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COLE'S WORLD OF MATHEMATICS
  • Home
  • YouTube Channel
    • All Playlists on YouTube
  • TI-84 Tutorials
  • M105 at IUK
    • TI-84 Tutorials
    • Chapter 5
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    • Chapter 8
    • Test Review
    • Released Exams & Quizzes
  • ACP Calculus at THS
    • Calculus Class Pictures
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    • Memorization Sheets
    • Chapter 1
    • Chapter 2
    • Chapter 3
    • Chapter 4
    • Chapter 5
    • Chapter 6
    • Chapter 7
    • Chapter 8
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  • Finite Math at THS
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    • Inductive & Deductive Reasoning Unit
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COLE'S WORLD OF MATHEMATICS
Introduction to Inductive & Deductive Reasoning
​Francis Bacon is credited with introducing inductive reasoning into scientific inquiry in the 17th century.  While he was the first to formalize the concept of a true scientific method, he did not do it without a little help.  The work of Nicolaus Copernicus (1473-1543) and Galileo Galilei (1563-1642) influenced Bacon tremendously.  Inductive reasoning begins with the specific details and observations and uses them to arrive at a principle to explain them.  What we now call the scientific method is largely inductive. 
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Francis Bacon (1561 - 1626)
 The Greek philosopher Aristotle is considered to be the father of deductive reasoning because he actually carved out the entire subject of logic for the first time. He identified the most common and crucial type of reasoning.  He defined for the first time what it means to prove something, to prove it or explain it, objectively, on the basis of facts.

Deductive reasoning is a logical process in which a conclusion is based on the concordance of multiple premises that are generally assumed to be true.
 
Aristotle’s classic example is as follows:
  • All mean are mortal.
  • Socrates is a man.
  • Therefore, Socrates is mortal.​
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Aristotle (384 - 322 BC)
In Aristotle’s example, sometimes referred to as a syllogism, the premises of the argument – that all men are mortal and that Socrates is a man – are true.  Because the premises establish that Socrates is an individual in a group whose members are all mortal, the inescapable conclusion is that Socrates must likewise be mortal.

Lecture Notes & Other Resources

TENTATIVE SCHEDULE FOR THE UNIT

VIDEO: Introduction to Inductive vs Deductive vs Abductive Reasoning

Inductive Reasoning - Day 1
The Path of a Billiard Ball

Inductive Reasoning - Day 2
More Billiard Ball Mathematics

Inductive Reasoning - Day 3
The Nature of Inductive Reasoning

1 cm Grid Paper

Inductive Reasoning WS
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VIDEO: How To Solve A Logic Problem
-----Mathematician Logic Problem
-----Online Logic Puzzle Website

-----Online Sudoku Puzzle Website

Sherlock Holmes
A Look at the Reasoning that Sherlock Holmes Uses

Sherlock Holmes Movie Analysis Paper

Two Minute Mysteries
-----The Case of the Angry Chef
-----The Case of the Attempted Murder
-----The Case of the Attic Suicide
-----The Case of the Balloon Man
-----The Case of the Bamboo Fence

Inductive & Deductive Reasoning Unit ASSESSMENT

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