# CHAPTER 10 VENN DIAGRAMS

Size: px
Start display at page:

Transcription

1 HATER 10 VENN DAGRAM NTRODUTON n the nineteenth-century, John Venn developed a technique for determining whether a categorical syllogism is valid or invalid. Although the method he constructed relied on the modern interpretation of universal statements, we can easily modify it for use on the older classical view of such statements. n the present chapter we will begin by explaining the technique as Venn originally developed it. Then later we will show you how to use it to determine validity on the older classical theory of categorical syllogisms. REREENTNG ATEGORAL YLLOGM WTH VENN DAGRAM The two overlapping rectangles above should be construed as representing two sets. The one on the left represents the set consisting in all of the things there are in the universe; while the one on the right represents all of the things there are in the universe. That part of the rectangle which overlaps with the rectangle represents those objects in the universe that are members of both sets. That portion of the rectangle that does not overlap with the rectangle represents all of the objects in the universe that are but not. While that portion of the rectangle that does not overlap with the rectangle represents all of the things in the universe that are but not. HADNG f we want to show that nothing is in a certain area we do this by shading that area. o, for example, if we want to say there are no s that are not s, we shade the area of the rectangle that does not overlap the area of the rectangle. We represent the claim that all are in this way. All are.

2 On the other hand, if we want to represent the claim that no s are s, we can do this by shading the area where the rectangle and rectangle overlap. No are. Finally, if we want to show that all are, or, in other words, there are no s that are not also s, we can shade the rightmost part of. All are. NDATNG THAT OMETHNG N AN AREA To show that something is in a certain area we place a capital X in that area. Thus, to say that there is something that is a member of, but not a member of, we place an X in the section of the rectangle that does not overlap with the rectangle. ome are not.

3 To say that something exists that belongs to both sets we place a capital X in the area where the two rectangles overlap. ome are. To represent that something is a member of, but not of, we place an X in the area of the rectangle that doesn't overlap the rectangle. ome are not. Finally, if we know that the set has something in it, but we don't know whether that thing is or is not also a member of, we will place a lower case x in both sets and then connect them with a line. Thus, the diagram below tells us that there is at least one member of, but it does not tell us whether that thing is, or is not, also a member of. There are some.

4 REREENTNG ATEGORAL YLLOGM o far we have been concerned with representing single statements in Venn diagrams. An argument, however, is not one statement, and a categorical syllogism is a type of argument. More specifically, a categorical syllogism is an argument that contains exactly two premises, both of which are categorical statements. The problem is how do we use Venn diagrams to represent categorical syllogisms? And how do we use them to decide whether such syllogisms are valid? erhaps the first thing to notice is that a categorical syllogism refers to three sets, rather than two. o, instead of two overlapping rectangles we will need three such rectangles. EXAMLE 1 ome schools are colleges. ome colleges are educational institutions. To decide whether the argument above is valid or invalid we must begin by representing both of the premises in the diagram. We represent the first premise by shading the area of schools that are not educational institutions. ome schools are colleges. ome colleges are educational institutions. Then we need to represent the second premise. This premise tells us that there is at least one school that is also a college. To express this in the diagram, we need to place an x in those areas where schools and colleges overlap. The only such area that has not been shaded, however, is the area where the three rectangles

5 overlap. o we know that something exists in this area. We must, therefore, place a capital X in this area and our diagram will then look like this: ome schools are colleges. ome colleges are educational institutions. All that remains is to evaluate whether the conclusion of the argument follows from its premises. f it does the argument is valid; otherwise it is invalid. learly the argument in question is valid. Let's try one more example. EXAMLE 2 ome schools are educational institutions. ome schools are colleges. ome colleges are educational institutions. To represent the first premise of this argument, we need to show that something is in the area of schools that are educational institutions. n the diagram there are, however, two areas that represent schools that are educational institutions and, unfortunately, the first premise doesn't tell us whether the schools that are educational institutions are, or are not, colleges. o we need to place a lowercase x in both areas and draw a line between them.

6 ome schools are educational institutions. ome schools are colleges. ome colleges are educational institutions. learly we have to represent the second premise in a similar way, except that we need to x-x the areas where schools and colleges overlap. Once we have done this our diagram will look like this: ome schools are educational institutions. ome schools are colleges. ome colleges are educational institutions. Evidently the conclusion of this argument does not follow from its premises since the conclusion informs us that something is definitely in the area where colleges and educational institutions overlap but the diagram doesn't show this. UNG VENN DAGRAM TO DETERMNE VALDTY ON THE LAAL VEW To use Venn diagrams to determine validity on the classical view we need to alter the above account. lassical logic evidently assumes that in sentences which express universal categorical statements, both the subject and predicate terms refer to existing objects. o on the classical view, the statement that all are entails that there exists an that is a. While the statement that no are entails not only that there exists an that is not a, but also that there exists a that is not an.

7 f we want to use Venn diagrams to determine validity on the classical view we need to add these assumptions to the diagram. o if the statement is an A-statement, besides shading the area of that is not, we must also add an X to the area where and overlap. Doing this, we obtain.... All are. On the other hand, if we want to represent the statement that no are, besides shading the area where the and rectangles overlap, we also need to place an X in the area of the rectangle that is not in the rectangle, and in the area of the rectangle that is not in the rectangle. Doing this we get: EXAMLE 1 No are. Let's see how this will work with some actual syllogisms. All colleges are schools. ome colleges are educational institutions.

8 The easiest way to handle this is to begin by representing the premises in the same way we would if we were adopting the modern perspective. Accordingly, we shade all of those areas of schools that are not educational institutions and of colleges that are not schools. Thus, we will shade the diagram as suggested below. (Notice that if this were the end of the matter we would have to evaluate the argument as invalid, since the conclusion does not follow from the premises.) All colleges are schools. ome colleges are educational institutions. However, we are not finished yet. We must now add the assumptions that the premises make about the sets referred to in their subject terms. Here this means that we must place a capital X in the area that represents colleges that are schools, since this is implied by the first premise. All colleges are schools. ome colleges are educational institutions. Normally, we would also have to place lowercase x-x in the two areas where schools and educational institutions overlap, since this is an assumption that the second premise commits us to. Here, however, since the earlier premise already commits us not only to the existence of some colleges, but also to existence of some schools, this is unnecessary. learly, our diagram shows that the argument is valid on the classical view.

9 NOTE: Any argument that is valid on the modern view will also be valid on the classical view; and any argument that is invalid on the classical view will also be invalid on the modern view. (The converses of these principles are, however, not true.) EXAMLE 2 B No schools are bars. ome bars are not educational institutions. As we suggested in the last example, we begin by representing the premises just as we would if we were adopting the modern view of syllogisms. Doing this, we get.... B No schools are bars. ome bars are not educational institutions. Now, however, we need to add the additional assumptions that the classical view makes about the premises. ince the first premise commits us to the existence of at least one school that is an educational institution, we need to represent this by placing a capital X in the un-shaded area where schools and educational institutions overlap.

10 No schools are bars. ome bars are not educational institutions. B To represent the presuppositions that classical logic makes about the second premise we must also add in our diagram that there exist some schools that are not bars and some bars that are not schools. However, we have already represented the first of these assumptions in the diagram. o all we need to do then is to represent the assumption that some bars exist that are not schools. We do this by x-ing the area of bars that are educational institutions and the area of bars that are not educational institutions, and drawing a line between them. No schools are bars. ome bars are not educational institutions. B nspecting the diagram we have now completed, we see that the conclusion of the argument does not follow from its premises. t is, therefore, invalid. A WORD OF WARNNG All of this may seem clear enough, and so long as the things we are reasoning about exist, the principles of classical logic are acceptable. When we begin reasoning about objects that don't exist, however, problems arise. First, the principle that the contradictory of any A statement must have the opposite truth-value of that statement does not work. Thus, suppose for example, the statement is that all unicorns are beautiful animals. This statement is false on the classical view, because there are no unicorns; while the contradictory, "ome unicorns are not beautiful animals," is also false for precisely the same reason. Moreover, both the -statement "ome unicorns are beautiful animals," and its contradictory "No unicorns are

13 EXERE nstructions: onstruct two Venn Diagrams on the syllogism below, one of which represents that argument on the modern view, and the other of which represents it on the classical perspective. Decide whether the argument is valid or invalid on each view. All vampires are bats. No vampires are hemophiliacs. ome hemophiliacs are not bats. nstructions: onstruct two Venn Diagrams on each of the arguments below, one of which represents that argument from the modern view, and the other of which represents it on the classical view. Determine whether the argument is valid or invalid on each of the two perspectives. 1. No diamonds are opals. No diamonds are sapphires. o no sapphires are opals. 2. ome islands are vacation resorts. All islands are paradises. o some paradises are vacation resorts. 3. All teachers are alcoholics. No alcoholics are politicians. o some politicians are not teachers. 4. No pleasurable experiences are headaches. All R audits are headaches. o no R audits are pleasurable experiences. 5. All dragons are fire hazards. No endangered species are fire hazards. o some endangered species are not dragons. 6. Only funny people are clowns. Funny people are never tedious oafs. o, all tedious oafs are non-clowns. A BRANTEAER nstructions: onstruct Venn-like Diagrams on the argument below and determine whether it is valid or invalid on both the classical and modern interpretations. ince all vampires are bats and some vampires are bloodsuckers, but no hemophiliacs are bats, it follows that some bloodsuckers are not hemophiliacs. LMTATON AND A ROLOGUE Although they are effective in determining the validity of many arguments containing quantifiers, both the syllogistic and diagrammatic approaches we have been exploring in the last two chapters are somewhat limited, most especially because they are unable to effectively evaluate arguments with premises involving two or more quantifiers. They cannot, for example, determine the validity of the argument that since everyone loves a lover and someone loves someone, it follows that everyone loves everyone. How these sorts of arguments are to be dealt with was not discovered until the invention of quantification theory in the early part of the twentieth century.

### Part 2 Module 4: Categorical Syllogisms

Part 2 Module 4: Categorical Syllogisms Consider Argument 1 and Argument 2, and select the option that correctly identifies the valid argument(s), if any. Argument 1 All bears are omnivores. All omnivores

### Philosophy 1100: Introduction to Ethics. Critical Thinking Lecture 1. Background Material for the Exercise on Validity

Philosophy 1100: Introduction to Ethics Critical Thinking Lecture 1 Background Material for the Exercise on Validity Reasons, Arguments, and the Concept of Validity 1. The Concept of Validity Consider

### 5.3 The Four Kinds of Categorical Propositions

M05_COI1396_13_E_C05.QXD 11/13/07 8:39 AM age 182 182 CHATER 5 Categorical ropositions Categorical propositions are the fundamental elements, the building blocks of argument, in the classical account of

### Complications for Categorical Syllogisms. PHIL 121: Methods of Reasoning February 27, 2013 Instructor:Karin Howe Binghamton University

Complications for Categorical Syllogisms PHIL 121: Methods of Reasoning February 27, 2013 Instructor:Karin Howe Binghamton University Overall Plan First, I will present some problematic propositions and

### SYLLOGISTIC LOGIC CATEGORICAL PROPOSITIONS

Prof. C. Byrne Dept. of Philosophy SYLLOGISTIC LOGIC Syllogistic logic is the original form in which formal logic was developed; hence it is sometimes also referred to as Aristotelian logic after Aristotle,

### Baronett, Logic (4th ed.) Chapter Guide

Chapter 6: Categorical Syllogisms Baronett, Logic (4th ed.) Chapter Guide A. Standard-form Categorical Syllogisms A categorical syllogism is an argument containing three categorical propositions: two premises

### 1 Clarion Logic Notes Chapter 4

1 Clarion Logic Notes Chapter 4 Summary Notes These are summary notes so that you can really listen in class and not spend the entire time copying notes. These notes will not substitute for reading the

### 13.6 Euler Diagrams and Syllogistic Arguments

EulerDiagrams.nb 1 13.6 Euler Diagrams and Syllogistic rguments In the preceding section, we showed how to determine the validity of symbolic arguments using truth tables and comparing the arguments to

### Deduction. Of all the modes of reasoning, deductive arguments have the strongest relationship between the premises

Deduction Deductive arguments, deduction, deductive logic all means the same thing. They are different ways of referring to the same style of reasoning Deduction is just one mode of reasoning, but it is

### Venn Diagrams and Categorical Syllogisms. Unit 5

Venn Diagrams and Categorical Syllogisms Unit 5 John Venn 1834 1923 English logician and philosopher noted for introducing the Venn diagram Used in set theory, probability, logic, statistics, and computer

### Selections from Aristotle s Prior Analytics 41a21 41b5

Lesson Seventeen The Conditional Syllogism Selections from Aristotle s Prior Analytics 41a21 41b5 It is clear then that the ostensive syllogisms are effected by means of the aforesaid figures; these considerations

### 9.1 Intro to Predicate Logic Practice with symbolizations. Today s Lecture 3/30/10

9.1 Intro to Predicate Logic Practice with symbolizations Today s Lecture 3/30/10 Announcements Tests back today Homework: --Ex 9.1 pgs. 431-432 Part C (1-25) Predicate Logic Consider the argument: All

### 7. Some recent rulings of the Supreme Court were politically motivated decisions that flouted the entire history of U.S. legal practice.

M05_COPI1396_13_SE_C05.QXD 10/12/07 9:00 PM Page 193 5.5 The Traditional Square of Opposition 193 EXERCISES Name the quality and quantity of each of the following propositions, and state whether their

### 6.5 Exposition of the Fifteen Valid Forms of the Categorical Syllogism

M06_COPI1396_13_SE_C06.QXD 10/16/07 9:17 PM Page 255 6.5 Exposition of the Fifteen Valid Forms of the Categorical Syllogism 255 7. All supporters of popular government are democrats, so all supporters

### SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Exam Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Draw a Venn diagram for the given sets. In words, explain why you drew one set as a subset of

### HANDBOOK (New or substantially modified material appears in boxes.)

1 HANDBOOK (New or substantially modified material appears in boxes.) I. ARGUMENT RECOGNITION Important Concepts An argument is a unit of reasoning that attempts to prove that a certain idea is true by

### HANDBOOK (New or substantially modified material appears in boxes.)

1 HANDBOOK (New or substantially modified material appears in boxes.) I. ARGUMENT RECOGNITION Important Concepts An argument is a unit of reasoning that attempts to prove that a certain idea is true by

### Philosophy 1100: Ethics

Philosophy 1100: Ethics Topic 1 - Course Introduction: 1. What is Philosophy? 2. What is Ethics? 3. Logic a. Truth b. Arguments c. Validity d. Soundness What is Philosophy? The Three Fundamental Questions

### Philosophy 57 Day 10. Chapter 4: Categorical Statements Conversion, Obversion & Contraposition II

Branden Fitelson Philosophy 57 Lecture 1 Branden Fitelson Philosophy 57 Lecture 2 Chapter 4: Categorical tatements Conversion, Obversion & Contraposition I Philosophy 57 Day 10 Quiz #2 Curve (approximate)

### Pastor-teacher Don Hargrove Faith Bible Church September 8, 2011

Pastor-teacher Don Hargrove Faith Bible Church http://www.fbcweb.org/doctrines.html September 8, 2011 Building Mental Muscle & Growing the Mind through Logic Exercises: Lesson 4a The Three Acts of the

### Transition to Quantified Predicate Logic

Transition to Quantified Predicate Logic Predicates You may remember (but of course you do!) during the first class period, I introduced the notion of validity with an argument much like (with the same

### Dr. Carlo Alvaro Reasoning and Argumentation Distribution & Opposition DISTRIBUTION

DISTRIBUTION Categorical propositions are statements that describe classes (groups) of objects designate by the subject and the predicate terms. A class is a group of things that have something in common

### Basic Concepts and Skills!

Basic Concepts and Skills! Critical Thinking tests rationales,! i.e., reasons connected to conclusions by justifying or explaining principles! Why do CT?! Answer: Opinions without logical or evidential

### SOME RADICAL CONSEQUENCES OF GEACH'S LOGICAL THEORIES

SOME RADICAL CONSEQUENCES OF GEACH'S LOGICAL THEORIES By james CAIN ETER Geach's views of relative identity, together with his Paccount of proper names and quantifiers, 1 while presenting what I believe

### HANDBOOK. IV. Argument Construction Determine the Ultimate Conclusion Construct the Chain of Reasoning Communicate the Argument 13

1 HANDBOOK TABLE OF CONTENTS I. Argument Recognition 2 II. Argument Analysis 3 1. Identify Important Ideas 3 2. Identify Argumentative Role of These Ideas 4 3. Identify Inferences 5 4. Reconstruct the

### Logic: A Brief Introduction. Ronald L. Hall, Stetson University

Logic: A Brief Introduction Ronald L. Hall, Stetson University 2012 CONTENTS Part I Critical Thinking Chapter 1 Basic Training 1.1 Introduction 1.2 Logic, Propositions and Arguments 1.3 Deduction and Induction

### Aquinas' Third Way Modalized

Philosophy of Religion Aquinas' Third Way Modalized Robert E. Maydole Davidson College bomaydole@davidson.edu ABSTRACT: The Third Way is the most interesting and insightful of Aquinas' five arguments for

### On the Aristotelian Square of Opposition

On the Aristotelian Square of Opposition Dag Westerståhl Göteborg University Abstract A common misunderstanding is that there is something logically amiss with the classical square of opposition, and that

### SAVING RELATIVISM FROM ITS SAVIOUR

CRÍTICA, Revista Hispanoamericana de Filosofía Vol. XXXI, No. 91 (abril 1999): 91 103 SAVING RELATIVISM FROM ITS SAVIOUR MAX KÖLBEL Doctoral Programme in Cognitive Science Universität Hamburg In his paper

### Logic Appendix: More detailed instruction in deductive logic

Logic Appendix: More detailed instruction in deductive logic Standardizing and Diagramming In Reason and the Balance we have taken the approach of using a simple outline to standardize short arguments,

### 1/19/2011. Concept. Analysis

Analysis Breaking down an idea, concept, theory, etc. into its most basic parts in order to get a better understanding of its structure. This is necessary to evaluate the merits of the claim properly (is

### What would count as Ibn Sīnā (11th century Persia) having first order logic?

1 2 What would count as Ibn Sīnā (11th century Persia) having first order logic? Wilfrid Hodges Herons Brook, Sticklepath, Okehampton March 2012 http://wilfridhodges.co.uk Ibn Sina, 980 1037 3 4 Ibn Sīnā

### Unit. Categorical Syllogism. What is a syllogism? Types of Syllogism

Unit 8 Categorical yllogism What is a syllogism? Inference or reasoning is the process of passing from one or more propositions to another with some justification. This inference when expressed in language

### PHI Introduction Lecture 4. An Overview of the Two Branches of Logic

PHI 103 - Introduction Lecture 4 An Overview of the wo Branches of Logic he wo Branches of Logic Argument - at least two statements where one provides logical support for the other. I. Deduction - a conclusion

### 6. Truth and Possible Worlds

6. Truth and Possible Worlds We have defined logical entailment, consistency, and the connectives,,, all in terms of belief. In view of the close connection between belief and truth, described in the first

### Study Guides. Chapter 1 - Basic Training

Study Guides Chapter 1 - Basic Training Argument: A group of propositions is an argument when one or more of the propositions in the group is/are used to give evidence (or if you like, reasons, or grounds)

### The Sea-Fight Tomorrow by Aristotle

The Sea-Fight Tomorrow by Aristotle Aristotle, Antiquities Project About the author.... Aristotle (384-322) studied for twenty years at Plato s Academy in Athens. Following Plato s death, Aristotle left

### In this section you will learn three basic aspects of logic. When you are done, you will understand the following:

Basic Principles of Deductive Logic Part One: In this section you will learn three basic aspects of logic. When you are done, you will understand the following: Mental Act Simple Apprehension Judgment

### Situations in Which Disjunctive Syllogism Can Lead from True Premises to a False Conclusion

398 Notre Dame Journal of Formal Logic Volume 38, Number 3, Summer 1997 Situations in Which Disjunctive Syllogism Can Lead from True Premises to a False Conclusion S. V. BHAVE Abstract Disjunctive Syllogism,

### Chapter 1. Introduction. 1.1 Deductive and Plausible Reasoning Strong Syllogism

Contents 1 Introduction 3 1.1 Deductive and Plausible Reasoning................... 3 1.1.1 Strong Syllogism......................... 3 1.1.2 Weak Syllogism.......................... 4 1.1.3 Transitivity

### PRACTICE EXAM The state of Israel was in a state of mourning today because of the assassination of Yztzak Rabin.

PRACTICE EXAM 1 I. Decide which of the following are arguments. For those that are, identify the premises and conclusions in them by CIRCLING them and labeling them with a P for the premises or a C for

### Informalizing Formal Logic

Informalizing Formal Logic Antonis Kakas Department of Computer Science, University of Cyprus, Cyprus antonis@ucy.ac.cy Abstract. This paper discusses how the basic notions of formal logic can be expressed

### 1.2. What is said: propositions

1.2. What is said: propositions 1.2.0. Overview In 1.1.5, we saw the close relation between two properties of a deductive inference: (i) it is a transition from premises to conclusion that is free of any

### TWO VERSIONS OF HUME S LAW

DISCUSSION NOTE BY CAMPBELL BROWN JOURNAL OF ETHICS & SOCIAL PHILOSOPHY DISCUSSION NOTE MAY 2015 URL: WWW.JESP.ORG COPYRIGHT CAMPBELL BROWN 2015 Two Versions of Hume s Law MORAL CONCLUSIONS CANNOT VALIDLY

### Part II: How to Evaluate Deductive Arguments

Part II: How to Evaluate Deductive Arguments Week 4: Propositional Logic and Truth Tables Lecture 4.1: Introduction to deductive logic Deductive arguments = presented as being valid, and successful only

### Introducing truth tables. Hello, I m Marianne Talbot and this is the first video in the series supplementing the Formal Logic podcasts.

Introducing truth tables Marianne: Hello, I m Marianne Talbot and this is the first video in the series supplementing the Formal Logic podcasts. Okay, introducing truth tables. (Slide 2) This video supplements

### Predicate logic. Miguel Palomino Dpto. Sistemas Informáticos y Computación (UCM) Madrid Spain

Predicate logic Miguel Palomino Dpto. Sistemas Informáticos y Computación (UCM) 28040 Madrid Spain Synonyms. First-order logic. Question 1. Describe this discipline/sub-discipline, and some of its more

### Deduction by Daniel Bonevac. Chapter 1 Basic Concepts of Logic

Deduction by Daniel Bonevac Chapter 1 Basic Concepts of Logic Logic defined Logic is the study of correct reasoning. Informal logic is the attempt to represent correct reasoning using the natural language

### What is a logical argument? What is deductive reasoning? Fundamentals of Academic Writing

What is a logical argument? What is deductive reasoning? Fundamentals of Academic Writing Logical relations Deductive logic Claims to provide conclusive support for the truth of a conclusion Inductive

Lecture 8: Refutation Philosophy 130 March 19 & 24, 2015 O Rourke I. Administrative A. Roll B. Schedule C. Exam #1 comments on difficult spots; if you have questions about this, please let me know D. Discussion

### Lecture 1: Validity & Soundness

Lecture 1: Validity & Soundness 1 Goals Today Introduce one of our central topics: validity and soundness, and its connection to one of our primary course goals, namely: learning how to evaluate arguments

### Empty Names and Two-Valued Positive Free Logic

Empty Names and Two-Valued Positive Free Logic 1 Introduction Zahra Ahmadianhosseini In order to tackle the problem of handling empty names in logic, Andrew Bacon (2013) takes on an approach based on positive

### Richard L. W. Clarke, Notes REASONING

1 REASONING Reasoning is, broadly speaking, the cognitive process of establishing reasons to justify beliefs, conclusions, actions or feelings. It also refers, more specifically, to the act or process

### INTERMEDIATE LOGIC Glossary of key terms

1 GLOSSARY INTERMEDIATE LOGIC BY JAMES B. NANCE INTERMEDIATE LOGIC Glossary of key terms This glossary includes terms that are defined in the text in the lesson and on the page noted. It does not include

### Logic: Deductive and Inductive by Carveth Read M.A. CHAPTER VIII

CHAPTER VIII ORDER OF TERMS, EULER'S DIAGRAMS, LOGICAL EQUATIONS, EXISTENTIAL IMPORT OF PROPOSITIONS Section 1. Of the terms of a proposition which is the Subject and which the Predicate? In most of the

### Reasoning SYLLOGISM. follows.

Reasoning SYLLOGISM RULES FOR DERIVING CONCLUSIONS 1. The Conclusion does not contain the Middle Term (M). Premises : All spoons are plates. Some spoons are cups. Invalid Conclusion : All spoons are cups.

### Lecture 2.1 INTRO TO LOGIC/ ARGUMENTS. Recognize an argument when you see one (in media, articles, people s claims).

TOPIC: You need to be able to: Lecture 2.1 INTRO TO LOGIC/ ARGUMENTS. Recognize an argument when you see one (in media, articles, people s claims). Organize arguments that we read into a proper argument

### Comments on Truth at A World for Modal Propositions

Comments on Truth at A World for Modal Propositions Christopher Menzel Texas A&M University March 16, 2008 Since Arthur Prior first made us aware of the issue, a lot of philosophical thought has gone into

### In more precise language, we have both conditional statements and bi-conditional statements.

MATD 0385. Day 5. Feb. 3, 2010 Last updated Feb. 3, 2010 Logic. Sections 3-4, part 2, page 1 of 8 What does logic tell us about conditional statements? When I surveyed the class a couple of days ago, many

### In Search of the Ontological Argument. Richard Oxenberg

1 In Search of the Ontological Argument Richard Oxenberg Abstract We can attend to the logic of Anselm's ontological argument, and amuse ourselves for a few hours unraveling its convoluted word-play, or

### 10.3 Universal and Existential Quantifiers

M10_COPI1396_13_SE_C10.QXD 10/22/07 8:42 AM Page 441 10.3 Universal and Existential Quantifiers 441 and Wx, and so on. We call these propositional functions simple predicates, to distinguish them from

### Lecture 3 Arguments Jim Pryor What is an Argument? Jim Pryor Vocabulary Describing Arguments

Lecture 3 Arguments Jim Pryor What is an Argument? Jim Pryor Vocabulary Describing Arguments 1 Agenda 1. What is an Argument? 2. Evaluating Arguments 3. Validity 4. Soundness 5. Persuasive Arguments 6.

### MCQ IN TRADITIONAL LOGIC. 1. Logic is the science of A) Thought. B) Beauty. C) Mind. D) Goodness

MCQ IN TRADITIONAL LOGIC FOR PRIVATE REGISTRATION TO BA PHILOSOPHY PROGRAMME 1. Logic is the science of-----------. A) Thought B) Beauty C) Mind D) Goodness 2. Aesthetics is the science of ------------.

### Philosophy 57 Day 10

Branden Fitelson Philosophy 57 Lecture 1 Philosophy 57 Day 10 Quiz #2 Curve (approximate) 100 (A); 70 80 (B); 50 60 (C); 40 (D); < 40 (F) Quiz #3 is next Tuesday 03/04/03 (on chapter 4 not tnanslation)

### 1. Immediate inferences embodied in the square of opposition 2. Obversion 3. Conversion

CHAPTER 3: CATEGORICAL INFERENCES Inference is the process by which the truth of one proposition (the conclusion) is affirmed on the basis of the truth of one or more other propositions that serve as its

### Geometry TEST Review Chapter 2 - Logic

Geometry TEST Review Chapter 2 - Logic Name Period Date Symbolic notation: 1. Define the following symbols. a b ~ c d e g a b c d a b c d 2. Consider the following legend: Let p = You love bananas. Let

### Review Deductive Logic. Wk2 Day 2. Critical Thinking Ninjas! Steps: 1.Rephrase as a syllogism. 2.Choose your weapon

Review Deductive Logic Wk2 Day 2 Checking Validity of Deductive Argument Steps: 1.Rephrase as a syllogism Identify premises and conclusion. Look out for unstated premises. Place them in order P(1), P(2),

### Woods, John (2001). Aristotle s Earlier Logic. Oxford: Hermes Science, xiv pp. ISBN

Woods, John (2001). Aristotle s Earlier Logic. Oxford: Hermes Science, xiv + 216 pp. ISBN 1-903398-20-5. Aristotle s best known contribution to logic is the theory of the categorical syllogism in his Prior

### IN DEFENSE OF THE SQUARE OF OPPOSITION

IN DEFENSE OF THE SQUARE OF OPPOSITION Scott M. Sullivan THE SQUARE OF OPPOSITION IN TRADITIONAL LOGIC is thought by many contemporary logicians to suffer from an inherent formal defect. Many of these

### Essential Logic Ronald C. Pine

Essential Logic Ronald C. Pine Chapter 11: Other Logical Tools Syllogisms and Quantification Introduction A persistent theme of this book has been the interpretation of logic as a set of practical tools.

### Ethical Consistency and the Logic of Ought

Ethical Consistency and the Logic of Ought Mathieu Beirlaen Ghent University In Ethical Consistency, Bernard Williams vindicated the possibility of moral conflicts; he proposed to consistently allow for

### 2.3. Failed proofs and counterexamples

2.3. Failed proofs and counterexamples 2.3.0. Overview Derivations can also be used to tell when a claim of entailment does not follow from the principles for conjunction. 2.3.1. When enough is enough

### Instructor s Manual 1

Instructor s Manual 1 PREFACE This instructor s manual will help instructors prepare to teach logic using the 14th edition of Irving M. Copi, Carl Cohen, and Kenneth McMahon s Introduction to Logic. The

### 2. Refutations can be stronger or weaker.

Lecture 8: Refutation Philosophy 130 October 25 & 27, 2016 O Rourke I. Administrative A. Schedule see syllabus as well! B. Questions? II. Refutation A. Arguments are typically used to establish conclusions.

### Chapter 4: Deduction and Logic

71 The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. There is no logical path to these laws; only intuition, resting

### In a previous lecture, we used Aristotle s syllogisms to emphasize the

The Flow of Argument Lecture 9 In a previous lecture, we used Aristotle s syllogisms to emphasize the central concept of validity. Visualizing syllogisms in terms of three-circle Venn diagrams gave us

### Suppressed premises in real life. Philosophy and Logic Section 4.3 & Some Exercises

Suppressed premises in real life Philosophy and Logic Section 4.3 & Some Exercises Analyzing inferences: finale Suppressed premises: from mechanical solutions to elegant ones Practicing on some real-life

### A Generalization of Hume s Thesis

Philosophia Scientiæ Travaux d'histoire et de philosophie des sciences 10-1 2006 Jerzy Kalinowski : logique et normativité A Generalization of Hume s Thesis Jan Woleński Publisher Editions Kimé Electronic

### Chapters 21, 22: The Language of QL ("Quantifier Logic")

Chapters 21, 22: The Language of QL ("Quantifier Logic") Motivation: (1) Fido is a cat. (2) All cats are scary. Valid argument! (3) Fido is scary. In PL: Let P = Fido is a cat. Q = All cats are scary.

### Quantifiers: Their Semantic Type (Part 3) Heim and Kratzer Chapter 6

Quantifiers: Their Semantic Type (Part 3) Heim and Kratzer Chapter 6 1 6.7 Presuppositional quantifier phrases 2 6.7.1 Both and neither (1a) Neither cat has stripes. (1b) Both cats have stripes. (1a) and

### CHAPTER THREE Philosophical Argument

CHAPTER THREE Philosophical Argument General Overview: As our students often attest, we all live in a complex world filled with demanding issues and bewildering challenges. In order to determine those

### Ling 98a: The Meaning of Negation (Week 1)

Yimei Xiang yxiang@fas.harvard.edu 17 September 2013 1 What is negation? Negation in two-valued propositional logic Based on your understanding, select out the metaphors that best describe the meaning

### THE FORM OF REDUCTIO AD ABSURDUM J. M. LEE. A recent discussion of this topic by Donald Scherer in [6], pp , begins thus:

Notre Dame Journal of Formal Logic Volume XIV, Number 3, July 1973 NDJFAM 381 THE FORM OF REDUCTIO AD ABSURDUM J. M. LEE A recent discussion of this topic by Donald Scherer in [6], pp. 247-252, begins

### The Appeal to Reason. Introductory Logic pt. 1

The Appeal to Reason Introductory Logic pt. 1 Argument vs. Argumentation The difference is important as demonstrated by these famous philosophers. The Origins of Logic: (highlights) Aristotle (385-322

### A Solution to the Gettier Problem Keota Fields. the three traditional conditions for knowledge, have been discussed extensively in the

A Solution to the Gettier Problem Keota Fields Problem cases by Edmund Gettier 1 and others 2, intended to undermine the sufficiency of the three traditional conditions for knowledge, have been discussed

### Gunky time and indeterminate existence

Gunky time and indeterminate existence Giuseppe Spolaore Università degli Studi di Padova Department of Philosophy, Sociology, Education and Applied Psychology Padova, Veneto Italy giuseppe.spolaore@gmail.com

### Logic Primer. Elihu Carranza, Ph.D. Inky Publication Napa, California

Logic Primer Elihu Carranza, Ph.D. Inky Publication Napa, California Logic Primer Copyright 2012 Elihu Carranza, Ph.D. All rights reserved. No part of this book may be reproduced or transmitted in any

Argument Mapping By James Wallace Gray 2/13/2012 Table of Contents Argument Mapping...1 Introduction...2 Chapter 1: Examples of argument maps...2 Chapter 2: The difference between multiple arguments and

### 1.5. Argument Forms: Proving Invalidity

18. If inflation heats up, then interest rates will rise. If interest rates rise, then bond prices will decline. Therefore, if inflation heats up, then bond prices will decline. 19. Statistics reveal that

### Revisiting the Socrates Example

Section 1.6 Section Summary Valid Arguments Inference Rules for Propositional Logic Using Rules of Inference to Build Arguments Rules of Inference for Quantified Statements Building Arguments for Quantified

### Critical Thinking. The Four Big Steps. First example. I. Recognizing Arguments. The Nature of Basics

Critical Thinking The Very Basics (at least as I see them) Dona Warren Department of Philosophy The University of Wisconsin Stevens Point What You ll Learn Here I. How to recognize arguments II. How to

### Broad on Theological Arguments. I. The Ontological Argument

Broad on God Broad on Theological Arguments I. The Ontological Argument Sample Ontological Argument: Suppose that God is the most perfect or most excellent being. Consider two things: (1)An entity that

### good philosopher gives reasons for his or her view that support that view in a rigorous way.

APHI 110 - Introduction to Philosophical Problems (#2488) TuTh 11:45PM 1:05PM Location: ED- 120 Instructor: Nathan Powers What is a person? What is a mind? What is knowledge? Do I have certain knowledge

### Handout 1: Arguments -- the basics because, since, given that, for because Given that Since for Because

Handout 1: Arguments -- the basics It is useful to think of an argument as a list of sentences.[1] The last sentence is the conclusion, and the other sentences are the premises. Thus: (1) No professors

### Logic: The Science that Evaluates Arguments

Logic: The Science that Evaluates Arguments Logic teaches us to develop a system of methods and principles to use as criteria for evaluating the arguments of others to guide us in constructing arguments

### REASONING SYLLOGISM. Subject Predicate Distributed Not Distributed Distributed Distributed

REASONING SYLLOGISM DISTRIBUTION OF THE TERMS The word "Distrlbution" is meant to characterise the ways in which terrns can occur in Categorical Propositions. A Proposition distributes a terrn if it refers

### 7.1. Unit. Terms and Propositions. Nature of propositions. Types of proposition. Classification of propositions

Unit 7.1 Terms and Propositions Nature of propositions A proposition is a unit of reasoning or logical thinking. Both premises and conclusion of reasoning are propositions. Since propositions are so important,

### Unit 4. Reason as a way of knowing. Tuesday, March 4, 14

Unit 4 Reason as a way of knowing I. Reasoning At its core, reasoning is using what is known as building blocks to create new knowledge I use the words logic and reasoning interchangeably. Technically,