# A Primer on Logic Part 1: Preliminaries and Vocabulary. Jason Zarri. 1. An Easy \$10.00? a 3 c 2. (i) (ii) (iii) (iv)

Size: px
Start display at page:

Download "A Primer on Logic Part 1: Preliminaries and Vocabulary. Jason Zarri. 1. An Easy \$10.00? a 3 c 2. (i) (ii) (iii) (iv)"

Transcription

1 A Primer on Logic Part 1: Preliminaries and Vocabulary Jason Zarri 1. An Easy \$10.00? Suppose someone were to bet you \$10.00 that you would fail a seemingly simple test of your reasoning skills. Feeling confident in your abilities, you accept. The test works like this: There are four cards, numbered (i) (iv). Each card has a letter on one side and a number on the other. Your goal is to check to see if the following claim is refuted by any of the cards. The claim is that, if a card has a vowel 1 on one side, then it has an odd number on the other. To win, you must turn over all of the cards you need to to check the claim, and no more than the cards you need to to check the claim. The cards are displayed like so: a 3 c 2 (i) (ii) (iii) (iv) Which of the cards do you need to turn over to check to see if the claim holds? Stop reading this essay for a minute and try to figure it out. I don t mind waiting. 1 In case you ve forgotten or are unsure which letters are vowels, they are a, e, i, o u, and (sometimes) y and w. 1

2 Okay, are you ready? The correct answer is that only cards (i) and (iv) should be turned over. If you re like most people, you got it wrong, in which case you would be out \$10.00! Card (i) should be turned over because it has the letter a, a vowel, showing. The claim you are testing says that, if a card has a vowel on one side, then it has an odd number on the other. Card (i) might have an odd number on the other side, in which case the claim has not been refuted. Then again, it might have an even number on the other side, in which case the claim has been refuted. Since you don t know whether the number on the other side of the card is odd or even, you need to turn it over. When presented with tests such as this, most people do indicate, correctly, that the card corresponding to this one should be turned over. For the other cards, the answer may not seem so obvious. Card (ii), however, should not be turned over. Given the way the test is set up, there may be a vowel or a consonant on the other side of the card. If the letter is a vowel, the claim is not refuted, for then there is indeed a vowel on one side and the number 3, an odd number, on the other. If the letter on the other side is a consonant, the claim is also not refuted, for it can only be refuted if there is a vowel on one side and an even number on the other. If there is a consonant on one side, it doesn t matter whether the number on the other side is odd or even. Card (iii) has the letter c a consonant showing, and so it too should not be turned over for the reason just given: If a card has a consonant on one side, it doesn t matter whether the number on the other side is odd or even. Finally, card (iv) should be turned over because it has a 2 showing, which is an even number. If the letter on the other side of the card is a consonant the claim is not refuted for a reason that should now be clear. But if the letter on the other side is a vowel, the claim is refuted, for it says that a card with a vowel on one side must have an odd number on the other. From the foregoing, one can see why cards (i) and (iv), and no others, need to be turned over in order to test the claim. The test to which you have just been subjected is called a Wason selection task. There are many different variants of it. When the claim being tested is relatively abstract, as it was here, 2

3 people tend to do poorly. When the claim is more concrete e.g., that if a person is under twenty one they can t legally drink beer people tend to do better. However, logic applies to all subject matter, both abstract and concrete. I have chosen to use an abstract claim so you can see how difficult it can be to think logically. 2. Arguments But what is it to think logically? By the time you ve finished reading this essay I hope to have provided you with an answer to this question. We shall begin in Part 1 by examining the notion of an argument. An argument, as we will understand it, is not a heated dispute between two or more people. Neither is it a more civil exchange between people with opposing views, as political debates are ideally supposed to be. Instead, we will regard an argument as a sequence of sentences. Not just any sentences will do, though. The sentences being considered here are declarative sentences, as opposed, for example, to interrogative sentences questions and imperative sentences commands. For the sake of brevity we will henceforth call declarative sentences statements. Unlike questions and commands, statements say something about the world. That is, they represent things as being a certain way, and are true if things are that way and false if they are not. So if I say that a certain cat is laying on a certain mat, I have made a statement, and what I said is true if the cat is laying on the mat, and false if it is not. In this respect statements differ from questions and commands. Questions may have right or wrong answers, and commands may be obeyed or disobeyed, but they are certainly neither true nor false. Arguments, then, are sequences of statements. They consist of a set of one or more premises, statements that are supposed to give support for a further statement which is called the conclusion. Consider the following argument, a variant of what is probably the oldest and most widely cited arguments in Western philosophy: 3

4 All humans are mortal. Socrates is human. Socrates is mortal. In this argument, the first two statements are the premises and the last is the conclusion. The line serves the purpose of marking off the premises of the argument from the conclusion. The premises give support to the conclusion in the sense that they entail it. We say that the premises of an argument entail its conclusion when it is impossible for all the premises to be true and the conclusion to be false. 2 You should be aware that the notion of entailment doesn t just apply to premises and conclusions. In general, it can apply to any statements or sets of statements, whether they can be thought of as being premises or conclusions or not. The only requirement is that one statement is entailed by another statement or set of statements in all and only those cases where it is impossible for the former statement to be false while the latter statement(s) are all true. In our sample argument, it is impossible for all humans to be mortal and for Socrates to be human, and for it also to be the case that Socrates is not mortal. It is important to realize that when I say that all humans are mortal I do not mean that the vast majority of humans are mortal, while failing to mention certain exceptions because they are few and far between. I mean that every single human is mortal, period. That being so, if all humans are mortal and Socrates is human, Socrates must be mortal. Hence, if it turns out that Socrates is not mortal, it follows that either not all humans are mortal, or that Socrates is not human, or perhaps both. Arguments such as this, in which the premises entail the conclusion, are called valid. If, in addition, all of the 2 There are other ways in which the premises of an argument can support its conclusion. In inductive arguments as opposed to deductive arguments, which we are considering here the premises may support the conclusion in the sense that their truth would render it more probable than it would otherwise be. We will say no more about inductive arguments in this essay. 4

5 premises of a valid argument are true the argument is also called sound. Since, by definition, all sound arguments are valid and have true premises, all sound arguments also have true conclusions. A word of caution is in order. Under no circumstances should you call an argument true. Besides the fact that philosophers and logicians never talk that way, there is the fact that when talking with someone your interlocutor may be unsure as to what exactly you mean by calling an argument true. You might mean that it is valid, or that it is also sound, or perhaps that its premises and conclusion are all true. Regarding this last possibility, it is important to note that an argument may have all true premises and a true conclusion while being invalid, unsound or both. 3 Consider the following argument: Most basketball players are over five feet tall. The Moon orbits the Earth. Aristotle was a philosopher. As things are, all three of these statements are true. Nevertheless, the premises of this argument do not entail the conclusion. Most basketball players could still have been over five feet tall, and the Moon could still have orbited the Earth, even if Aristotle had chosen to be a fisherman instead of a philosopher. Thus both premises of this argument could have been true even though its conclusion was false, making it invalid and unsound. 3 An argument that is unsound may still be valid, but one or more of its premises must be false if they were all true, the argument would be sound after all. When an argument is both valid and unsound, its conclusion may or may not be true. An example of a valid but unsound argument is: If the Earth is flat then the Earth doesn t have an equator. The Earth is flat. The Earth doesn t have an equator. In this case the first premise is true, the second premise is false, and the conclusion is false. 5

6 3. Consistency and Inconsistency I will now introduce two other logical notions, those of consistency and inconsistency. While they do not directly concern arguments, it is important for you to become acquainted with them. A set of statements is consistent if it is possible for all of the statements that compose it to be true together. Correspondingly, a set of statements is inconsistent if it is not possible for all of the statements that compose it to be true together. Alternatively, we can understand consistency and inconsistency in terms of entailment: A set of statements is consistent if no member of the set, or two or more members taken together, entail that any member of the set is false, otherwise the set is inconsistent. To make these notions clear, consider the following set: 1. No man is both tall and fat. 2. Chris is tall. 3. Chris is fat. 4. Chris is a man. It doesn t take much thought to realize that this set is inconsistent. If Chris is tall, fat, and a man, then some man is both tall and fat, which is precisely what statement (1) denies. So statements (1) (4) cannot all be true, and are inconsistent by the first definition of inconsistency. The set consisting of (2) (4) entails that (1) is false, and (1) entails that at least one of (2), (3) and (4) is false, although it is consistent with any one of them taken by itself, and also with any two of them taken together. So the set is also inconsistent by the second definition. 6

7 Now consider this set: 5. Jones is sitting and Jones is not sitting. 6. All whales are mammals. 7. Mt. Everest is the world s tallest mountain. This set is also inconsistent by either definition of inconsistent. The reason is that (5) cannot be true provided we understand it as saying that Jones is both sitting and not sitting at the same time. Granting that, since (5) cannot be true by itself, it cannot be true together with (6) and (7) either. Furthermore, because (5) cannot be true, every statement entails that (5) is false, including (5) itself! 4 We may say that (5) is self-inconsistent. We may also say that self-inconsistent statements are infectious, because their inconsistency spreads: Any set of statements that contains a self-inconsistent statement is also inconsistent, even if all the other statements in the set are consistent with themselves and each other. 4. Conclusion Now that we have some understanding of some basic logical notions we can move on. In Part 2 I ll discuss argument schemas, abstract forms or patterns that different arguments have in common. We ll learn how to tell which schemas are valid and why. 4 Recall that one statement entails another when it is impossible for the former to be true while the latter is false. Since (5) cannot be true, it is necessarily false. So the statement (5) is false is necessarily true, and no statement can be true while it is false, for it is necessarily true. Thus every statement entails the statement (5) is false, and by extension every statement entails the falsity of (5). 7

### ELEMENTS OF LOGIC. 1.1 What is Logic? Arguments and Propositions

Handout 1 ELEMENTS OF LOGIC 1.1 What is Logic? Arguments and Propositions In our day to day lives, we find ourselves arguing with other people. Sometimes we want someone to do or accept something as true

### Introduction to Philosophy Crito. Instructor: Jason Sheley

Introduction to Philosophy Crito Instructor: Jason Sheley Recall again our steps for doing philosophy 1) What is the question? 2) What is the basic answer to the question? 3) What reasons are given for

### 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

### BASIC CONCEPTS OF LOGIC

1 BASIC CONCEPTS OF LOGIC 1. What is Logic?... 2 2. Inferences and Arguments... 2 3. Deductive Logic versus Inductive Logic... 5 4. Statements versus Propositions... 6 5. Form versus Content... 7 6. Preliminary

### 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.

### 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

### Logic for Computer Science - Week 1 Introduction to Informal Logic

Logic for Computer Science - Week 1 Introduction to Informal Logic Ștefan Ciobâcă November 30, 2017 1 Propositions A proposition is a statement that can be true or false. Propositions are sometimes called

### 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

### How to Write a Philosophy Paper

How to Write a Philosophy Paper The goal of a philosophy paper is simple: make a compelling argument. This guide aims to teach you how to write philosophy papers, starting from the ground up. To do that,

### 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,

### Skim the Article to Find its Conclusion and Get a Sense of its Structure

Pryor, Jim. (2006) Guidelines on Reading Philosophy, What is An Argument?, Vocabulary Describing Arguments. Published at http://www.jimpryor.net/teaching/guidelines/reading.html, and http://www.jimpryor.net/teaching/vocab/index.html

### 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

### Chapter 1 - Basic Training

Logic: A Brief Introduction Ronald L. Hall, Stetson University Chapter 1 - Basic Training 1.1 Introduction In this logic course, we are going to be relying on some mental muscles that may need some toning

### A Brief Introduction to Key Terms

1 A Brief Introduction to Key Terms 5 A Brief Introduction to Key Terms 1.1 Arguments Arguments crop up in conversations, political debates, lectures, editorials, comic strips, novels, television programs,

### Truth At a World for Modal Propositions

Truth At a World for Modal Propositions 1 Introduction Existentialism is a thesis that concerns the ontological status of individual essences and singular propositions. Let us define an individual essence

### BASIC CONCEPTS OF LOGIC

BASIC CONCEPTS OF LOGIC 1. What is Logic?...2 2. Inferences and Arguments...2 3. Deductive Logic versus Inductive Logic...5 4. Statements versus Propositions...6 5. Form versus Content...7 6. Preliminary

### PHI 1500: Major Issues in Philosophy

PHI 1500: Major Issues in Philosophy Session 3 September 9 th, 2015 All About Arguments (Part II) 1 A common theme linking many fallacies is that they make unwarranted assumptions. An assumption is a claim

### Tutorial A02: Validity and Soundness By: Jonathan Chan

A02.1 Definition of validity Tutorial A02: Validity and Soundness By: One desirable feature of arguments is that the conclusion should follow from the premises. But what does it mean? Consider these two

### 6: DEDUCTIVE LOGIC. Chapter 17: Deductive validity and invalidity Ben Bayer Drafted April 25, 2010 Revised August 23, 2010

6: DEDUCTIVE LOGIC Chapter 17: Deductive validity and invalidity Ben Bayer Drafted April 25, 2010 Revised August 23, 2010 Deduction vs. induction reviewed In chapter 14, we spent a fair amount of time

### 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

### 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

### Philosophy Introduction to Philosophy Jeff Speaks What is philosophy?

Philosophy 10100 Introduction to Philosophy Jeff Speaks jspeaks@nd.edu What is philosophy? What is philosophy? Philosophy comes from the ancient Greek φιλοσοφία philosophia. philosophia = philo + sophia

### 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

### Intro Viewed from a certain angle, philosophy is about what, if anything, we ought to believe.

Overview Philosophy & logic 1.2 What is philosophy? 1.3 nature of philosophy Why philosophy Rules of engagement Punctuality and regularity is of the essence You should be active in class It is good to

### The Relationship between the Truth Value of Premises and the Truth Value of Conclusions in Deductive Arguments

The Relationship between the Truth Value of Premises and the Truth Value of Conclusions in Deductive Arguments I. The Issue in Question This document addresses one single question: What are the relationships,

### 1.6 Validity and Truth

M01_COPI1396_13_SE_C01.QXD 10/10/07 9:48 PM Page 30 30 CHAPTER 1 Basic Logical Concepts deductive arguments about probabilities themselves, in which the probability of a certain combination of events is

### HOW TO ANALYZE AN ARGUMENT

What does it mean to provide an argument for a statement? To provide an argument for a statement is an activity we carry out both in our everyday lives and within the sciences. We provide arguments for

### Argumentation Module: Philosophy Lesson 7 What do we mean by argument? (Two meanings for the word.) A quarrel or a dispute, expressing a difference

1 2 3 4 5 6 Argumentation Module: Philosophy Lesson 7 What do we mean by argument? (Two meanings for the word.) A quarrel or a dispute, expressing a difference of opinion. Often heated. A statement of

### 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

### 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

### CRITICAL THINKING (CT) MODEL PART 1 GENERAL CONCEPTS

Fall 2001 ENGLISH 20 Professor Tanaka CRITICAL THINKING (CT) MODEL PART 1 GENERAL CONCEPTS In this first handout, I would like to simply give you the basic outlines of our critical thinking model

### Moore on External Relations

Moore on External Relations G. J. Mattey Fall, 2005 / Philosophy 156 The Dogma of Internal Relations Moore claims that there is a dogma held by philosophers such as Bradley and Joachim, that all relations

### Overview of Today s Lecture

Branden Fitelson Philosophy 12A Notes 1 Overview of Today s Lecture Music: Robin Trower, Daydream (King Biscuit Flower Hour concert, 1977) Administrative Stuff (lots of it) Course Website/Syllabus [i.e.,

### What we want to know is: why might one adopt this fatalistic attitude in response to reflection on the existence of truths about the future?

Fate and free will From the first person point of view, one of the most obvious, and important, facts about the world is that some things are up to us at least sometimes, we are able to do one thing, and

### 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

### 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

### Fatalism and Truth at a Time Chad Marxen

Stance Volume 6 2013 29 Fatalism and Truth at a Time Chad Marxen Abstract: In this paper, I will examine an argument for fatalism. I will offer a formalized version of the argument and analyze one of the

### Mr Vibrating: Yes I did. Man: You didn t Mr Vibrating: I did! Man: You didn t! Mr Vibrating: I m telling you I did! Man: You did not!!

Arguments Man: Ah. I d like to have an argument, please. Receptionist: Certainly sir. Have you been here before? Man: No, I haven t, this is my first time. Receptionist: I see. Well, do you want to have

### A. Problem set #3 it has been posted and is due Tuesday, 15 November

Lecture 9: Propositional Logic I Philosophy 130 1 & 3 November 2016 O Rourke & Gibson I. Administrative A. Problem set #3 it has been posted and is due Tuesday, 15 November B. I am working on the group

### 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

### PHILOSOPHY 102 INTRODUCTION TO LOGIC PRACTICE EXAM 1. W# Section (10 or 11) 4. T F The statements that compose a disjunction are called conjuncts.

PHILOSOPHY 102 INTRODUCTION TO LOGIC PRACTICE EXAM 1 W# Section (10 or 11) 1. True or False (5 points) Directions: Circle the letter next to the best answer. 1. T F All true statements are valid. 2. T

### 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.

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

### To better understand VALIDITY, we now turn to the topic of logical form.

LOGIC GUIDE 2 To better understand VALIDITY, we now turn to the topic of logical form. LOGICAL FORM The logical form of a statement or argument is the skeleton, or structure. If you retain only the words

### 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,

### 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 ------------.

### What are Truth-Tables and What Are They For?

PY114: Work Obscenely Hard Week 9 (Meeting 7) 30 November, 2010 What are Truth-Tables and What Are They For? 0. Business Matters: The last marked homework of term will be due on Monday, 6 December, at

### Semantic Foundations for Deductive Methods

Semantic Foundations for Deductive Methods delineating the scope of deductive reason Roger Bishop Jones Abstract. The scope of deductive reason is considered. First a connection is discussed between the

### Introduction to Logic

University of Notre Dame Spring, 2017 Arguments Philosophy has two main methods for trying to answer questions: analysis and arguments Logic is the the study of arguments An argument is a set of sentences,

### Final Paper. May 13, 2015

24.221 Final Paper May 13, 2015 Determinism states the following: given the state of the universe at time t 0, denoted S 0, and the conjunction of the laws of nature, L, the state of the universe S at

### Critical Thinking is:

Logic: Day 1 Critical Thinking is: Thinking clearly and following rules of logic and rationality It s not being argumentative just for the sake of arguing Academics disagree about which departments do

### Introduction to Philosophy

Introduction to Philosophy Philosophy 110W Russell Marcus Hamilton College, Fall 2013 Class 1 - Introduction to Introduction to Philosophy My name is Russell. My office is 202 College Hill Road, Room 210.

### The Cosmological Argument for the Existence of God

The Cosmological Argument for the Existence of God Some preliminaries: The essence of being a Christian is to have a personal relationship with Jesus Christ, the risen Son of God. It is through Christ

### Consciousness might be defined as the perceiver of mental phenomena. We might say that there are no differences between one perceiver and another, as

2. DO THE VALUES THAT ARE CALLED HUMAN RIGHTS HAVE INDEPENDENT AND UNIVERSAL VALIDITY, OR ARE THEY HISTORICALLY AND CULTURALLY RELATIVE HUMAN INVENTIONS? Human rights significantly influence the fundamental

### Subjective Logic: Logic as Rational Belief Dynamics. Richard Johns Department of Philosophy, UBC

Subjective Logic: Logic as Rational Belief Dynamics Richard Johns Department of Philosophy, UBC johns@interchange.ubc.ca May 8, 2004 What I m calling Subjective Logic is a new approach to logic. Fundamentally

### By submitting this essay, I attest that it is my own work, completed in accordance with University regulations. Minh Alexander Nguyen

DRST 004: Directed Studies Philosophy Professor Matthew Noah Smith By submitting this essay, I attest that it is my own work, completed in accordance with University regulations. Minh Alexander Nguyen

PHILOSOPHY ESSAY ADVICE One: What ought to be the primary objective of your essay? The primary objective of your essay is not simply to present information or arguments, but to put forward a cogent argument

### Academic argument does not mean conflict or competition; an argument is a set of reasons which support, or lead to, a conclusion.

ACADEMIC SKILLS THINKING CRITICALLY In the everyday sense of the word, critical has negative connotations. But at University, Critical Thinking is a positive process of understanding different points of

### Critical Thinking 5.7 Validity in inductive, conductive, and abductive arguments

5.7 Validity in inductive, conductive, and abductive arguments REMEMBER as explained in an earlier section formal language is used for expressing relations in abstract form, based on clear and unambiguous

### Introduction to Philosophy

Introduction to Philosophy PHIL 2000--Call # 41480 Kent Baldner Teaching Assistant: Mitchell Winget Discussion sections ( Labs ) meet on Wednesdays, starting next Wednesday, Sept. 5 th. 10:00-10:50, 1115

### Logic Book Part 1! by Skylar Ruloff!

Logic Book Part 1 by Skylar Ruloff Contents Introduction 3 I Validity and Soundness 4 II Argument Forms 10 III Counterexamples and Categorical Statements 15 IV Strength and Cogency 21 2 Introduction This

### Introduction to Logic

University of Notre Dame Fall, 2015 Arguments Philosophy is difficult. If questions are easy to decide, they usually don t end up in philosophy The easiest way to proceed on difficult questions is to formulate

### Introduction Symbolic Logic

An Introduction to Symbolic Logic Copyright 2006 by Terence Parsons all rights reserved CONTENTS Chapter One Sentential Logic with 'if' and 'not' 1 SYMBOLIC NOTATION 2 MEANINGS OF THE SYMBOLIC NOTATION

### Chapter 9- Sentential Proofs

Logic: A Brief Introduction Ronald L. Hall, Stetson University Chapter 9- Sentential roofs 9.1 Introduction So far we have introduced three ways of assessing the validity of truth-functional arguments.

### Anthony P. Andres. The Place of Conversion in Aristotelian Logic. Anthony P. Andres

[ Loyola Book Comp., run.tex: 0 AQR Vol. W rev. 0, 17 Jun 2009 ] [The Aquinas Review Vol. W rev. 0: 1 The Place of Conversion in Aristotelian Logic From at least the time of John of St. Thomas, scholastic

### 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

### Handout 2 Argument Terminology

Handout 2 Argument Terminology 1. Arguing, Arguments, & Statements Open Question: What happens when two people are in an argument? An argument is an abstraction from what goes on when people arguing. An

### 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

### Philosophical Arguments

Philosophical Arguments An introduction to logic and philosophical reasoning. Nathan D. Smith, PhD. Houston Community College Nathan D. Smith. Some rights reserved You are free to copy this book, to distribute

### 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

### A BRIEF INTRODUCTION TO LOGIC FOR METAPHYSICIANS

A BRIEF INTRODUCTION TO LOGIC FOR METAPHYSICIANS 0. Logic, Probability, and Formal Structure Logic is often divided into two distinct areas, inductive logic and deductive logic. Inductive logic is concerned

### PHLA10F 2. PHLA10F What is Philosophy?

2 What is Philosophy? What is Philosophy? Philosophical Questions Fundamental General Conceptual Analysis Why no Philosophical Labs? Thought experiments The Hand Off No mystic gurus! Plato What is an argument?

### Kripke on the distinctness of the mind from the body

Kripke on the distinctness of the mind from the body Jeff Speaks April 13, 2005 At pp. 144 ff., Kripke turns his attention to the mind-body problem. The discussion here brings to bear many of the results

### 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

### Validity & Soundness LECTURE 3! Critical Thinking. Summary: In this week s lectures, we will learn! (1) What it is for an argument to be valid.

Critical Thinking Norva Y S Lo Produced by Norva Y S Lo Edited by Andrew Brennan LECTURE 3! Validity & Soundness Summary: In this week s lectures, we will learn! (1) What it is for an argument to be. (2)

### 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

### Criticizing Arguments

Kareem Khalifa Criticizing Arguments 1 Criticizing Arguments Kareem Khalifa Department of Philosophy Middlebury College Written August, 2012 Table of Contents Introduction... 1 Step 1: Initial Evaluation

### Philosophy 220. Truth Functional Properties Expressed in terms of Consistency

Philosophy 220 Truth Functional Properties Expressed in terms of Consistency The concepts of truth-functional logic: Truth-functional: Truth Falsity Indeterminacy Entailment Validity Equivalence Consistency

### Ibuanyidanda (Complementary Reflection), African Philosophy and General Issues in Philosophy

HOME Ibuanyidanda (Complementary Reflection), African Philosophy and General Issues in Philosophy Back to Home Page: http://www.frasouzu.com/ for more essays from a complementary perspective THE IDEA OF

### Example Arguments ID1050 Quantitative & Qualitative Reasoning

Example Arguments ID1050 Quantitative & Qualitative Reasoning First Steps to Analyzing an Argument In the following slides, some simple arguments will be given. The steps to begin analyzing each argument

### Writing the Persuasive Essay

Writing the Persuasive Essay What is a persuasive/argument essay? In persuasive writing, a writer takes a position FOR or AGAINST an issue and writes to convince the reader to believe or do something Persuasive

### Proofs of Non-existence

The Problem of Evil Proofs of Non-existence Proofs of non-existence are strange; strange enough in fact that some have claimed that they cannot be done. One problem is with even stating non-existence claims:

### Argumentative Analogy versus Figurative Analogy

Argumentative Analogy versus Figurative Analogy By Timo Schmitz, Philosopher As argumentative analogy or simply analogism (ἀναλογισµός), one calls the comparison through inductive reasoning of at least

### Illustrating Deduction. A Didactic Sequence for Secondary School

Illustrating Deduction. A Didactic Sequence for Secondary School Francisco Saurí Universitat de València. Dpt. de Lògica i Filosofia de la Ciència Cuerpo de Profesores de Secundaria. IES Vilamarxant (España)

### THE CAMBRIDGE SOLUTION TO THE TIME OF A KILLING LAWRENCE B. LOMBARD

THE CAMBRIDGE SOLUTION TO THE TIME OF A KILLING LAWRENCE B. LOMBARD I. Introduction Just when we thought it safe to ignore the problem of the time of a killing, either because we thought the problem already

### Chapter 8 - Sentential Truth Tables and Argument Forms

Logic: A Brief Introduction Ronald L. Hall Stetson University Chapter 8 - Sentential ruth ables and Argument orms 8.1 Introduction he truth-value of a given truth-functional compound proposition depends

### 15. Russell on definite descriptions

15. Russell on definite descriptions Martín Abreu Zavaleta July 30, 2015 Russell was another top logician and philosopher of his time. Like Frege, Russell got interested in denotational expressions as

### Basic Concepts and Distinctions 1 Logic Keith Burgess-Jackson 14 August 2017

Basic Concepts and Distinctions 1 Logic Keith Burgess-Jackson 14 August 2017 Terms in boldface type are defined somewhere in this handout. 1. Logic is the science of implication, or of valid inference

### Philosophy 1100: Introduction to Ethics. Critical Thinking Lecture 2. Background Material for the Exercise on Inference Indicators

Philosophy 1100: Introduction to Ethics Critical Thinking Lecture 2 Background Material for the Exercise on Inference Indicators Inference-Indicators and the Logical Structure of an Argument 1. The Idea

### Lecture 4.2 Aquinas Phil Religion TOPIC: Aquinas Cosmological Arguments for the existence of God. Critiques of Aquinas arguments.

TOPIC: Lecture 4.2 Aquinas Phil Religion Aquinas Cosmological Arguments for the existence of God. Critiques of Aquinas arguments. KEY TERMS/ GOALS: Cosmological argument. The problem of Infinite Regress.

### The Principle of Sufficient Reason and Free Will

Stance Volume 3 April 2010 The Principle of Sufficient Reason and Free Will ABSTRACT: I examine Leibniz s version of the Principle of Sufficient Reason with respect to free will, paying particular attention

### Worksheet Exercise 1.1. Logic Questions

Worksheet Exercise 1.1. Logic Questions Date Study questions. These questions do not have easy answers. (But that doesn't mean that they have no answers.) Just think about these issues. There is no particular

### ARGUMENTS. Arguments. arguments

ARGUMENTS Arguments arguments 1 Argument Worksheet 1. An argument is a collection of propositions with one proposition, the conclusion, following from the other propositions, the premises. Inference is

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

### Ayer on the criterion of verifiability

Ayer on the criterion of verifiability November 19, 2004 1 The critique of metaphysics............................. 1 2 Observation statements............................... 2 3 In principle verifiability...............................

### Appendix: The Logic Behind the Inferential Test

Appendix: The Logic Behind the Inferential Test In the Introduction, I stated that the basic underlying problem with forensic doctors is so easy to understand that even a twelve-year-old could understand

### Three Kinds of Arguments

Chapter 27 Three Kinds of Arguments Arguments in general We ve been focusing on Moleculan-analyzable arguments for several chapters, but now we want to take a step back and look at the big picture, at

### On Priest on nonmonotonic and inductive logic

On Priest on nonmonotonic and inductive logic Greg Restall School of Historical and Philosophical Studies The University of Melbourne Parkville, 3010, Australia restall@unimelb.edu.au http://consequently.org/