Download - Geometry unit 2.1
Deduction:Deduction: reasoning from general premises, which are known or presumed to be known, to more specific, certain conclusions.
Induction:Induction: the process of observing data, recognizing patterns and making a generalization of your observations.
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: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:Induction: commonly known as
“informal logic,” or “everyday argument”
involves drawing uncertain inferences, based on probabilistic reasoning.
the conclusions reached are probable, reasonable, plausible, believable.
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 if the premises are true, then the 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
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.
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.”
Bessie
tortoisesvegetarian animals
All tortoises fall in the circle of animals that are vegetarians
Bessie falls into the circle of animals that are tortoises
Thus, Bessie must be a vegetarian
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:
A. all wooden houses are found in Canada
B. Everyone lives in a wooden house
C. Some Canadians live in wooden houses
D. No one lives in Canada
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”?
A. Person L is taller than JB. Person X is taller than
JC. Person J is taller than LD. Person J is taller than
ME. Person M is taller than
Y
Solution: Answer CSolution: Answer CM < Y < L < XM < Y < L < XSo, if J is taller than L,So, if J is taller than L,Y must be shorter than JY must be shorter than J
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. Julie 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?
A. pineapple, onions, cheese, mushrooms, sausage
B. cheese, sausage, ham, olives, pineapple
C. cheese, mushrooms, ham, onions, pineapple
D. sausage, mushrooms, onions, cheese, and ham.
cheese
mushroom
olive
ham sausage
onion
pineapple
Fifi Yes
Mona No
Rex then ham
if sausage
Note: the statement “if sausage, then ham” doesn’t imply “If ham then sausage.” The obverse doesn’t necessarily follow.
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.
fallacious cogent
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