What Is Deductive Reasoning? | Definition & Examples
Deductive reasoning involves forming a specific conclusion from general premises.
A deductive argument typically starts with a broad principle, applies it to a particular situation or example, and leads to an inevitable conclusion.
- Premise: All humans are mortal.
- Premise: Socrates is human.
- Conclusion: Therefore, Socrates is mortal.
This classic example of deductive reasoning begins with a broad principle and then applies that principle to a particular person. The premises lead inevitably to the conclusion, which makes a more specific claim than the premises.
Deduction is the mode of reasoning used in formal logic, which has applications in mathematics, logic, science, and law. In everyday decision-making and thought processes, deductive reasoning often falls into the category of “common sense” thinking.
Table of contents
- What is deductive reasoning?
- Deductive reasoning vs inductive reasoning
- Deductive reasoning examples
- Types of deductive reasoning in logic and argumentation
- Valid vs invalid deductive arguments
- Deductive reasoning and logical fallacies
- Hypothetico-deductive reasoning in research
- Frequently asked questions about deductive reasoning
What is deductive reasoning?
Deductive reasoning is the process of applying broad rules, hypotheses, or truths, to specific situations to form conclusions that must follow logically. It’s used to establish proofs, test hypotheses, and verify classifications.
In daily life, we use deductive reasoning in problem-solving, decision-making, pattern recognition, and categorization to draw logical conclusions from established rules or observations.
Deductive reasoning is often defined in contrast to inductive reasoning.
Deductive reasoning vs inductive reasoning
Deductive reasoning moves from general to specific, whereas inductive reasoning moves from specific to general.
- Deductive reasoning: Applying broad principles to specific instances
- Example: “All marine mammals breathe air. Dolphins are marine mammals. Therefore, dolphins breathe air.”
- Inductive reasoning: Inferring broad hypotheses from specific data or observations
- Example: “Societies with higher education funding experience better economic growth; therefore, boosting education funding will enhance economic growth.”
Induction involves drawing conclusions that extend beyond the scope of the initial premises and can be further supported by empirical evidence. Deduction, however, produces conclusions that can be inferred from the premises alone, providing certainty without the need for additional testing.
In contrast with deduction, all forms of ampliation yield conclusions that extend beyond the scope of the premises and can be strengthened by further evidence.
Deductive reasoning examples
Examples of deductive reasoning are common in day-to-day life. For instance, every time we make calculations, we use deduction.
- All items are subject to a 10% sales tax.
- A box of cereal costs $7.
- Therefore, the sales tax on the item is $0.70, making the total cost $7.70.
This argument deduces the specific outcome (the total cost of the cereal) from a general rule (10% sales tax), demonstrating a clear, logical progression from the premises to the conclusion.
In casual communication, it’s rare to see deductive reasoning presented in the form of an explicit argument.
However, it’s relatively common to find explicit examples of deductive arguments in certain professional and academic domains such as mathematics, logic, law, and science.
- If an entity requires a host to reproduce and metabolize, it is not alive.
- Viruses require a host to reproduce and cannot sustain metabolism independently.
- Therefore, viruses are nonliving.
A deductive argument can be made for the idea that viruses are not living creatures based on one prevalent definition of life. The argument is deductive because it applies a broad definition to a specific case (viruses).
In programming, computers use deduction to draw logical conclusions based on given rules or conditions.
- All values greater than 100 are considered outliers.
- 124 is greater than 100.
- Therefore, 124 is an outlier.
Computers use deductive reasoning for many of their processes, applying programmed rules or conditions to data, allowing them to make logical inferences and draw conclusions based on given information.
In law, deductive reasoning is commonly used to apply established legal principles to specific cases or situations.
Lawyers and judges deduce logical conclusions from legal rules, statutes, precedents, and evidence.
- All contracts require mutual consent from both parties to be legally binding.
- This contract was not signed by representatives from both parties.
- Therefore, the contract is not legally binding.
In this legal scenario, the conclusion about a specific contract is logically deduced from the broad legal principle in the first premise.
Types of deductive reasoning in logic and argumentation
Deduction is central to formal logic and is expressed through formal arguments, or syllogisms, which comprise two premises followed by a conclusion that must be true if the premises are true.
There are three main categories of syllogisms:
- Hypothetical syllogisms (or conditional syllogisms) form inferences from conditional (if—then) statements (e.g., “If a shape is an octagon, then it has 8 sides. This shape does not have 8 sides. Therefore, this shape is not an octagon.”); examples include modus ponens and modus tollens
- Disjunctive syllogisms involve using disjunctive (either—or) statements to infer conclusions about mutually exclusive options (e.g., “A light switch is either on or off. It is not off. Therefore, it is on.”)
- Categorical syllogisms compare categories and describe their relationships using terms such as “all,” “some,” or “no” (e.g., “No human has a tail. Spider monkeys have tails. Therefore, spider monkeys are not human.”)
When properly formed, syllogisms are valid, but structural flaws render them invalid.
Valid vs invalid deductive arguments
A well-constructed formal argument is considered valid (as opposed to invalid, or fallacious). If an argument is valid, it’s impossible to affirm the premises and deny the conclusion without a contradiction. In other words:
- In a valid argument, if the premises are true, the conclusion must also be true.
- In an invalid argument, the conclusion does not logically follow from the premises (and in this case, the argument commits a formal fallacy).
If an argument has a valid structure and its premises are factually correct, then the argument is also considered sound.
Deductive reasoning and logical fallacies
Flawed attempts at deductive reasoning lead to formal logical fallacies. Also known by their Latin name, non sequitur fallacies, formal fallacies are structural errors that render an argument invalid.
Examples of deductive fallacies, or formal logical fallacies, include the following:
- Denying the antecedent: Concluding that an effect won’t happen because a certain cause (the antecedent) didn’t occur
- Affirming the consequent: Assuming a certain cause occurred because an expected effect (the consequent) is observed
- Fallacy of the undistributed middle: Asserting that two things are related solely because they share a common property (the “middle term”)
Hypothetico-deductive reasoning in research
Researchers rely on hypothetico-deductive reasoning to test theories and hypotheses. This method of scientific inquiry involves several steps:
- Formulation: Form a falsifiable hypothesis (i.e., one that can be tested and disproved with empirical evidence) based on observations or established knowledge.
- Deduction: Predict outcomes that should logically follow from the truth of the hypothesis.
- Testing: Conduct experiments to test the predictions.
- Analysis: Evaluate the results. If the prediction turns out to be true, the hypothesis is strengthened. If the prediction is false, the hypothesis may be re-tested or rejected.
Hypothetico-deductive reasoning: If the hypothesis is true, city dwellers exposed to plant life should be tested as having lower levels of stress hormones than those in areas devoid of plants.
Deductive reasoning allows researchers to predict specific outcomes that would logically follow from the truth of the hypothesis.
Frequently asked questions about deductive reasoning
- What is an example of deductive reasoning?
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An example of deductive reasoning in real life is a student forming conclusions about shapes and angles based on the laws of geometry.
- The sum of any triangle’s interior angles is 180°.
- Two angles in a given triangle are 50° and 60°.
- The third angle is 70°.
Deductive reasoning applies a general rule to a specific case to draw a conclusion.
- Why is deductive reasoning important?
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Deductive reasoning is a crucial part of critical thinking, especially in domains such as philosophy, mathematics, and science. It allows us to make predictions and evaluate theories objectively.
Deductive arguments provide frameworks for testing hypotheses (typically developed through inductive reasoning) and allow us to establish conclusions with logical certainty.
- Why is deductive reasoning stronger than inductive reasoning?
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Deductive reasoning is considered stronger than inductive reasoning in a specific sense:
If a deductive argument’s premises are factually correct, and its structure is valid, then its conclusion is guaranteed to be true.
An inductive argument, in contrast, can only suggest the strong likelihood of its conclusion
- What is the difference between inductive and deductive reasoning?
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Inductive reasoning and deductive reasoning are the two most prominent approaches to critical thinking and argumentation. Each plays a crucial role in reasoning and argumentation, but they serve different functions:
- Inductive reasoning relies on specific observations to form general conclusions. Example: “The sun has risen every day of my life; therefore, the sun will always rise every day.”
- Cannot prove a conclusion with absolute certainty
- Can result in informal logical fallacies (i.e., errors of content)
- Deductive reasoning (or formal reasoning) relies on general principles to form specific conclusions. Example: “All humans are mortal. Socrates was human. Therefore, Socrates was mortal.
- Can prove a conclusion with absolute certainty if the premises are true and the argument has a valid form
- Can result in formal logical fallacies (i.e., errors of form)
- Inductive reasoning relies on specific observations to form general conclusions. Example: “The sun has risen every day of my life; therefore, the sun will always rise every day.”
