Deductive Arguments vs. Inductive Arguments

CATEGORICAL DEDUCTION(A deduction about categories of things.)

"All A's are B's" "No A's are B's" "Some A's are B's (not all A's are non-B's)" "Some A's are not B's (not all A's are B's)." For example, All students here (category 1) are college students (category 2). All college students are people above the age of five (category 3). Therefore, all students here are above the age of five.

Common patterns of Deductive Argument

1. HYPOTHETICAL DEDUCTION 2. CATEGORICAL DEDUCTION 3. ARGUMENT BY ELIMINATION (The Either-Or Argument) 4. ARGUMENT BASED ON MATHEMATICS 5. ARGUMENT BASED ON DEFINITION 6. ARGUMENT BY EXAMPLE

COMMON PATTERNS OF INDUCTIVE ARGUMENT

1. INDUCTIVE GENERALIZATION 2. ARGUMENT FROM STATISTICS 3. ARGUMENT FROM AUTHORITY 4. ARGUMENT FROM ANALOGY 5. CAUSE-AND-EFFECT ARGUMENT

ARGUMENT FROM ANALOGY

An argument for an additional SIMILARITY between things based on some already-known similarities between them. The word "similarly" often shows up as an indicator-word for this type of argument.

CAUSE & EFFECT ARGUMENT

An argument from observed patterns to a cause - effect connection, or from an observed event to a presumed cause, or arguing from an observed cause to a likely effect. In 12 Angry Men, when the fan finally works, baseball tickets juror concludes, "Hey! Look at that. It must have been on the same switch with the light."

ARGUMENT FROM AUTHORITY

An argument that supports a conclusion based on the authority, or reliability, of the source from which it came. This is generally the sort of argument you make when you cite your sources in a research paper. This sort of argument can include citing books, articles, speakers, street signs, the medical community, etc.

ARGUMENT BASED ON DEFINITION

Any conclusion that follows by definition is part of a deductive argument. Ex. Rob is a bachelor. Therefore, Rob is single. OR - "I didn't steal it. I just took it without the owners' permission." "That IS stealing!" OR Yogi Berra: "Slump? I ain't in no slump. ... I just ain't hitting." Response: "That's just what slump means."

MOST ARGUMENTS

Are very clearly deductive or inductive based on matching one of the common patterns or having clear indicator words. The Principle of Charity does not come in at all.

Deductive Argument

Claims that the premises support the conclusion absolutely, or 100%. The author intends the premises to support the conclusion absolutely. The argument claims that the conclusion can't be false IF all the premises are true. (Of course, the conclusion can be false if some premise is false.)

Inductive Argument

Claims that the premises support the conclusion, but only with some degree of probability. The author intends the premises to support the conclusion, but only with some degree of probability. The argument claims that the conclusion is probably true IF all the premises are true. (Of course, if some premise is false, the conclusion can be improbable.)

ARGUMENT FROM STATISTICS

Ex. 93% of students know the capital of Georgia, and Ella is a student. Therefore, Ella probably (93% probability) knows the capital of Georgia. OR - Therefore, about 93% of my critical thinking students know the capital of Georgia. • Note that the "statistic" does not have to be presented numerically! Statistical concepts can be expressed in many different ways, such as: 1. Almost all towns and cities have a public library, 2. Most college students have downloaded MP3's, 3. A large majority of Americans own televisions, 4. Virtually all Americans approve of the U.S. Constitution, 5. A majority of U.S. Senators are male.

ARGUMENT BASED ON MATHEMATICS:

Ex. Rosa is taller than Jake, and Jake is taller than Angela. Therefore, Rosa is taller than Angela. This is really a type of argument based on definition, where the relevant definitions are of mathematical terms (taller than, greater than, equal to, etc.)

Deductive Argument EXAMPLES

Example: 100% (All) of my uncles are retired, and this guy next to me is one of my uncles. Therefore, this guy is retired. (The premises guarantee the conclusion) All members of the club are allowed in the pool. Abernathy is allowed in the pool. Therefore, Abernathy is a member of the club. (*NOTE: In this argument, the premises don't actually support the conclusion, because it could be that some non-members are allowed in as well. But it's deductive because the format of the argument makes it clear that the premises were meant to guarantee the conclusion. They just don't, due to a mistake in reasoning.)

Inductive Argument EXAMPLES

Example: 95% of college students have a drivers license, and Ella is a college student. Therefore, Ella probably (95% probability) has a drivers license. (The premises give strong support, but less than 100%, to the conclusion) Example: Sue missed the first quiz. Therefore, Sue will probably miss the second quiz next week. (*NOTE: The premises don't actually make the conclusion probable, but they were obviously meant to give probability to the conclusion, so it is inductive.)

INDUCTIVE GENERALIZATION

From the particular (cases) to the general (conclusion). Supporting a general principle (all / almost all / most A's are B's) based on a number of particular examples (this A is B, that A is B, that other A is B, etc. etc.), usually referred to as the SAMPLE. This sort of argument gives us statistical claims in the conclusion and is the method used in polls and surveys. The conclusion is always a more general claim than the premises in this argument.

ARGUMENT BY ELIMINATION

Given two or more options, and eliminating all but one, you can infer the one remaining must be true. Ex. Either A or B. Not B. Therefore, A.

The Principle of Charity EXAMPLES

If what they've said would make a lousy argument but you can plausibly interpret it as a non-argument, give the speaker or writer the benefit of the doubt and assume they meant it as a non-argument. If a passage can reasonably be interpreted as a deductive argument or as an inductive argument (keep in mind there are limits to what counts as a reasonable interpretation), and it does not work as a good deduction but it is a good induction, give the speaker or writer the benefit of the doubt and assume they meant it as inductive.

Hypothetical Deduction(A deduction involving hypothetical/conditional (if A-then B) statements.)

Makes an absolute 100% connection between A and B (unless it is qualified by terms such as "probably' or "maybe" - then it would set up an inductive argument). The absolute if-then connection sets up a deductive argument.

Logically CORRECT

Modus Ponens (The "Placing Mode," affirming A) If A, then B (A=antecedent; B=consequent) A Therefore, B Modus Tollens (The "Taking Mode," denying B)) If A, then B Not B Therefore, Not A Chain Argument If A, then B If B, then C Therefore, if A, then C

Logically INCORRECT

The Fallacy of Denying the Antecedent (A) If A, then B not A Therefore, not B The Fallacy of Affirming the Consequent (B) If A, then B B Therefore, A

ARGUMENT BY EXAMPLE

When an example of something actually happening is used to prove that it is possible, that is a deductive argument. For example, if someone argues that it is possible for a person as young as 10 to graduate from college by citing the case of Michael Kearney, that is deductive proof

The Principle of Charity

When interpreting someone's spoken or written words, a critical thinker will give the best interpretation possible.