Deductive Argument Forms

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As you may recall, the goal of a deductive inference is to affirm some conclusion with absolute certainty. To achieve this, specific argument forms are typically employed. For example, if you can show that someone that an "if...then" relationship holds between to claims (A--> B) and then you can show that the first claim, A, is true, then it must be the case that B is true. Just try creating examples of this pattern to see for yourself.

For example,

P1. If Tim is a new student, then he should expect to feel confused.

P2. Tim is a new student

C: Tim should expect to feel confused.

or,

P1. If wishes were horses, then pigs would fly.

P2. Pigs can't fly.

C: Wishes aren't horses.

These two arguments both follow deductive valid patterns. In the first the pattern is

P1. A --> B

P2. A

C: B

In the second, the pattern is

P1. A --> B

P2. Not B

C: Not A

Because these are valid patterns, if the premises are true, the conclusion of the argument must be true. Recall that validity is the property of deductive arguments that guarantees that the premises will never be true while the conclusion is false. Within logic (see "Propositional Logic") this is explained in terms of the truth table for the argument. Here, we simply introduce the patterns which the tables demonstrate to be valid. As you work on your own rationales and your reconstructions of other's rationales, you should see if the arguments fit these patterns.

1. Modus Pollens

1. P --> Q

2. P

C. Q

2. Modus Tollens

1. P --> Q

2. ~Q

C. ~P

3. Disjunctive Syllogism

1. P v Q

2. ~P

C. Q

4. Hypothetical Syllogism

1. P --> Q

2. Q --> R

C. P --> R

5. Double Negation

1. ~~P

C: P

The first two patterns, Modus Ponens and Modus Tollens, come up alot in reconstruction. One of the most basic ways to get an argument going is to connect two claims in a conditional (if ... then) structure.

Disjunctive Syllogism involves affirming that two claims are in an "either or" relationship. In the second premise, you deny the truth of one of the claims and then conclude the other. Again, this is a pattern you will see within rationales as you become more sensitive to argumentative patterns.

Hypothetical Syllogism may remind you of the "transitive property" in math (for example, if 3 is greater than 2 and 2 is greater than 1, then 3 is greater than 1). In this case, it simply affirms that "chain reasoning" is valid.

While this is a basic set of patterns, there are others. The choice of valid argument patterns within a deductive logic depends in part upon the goals of the logician. Our own goals in noticing logical patterns is more practical -- to be able to identify the patterns in reflective contexts as a means of offering. For this reason, we have chosen a basic set of patterns that are roughly intuitive.