# DEDUCTIVE REASONING

### Deduction can lead to conclusions or predictions based on existing knowledge.

DEFINITION: Deductive reasoning can construct arguments that are "truth preserving" (Layman, 2005; Giere, 2006). Truth preserving means that the truth of conclusions is contained within the  "sphere” (i.e. the domain, range, scope) of true premises. Therefore, if the sphere of the premises includes the conclusion, and the premises are true, then the conclusion will also be true.

Deductive reasoning is useful for making predictions based on things that we already know. For example, we could make the simple argument:

PREMISE: The sun always comes up in the morning

CONCLUSION: Therefore, tomorrow morning the sun will come up.

Because we know that the sun always comes in the morning (i.e. it's a "fact"), we can conclude that the sun will come up tomorrow. The sphere of the premises (all mornings) includes the conclusion (tomorrow morning). Therefore, if it is true that the sun always comes up in the morning, then the truth will be "preserved" and apply to tomorrow morning.

Formal logic and mathematics both use deductive reasoning. Similar to mathematical proofs, deductive reasoning can establish the truth of conclusions based on appropriate and true premises. For example,

PREMISE: All mammals have hair

PREMISE: No lizards have hair

CONCLUSION: Therefore, no lizards are mammals.

The premises of the preceding argument are termed "categorical" premises because they apply generally to large categories of things (e.g. mammals and lizards, respectively). Consider also the following argument:

PREMISE: No mammals lay eggs

PREMISE: Echidnas lay eggs

CONCLUSION: Therefore, echidnas are not mammals.

Does the second argument seem reasonable?

Based on the facts (premises) presented to you, it is reasonable to conclude that echidnas are not mammals, because echidnas lay eggs and mammals don't. The argument is a valid example of deductive reasoning because the conclusion follows reasonably from premises that are demonstrably true or false.

HOWEVER, premises are not always true! Echidnas do lay eggs, but they also ARE mammals (Nicol and Andersen, 2007). The first premise of the argument is false: some mammals actually DO lay eggs. Therefore, the conclusion of the argument is also false.

Some useful terminology can help to understand deductive arguments.

DEFINITION: A "valid" deductive argument is a deductive argument where IF the premises are true, then the conclusion is also true (Cavender and Kahane, 2018).

Validity depends on the structure of the deductive reasoning. If a deductive argument is structured in a valid way, then true premises will lead to true conclusions. Valid arguments are therefore "truth preserving."

DEFINITION:  A "sound" deductive argument is a valid argument with true premises (Cleave, 2016).

Soundness depends on the content and the structure of deductive reasoning. To be sound, an argument must be well-structured and also must have true premises.

Therefore, the argument about echidnas WAS valid because the conclusion would reasonably follow from true premises. However, the argument was NOT sound because not all of the premises were true.

Deductive reasoning is critical for science (Popper, 1934). Specifically, SYLLOGISMS represent the simplest deductive arguments. Using GRAPHICAL FRAMEWORKS can help to put deductive reasoning into practice. However, when constructing arguments, we must be sure to avoid using deductive FALLACIES.