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Formal Versus Informal Logic. Deductive Versus Inductive Forms of Reasoning. Two basic categories of human reasoning. Deduction: reasoning from general premises, which are known or presumed to be known, to more specific, certain conclusions.

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formal versus informal logic

Formal Versus Informal Logic

Deductive Versus Inductive

Forms of Reasoning

two basic categories of human reasoning
Two basic categoriesof human reasoning
  • Deduction: reasoning from general premises, which are known or presumed to be known, to more specific, certain conclusions.
  • Induction: reasoning from specific cases to more general, but uncertain, conclusions.
  • Both deductive and inductive arguments occur frequently and naturally…both forms of reasoning can be equally compelling and persuasive, and neither form is preferred over the other (Hollihan & Baske, 1994).
deduction vs induction
Deduction:

commonly associated with “formal logic.”

involves reasoning from known premises, or premises presumed to be true, to a certain conclusion.

the conclusions reached are certain, inevitable, inescapable.

Induction

commonly known as “informal logic,” or “everyday argument”

involves drawing uncertain inferences, based on probabalistic reasoning.

the conclusions reached are probable, reasonable, plausible, believable.

Deduction Vs. Induction
deductive versus inductive reasoning
Deduction

It is the form or structure of a deductive argument that determines its validity

the fundamental property of a valid, deductive argument is that ifthe premises are true, thenthe conclusion necessarily follows.

The conclusion is said to be “entailed” in, or contained in, the premises.

example: use of DNA testing to establish paternity

Induction

By contrast, the form or structure of an inductive argument has little to do with its perceived believability or credibility, apart from making the argument seem more clear or more well-organized.

The receiver (or a 3rd party) determines the worth of an inductive argument

Deductive VersusInductive Reasoning
inductive or deductive reasoning
A sample of fifty motorists who were stopped by the CHP at a sobriety checkpoint on a Saturday at midnight revealed that one in four drivers were either uninsured, intoxicated, or both. Thus, if you get involved in an accident on the freeway there is a 25% chance the other motorist will be drunk or uninsured.

The Law of the Sea treaty states that any vessel beyond a 12 mile limit is in international waters. The treaty also states that any vessel in international waters cannot be legally stopped or boarded. Therefore, when the U.S. Coast Guard intercepts boats coming from Cuba or Haiti more than 12 miles from the U.S. coast, it is violating the Law of the Sea.

Inductive or deductive reasoning?
sample deductive and inductive arguments
Example of Deduction

major premise:All tortoises are vegetarians

minor premise:Bessie is a tortoise

conclusion:Therefore, Bessie is a vegetarian

Example of Induction

Boss to employee: “Biff has a tattoo of an anchor on his arm. He probably served in the Navy.”

Sample Deductive and Inductive Arguments
sample venn diagram of a deductive argument
sample “Venn diagram”of a deductive argument

vegetarian animals

tortoises

Thus, Bessie must be a vegetarian

All tortoises fall in the circle of animals that are vegetarians

Bessie falls into the circle of animals that are tortoises

Bessie

other types of deductive arguments
Suppose every place in the world that people live is represented by the blue space inside the rectangle. Suppose the long pink oval represents all the wooden houses in the world. And, suppose the green circle represents Canada. The most logical conclusion one can draw from the figure is:

all wooden houses are found in Canada

Everyone lives in a wooden house

Some Canadians live in wooden houses

No one lives in Canada

Other types ofdeductive arguments
other types of deductive arguments9
Suppose the following statements are all true:

Person L is shorter than person X

Person Y is shorter than person L

Person M is shorter than person Y

What additional piece of information would be required to conclude that “Person Y is shorter than Person J”?

Person L is taller than J

Person X is taller than J

Person J is taller than L

Person J is taller than M

Person M is taller than Y

Other types ofdeductive arguments

Solution: Answer C

M < Y < L < X

So, if J is taller than L,

Y must be shorter than J

other types of deductive arguments10
A mother wants to order one large pizza, with exactly 5 toppings for her three picky children. She can choose from 7 toppings; cheese, mushrooms, olives, ham, sausage, onions, and pineapple.

Fifi says there has to be pineapple

Mona says there cannot be any olives

Rex says that if there is going to be sausage, then there has to be ham too.

Which combination of toppings should she select if she is to satisfy all three children’s combined demands?

pineapple, onions, cheese, mushrooms, sausage

cheese, sausage, ham, olives, pineapple

cheese, mushrooms, ham, onions, pineapple

sausage, mushrooms, onions, cheese, and ham.

Other types ofdeductive arguments
the five topping solution
the five topping solution

Note: the statement “if sausage, then ham” doesn’t imply “If ham then sausage.” The obverse doesn’t necessarily follow.

deduction versus induction continued
Deductive reasoning is either “valid” or “invalid.” A deductive argument can’t be “sort of” valid.

If the reasoning employed in an argument is valid and the argument’s premises are true, then the argument is said to be sound.

valid reasoning + true premises = sound argument

Inductive reasoning enjoys a wide range of probability; it can be plausible, possible, reasonable, credible, etc.

the inferences drawn may be placed on a continuum ranging from cogent at one end to fallacious at the other.

Deduction Versus Induction---continued

fallacious

cogent

deduction versus induction still more
Deductive reasoning is commonly found in the natural sciences or “hard” sciences, less so in everyday arguments

Occasionally, everyday arguments do involve deductive reasoning:

Example: “Two or more persons are required to drive in the diamond lane. You don’t have two or more persons. Therefore you may not drive in the diamond lane”

Inductive reasoning is found in the courtroom, the boardroom, the classroom, and throughout the media

Most, but not all everyday arguments are based on induction

Examples: The “reasonable person” standard in civil law, and the “beyond a reasonable doubt” standard in criminal law

Deduction Versus Induction--still more