[MMW] M3 - Problem Solving and Reasoning

**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

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* *“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