Deduction and Induction

Truth and Reasoning All arguments have two basic elements: statements and inferences. Statements are true or false. Inferences have to do with what “follows from” a given set of statements.

The following argument (p.54) has a reasoning problem: P1: All cats are animals P2: All dogs are animals Con: All cats are dogs. 1. Each statement is, individually, true. 2. Since we know the conclusion is false, we know there must be some problem with the reasoning in this argument.

The following argument (p. 49) has a truth problem: P1: The vast majority of Rose Bowl games have been played in freezing cold weather. Con: Probably the next Rose Bowl game will be played in freezing cold weather

Which is wrong with the following argument? P1: If human rights are recognized, then civilization flourishes. P2: If equality prevails, then civilization flourishes. Con: If human rights are recognized, then equality will prevail. Note: you might agree that the conclusion is true, and maybe it is. But it’s truth does not follow from the two premises.

Deduction and Induction are characteristics of inferences. In a good deductive argument, the conclusion follows with certainty. There is no information in the conclusion that is not already in the premises. In a good inductive argument, the conclusion follows with probability. There is information in the conclusion that is not already in the premises.

Some Examples of Deduction Inferences from (non-statistical) math: certain statements and operations entail conclusions. Inferences from definition: the meaning of words in the premises entails the truth of the conclusion. Disjunctive syllogism: eliminating one of two options leaves only the other.

Some Examples of Induction Predictions: need I say more?  Generalizations: information in the conclusion by definition is broader than information offered in the premises. Causal inferences: these strive for, but cannot achieve, necessity.

Two Common Confusions about Deduction and Induction 1. “Certainty” and “Probability” are meant logically, not psychologically. Psychological certainty is a state of mind; it expresses something about your attitude toward a statement. Logical certainty is a characteristic of arguments; it arises from a relationship between statements. 2. It is not essential that a deductive inference be drawn from the general to the particular; nor is it essential that an inductive inference be drawn from particular to general.

Two Final Suggestions 1. Your only concern, in determining what kind of inference is presented, is how the conclusion follows from the premise(s). Ignore questions of actual truth. 2. If you are still unsure about the nature of the inference after applying the “reasonable person” test, interpret the inference as inductive.

The Language of Logical Evaluation Deductive and Inductive Terminology

Content v. Inference Only premises can be true or false Only inferences can be valid/strong or invalid/weak. Logical terminology develops to reflect this distinction between determining truth and determining acceptable reasoning.

In ordinary contexts, we say “good” arguments In ordinary contexts, we say “good” arguments. In logical contexts, we must clarify what kind of good argument we mean.

In ordinary contexts, we say “good” arguments In ordinary contexts, we say “good” arguments. In logical contexts, we must also show that our kind of argument passes the two essential tests of any argument.

Deductive Reasoning (Soundness) Valid arguments – If the premises were true, then the conclusion must be true Sound arguments – the premises are, actually, true; and the conclusion must then be true

Inductive Reasoning (Cogency) Strong arguments – If the premises were true, then the conclusion is probably true Cogent arguments – the premises are, actually, true; so the conclusion is probably true (although could always be false).

Summary All “good” arguments must have both true premises and good reasoning. The standards for “good” reasoning differ for deductive and inductive reasoning. Sound arguments = true premises and valid deductive reasoning Cogent arguments – true premises and strong inductive reasoning.