# INDUCTIVE REASONING

### Inductive reasoning can lead to new knowledge.

__DEFINITION__: Inductive reasoning constructs arguments that are "knowledge expanding" (Giere, 2006). *Knowledge expanding* means that conclusions of arguments *exceed* the sphere of the premises. In experimental science, inductive reasoning typically involves *generalizing* based on a set of observations (although other forms of induction such as analogies are possible; Moore and Parker, 2017).

For example, we could construct an inductive argument about why we are confident that the sun comes up in the morning:

__PREMISE__: Every morning for recorded history, the sun has come up.

__CONCLUSION__: Therefore, the sun always comes up in the morning.

Our set of observations is all days in recorded history where the sun has come up (hundreds of thousands). From our repeated observations, we conclude the more general statement that the sun always comes up in the morning.

__QUESTION__: Is it reasonable to consider the statement "the sun always comes up in the morning" to be *true*?

Clearly, inductive reasoning is very *useful*. Once we have confidence in a statement like "the sun always comes up in the morning," then we can use the statement to make predictions and plans. For example, we can count on having enough light tomorrow morning to safely bike to work.

We can use inductive reasoning to come to LOTS of conclusions to try to expand our knowledge. For example, three more arguments that also use inductive reasoning could be:

1) __PREMISE__: All pigeons in central park are black.

__CONCLUSION__: Therefore, all pigeons are black.

2) __PREMISE__: All of the students who come to office hours really like my class.

__CONCLUSION__: All of the students in my class really like the class.

3) __PREMISE__: I always run red lights.

__CONCLUSION__: Everyone always runs red lights.

Are all of the conclusions of these three inductive arguments true?

It might seem that there are some problems with the three inductive arguments listed above. For the first argument, it may not seem reasonable to extrapolate from one population to an entire species (i.e. pigeons). For the second argument, it seems entirely possible that students who don't like the class simply do not come to office hours. The third argument crosses the line to ridiculousness: judging everyone's behavior on one person is clearly not reasonable (even if the person is you). Therefore, not all inductive arguments lead to true conclusions. Inductive arguments may lead to __false__ conclusions *even if* all of the premises are true!

Because the conclusions of inductive arguments can be false even if all of the premises are true, we might be tempted to dismiss induction altogether as fallacious reasoning. However, there is one slight problem:

__Induction is the only way we understand anything about the universe (__Hume, 1748

__)!__

As pointed out by the philosopher David Hume, we ultimately acquire ALL of our general understanding from inductive reasoning (although all knowledge we acquire is also influenced by the way we acquire and process information leading to intrinsic biases; Kant, 1787). Statements such as "the sun always comes up in the morning" are developed *inductively* from observations. Even the most rigorous deductive frameworks need induction to generate hypotheses and rules. Therefore, it is important to understand the possibilities and limitations of inductive reasoning.

1) __POSSIBILITIES__

Inductive reasoning allows us to expand our knowledge. Through observation and inductive reasoning, we can develop new generalizations. Additional observations that are consistent with our generalizations can *strengthen our confidence* in the generalizations.

In science, we often term generalizations "hypotheses." One role of hypotheses is to act as explanations or models of the world we live in (Giere, 2001). Inductive reasoning is one way of gaining confidence that our explanations/models of the world are useful (or "true"). We often seek to find a convergence (or "consilience") of different types of evidence that __all__ support the same explanation or model in different ways. Therefore, induction is one way of gaining confidence that hypotheses are useful models of the world.

Consequently, inductive arguments form a continuum. "Weak" arguments have little evidentiary support (few observations supporting the argument). "Strong" inductive arguments have strong evidentiary support (many diverse observations supporting the argument). Structured investigation (e.g. using Hill's Criteria) can result in more and more observations that support an inductive argument (Hill, 1965).

Therefore, strong inductive arguments (and consequently knowledge about the world) is *possible*.

2) __LIMITATIONS__

Inductive reasoning is limited because we cannot "prove" (know with 100% certainty) *anything* through inductive reasoning! Inductive reasoning is limited in the same way that deductive arguments cannot "Affirm the Consequent."

For example, induction could be seen as many deductive arguments together:

__PREMISE__: Hypothesis H1 Leads to predictions A,B,C,D,E,F,G

__PREMISE__: Observations A',B',C',D',E',F' and G' are __consistent__ with predictions A,B,C,D,E,F,G

__CONCLUSION__: Observations A',B',C',D',E',F' and G' *support* Hypothesis H1.

However, because the argument has the same structure as arguments that "Affirm the Consequent," the argument is NOT deductively valid and therefore NOT necessarily truth preserving. We CANNOT be 100% sure of anything we determine through inductive reasoning.

The implications of the limitations of inductive reasoning are __enormous__ (as identified by David Hume). We CANNOT be 100% sure even of statements like "the sun always comes up in the morning" (Hume, 1748). It is *possible* that that there is some quirky law of physics that will cause the sun to *not* come up on the morning of October 20, 3040 because it is such a nice number. Moreover, it might be impossible for us to discover the law before 10/20/3040. However, we cannot prove that something does NOT exist either. Because there are an infinite number of things that are possible but we simply don't know, we cannot be 100% sure of even the most certain information that we have.

In terms of science, there is no way to "prove" hypotheses using induction for the same reason that there is no way to "prove" hypotheses using deduction. There is simply no way of being 100% certain of ANYTHING in science. Therefore, although "proof" remains useful and valid in the realms of mathematics and formal logic, in experimental science we can only __strengthen our confidence__ in particular models, not achieve the certainty of "proof" (Giere, 2006).

Consequently, the terms "valid" and "sound" *do not apply* to inductive arguments. Inductive arguments cannot be either valid or sound, only "strong," "weak," or some intermediate judgment of strength (Layman, 2005). The word "prove" should be reserved for mathematics, and should not be used when discussing empirical conclusions.

Similar to deductive reasoning, inductive reasoning has common flaws that are sometimes called "INDUCTIVE FALLACIES." Knowing about common inductive fallacies may help to identify and avoid them when making inductive arguments.