)

So in a nutshell, deductive reasoning means arriving at a guaranteed conclusion based on facts. It

should also be noted that in deductive reasoning, if you change the premise(s), you change the con-

clusion.

A key indication that an argument is deductive rather than inductive is if words such as must,

certainly, and necessarily are used in the argument.

Two other components of deductive arguments are known as validity and soundness. The example

above is considered to be valid and sound. While these two components are rather simple conceptu-

ally, they can be difficult to grasp. Adding to the confusion is that the words “valid” and “sound”

generally mean the same thing in everyday language. To keep it simple, think of these words more

as designations (names) than definitions when describing a deductive argument. Let me explain each

one separately.

An argument is “valid” if and only if it is logically impossible for its conclusion to be false when

all of its premises are true.1 The use of the word “valid” here is simply referring to the form the

argument takes. For example, consider the form of the same example I just used:

Example 1: Valid Argument

1. All A are B;

2. C is equal to A;

3. Therefore, C is equal to B.

1. All men (A) have minds (B). (true premise)

2. DaVinci (C) was a man (A). (true premise)

3. DaVinci (C) had a mind (B). (true conclusion)

With this example, if the premises are true, the conclusion must also be true. Therefore, this

argument is considered to have a valid form and is called a “valid” argument.

Conversely, an argument is “invalid” if it is logically possible for its conclusion to be false even

when all of its premises are true. Again, the use of the word “invalid” here is simply referring to the

form the argument takes. An example of invalid form from Example 1 would be:

1 California State University, Northridge, http://www.csun.edu/~vcoao087/200/Validity.pdf.

Segment 2: Deductive vs. Inductive Reasoning

Example 2: Invalid Argument

1. All A are B;

2. C is equal to B;

3. Therefore, C is equal to A.

1. All men (A) have minds (B). (true premise)

2. DaVinci (C) had a mind (B). (true premise)

3. DaVinci (C) was a man (A). (not necessarily a

true conclusion)

At first glance, the second example still seems to make sense. However, what if we are talking

about DaVinci’s mother? It’s a possibility and therefore, the argument is “invalid” because the con-

clusion could be false even though the premises are true. Of course, one or more of the premises

could also be false, but it wouldn’t change anything. The argument would still be considered “inva-

lid.” Please also note that the format of the argument on the left side of Example 2 is good. The

problem is with the wording on the right side.

Again, an argument is “valid” if and only if it is logically impossible for its conclusion to be false

when all of its premises are true. With this in mind, it is important to note that just because the

premises are false doesn’t mean that the form of the argument is invalid. You have to think of a valid

argument in this way: If the premises were in fact true, then the conclusion would also be true. To

illustrate this, ponder the examples of valid arguments below.1 If the premises were in fact true,

then the conclusion would be true as well. Don’t let the fact that some of the premises are false

confuse you. All we’re looking at here is the form of the argument. We do not yet care if the premises

are right or wrong (that will come next).

Example 31 Example 41

All whales are fish. (False)

All fish are cold-blooded. (True)

Therefore, all whales are cold-blooded. (False)

All whales are fish. (False)

All fish live in water. (True)

So, all whales live in water. (True)

Example 51 Example 61

All whales are fish. (False)

All fish suckle their young. (False)

Therefore, all whales suckle their young. (True)

All whales are mammals. (True)

All mammals suckle their young. (True)

So, all whales suckle their young. (True)

Each of these arguments represents valid form even though some have false premises and one has

a false conclusion. Each argument is valid because if all its premises were in fact true, its conclusion

would also have to be true. Take number 3 above for example. If it were true that whales are fish,

and if fish are cold blooded, then the conclusion that whales are cold blooded would logically have

to be true as well. Therefore, the argument is valid.

Now, let’s address the issue that some of these arguments actually have false premises. This brings

us to the component of “soundness.” An argument is considered to be “sound” if and only if it is valid

1 Source: California State University, Northridge, http://www.csun.edu/~vcoao087/200/Validity.pdf.

Segment 2: Deductive vs. Inductive Reasoning

and all of its premises are true, otherwise, it is “unsound.” Using the examples just above, we already

know that the form is valid, so the next thing to do is to ask which examples have premises that are

all true. Obviously, only number 6 qualifies because it is the only one that is completely true. There-

fore, number 6 is considered to be a “sound” argument whereas the others are considered to be

“unsound” arguments.

Just for added clarity regarding “valid” and “sound,” the two previous paragraphs state that Ex-

amples 3 - 6 above are valid, but only Example 6 is sound. Therefore, a deductive argument that is

valid is not necessarily logically sound.

Deductive arguments are somewhat limited in nature because they produce no new information;

they are limited to known facts and simply rearrange the same information. For example, if you

change the premise(s), you change the conclusion. Deductive reasoning is often used in mathematics

and for certain scientific purposes. This is why inductive reasoning is also necessary in many, if not

most, critical thinking situations. Inductive arguments have much broader application because they

are not limited to facts.

Inductive Reasoning

Inductive reasoning/arguments are also called “ampliative” reasoning/arguments. An inductive

argument is one that, if the premises are true, the conclusion is likely to also be true. Notice how

this differs from a deductive argument which says that the conclusion must be true if the premises

are true. It should also be noted that unlike deductive reasoning, with inductive reasoning, if you

change the premise(s), you may or may not also change the

conclusion. In some cases of inductive reasoning, if you

change a premise(s), the likely conclusion may not change.

An example of an inductive argument would be:

1. Socrates was Greek. (premise)

2. Most Greeks eat fish. (premise)

3. Socrates ate fish. (conclusion)1

In this example, both premises represent strong evidence

which, in turn, suggest that the conclusion is probable or

likely. However, it is still possible for the conclusion to be false—especially if Socrates hated fish.

So in a nutshell, inductive reasoning means arriving at a probable conclusion based on strong

evidence.

A key indication that an argument is inductive rather than deductive is if words such as probably,

likely, possibly, potentially, good reason to believe that, and reasonably are used in the argument.

Validity and soundness are not used with inductive arguments, but “cogent” is. An inductive ar-

gument is considered cogent when the premises are true and the evidence is strong. It corresponds

to the deductive word “sound.”

1 About.com. http://atheism.about.com/od/criticalthinking/a/deductivearg.htm.

Huh? Deductive Reasoning

If the premises are true,

the conclusion is logically

guaranteed to also be

true.

Inductive Reasoning

If the premises are true, the conclusion

is likely to also be true.

Segment 2: Deductive vs. Inductive Reasoning

Formal vs. Informal Reasoning

Two other terms you should be aware of are formal and informal reasoning. Formal reasoning is

simply deductive reasoning because it employs a logical “form.” Informal reasoning is simply the act

of thinking, hence, inductive reasoning. Both can be forms of critical thinking.

Inference

A word often associated with critical thinking is “inference” which means to derive a conclusion

by deductive or inductive reasoning. “Infer” is similar to “imply,” but the usage is different depending

on the perspective. “Imply” means to state something indirectly, whereas “infer” means to draw a

conclusion. As is discussed in Course G100: Personal and Professional Intercommunication Skills,

every message has a sender and a receiver. The sender “implies” and the receiver “infers.” In other

words, to imply means to put a suggestion into a message while to infer means to take a suggestion

out of a message. For example:

Wrong: Are you inferring that our consciousness survives death?

Right: Are you implying that our consciousness survives death?

Wrong: I imply from what you are saying that the mind is actually nonlocal.

Right: I infer from what you are saying that the mind is actually nonlocal.

Wrong: The writer inferred that unconditional love was, in fact, conditional.

Right: The writer implied that unconditional love was, in fact, conditional.

Wrong: The conclusion is inferred by the premises.

Right: The conclusion is implied by the premises.

Wrong: Based on the premises, we can imply a conclusion.

Right: Based on the premises, we can infer a conclusion.

We generally use the terms infer or inference in conjunction with deductive or inductive reason-

ing, but “imply” may also be fitting depending on the context.

PRACTICE MAKES PERFECT

Now that we’ve explained and explored the basic nature of critical thinking, we will apply these

skills in the next segment by reasoning on a few examples.

Please note that in the video below, “inductive” arguments are referred to as “ampliative” ar-

guments.

Segment 2 Supplemental Video: Critical Thinking Fundamentals 1

NOTE: Before proceeding to the next section, please listen to the audio above on

the Course Page for a supplemental discussion of this section. This audio is part of

the course.

1 Video Source: youtube.com/watch?v=Cum3k-Wglfw