Chapter 23: Enthymemes, Argument Chains, and Other Hazards

Enthymemes (pp ) Enthymemes –An enthymeme is an argument with a missing premise or conclusion –Appeal to the argument forms to determine what must be missing –Identify the form and fill in what must be missing. If you’re given, “If Juan went to the dance, then Lottie went to the dance. So, Lottie went to the dance.” The only argument form with which we are familiar that will allow you to reach the consequent as a conclusion is affirming the antecedent. So, the missing premise must be “Juan went to the dance.”

Enthymemes (pp ) Assume you are given “Either Ana went to the game or Brutus went to the dance, and Brutus didn’t go to the dance.” No conclusion is stated. It has to be a case of disjunctive syllogism — that’ the only form that fits this pattern. So, the conclusion has to be “Ana went to the game.” Either Ana went to the game or Brutus went to the dance. Ana went to the game, so, …” nothing follows. It has to be an instance of improper exclusive disjunctive syllogism, which is a fallacy. If you confront a fallacious argument without a conclusion, point out that the form is fallacious and stress that nothing follows. If you are given “If Luis likes licorice, then Maria likes chocolate. So Luis likes licorice.” You will acknowledge that it is an instance of the fallacy of affirming the consequent. You might note what the assumed premise is “Maria likes chocolate,” but you should stress that it is a fallacious argument.

Enthymeme Examples (pp ) Rhetorical questions –If you have a rhetorical question, a question that assumes a determinate answer, treat it as if it is a statement. –If you’re given, “Aren’t dogs carnivores? And if dogs are carnivores, doesn’t that imply dogs like steaks? So, mustn’t we conclude that dogs like steaks?” you can treat it as, “Dogs are carnivores. If dogs are carnivores, then dogs like steaks. So, dogs like steaks.”

Enthymeme Examples (pp ) Dilemmas –Often the antecedents of the two conditional statements in a constructive dilemma are contradictories and the consequent is the same. –If two statements are contradictories, one statement is true and the other is false. –If you reach a conclusion of the form, “Either p or p” (p v p), the statement is logically equivalent to p. If the antecedents are contradictories, it often happens that the disjunctive premise is unstated. If the consequent is in both conditionals the same, for example, ‘p’, it often will be stated as a simple statement, p, rather than as the disjunction, “p or p.” Example: “If you vote in the next election, taxes will rise; and if you don’t vote in the next election, taxes will rise. So, taxes will rise.”

Enthymeme Examples (pp ) Unclear statements of an argument form –Arguments are often stated unclearly. Often you will be able to reconstruct the argument as a valid deductive argument, often an affirming the antecedent, denying the consequent, disjunctive syllogism, or one of the dilemmas. You should always restate the argument in as strong a fashion as possible. So, restate the argument as a valid deductive argument so long as all the proposed premises are true or, at least, reasonably can be assumed to be true.

Argument Chains (pp ) As we noticed in Chapter 9, often the conclusion of one argument is a premise for another. Often the intermittent conclusions are unstated. You put together the various elements like pieces of a puzzle, following the various argument forms. Typically if you are asked to find the “final conclusion” it is either a simple statement found in the premises or the denial of such a simple statement.

Argument Chains: Example You are given: –If Boris builds boats from birch bark, then Angela angles ably for tasty trout. If Constance cares constantly for convoluted cats, then Danielle drags druids down dry drives. Either Boris builds boats from birch bark or Constance cares constantly for convoluted cats. Danielle does not drag druids down dry drives. If Angela angles ably for tasty trout, then Ethel eats enchiladas energetically. So, … The conclusion is “Ethel eats enchiladas energetically.” You might conjoin the first two premises, do a constructive dilemma from the conjunction and premise 3 (concluding that “Either Angela or Danielle”), a disjunctive syllogism from that conclusion and premise 4 (concluding that “Angela”), and an affirming the antecedent from that conclusion and premise 5 to reach the conclusion that Ethel eats enchiladas energetically. Or you might do a denying the consequent from premises 2 and 4 (concluding that “Not Constance”), a disjunctive syllogism from the conclusion and premise 3 (concluding that “Boris”), an affirming the antecedent from the conclusion and premise 1 (concluding that “Angela”), and an affirming the antecedent from the conclusion and premise 5 to reach the conclusion that Ethel eats enchiladas energetically. Or you might conclude that “If Boris then Ethel” from premises 1 and 5, followed by concluding that “Not Constance” from premises 3 and 4, followed by “Boris” from “Not Constance” and premise 3, and, finally “Ethel” from “If Boris than Ethel” and “Boris”.

Argument Chains: Example When looking for the consequences of a set of premises, it often makes the task clearer to work it through symbolically. Often there are several ways to figure out the conclusion. 1. B  A 2. C  D 3. B v C 4. ~D 5. A  E 6. (B  A) & (C  D)1,2 Conj. 7. A v D6,3 CD 8. A7,4 DS 9. E5, 8 AA or 6 ~C2,4 DC 7. B3,6 DS 8. A1,7 AA 9. E5,8 AA Can you find another?