Mr. Cervone. History of Logic - Aristotle Aristotle Greek philosopher 384 BC – 322 BC Born in Stageira, Chalcidice (Thessaloniki – Greece) Studied at.

Slides:

Advertisements

Similar presentations

12.2: And and Or in Logic 1/17/ : And, Or and Not in Logic Expectations: L3.2.1:Know and use the terms of basic logic (e.g., proposition, negation,

Advertisements

Geometry Chapter 2 Terms.

Introduction to Symbolic Logic

HISTORY OF LOGIC BY JOHN NAGUIB. What is Logic? The science or study of how to evaluate arguments and reasoning. “Logic is new and necessary reasoning”

So far we have learned about:

SEVENTH EDITION and EXPANDED SEVENTH EDITION

TR1413: Discrete Mathematics For Computer Science Lecture 1: Mathematical System.

The Arithmetic of Reasoning: Logic and Boolean Algebra -Jeff Johnson -Mike Grassel.

CLASS VI. What is Geometry????!!!?? Geometry is the branch of mathematics which deals with the properties and relations of lines, angles, surfaces and.

KATE, ANDREW, JACOB THE ATOM- PHILOSOPHERS POINT OF VIEW.

What is logic? Logic is the science of how to evaluate arguments and reasoning. Critical thinking is a process of evaluation which uses logic to separate.

Unit 2 Reasoning & Proof.

Chapter 2 Midterm Review

Greek Philosophers, Scientists and Mathematicians.

Chapter 2 Section 5 - Slide 1 Copyright © 2009 Pearson Education, Inc. AND.

Chapter 2 Reasoning and Proof. AIM: Introduction to Logic What types of statements are considered mathematical ? Statements in which truth value (either.

نیت میں نیت کرتا ہوں کہ اس ڈھائی گھنٹے کی کلاسس سے کچھ مفید اور نیا سیکھوں گا اور اسے اپنی زندگی میں استعمال کروں گا. اور اس مقصد.

Computer Science 210 Computer Organization Introduction to Boolean Algebra.

Logic Geometry Unit 11, Lesson 5 Mrs. Reed. Definition Statement – a sentence that is either true or false. Example: There are 30 desks in the room.

Points, Lines, and Planes 1.2 Ms. Verdino. What will we be learning today? SPI : Use definitions, basic postulates, and theorems about points,

Boolean Algebra. Boolean algebra (or Boolean logic) is a logical calculus of truth values, developed by George Boole in the late 1830s. It created a notation.

Euclid and the “elements”. Euclid (300 BC, 265 BC (?) ) was a Greek mathematician, often referred to as the "Father of Geometry”. Of course this is not.

Greek Philosophy and History

Thinking Mathematically

6.1 Logic Logic is not only the foundation of mathematics, but also is important in numerous fields including law, medicine, and science. Although the.

A logical puzzle Given situation: Three women stand behind each other. Each one carries a hat on her head and sees only the hats of the person(s) standing.

Chapter 3 Section 1 - Slide 1 Copyright © 2009 Pearson Education, Inc. AND.

Logic Eric Hoffman Advanced Geometry PLHS Sept

Logic The Lost Art of Argument. Logic - Review Proposition – A statement that is either true or false (but not both) Conjunction – And Disjunction – Or.

Laws of Boolean Algebra Commutative Law Associative Law Distributive Law Identity Law De Morgan's Theorem.

Eculid By: Kaitlin Johnson.

Philosophy in Ancient Greece. Greek Philosophy Philosophy= love of wisdom Importance of reason – The Greeks began to be concerned with “life questions”

Important Concepts Postulates The geometry concepts that you are going to study through this course are largely based on ideas set forth more than.

Use Similar Right Triangles

GREEK PHILOSOPHERS I can explain the importance of the Greek philosophers; Socrates, Plato, and Aristotle.

Solve 7n – 2 = 5n + 6. Example 1: Solving Equations with Variables on Both Sides To collect the variable terms on one side, subtract 5n from both sides.

Review Find a counter example for the conjecture Given: JK = KL = LM = MJ Conjecture: JKLM forms a square.

Activity 1 Points, Lines, and Planes Section 1.1.

 Statement - sentence that can be proven true or false  Truth value – true or false  Statements are often represented using letters such as p and q.

Chapter 1 Logic and proofs

Geometry: Section 2.4 Algebraic Reasoning. What you will learn: 1. Use Algebraic Properties of Equality to justify the steps in solving an equation. 2.

•. Geometry is by far the. oldest branch of. mathematics. •

CPS120 Introduction to Computer Science

Computer Science 210 Computer Organization

Thinking Mathematically

Definitions and Biconditional Statements

Objectives Identify, name, and draw points, lines, segments, rays, and planes. Apply basic facts about points, lines, and planes.

Geometry Pre-AP BOMLA LacyMath 10/6.

COMPUTING FUNDAMENTALS

Euclid The Elements “There is no royal road to Geometry.”

JavaScript conditional

Sec. 2.3: Apply Deductive Reasoning

PYTHAGOREAN THEOREM VOCABULARY.

Section 3.1 Statements and Logical Connectives

Computer Science 210 Computer Organization

Greek Philosophers The Big Three.

(1.4) An Introduction to Logic

Pythagorean Theorem a²+ b²=c².

Or how to put your search together by using connectors

Objectives Identify, name, and draw points, lines, segments, rays, and planes. Apply basic facts about points, lines, and planes.

1-1 Vocabulary undefined term point line plane collinear coplanar

Inductive Reasoning and Conjecture, and Logic

PYTHAGOREAN THEOREM VOCABULARY.

And represent them using Venn Diagrams.

Logic of Informatics Introduction.

Millennium High School Agenda Calendar

Objectives Identify, name, and draw points, lines, segments, rays, and planes. Apply basic facts about points, lines, and planes.

2-2 Logic Vocab Statement: A sentence that is either true or false

Presentation transcript:

Mr. Cervone

History of Logic - Aristotle Aristotle Greek philosopher 384 BC – 322 BC Born in Stageira, Chalcidice (Thessaloniki – Greece) Studied at Plato’s Academy of Athens since he was 18 Father of logic Believed that logic should be build out of syllogism

History of Logic - Syllogism Syllogism: Starting from true statements followed by statements that must be true as well I.e. “If all monkeys are primates, and all primates are mammals, then all monkeys are mammals”. Learn new knowledge based on old knowledge

History of Logic – George Boole George Boole English mathematician & phylosopher 11/2/1815 – 12/8/1864 Inventor of Boolean Logic Gave rise to computer science

History of Logic – Boolean Logic Boolean Logic Truth values 0 and 1 Conjunction Disjunction Negation

Logic & Geometry What is Geometry? Branch of mathematics that defines and relates the basic properties and measurement of line segments and angles I.e. All angles in a triangle add up to 180°, etc. What does Logic have to do with Geometry? investigate how these geometric properties interact to form a logical system logical system must start with generally accepted terms and concepts that are building blocks of the system.

Logic & Geometry Truth: Begin somewhere with truths that are accepted without argument  Axioms I.e. Point is that which has no part I.e. Line is breathless length I.e. Set as a collection of objects I.e. Plane as a set of points forming a surface

What is Logic Examples SentenceType The Brooklyn Bridge is in New YorkTrue mathematical sentence (T) The capital of California is Los AngelesFalse mathematical sentence (F) Did you have soccer practice today?Nonmathemtical sentence 19-2Nonmathemtical sentence 5x = 10Open sentence: the variable is x Jenny found it behind the sofaOpen sentence: the variable is it

Negation Examples The negation of a statement always has the opposite truth value of the given or original statement and is usually formed by adding the word not to the given statement.