Today s Lecture 1/28/10
|
|
- Shawn Parsons
- 6 years ago
- Views:
Transcription
1 Chapter 7.1! Symbolizing English Arguments! 5 Important Logical Operators!The Main Logical Operator Today s Lecture 1/28/10
2 Quiz State from memory (closed book and notes) the five famous valid forms and their names. --be sure your name is on your paper
3 Announcements Homework -- Ex 7.1 pgs Part A and B (All) Quiz on Tuesday (Feb 2nd) --state from memory each logical operator, its translation, and its corresponding type of compound statement. See the table on p (Example: ~ not negation) Book Issues Adding the Course
4 Validity v. Invalidity Again An argument is valid if and only if it s impossible for all of the premises to be true while the conclusion is false. An argument is invalid if and only if it is possible for all of the premises to be true while the conclusion is false.
5 Validity v. Invalidity Again --Our task shortly is to study a particular mechanical method for determining whether an argument is either valid or invalid. --It will be the method of Truth Tables.
6 --But before we can employ this mechanical method, it's essential that we be able to represent English arguments using a symbolic notation. --To do this we need to learn all that is involved with translating English statements into symbols.
7 Atomic v. Compound Statements An atomic statement is one that does not have any other statement as a component. Examples!Grass is green.!the library is adjacent to Sierra Tower.!Tennis is challenging.
8 Atomic v. Compound Statements A compound statement is one that has at least one atomic statement as a component. Examples! It is false that grass is red.! The library is adjacent to Sierra Tower and I am hungry.! If tennis is challenging, then tennis players have a reason to practice.
9 Atomic Statements: Symbolize Atomic Statements with a single upper case letter. B: Brass is a mixed metal. C: Cathy called in sick. N: Nadal wins trophies T: Thought is mysterious.
10 Compound Statements Symbolize Compound Statements by first symbolizing their Atomic Constituents, and then their logical words. (logical words: it s not the case that, and, or, if, then, if and only if, and their stylistic variants) (We will just symbolize the Atomic Constituents for now) Example: It is false that grass is red. It is false that G.
11 Compound Statements More examples of partially translated compound Statements: The library is adjacent to Sierra Tower and I am hungry -- L and I If tennis is challenging, then tennis players have a reason to practice -- If T, then P
12 Symbolizing the Logical Words Operator ~ Name tilde Translates not Compound Type negation dot and conjunction v vee or disjunction " arrow if, then conditional! double-arrow If and only if biconditional
13 ~ NEGATIONS
14 Symbolizing Negations Grass is not red (R: Grass is red) is symbolized as this is our scheme of ~ R abbreviation It is not the case that grass is red ~ R It is false that grass is red ~ R
15 Negations of Compound Statements It is false that Dallas wins and Phoenix wins is symbolized as ~ (D P) (D: Dallas wins P: Phoenix wins) It s not true that if Dallas wins, then Phoenix wins ~ (D " P) The following is false: either Dallas wins or Phoenix wins. ~ (D # P)
16 Parentheses are Important It is false that Dallas wins and Phoenix wins ~ (D P) -- this a negation (this says that it s not the case that both of them win; it leaves us agnostic as to who actually wins; maybe both of them don t win) If we didn t use parentheses we would get ~ D P -- this is a conjunction, not a negation (this says that Dallas does not win and Phoenix wins)
17 Parentheses are Important It s not the case that if Dallas wins then Phoenix wins. ~(D " P) -- this is a negation (this says that Dallas winning does not entail Phoenix winning) If we didn t use parentheses we would get: ~D " P -- this is a conditional, not a negation (this says if Dallas doesn t win, then Phoenix wins)
18 Main Logical Operator The most important step in knowing where to place parentheses is finding the main logical operator (i.e. main connective) in the English statement. This lets you know what kind of compound statement it is, be it a negation or conditional, or disjunction, etc.
19 Main Logical Operator The main logical operator is, roughly, the operator that governs (or connects) the entire statement. Finding the main operator depends upon your ability to see what the statement is saying. This just takes practice. More will be said concerning main operators and parentheses later.
20 Back to Negations Again, all of these are examples of negations: ~ (D P) ~(D "P) ~(D # P) The ~ is the main logical operator
21 CONJUNCTIONS
22 Symbolizing Conjunctions Grass is purple and life is good. (G: grass is purple; L: life is good) G L
23 Stylistic Variants of and! Grass is purple but life is good.! Grass is purple; however life is good.! Grass is purple yet life is good.! Although grass is purple, life is good.! While grass is purple, life is good.! Grass is purple; nevertheless life is good. Still, G L
24 Not all uses of 'and' are conjunctions Not all uses of the English term 'and convey a conjunction. If they did, then we would be able to translate the statements in question into conjunctions and capture the essential meaning of the English statement. But we are unable to do this in all cases. For example
25 Not all uses of 'and' are conjunctions! Sometimes and indicates temporal order! Sometimes and indicates a relationship -Sarah cracked the safe and took the money. -You made a joke and I laughed. -Dave and Val are married. - Dave and Val moved the couch.
26 These are all Conjunctions P Q P ~(Q # R) (P " Q) (Q " P) The is the main operator ~P [Q # (R " S) ] [Q " (P # R)] S (P # Q) (R " S) The is the main operator
27 # DISJUNCTIONS
28 Symbolizing Disjunctions 1. Grass is green or pizza is edible. (G: Grass is green; P: pizza is edible) G # P 2. Alfred will not pass tomorrow or Alfred will study tonight (P: Alfred will pass tomorrow; S: Alfred will study tonight) ~P # S
29 Stylistic Variants of or Alfred will not pass tomorrow and/or Alfred will study tonight. Alfred will not pass tomorrow or Alfred will study tonight (or both). Alfred will not pass tomorrow unless Alfred will study tonight. Still ~P # S
30 Inclusive OR either P or Q (or both) Sometimes when people make a disjunctive claim, they intend the or to be read inclusively. e.g. If you want to live under my roof, either you get a job or you go to college. **The parent will not be bothered if you do both. Exclusive OR either P or Q (but not both) Sometimes when people make a disjunctive claim, they intend the or to be read exclusively. e.g. You may have the soup or you may have the salad. **The waitress will be bothered if you say both.
31 Logicians Treat or as Inclusive We will treat or as inclusive in the absence of a context that suggests an exclusive reading. There is, however, a way of translating an exclusive or which is, again, P or Q (but not both) Consider: You may have the soup or you may have the salad, but not both. Q: How would you translate this?
32 Exclusive OR You may have soup or you may have salad, but not both. (S: you may have soup; L: you may have salad) (S # L) ~(S L)
33 'Neither-Nor' is Not a Disjunction! Neither Simon nor Garfunkel is sad. S: Simon is sad. G: Garfunkel is sad. Two Equivalent Readings 1. ~ (S # G) 2. ~S ~G
34 These are all Disjunctions P # Q P # ~(Q R) (P " Q) # (Q P) The # is the main operator ~P #[Q (R " S) ] [Q " (P # R)] # S (P # Q) #(R " S) The # is the main operator
35 " CONDITIONALS
36 Symbolizing Conditionals If Lisa is identical to an immaterial soul, then Lisa is essentially invisible. L: Lisa is identical to an immaterial soul I: Lisa is essentially invisible L " I If Lisa is identical to a material body, then Lisa is not essentially invisible. M: Lisa is identical to a material body I: Lisa is essentially invisible M " ~I
37 Some Stylistic variants of 'if-then' If Gizmo is a cat, then Gizmo is a mammal! Gizmo is a cat only if Gizmo is a mammal.! Assuming that Gizmo is a cat, Gizmo is a mammal.! Gizmo is a mammal if Gizmo is a cat G: Gizmo is a cat; M: Gizmo is a mammal G " M (Note: there are other stylistic variants. See p. 286)
38 A note on only if The term Only if (unlike if ) introduces a consequent; the antecedent precedes the only if Remember ANTECEDENT only if CONSEQUENT The term only if intuitively (naturally) introduces a necessary condition (or a requirement). Since the consequent of a conditional is a necessary condition for the antecedent, it s a bit easier to see how only if introduces a consequent.
39 Sufficient and Necessary Conditions Sufficient Conditions " P " Q is claiming that the occurrence of P is sufficient condition for Q. " A sufficient condition is a condition that guarantees that a statement is true (or that a phenomenon will occur). Necessary Conditions " P " Q is also claiming that the occurrence of Q is a necessary condition for P. " A necessary condition is a condition that, if lacking, guarantees that a statement is false (or that a phenomenon will not occur).
40 Some Examples --If Alex knows he has hands, then Alex believes he has hands. Knowing something is sufficient for believing it. --Alex knows he has hands only if Alex has good reason to believe he has hands. Having good reason to believe something is a necessary condition on having knowledge of it. --Given that one has a conscious pain, one is aware of the pain. Being conscious of pain is sufficient for being aware of pain. --You can legally drink only if you are at least 21. Being at least 21 is a necessary condition on being able to legally drink.
41 These are all Conditionals P " Q P " ~(Q # R) (P " Q) " (Q " P) ~P "[Q # (R " S) ] [Q (P # R)] " S (P Q) " (R " S) The " is the main operator The " is the main operator
42 Unless can be translated by the " as well as the # Depending on the intent of the speaker, 'Alfred will not pass tomorrow unless Alfred will study tonight' could read: If Alfred will study tonight, then it s false that he won t pass tomorrow (i.e. he will pass) S" ~~P (or S " P). This corresponds to the exclusive reading of 'or' in that the intent is not to say that Alfred could very well study and not pass. For if he studies tonight, he will pass tomorrow.
43 Unless can be translated by the " as well as the # 'Alfred will not pass tomorrow unless Alfred will study tonight' could read: If Alfred will not study tonight, then Alfred will not pass tomorrow ~S " ~P This corresponds to the inclusive reading of 'or' in that it leaves open the possibility that he could study and not pass. The conditional just says that if he doesn't study tonight, he won't pass. It doesn't automatically follow from this that if he does study, he will pass.
44 Unless can be translated by the " as well as the # Since we are sticking with an inclusive reading of or (and unless), p unless q (where p and q stand for any statement, compound or atomic) should be symbolized as: ~q " p
45 ! Biconditionals
46 Symbolizing Biconditionals Leslie is in her 30 s if and only if Leslie is between the ages of L: Leslie is in her 30 s A: Leslie is between the ages of L! A
47 Symbolizing Biconditionals Jon is a bachelor if and only if Jon is not married and Jon is a male. B: Jon is a bachelor M: Jon is a male R: Jon is married Q: How would you symbolize this?
48 Symbolizing Biconditionals Jon is a bachelor if and only if Jon is not married and Jon is a male. B: Jon is a bachelor M: Jon is a male R: Jon is married B! (~R M)
49 Stylistic variant of if and only if Leslie is in her 30 s just in case Leslie is between the ages of L: Leslie is in her 30 s A: Leslie is between the ages of M! A
50 These are all Biconditionals P! Q P! ~(Q R) (P " Q)! (Q P) ~P! [Q (R " S) ] [Q " (P # R)]! S (P # Q)! (R " S)
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
More information9.1 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
More informationPART III - Symbolic Logic Chapter 7 - Sentential Propositions
Logic: A Brief Introduction Ronald L. Hall, Stetson University 7.1 Introduction PART III - Symbolic Logic Chapter 7 - Sentential Propositions What has been made abundantly clear in the previous discussion
More informationLogic: A Brief Introduction
Logic: A Brief Introduction Ronald L. Hall, Stetson University PART III - Symbolic Logic Chapter 7 - Sentential Propositions 7.1 Introduction What has been made abundantly clear in the previous discussion
More informationA. 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
More informationChapter 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
More informationA 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
More informationINTERMEDIATE 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
More informationLogic 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,
More informationLOGIC ANTHONY KAPOLKA FYF 101-9/3/2010
LOGIC ANTHONY KAPOLKA FYF 101-9/3/2010 LIBERALLY EDUCATED PEOPLE......RESPECT RIGOR NOT SO MUCH FOR ITS OWN SAKE BUT AS A WAY OF SEEKING TRUTH. LOGIC PUZZLE COOPER IS MURDERED. 3 SUSPECTS: SMITH, JONES,
More informationLogicola Truth Evaluation Exercises
Logicola Truth Evaluation Exercises The Logicola exercises for Ch. 6.3 concern truth evaluations, and in 6.4 this complicated to include unknown evaluations. I wanted to say a couple of things for those
More informationLogic & Proofs. Chapter 3 Content. Sentential Logic Semantics. Contents: Studying this chapter will enable you to:
Sentential Logic Semantics Contents: Truth-Value Assignments and Truth-Functions Truth-Value Assignments Truth-Functions Introduction to the TruthLab Truth-Definition Logical Notions Truth-Trees Studying
More informationLecture 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.
More informationWorkbook Unit 3: Symbolizations
Workbook Unit 3: Symbolizations 1. Overview 2 2. Symbolization as an Art and as a Skill 3 3. A Variety of Symbolization Tricks 15 3.1. n-place Conjunctions and Disjunctions 15 3.2. Neither nor, Not both
More informationPhilosophy 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
More informationLogic 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
More informationChapter 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.
More informationA Romp through the Foothills of Logic: Session 2
A Romp through the Foothills of Logic: Session 2 You might find it easier to understand this podcast if you first watch the short podcast Introducing Truth Tables. (Slide 2) Right, by the time we finish
More informationPhilosophy 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
More informationPHILOSOPHY 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
More informationHANDBOOK (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
More informationStudy 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)
More information7.1. 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,
More informationSymbolic Logic. 8.1 Modern Logic and Its Symbolic Language
M08_COPI1396_13_SE_C08.QXD 10/16/07 9:19 PM Page 315 Symbolic Logic 8 8.1 Modern Logic and Its Symbolic Language 8.2 The Symbols for Conjunction, Negation, and Disjunction 8.3 Conditional Statements and
More informationPart 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
More informationChapter 3: More Deductive Reasoning (Symbolic Logic)
Chapter 3: More Deductive Reasoning (Symbolic Logic) There's no easy way to say this, the material you're about to learn in this chapter can be pretty hard for some students. Other students, on the other
More informationAn Introduction to. Formal Logic. Second edition. Peter Smith, February 27, 2019
An Introduction to Formal Logic Second edition Peter Smith February 27, 2019 Peter Smith 2018. Not for re-posting or re-circulation. Comments and corrections please to ps218 at cam dot ac dot uk 1 What
More informationKRISHNA KANTA HANDIQUI STATE OPEN UNIVERSITY Patgaon, Ranigate, Guwahati SEMESTER: 1 PHILOSOPHY PAPER : 1 LOGIC: 1 BLOCK: 2
GPH S1 01 KRISHNA KANTA HANDIQUI STATE OPEN UNIVERSITY Patgaon, Ranigate, Guwahati-781017 SEMESTER: 1 PHILOSOPHY PAPER : 1 LOGIC: 1 BLOCK: 2 CONTENTS UNIT 6 : Modern analysis of proposition UNIT 7 : Square
More informationSituations 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,
More informationPhilosophy 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
More informationHANDBOOK (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
More informationA Primer on Logic Part 1: Preliminaries and Vocabulary. Jason Zarri. 1. An Easy $10.00? a 3 c 2. (i) (ii) (iii) (iv)
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
More informationRosen, Discrete Mathematics and Its Applications, 6th edition Extra Examples
Rosen, Discrete Mathematics and Its Applications, 6th edition Extra Examples Section 1.1 Propositional Logic Page references correspond to locations of Extra Examples icons in the textbook. p.2, icon at
More informationPHIL 115: Philosophical Anthropology. I. Propositional Forms (in Stoic Logic) Lecture #4: Stoic Logic
HIL 115: hilosophical Anthropology Lecture #4: Stoic Logic Arguments from the Euthyphro: Meletus Argument (according to Socrates) [3a-b] Argument: Socrates is a maker of gods; so, Socrates corrupts the
More informationAlso, in Argument #1 (Lecture 11, Slide 11), the inference from steps 2 and 3 to 4 is stated as:
by SALVATORE - 5 September 2009, 10:44 PM I`m having difficulty understanding what steps to take in applying valid argument forms to do a proof. What determines which given premises one should select to
More informationHANDBOOK. 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
More information9 Methods of Deduction
M09_COPI1396_13_SE_C09.QXD 10/19/07 3:46 AM Page 372 9 Methods of Deduction 9.1 Formal Proof of Validity 9.2 The Elementary Valid Argument Forms 9.3 Formal Proofs of Validity Exhibited 9.4 Constructing
More informationAn alternative understanding of interpretations: Incompatibility Semantics
An alternative understanding of interpretations: Incompatibility Semantics 1. In traditional (truth-theoretic) semantics, interpretations serve to specify when statements are true and when they are false.
More informationTransition 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
More informationSemantic Entailment and Natural Deduction
Semantic Entailment and Natural Deduction Alice Gao Lecture 6, September 26, 2017 Entailment 1/55 Learning goals Semantic entailment Define semantic entailment. Explain subtleties of semantic entailment.
More information4.1 A problem with semantic demonstrations of validity
4. Proofs 4.1 A problem with semantic demonstrations of validity Given that we can test an argument for validity, it might seem that we have a fully developed system to study arguments. However, there
More informationChapter 3: Basic Propositional Logic. Based on Harry Gensler s book For CS2209A/B By Dr. Charles Ling;
Chapter 3: Basic Propositional Logic Based on Harry Gensler s book For CS2209A/B By Dr. Charles Ling; cling@csd.uwo.ca The Ultimate Goals Accepting premises (as true), is the conclusion (always) true?
More informationChapter 6, Tutorial 1 Predicate Logic Introduction
Chapter 6, Tutorial 1 Predicate Logic Introduction In this chapter, we extend our formal language beyond sentence letters and connectives. And even beyond predicates and names. Just one small wrinkle,
More information2.1 Review. 2.2 Inference and justifications
Applied Logic Lecture 2: Evidence Semantics for Intuitionistic Propositional Logic Formal logic and evidence CS 4860 Fall 2012 Tuesday, August 28, 2012 2.1 Review The purpose of logic is to make reasoning
More information1. Introduction Formal deductive logic Overview
1. Introduction 1.1. Formal deductive logic 1.1.0. Overview In this course we will study reasoning, but we will study only certain aspects of reasoning and study them only from one perspective. The special
More information15. 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
More informationIn Defense of The Wide-Scope Instrumental Principle. Simon Rippon
In Defense of The Wide-Scope Instrumental Principle Simon Rippon Suppose that people always have reason to take the means to the ends that they intend. 1 Then it would appear that people s intentions to
More informationIn 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
More informationPHI 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
More information3. Negations Not: contradicting content Contradictory propositions Overview Connectives
3. Negations 3.1. Not: contradicting content 3.1.0. Overview In this chapter, we direct our attention to negation, the second of the logical forms we will consider. 3.1.1. Connectives Negation is a way
More informationArtificial Intelligence: Valid Arguments and Proof Systems. Prof. Deepak Khemani. Department of Computer Science and Engineering
Artificial Intelligence: Valid Arguments and Proof Systems Prof. Deepak Khemani Department of Computer Science and Engineering Indian Institute of Technology, Madras Module 02 Lecture - 03 So in the last
More information3.5_djj_004_Notes.notebook. November 03, 2009
IN CLASS TUE, 10. 27.09,THU, 10.29.09, & TUE. 11.03.09 Section 3.5: Equivalent Statements, Variations of Conditional Statements, and De Morgan's Laws (Objectives 1 5) Equivalent Statements: statements
More informationCHAPTER ONE STATEMENTS, CONNECTIVES AND EQUIVALENCES
CHAPTER ONE STATEMENTS, CONNECTIVES AND EQUIVALENCES A unifying concept in mathematics is the validity of an argument To determine if an argument is valid we must examine its component parts, that is,
More informationLogic 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
More informationGeometry 2.3.notebook October 02, 2015
Do Now Write the converse of each true statement. If true, combine the statements to write a true biconditional. If the converse is false, give a counterexample. a) If an angle measures 30 o, then it is
More informationLGCS 199DR: Independent Study in Pragmatics
LGCS 99DR: Independent Study in Pragmatics Jesse Harris & Meredith Landman September 0, 203 Last class, we discussed the difference between semantics and pragmatics: Semantics The study of the literal
More informationWhat 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
More informationA romp through the foothills of logic Session 3
A romp through the foothills of logic Session 3 It would be a good idea to watch the short podcast Understanding Truth Tables before attempting this podcast. (Slide 2) In the last session we learnt how
More informationLecture 4: Deductive Validity
Lecture 4: Deductive Validity Right, I m told we can start. Hello everyone, and hello everyone on the podcast. This week we re going to do deductive validity. Last week we looked at all these things: have
More information3.3. Negations as premises Overview
3.3. Negations as premises 3.3.0. Overview A second group of rules for negation interchanges the roles of an affirmative sentence and its negation. 3.3.1. Indirect proof The basic principles for negation
More informationOverview 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.,
More informationConditionals II: no truth conditions?
Conditionals II: no truth conditions? UC Berkeley, Philosophy 142, Spring 2016 John MacFarlane 1 Arguments for the material conditional analysis As Edgington [1] notes, there are some powerful reasons
More informationExposition of Symbolic Logic with Kalish-Montague derivations
An Exposition of Symbolic Logic with Kalish-Montague derivations Copyright 2006-13 by Terence Parsons all rights reserved Aug 2013 Preface The system of logic used here is essentially that of Kalish &
More informationAnnouncements & Such
Branden Fitelson Philosophy 12A Notes 1 Announcements & Such Miles Davis & John Coltrane: So What Administrative Stuff Permanent locations for all sections are now known (see website). HW #1 is due today
More informationIs the law of excluded middle a law of logic?
Is the law of excluded middle a law of logic? Introduction I will conclude that the intuitionist s attempt to rule out the law of excluded middle as a law of logic fails. They do so by appealing to harmony
More informationUnit. 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
More informationA Liar Paradox. Richard G. Heck, Jr. Brown University
A Liar Paradox Richard G. Heck, Jr. Brown University It is widely supposed nowadays that, whatever the right theory of truth may be, it needs to satisfy a principle sometimes known as transparency : Any
More informationNatural Deduction for Sentence Logic
Natural Deduction for Sentence Logic Derived Rules and Derivations without Premises We will pursue the obvious strategy of getting the conclusion by constructing a subderivation from the assumption of
More informationb) The meaning of "child" would need to be taken in the sense of age, as most people would find the idea of a young child going to jail as wrong.
Explanation for Question 1 in Quiz 8 by Norva Lo - Tuesday, 18 September 2012, 9:39 AM The following is the solution for Question 1 in Quiz 8: (a) Which term in the argument is being equivocated. (b) What
More information2.3. 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
More informationThe antecendent always a expresses a sufficient condition for the consequent
Critical Thinking Lecture Four October 5, 2012 Chapter 3 Deductive Argument Patterns Diagramming Arguments Deductive Argument Patterns - There are some common patterns shared by many deductive arguments
More informationKripke 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
More informationDay 3. Wednesday May 23, Learn the basic building blocks of proofs (specifically, direct proofs)
Day 3 Wednesday May 23, 2012 Objectives: Learn the basics of Propositional Logic Learn the basic building blocks of proofs (specifically, direct proofs) 1 Propositional Logic Today we introduce the concepts
More informationBASIC 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
More informationIllustrating 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)
More informationComplications 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
More informationTo 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
More informationHomework: read in the book pgs and do "You Try It" (to use Submit); Read for lecture. C. Anthony Anderson
Philosophy 183 Page 1 09 / 26 / 08 Friday, September 26, 2008 9:59 AM Homework: read in the book pgs. 1-10 and do "You Try It" (to use Submit); Read 19-29 for lecture. C. Anthony Anderson (caanders@philosophy.ucsb.edu)
More informationSelections 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
More information1.5. 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
More informationThere are two common forms of deductively valid conditional argument: modus ponens and modus tollens.
INTRODUCTION TO LOGICAL THINKING Lecture 6: Two types of argument and their role in science: Deduction and induction 1. Deductive arguments Arguments that claim to provide logically conclusive grounds
More informationFaith indeed tells what the senses do not tell, but not the contrary of what they see. It is above them and not contrary to them.
19 Chapter 3 19 CHAPTER 3: Logic Faith indeed tells what the senses do not tell, but not the contrary of what they see. It is above them and not contrary to them. The last proceeding of reason is to recognize
More informationLecture 3. I argued in the previous lecture for a relationist solution to Frege's puzzle, one which
1 Lecture 3 I argued in the previous lecture for a relationist solution to Frege's puzzle, one which posits a semantic difference between the pairs of names 'Cicero', 'Cicero' and 'Cicero', 'Tully' even
More informationGENERAL NOTES ON THIS CLASS
PRACTICAL LOGIC Bryan Rennie GENERAL NOTES ON THE CLASS EXPLANATION OF GRADES AND POINTS, ETC. SAMPLE QUIZZES SCHEDULE OF CLASSES THE SIX RULES OF SYLLOGISMS (and corresponding fallacies) SYMBOLS USED
More informationPhilosophical Perspectives, 14, Action and Freedom, 2000 TRANSFER PRINCIPLES AND MORAL RESPONSIBILITY. Eleonore Stump Saint Louis University
Philosophical Perspectives, 14, Action and Freedom, 2000 TRANSFER PRINCIPLES AND MORAL RESPONSIBILITY Eleonore Stump Saint Louis University John Martin Fischer University of California, Riverside It is
More informationResponses to the sorites paradox
Responses to the sorites paradox phil 20229 Jeff Speaks April 21, 2008 1 Rejecting the initial premise: nihilism....................... 1 2 Rejecting one or more of the other premises....................
More informationChapter 2. A Little Logic
Chapter 2. A Little Logic 2.1 An Intuitive Distinction: Logic can be regarded as the study of certain specific properties and relations among sentences. Those properties and relations are ultimately specified
More informationIdentity and Plurals
Identity and Plurals Paul Hovda February 6, 2006 Abstract We challenge a principle connecting identity with plural expressions, one that has been assumed or ignored in most recent philosophical discussions
More informationDeduction. 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
More informationELEMENTS 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
More informationBASIC 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
More informationMoore 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
More informationTesting semantic sequents with truth tables
Testing semantic sequents with truth tables Marianne: Hi. I m Marianne Talbot and in this video we are going to look at testing semantic sequents with truth tables. (Slide 2) This video supplements Session
More informationTutorial 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
More information1 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
More informationInstructor 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
More informationLogic: 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
More informationBasic 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
More informationWhat 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
More informationPhilosophy 12 Study Guide #4 Ch. 2, Sections IV.iii VI
Philosophy 12 Study Guide #4 Ch. 2, Sections IV.iii VI Precising definition Theoretical definition Persuasive definition Syntactic definition Operational definition 1. Are questions about defining a phrase
More information