Deductive & Inductive Arguments

Categorical syllogism

A deductive argument about category relationships. Composed of categorical (absolute) statements "All S are P," "No S are P," "Some S are P (it is not the case that no S are P)," or "Some S are not P (not all S are P)."

Hypothetical syllogism

A deductive argument containing one or more hypothetical, or conditional ("if -then"), statements. Common forms include Modus Ponens, Modus Tollens, Chain Argument, the Fallacy of Denying the Antecedent, and the Fallacy of Affirming the Consequent.

Deductive & Inductive Arguments

All arguments are either deductive or non-deductive (i.e., inductive)

Cause and Effect Argument

An argument claiming a causal relationship exists based on observed patterns, or an argument from a presumed causal connection to a conclusion (often a prediction).

Argument by Mathematics

An argument claiming that the conclusion follows as a matter of mathematical necessity.

Argument by Definition

An argument claiming that the definition of some term(s) in the premises guarantees the truth of the conclusion.

Deductive argument

An argument claiming that the premises support the conclusion absolutely, or 100%, with rigorous, inescapable logic. The argument claims that, if all premises are true, the conclusion cannot be false. Alternately it claims that, if the conclusion is false, there must be at least one false premise.

Inductive argument

An argument claiming that the premises support the conclusion, but only with some degree of probability. The argument claims that, if the premises are true, the conclusion is probably true (but not guaranteed).

Predictive argument

An argument for a conclusion about a future event. Logical support for predictions is ultimately inductive, almost always Argument by Analogy or Cause and Effect Argument.

Argument by Analogy

An argument from some known similarities among a group of objects or events to some likely additional point of similarity.

Inductive generalization

An argument reasoning from an observed sample to the broader, general, population.

Argument from Statistics

An argument starting with a general statistical claim (less than 100%) and reasoning to a sub-class or individual member of the reference class.

Argument by Elimination

An argument starting with a set of either-or options, eliminating all but one, concluding that the one option remaining is true. Often called process of elimination.

Argument from Authority (a reliable source)

An argument supporting a conclusion by citing the reliability (authority) of the source of the claims in the conclusion.

Inference to the Best Explanation

An argument that supports its conclusion as the best available explanation for the evidence. Usually, but not always, a causal argument.

Common deduction indicator words

It follows necessarily/certainly/definitely/absolutely, it must be the case, it cannot be false that ... (BEWARE, many people OVERSTATE their case, using deductive terms in clearly inductive arguments.)

Inductive Relevance

One statement (A) is inductively (logically) RELEVANT to another statement (B) if and only if the truth of A either increases or decreases the likelihood of B. A fact must be logically relevant to count as evidence for or against a claim.

Common induction indicator words

Probably, most likely, chances are, odds are, one would be expect ...

The Principle of Charity

When interpreting someone's spoken or written words, one should give the interpretation that renders the statement as reasonable and strong as the wording allows.