Skill Sheet #1: Good and Bad Arguments

1. An argument is a set of statements including premise(s) and conclusion(s). An argument is not the same as an assertion and is not identical to its conclusion. Arguments are not true or false. One appraises the truth and falsity of their premises and conclusions and the logical relation between their premise(s) and conclusion(s).

2. A valid argument is an argument in which the conclusion follows from the premises. The conclusion of an argument is said "to follow from" its premises when it is impossible for its premises to be true and for its conclusion to be false. If all the premises in a valid argument are true, then its conclusion must be true, too. If the conclusion of a valid argument is false, then at least one of its premises must be false. An argument that goes wrong because its conclusion does not follow from its premises is called "invalid."

3. A sound argument is thus an argument in which it is both the case that the premises are true and that the conclusion follows from the premises. Arguments can go wrong in two ways: they may include false premises and their conclusions can fail to follow from their premises. An argument that goes wrong in either of these two ways is called "unsound." Every sound argument is valid, but some valid arguments are unsound. Every invalid argument is unsound, but some unsound arguments are valid.

4. An argument A made by a person P is rationally persuasive to another person Q if and only if A is valid and both P and Q believe that A is sound.

5. A particularly powerful technique for the appraisal of arguments is to reformulate them so that they are literally valid. Often this requires one to supply implicit premises. Consider the following trival example. Suppose someone were to write, "Dan Hausman could not be a philosopher, because he doesn't have a beard." One can reformulate this as: (1) All philosophers have beards. (2) Dan Hausman does not have a beard. therefore (3) Dan Hausman is not a philosopher. In reformulating the argument as literally valid, one can then focus on the truth or falsity of premises, and one is forced to notice that the argument relies on the unstated premise (1).

Examples : Decide whether each of the following examples is valid and whether each is sound.

(a) 1. No one gets an A in Phil 341 unless he or she works hard.

2. George works hard.

3. George gets an A.

(b) 1. All teachers have beards.

2. Dan Hausman is a teacher.

3. Dan Hausman has a beard.

(c) 1. All teachers are under 50.

2. Dan Hausman is a teacher.

3. Dan Hausman is under 50

(d) 1. Some humans teach philosophy.

2. Dan Hausman teaches philosophy.

3. Dan Hausman is a human.

(e) 1. Some humans teach philosophy.

2. Dan Hausman is a human.

3. Dan Hausman teaches philosophy.

(f) 1. Abortion is wrong.

2. Abortion is wrong.

(g) 1. All humans will die.

2. All pigs will die.

3. Dan Hausman is a pig.

4. Dan Hausman will die.

(h) 1. All humans will die.

2. All pigs will die.

3. Dan Hausman is a human.

4. Dan Hausman will die.

(i) 1. Pigs have four legs.

2. Milk comes from cows.

3. Bill Clinton is from Arkansas.

(j) 1. All Mary's marbles are round.

2. None of Mary's marbles are square.