Deductive Argument Crash Course

Weston, Anthony. A Rulebook for Arguments. 4th ed. Indianapolis: Hackett Pub., 2009. Kindle Electronic Edition.
Chapter 6, “Deductive Arguments” pp. 37-48

A deductive argument is another commonly used type of argument. “A (properly formed) deductive argument is an argument of such a form that if its premises are true, the conclusion must be true too” (Weston 2009, 37). Other types of arguments do not guarantee the conclusion. Weston observes that we can rarely be completely certain of the premises, so there may be some doubt. He begins listing different types of deductive arguments on p. 38 beginning with his “rule 22.”

22 Modus ponens  If p then q.  P. Therefore, Q.
23 Modus tollens  If p then q.  Not Q.  Therefore, not P.
24 (Ibid., 40) Hypothetical syllogism  If p then q.  If q the r. Therefore, if P then R.
25 Disjunctive syllogism  P or Q.   Not P.  Therefore, Q.
26 (Ibid., 42) Dilemma   P or Q.  If P then R. If Q then S. Therefore R or S.
27 (Ibid., 43)  Reductio ad absurdum   This is a variety of Modus Tollens. Assuming Q is “absurd” P must be true after all.
28  (Ibid., 44)  Deductive arguments in several steps  It is possible to string several different deductive arguments together to demonstrate each premise. Weston gives an example from Sherlock Holmes on pp. 44ff.