### DEDUCTIVE REASONING

Deduction is one of those terms that can be misleading because of differences between its technical use in a logic course and how it is used in other settings. Sherlock Holmes, for instance, did not engage in deductive reasoning in a technical sense even though he often deduces who is the murderer from a set of clues.

So what is this technical sense? It is this: one statement can be deduced from one or more other statements when there is a pattern in how they are stated that makes it impossible for the conclusion to be false when its premises are true. For instance, given that everything black is sweet and salt is black, it follows that salt is sweet. However, if we said that everything sweet is white and sugar is white, it would not follow that sugar is sweet. The statement that salt is sweet is what we would call a valid conclusion (even though it is false) and the statement that sugar is sweet would be an invalid conclusion (even though it is true.)

Please note we are not talking about psychological processes--how we actually think and thus how we make our inferences on the basis of evidence available to us. Instead, by using the word reasoning we are looking at how statements (which do not have to be expressed as separate sentences) are interconnected. In propositional logic (when we work with the variables P,Q, and so on) the relationships are between entire statements. In predicate or quantifier logic we are often working with just parts of the statements (as in the way in which we handle the terms black, sweet, sugar, and salt in the examples).

In formal logic we are interested in patterns that could be represented just with letters (what we in fact do with symbolic logic). In informal logic we are more concerned with the broader picture of reasonable and unreasonable inferences, and the reasonableness (or probability) of a conclusion does depend on the content of the premises (the statement of the evidence) in a way that does not happen with formal logic.

The term valid, then, is not the same as the term true, but instead refers to an entire argument (or its conclusion) when because of the pattern true premises could not imply (or entail) a false conclusion. For there to be a false conclusion in a valid argument there would also have to be at least one false premise. Still another way of putting this is that it would be inconsistent to have true premises and a false conclusion, and this is an idea we make use of in testing for validity.

What you probably already recognize is that an argument can exist without disagreement since, in the sense in which we use the word in logic, it refers simply to any arrangement in which a statement (the conclusion) is said to be true, either because it is a tautology or because having it be false would be inconsistent with other statements presented as its premises. Also, a conclusion does not have to be expressed at the end of a sentence or paragraph: "Jane must have passed because she did study and anyone who studied would pass" is an argument in which the conclusion is expressed first.