REASONING
Essence of reasoning: search for truth
We can consider something to be true if the available evidence seems to verify it. The more evidence we have, the stronger our conclusion can be
“You can’t prove the truth, but using deductive and inductive reasoning, you can get close.”
search for truth
essence of reasoning
deductive
inductive
types of reasoning
inductive reasoning
Drawing conclusions from facts using logic
If an inductive argument is strong, the truth of the premise would mean the conclusion is likely
If the inductive argument is weak, the logic connecting the premise and conclusion is incorrect
Observations and real life experiences
Specific to general
AKA Scientific Method
scientific method
inductive reasoning is also known as ______
generalized
statistical
sample
analogous
predictive
casual inference
5 types of inductive reasoning
generalized
draws a conclusion from a generalization
“All the swans I have seen are white; therefore, all swans are probably white.”
statistical
Draws a conclusion based on statistics
Generalization
“95% of swans are white; therefore, a randomly selected swan will probably be white”
sample
Draws a conclusion about one group based on a different sample group
1 group
“There are ten swans in this pond and are all white; therefore, the swans in my neighbor’s pond are probably also white”
analogous
Draws a conclusion based on shared properties of two groups
2 groups
“All Aylesbury ducks are white. Swans are similar to Aylesbury ducks. Therefore, all swans are probably white.”
predictive
Draws a conclusion based on a prediction made using a past sample
Past sample
“I visited this pond last year and all the swans were white. Therefore, when I visit again, all the swans will probably be white.”
causal inference
Draws a conclusion based on casual connection
Cause and effect
“All the swans in this pond are white. I just saw a white bird in the pond. The bird was probably a swan.”
deductive reasoning
Begins with a broad truth (the major premise), followed by the more specific statement (the minor premise), then the conclusion
Black and white; a conclusion is either true or false, and cannot be partly true or partly false
General to specific
inductive - predictive
Terry is always with James. Terry came to the party today so James must also be at the party.
is this inductive or deductive?
inductive
I see fireflies in my backyard every summer. This summer, I will probably see fireflies in my backyard.
deductive
Everytime I see Terry, James is with him, therefore Terry and James must always be together.
\n is this inductive or deductive?
intuition
Representation, an explanation, or an interpretation directly accepted by us as something normal, self-evident, intrinsically meaningful, like a simple, given fact
proof
An inferential argument for a mathematical statement
In the argument, other previously established statements, such as theorems, can be used
In principle, a proof can be traced back to self-evident or assumed statements, known as axioms, along with accepted rules of inference
certainty
Perfect knowledge that has total security from error, or the mental state of being without doubt
Objectively defined, certainty is total continuity and validity of all foundational inquiry, to the highest degree of precision
Something is certain only if no skepticism can occur
understand the problem
devise a plan
carry out the plan
look back
Polya’s 4 Steps in Problem Solving