Disjunctive Syllogism | Definition & Examples

A disjunctive syllogism is an argument with two premises and a conclusion that describes an either–or relationship. The conclusion is derived through a process of elimination when one of the two options is negated.

Disjunctive syllogism example
  • A shape is either a hexagon or an octagon.
  • The shape is not a hexagon.
  • Therefore, the shape is an octagon.

This argument fits the structure of a disjunctive syllogism because it presents a choice between two options (hexagon or octagon), negates one (hexagon), and concludes by affirming the other (octagon).

Disjunctive syllogisms are typically used in formal logic, but mathematics, computer programming, and other disciplines often use the same pattern of reasoning expressed in different ways.

Continue reading: Disjunctive Syllogism | Definition & Examples

Hypothetical Syllogism | Definition & Examples

Hypothetical syllogisms are arguments in formal logic that deduce conclusions from conditional (if–then) statements.

Hypothetical syllogism example
  • Premise: If an animal has exactly six legs, then it is an insect.
  • Premise: And if an animal is an insect, then it has three body segments (head, thorax, and abdomen).
  • Conclusion: Therefore, if an animal has six legs, then it also has three body segments.

This is an example of a hypothetical syllogism that includes a conditional (if–then) statement in each premise. The conclusion follows from the premises with logical certainty.

Syllogisms are typically found in contexts such as formal logic, but syllogistic reasoning is also applied in fields like science and mathematics.

Continue reading: Hypothetical Syllogism | Definition & Examples

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.

Premises in deductive reasoning example
  • 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.

Continue reading: What Is Deductive Reasoning? | Definition & Examples

What Is a Syllogism? | Definition & Examples

A syllogism is an argument that consists of two premises and a conclusion. Syllogisms express deductive reasoning, forming specific conclusions from general principles.

Syllogism example
  • No fish can survive without water.
  • Sharks are fish.
  • Therefore, sharks cannot survive without water.

The main purpose of a syllogism is to prove a conclusion with logical certainty.

Syllogisms are typically found in academic and professional domains, such as formal logic and mathematics. We often use syllogistic reasoning to make decisions in everyday life even if we don’t often express these thoughts verbally.

Continue reading: What Is a Syllogism? | Definition & Examples

What Is Modus Tollens? | Definition & Examples

Modus tollens is a valid form of deductive argument also known as denying the consequent.

Used in formal logic, modus tollens is a type of hypothetical syllogism that involves an if–then statement followed by a negation of the “then” statement (i.e., the consequent). It is typically expressed as follows:

  • If P, then Q.
  • Not Q.
  • Therefore, not P.
Modus tollens example
  • If an object is made of iron, it will be attracted to a magnet.
  • This object is not attracted to a magnet.
  • Therefore, this object is not made of iron.

Modus tollens is used to demonstrate that a hypothesis is false when a necessary condition is not met.

Continue reading: What Is Modus Tollens? | Definition & Examples

What Is Modus Ponens? | Definition & Examples

Modus ponens is a type of conditional syllogism that takes the following form:

  • If P, then Q.
  • P.
  • Therefore, Q.

Arguments that correctly apply this form are valid, meaning that the conclusion follows logically from the premises.

Modus ponens example
  • If Socrates is human, then Socrates is mortal.
  • Socrates is human.
  • Therefore, Socrates is mortal.

The reasoning expressed in modus ponens and other formal arguments is especially crucial in contexts such as philosophical debates, legal reasoning, scientific research, mathematical proofs, computer science, and natural language processing.

Continue reading: What Is Modus Ponens? | Definition & Examples

What Is Black-and-White Thinking? | Examples & Meaning

Black-and-white thinking is the tendency to categorize people, situations, and ideas in extreme, absolute terms, such as “good vs. evil,” leaving no room for nuance or neutrality.

Black-and-white thinking examples
“If you don’t support everything our party does, you are effectively working for the opposition.”

“If you want to place any limits on speech, then you don’t support freedom of speech at all.”

“This book is terrible because the author portrays the villain in a sympathetic light.”

“If a painting isn’t both realistic and aesthetically pleasing, it’s not art.”

In reasoning and argumentation, engaging in black-and-white thinking makes people vulnerable to certain logical fallacies. In creative writing and other artistic forms, black-and-white thinking can limit creativity and depth, reducing the complexity of characters, plots, and themes.

Continue reading: What Is Black-and-White Thinking? | Examples & Meaning

What Is a Premise? | Definition & Examples

Premises are the key points made in support of an argument’s conclusion. They play a crucial role in all forms of reasoning.

Premise in argumentation example
Premise: All even numbers are divisible by 2.

Premise: 4 is divisible by 2.

Conclusion: Therefore, 4 is an even number.

“Premise” can also refer to the background situation that sets up a story or joke. This more colloquial use of the term is common in discussions of literature and the performing arts.

Continue reading: What Is a Premise? | Definition & Examples

What Is Analogical Reasoning? | Definition & Examples

Analogical reasoning involves identifying similarities between different situations or concepts to make inferences or solve problems. It is sometimes classified as a subcategory of inductive reasoning.

Using analogical reasoning, we can draw upon existing knowledge and patterns to understand new or unfamiliar situations, applying solutions or insights from one context to another.

Analogical reasoning example
In discussions of potential limitations on free speech, hate speech is often compared to shouting “fire” in a crowded theater. Just as falsely shouting “fire” can create a dangerous situation by inciting panic and resulting in real-world harm, hate speech online can also have dire consequences, fueling violence and discrimination.

This argument exemplifies analogical reasoning because it involves observing one similarity between two distinct scenarios (i.e., two very different forms of speech that can both result in physical harm) and arguing for another similarity (i.e., that both should be banned).

Analogy-based reasoning plays an important role in problem-solving, decision-making, and creative thinking.

Try QuillBot’s free Paraphrasing Tool

Continue reading: What Is Analogical Reasoning? | Definition & Examples

What Is Abductive Reasoning? | Definition & Examples

Abductive reasoning involves observing a phenomenon and inferring the most likely explanation or cause.

This type of analysis is commonly used in both research and everyday problem-solving to generate plausible interpretations for specific incidents that involve uncertainty.

Abductive reasoning example
A doctor observes a patient’s symptoms and infers which condition is the most likely cause.

Try QuillBot’s free paraphraser

Continue reading: What Is Abductive Reasoning? | Definition & Examples

What Is Inductive Reasoning? | Definition & Examples

Inductive reasoning involves making broad generalizations based on specific observations.

Induction is used in various academic and professional settings, as well as informal everyday conversations and tasks. This type of reasoning is especially relevant to problems involving pattern recognition, prediction, and decision-making.

Inductive reasoning example
Specific observation: All swans at the local park are white.

Generalization: Therefore, all swans everywhere are probably white.

This inference might seem reasonable based on the available evidence. However, the sample of swans at the local park is too small to merit such a broad conclusion. Studying a geographically diverse sample would show that there are non-white swans, including the black swans of Australia.

Inductive reasoning often relies on the assumption that observed cases (e.g., white swans in a local park) are representative of all cases (e.g., all swans everywhere). This assumption is a common source of errors, or logical fallacies, in inductive reasoning.

Try QuillBot’s free paraphraser

Continue reading: What Is Inductive Reasoning? | Definition & Examples