5 Categorical Syllogisms

Slides:

Advertisements

Similar presentations

Geometry Chapter 2 Terms.

Advertisements

Venn Diagram Technique for testing syllogisms

Chapter 3 Introduction to Logic © 2008 Pearson Addison-Wesley.

Chapter 2 By: Nick Holliday Josh Vincz, James Collins, and Greg “Darth” Rader.

Four Rules of Aristotelian Logic 1. Rule of Identity: A is A 2. Rule of Non-Contradiction: A is not (-A) 3. Rule of Excluded Middle: Either A or (-A)

Rules of Inferences Section 1.5. Definitions Argument: is a sequence of propositions (premises) that end with a proposition called conclusion. Valid Argument:

Deductive Arguments: Categorical Logic

1 Philosophy 1100 Title:Critical Reasoning Instructor:Paul Dickey Website:

Chapter 1 The Logic of Compound Statements. Section 1.3 Valid & Invalid Arguments.

Contrapositive and Inverse

Critical Thinking Lecture 9 The Square of Opposition By David Kelsey.

Philosophy 1100 Today: Hand Back “Nail that Claim” Exercise! & Discuss

Categorical Syllogisms Always have two premises Consist entirely of categorical claims May be presented with unstated premise or conclusion May be stated.

Syllogistic Logic 1. C Categorical Propositions 2. V Venn Diagram 3. The Square of Opposition: Tradition / Modern 4. C Conversion, Obversion, Contraposition.

Immediate Inference Three Categorical Operations

Proof by Deduction. Deductions and Formal Proofs A deduction is a sequence of logic statements, each of which is known or assumed to be true A formal.

Chapter 3 Section 4 – Slide 1 Copyright © 2009 Pearson Education, Inc. AND.

Copyright © 2008 Pearson Education, Inc. Chapter 1.

2.5 Verifying Arguments Write arguments symbolically. Determine when arguments are valid or invalid. Recognize form of standard arguments. Recognize common.

CATEGORICAL PROPOSITIONS, CHP. 8 DEDUCTIVE LOGIC VS INDUCTIVE LOGIC ONE CENTRAL PURPOSE: UNDERSTANDING CATEGORICAL SYLLOGISMS AS THE BUILDING BLOCKS OF.

Section 3.5 Symbolic Arguments

Philosophy 148 Chapter 7. AffirmativeNegative UniversalA: All S are PE: No S is P ParticularI: Some S is PO: Some S is not P.

2.3Logical Implication: Rules of Inference From the notion of a valid argument, we begin a formal study of what we shall mean by an argument and when such.

Question of the Day!  We shared a lot of examples of illogical arguments!  But how do you make a LOGICAL argument? What does your argument need? What.

Chapter 18: Conversion, Obversion, and Squares of Opposition

4 Categorical Propositions

From conclusions by applying the laws of logic. Symbolic Notation Conditional statement If p, then qp ⟶q Converseq⟶p Biconditional p ⟷ q.

Section 2-2: Conditional Statements. Conditional A statement that can be written in If-then form symbol: If p —>, then q.

Equivalent Fractions.

CATEGORICAL SYLLOGISMS

Venn Diagrams Truth Sets & Valid Arguments Truth Sets & Valid Arguments Truth Tables Implications Truth Tables Implications Truth Tables Converse, Inverse,

Critical Thinking Lecture 9 The Square of Opposition

Chapter 19: Living in the Real World. Introductory Remarks (p. 190) The joy and misery of ordinary English is that you can say the same thing in many.

Section 2.2 Analyze Conditional Statements. What is an if-then statement? If-then statements can be used to clarify statements that may seem confusing.

Inverse, Contrapositive & indirect proofs Sections 6.2/6.3.

Section 2.3: Deductive Reasoning

Section 2.1 Geometric Statements. Definitions: Conditionals, Hypothesis, & Conclusions: A conditional statement is a logical statement that has two parts:

5-Minute Check Converse: Inverse: Contrapositive: Hypothesis: Conclusion: The measure of an angle is less than 90  The angle is acute If an angle is.

Section 2.2 Homework Quiz Question Put the following Conditional Statement into If Then Form: All birds have feathers.

Venn Diagram Technique for testing syllogisms

OTCQ True or False An Isosceles triangle has 2 congruent sides and no congruent angles. An Equiangular triangle has three angles that measure 70◦. A right.

a valid argument with true premises.

Methods of proof Section 1.6 & 1.7 Wednesday, June 20, 2018

5 Categorical Syllogisms

Venn Diagrams 1= s that are not p; 2= s that are p; 3= p that are not s S P.

Methods of Proof A mathematical theorem is usually of the form pq

5.1 Standard Form, Mood, and Figure

5 Categorical Syllogisms

Principles of Computing – UFCFA3-30-1

Chapter 8 Logic Topics

Conditional Statements

Confirmation The Raven Paradox.

Philosophy 1100 Class #8 Title: Critical Reasoning

Critical Thinking Lecture 9 The Square of Opposition

Section 3.5 Symbolic Arguments

Chapter 3 Introduction to Logic 2012 Pearson Education, Inc.

3.5 Symbolic Arguments.

Philosophy 1100 Title: Critical Reasoning Instructor: Paul Dickey

Conditional Original IF-THEN statement.

Premise: If it’s a school day, then I have Geometry class.

X X X X Logical relations among categorical propositions S P S P S P

Philosophy 1100 Class #9 Title: Critical Reasoning

Logic and Reasoning.

Conditional Statements Section 2.3 GEOMETRY

Chapter 3 Introduction to Logic © 2008 Pearson Addison-Wesley.

If there is any case in which true premises lead to a false conclusion, the argument is invalid. Therefore this argument is INVALID.

3.5 Symbolic Arguments.

If there is any case in which true premises lead to a false conclusion, the argument is invalid. Therefore this argument is INVALID.

Presentation transcript:

5 Categorical Syllogisms 5.4 Reducing the Number of Terms

Reducing the Number of Terms This section is really just about using Conversion, Obversion, and Contraposition to get arguments into standard form. Let’s review what these operations work on: Conversion (E and I) Obversion (A, E, I, and O) Contraposition (A and O)

Reducing the Number of Terms All P are non-W Some E are W Some non-P are not non-E How many terms are there? ____ How many can there be in a Standard Form Categorical Syllogism? ____ How can we fix the argument? ____

Reducing the Number of Terms On premise one, what operation will result in a logically equivalent form, while reducing the number of terms in the argument?

Reducing the Number of Terms All P are non-W --- obversion ---> No P are W Cool. How about the conclusion, Some non-P are not non-E ? What would get rid of the complexity?

Reducing the Number of Terms Some non-P are not non-E --- Contraposition ---> Some E are not P So, putting the argument back together, All P are non-W Some E are W Some non-P are not non-E Obversion  Contraposition  No P are W Some E are W Some E are not P Test this argument using Venn or 5 Rules