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.
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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.
Deductive reasoning applies a general rule to a specific case to draw a conclusion.
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There are three main types of syllogisms in classical logic:
Each incorporates the law of syllogism. The main distinction between them is the relationships expressed by their premises. The main distinction between them is the relationships expressed by their premises.
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A literary syllogism mirrors formal logic by presenting two premises, often implicit, followed by a conclusion, enhancing a narrative’s depth and complexity.
For example, in To Kill a Mockingbird, Atticus Finch’s argument that all humans are created equal, coupled with evidence of Tom Robinson’s innocence, leads to the conclusion that Tom should be acquitted.
In other areas, like mathematics, the law of syllogism is used in proofs or reasoning.
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“Syllogism” has several near-synonyms:
For example, in math, the law of syllogism could be thought of as the “law of deductive reasoning.”
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The word “syllogism” is pronounced SIL-uh-jiz-uhm (IPA: /ˈsɪləˌdʒɪzəm/).
This word is sometimes used on its own or in phrases, like law of syllogism.
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Modus tollens is not a logical fallacy; it is a valid approach to deductive reasoning.
However, syllogisms such as modus tollens are often conflated with formal logical fallacies (or non sequitur fallacies).
The two fallacies that are most easily conflated with modus tollens are affirming the consequent and denying the antecedent.
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A contrapositive negates and reverses a conditional (if–then) statement. For example, the contrapositive for the statement “If P, then Q” is “If not Q, then not P.”
Modus tollens validates the contrapositive, demonstrating that “not P” follows logically from “not Q” as follows:
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“Modus tollens” translates to “method of denying” in English.
In contrast, the Latin term “modus ponens” means “method of affirming.” Both refer to types of syllogisms.
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Modus ponens is not a logical fallacy; it is a valid form of deductive reasoning. Also known as “affirming the antecedent,” it employs a straightforward logical structure:
However, flawed attempts at forming a syllogism often result in formal logical fallacies, such as denying the antecedent, which resembles modus ponens in form but fails to provide logical certainty:
Although the two arguments look similar, denying the antecedent is an invalid form of argument.
Continue reading: Is modus ponens a fallacy?
