Chapter 3: Basic Propositional Logic. Based on Harry Gensler s book For CS2209A/B By Dr. Charles Ling;


 Silas Daniels
 4 years ago
 Views:
Transcription
1 Chapter 3: Basic Propositional Logic Based on Harry Gensler s book For CS2209A/B By Dr. Charles Ling;
2 The Ultimate Goals Accepting premises (as true), is the conclusion (always) true? Is the reasoning process valid? Premises: If you smoke, you can get lung cancer. You do not smoke. Conclusion: you cannot get lung cancer. Premises: If it rains and your tent leaks, your sleeping bag will get wet. Your sleeping bag did not get wet. Your tent leaks. Conclusion: it did not rain. Formalize and automate the deduction process First: how to express premises and conclusions?
3 3.1 Translation from English to Logic Need a (formal) language to deal with simple statements that may be true and false: use capital letters (P, Q, ) They are called propositions deal with ifthen, and, or, not, etc. in NL
4 WellFormed Formula (wff) 1. Any capital letter is a wff. 2. The result of prefixing any wff with ~ is a wff. 3. The result of joining any two wffs by or or or and enclosing the result in ( ) is a wff. Examples and usual meaning of connectives in NL
5 Parentheses are important
6 Examples of Invalid wff p, p q, p and q (~P), (Q), ((R)) P Q, P Q R, (P Q R) If p then q Logic (including wff) is very precise
7 Some useful rules in translation Rule: put ( wherever you see both, either, or if.
8 Rule: Group together parts on either side of a comma.
9 Rule: have your capital letters stand for whole statements
10 Exercise (also LogiCola C (EM & ET)) 1. Not both A and B. 2. Both A and either B or C. 3. Either both A and B or C. 4. If A, then B or C. 5. If A then B, or C. 6. If not A, then not either B or C. 7. If not A, then either not B or C. 8. Either A or B, and C. 9. Either A, or B and C. 10. If A then not both not B and not C. 11. If you get an error message, then the disk is bad or it s a Macintosh disk. 12. If I bring my digital camera, then if my batteries don t die then I ll take pictures of my backpack trip and put the pictures on my Web site.
11 Exercise LogiCola C (EM & ET)
12 LogiCola CET
13 OK if you use LogiCola notations in assignment and quiz
14 3.2 Simple truth tables: the meaning/semantics of wff A truth table gives a logical diagram for a wff. It lists all possible truthvalue combinations for the letters and says whether the wff is true or false in each case. Define connectives first
15
16
17 Reallife or may have different meanings You can have allyoucaneat soup or salad and bread. Inclusive or. Exclusive or : A or B but not both = ((A B) ~(A B)) Most logic books treat either A or B as exclusive or but this textbook treats either A or B as (A B)
18
19 Some interesting examples of if If A then B does NOT imply A but is often taken otherwise. In Death on the Nile If I did not sleep, if I walked on the deck, I might see who killed her The Conservatives have issued another apology, this time for comments caught on video Wednesday by an assistant to Transport Minister Lawrence Cannon. The exchange was caught on video and broadcast Wed. by the Aboriginal Peoples Television Network. If you behave and you're sober and there's no problems and if you don't do a sit down and whatever, I don't care, said Mr. Cannon's assistant Darlene Lannigan to Mr. Matchewan. Are you calling me an alcoholic? replied Mr. Matchewan. She later added: One of them showed up the other day and was drinking.
20
21 3.3 Truth evaluations We can calculate the truth value of a wff if we know the truth value of its letters. LogiCola D (TM & TH)
22 3.3a Exercise Assume that A=1 and B=1 (A and B are both true) while X=0 and Y=0 (X and Y are both false). Calculate the truth value of each wff below.
23 3.4 Unknown evaluations We can sometimes figure out a formula s truth value even if we don t know the truth value of some letters. Exercise LogiCola D (UE, UM, & UH) T=1 (T is true), F=0 (F is false), and U=?
24 3.5 Complex truth tables A formula with n distinct letters has 2 n possible truthvalue combinations:
25
26 The truth table for (P ~P) is true in all cases which makes the formula a tautology the law of the excluded middle, says that every statement is true or false (no other status, such as maybe true ). This law holds in propositional logic The truth table for (P ~P) is false in all cases which makes the formula a selfcontradiction Otherwise, the formula is a contingent (either true of false; we do not know which one). 3.5a Exercise LogiCola D (FM & FH)
27 Logical Paradox Everything I say is a lie. Is this a lie? Barber paradox: An adult male barber shaves all and only men who do not shave themselves. Does he shave himself? One thing is certain in this world: nothing is certain.
28 3.6 The truthtable test To prove a propositional argument (given premises and conclusion) Construct a truth table showing the truth value of the premises and conclusion for all possible cases. The argument is valid if and only if for all rows (cases) that the premises are all true, the conclusion is also true. Otherwise, the argument is invalid.
29 If you re a dog, then you re an animal. You re not a dog. You re not an animal So, cannot conclude (or invalid to deduce) you re not an animal
30 Shortcut table: do it faster Letter comb P1 P2 P3 C If any Pi is 0, no need to evaluate other P s and C (ignore this row and continue the table) If C is 1, no need to evaluate any Pi (ignore this row and continue the table) If C is 0, must evaluate Ps. If all Pi are 1, stop the table. The argument is invalid. If the above case does not happen when you complete the table, the argument is valid.? a Exercise LogiCola D (AE, AM, & AH)
31 A Note Reasoning (or argument) is valid or invalid, not true or false When valid conclusion cannot be drawn: not the same as drawing the negated conclusion. Previous example: invalid to conclude you are an animal In court, given evidence, if I can prove you are guilty, then you are guilty is true. But if I cannot prove you are guilty, then you can be either guilty or innocent.
32 3.6a Exercise (selected) 3. If television is always right, then Anacin is better than Bayer. If television is always right, then Anacin isn t better than Bayer. Television isn t always right. [Use T and B.] 4. If it rains and your tent leaks, then your down sleeping bag will get wet. Your tent won t leak. Your down sleeping bag won t get wet. [Use R, L, and W.] 7. If ethics depends on God s will, then something is good because God desires it. Something isn t good because God desires it. (Instead, God desires something because it s already good.) Ethics doesn t depend on God s will. [Use D and B; this argument is from Plato s Euthyphro.] 9. I ll go to Paris during spring break if and only if I ll win the lottery. I won t win the lottery. I won t go to Paris during spring break. [Use P and W.]
33 If an argument passes the truthtable test, it means that the premises entails the conclusion (in semantics). The truthtable test can get tedious for long arguments. Arguments with 6 letters may need 64 lines and ones with 10 letters need 1024 lines Can we do it based only on syntax? Yes, see 3.10, Chapter 4,
34 3.7 The truthassignment test Take a propositional argument. Set each premise to 1 and the conclusion to 0. The argument is VALID if and only if no consistent way of assigning 1 and 0 to the letters will make this work so we can t make the premises all true and conclusion false. You REFUTE the argument if you can find such an assignment Again, this does not prove the negated conclusion.
35 Is this method easier than the truthtable test? Exercise LogiCola E (S); E (E)
36
37 Read Chapter 3.8 by yourselves Read Chapter 3.9 by yourselves 3.8a Exercise LogiCola C (HM & HT) 3.9a Exercise LogiCola E (F I)
38 Some extra topics See extra slides posted Adequate set of connectives (set2)
39 3.10/3.11 Srules, Irules Inference rules, which state that certain formulas can be derived with validity from certain other formulas, mechanically Deduce, formally deducible : Will be building blocks for formal proofs Also check mechanically if a proof is valid They reflect common forms of reasoning What we hope to have (see later) Everything that is deduced is indeed valid. Sound Everything that is valid can be deduced. Complete
40 Each P and Q can match with any wff. E.g., (A (B C)) 3.10a Exercise LogiCola F (SE & SH)
41
42 All Srules Also: P ~ ~ P
43 Modus Ponens Modus Tolens 3.11a Exercise LogiCola F (IE & IH)
44
45 3.12 Combining S and Irules 3.12a Exercise LogiCola F (CE & CH)
46 3.13 Extended inferences
47 Exercise
48 Rules you can use
49 Sound but Incomplete These rules are certainly sound But incomplete Cannot prove these Next chapter: sound and complete proof system
50 3.14 Logic and computers Boolean Logic: used to design circuits in computers and digital devices Automated logical deduction, automated proof system Logic Programming: a logicbased declarative programming language AI: knowledge representation, reasoning, planning Hoare Logic: correctness of computer programs
Artificial 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 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 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 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 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 informationChapter 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
More informationWhat are TruthTables and What Are They For?
PY114: Work Obscenely Hard Week 9 (Meeting 7) 30 November, 2010 What are TruthTables and What Are They For? 0. Business Matters: The last marked homework of term will be due on Monday, 6 December, at
More informationArtificial Intelligence Prof. P. Dasgupta Department of Computer Science & Engineering Indian Institute of Technology, Kharagpur
Artificial Intelligence Prof. P. Dasgupta Department of Computer Science & Engineering Indian Institute of Technology, Kharagpur Lecture 9 First Order Logic In the last class, we had seen we have studied
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 truthvalue of a given truthfunctional compound proposition depends
More informationLogic I or Moving in on the Monkey & Bananas Problem
Logic I or Moving in on the Monkey & Bananas Problem We said that an agent receives percepts from its environment, and performs actions on that environment; and that the action sequence can be based on
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 informationModule 5. Knowledge Representation and Logic (Propositional Logic) Version 2 CSE IIT, Kharagpur
Module 5 Knowledge Representation and Logic (Propositional Logic) Lesson 12 Propositional Logic inference rules 5.5 Rules of Inference Here are some examples of sound rules of inference. Each can be shown
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 informationBeyond Symbolic Logic
Beyond Symbolic Logic 1. The Problem of Incompleteness: Many believe that mathematics can explain *everything*. Gottlob Frege proposed that ALL truths can be captured in terms of mathematical entities;
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 informationInformalizing 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
More informationDeduction 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
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 reposting or recirculation. Comments and corrections please to ps218 at cam dot ac dot uk 1 What
More informationIntroducing 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
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 informationRevisiting 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
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 informationCHAPTER 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
More informationA 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,
More informationReductio ad Absurdum, Modulation, and Logical Forms. Miguel LópezAstorga 1
International Journal of Philosophy and Theology June 25, Vol. 3, No., pp. 5965 ISSN: 2333575 (Print), 23335769 (Online) Copyright The Author(s). All Rights Reserved. Published by American Research
More informationMATH1061/MATH7861 Discrete Mathematics Semester 2, Lecture 5 Valid and Invalid Arguments. Learning Goals
MAH1061/MAH7861 Discrete Mathematics Semester 2, 2016 Learning Goals 1. Understand the meaning of necessary and sufficient conditions (carried over from Wednesday). 2. Understand the difference between
More informationThe way we convince people is generally to refer to sufficiently many things that they already know are correct.
Theorem A Theorem is a valid deduction. One of the key activities in higher mathematics is identifying whether or not a deduction is actually a theorem and then trying to convince other people that you
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 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 informationArtificial Intelligence Prof. P. Dasgupta Department of Computer Science & Engineering Indian Institute of Technology, Kharagpur
Artificial Intelligence Prof. P. Dasgupta Department of Computer Science & Engineering Indian Institute of Technology, Kharagpur Lecture 10 Inference in First Order Logic I had introduced first order
More informationDoes Deduction really rest on a more secure epistemological footing than Induction?
Does Deduction really rest on a more secure epistemological footing than Induction? We argue that, if deduction is taken to at least include classical logic (CL, henceforth), justifying CL  and thus deduction
More informationLogic. A Primer with Addendum
Logic A Primer with Addendum The Currency of Philosophy Philosophy trades in arguments. An argument is a set of propositions some one of which is intended to be warranted or entailed by the others. The
More informationAnnouncements. CS243: Discrete Structures. First Order Logic, Rules of Inference. Review of Last Lecture. Translating English into FirstOrder Logic
Announcements CS243: Discrete Structures First Order Logic, Rules of Inference Işıl Dillig Homework 1 is due now Homework 2 is handed out today Homework 2 is due next Tuesday Işıl Dillig, CS243: Discrete
More informationLing 98a: The Meaning of Negation (Week 1)
Yimei Xiang yxiang@fas.harvard.edu 17 September 2013 1 What is negation? Negation in twovalued propositional logic Based on your understanding, select out the metaphors that best describe the meaning
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 informationAnnouncements. CS311H: Discrete Mathematics. First Order Logic, Rules of Inference. Satisfiability, Validity in FOL. Example.
Announcements CS311H: Discrete Mathematics First Order Logic, Rules of Inference Instructor: Işıl Dillig Homework 1 is due now! Homework 2 is handed out today Homework 2 is due next Wednesday Instructor:
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 informationParadox of Deniability
1 Paradox of Deniability Massimiliano Carrara FISPPA Department, University of Padua, Italy Peking University, Beijing  6 November 2018 Introduction. The starting elements Suppose two speakers disagree
More informationLOGIC ANTHONY KAPOLKA FYF 1019/3/2010
LOGIC ANTHONY KAPOLKA FYF 1019/3/2010 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 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 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 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 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 informationCHAPTER 1 A PROPOSITIONAL THEORY OF ASSERTIVE ILLOCUTIONARY ARGUMENTS OCTOBER 2017
CHAPTER 1 A PROPOSITIONAL THEORY OF ASSERTIVE ILLOCUTIONARY ARGUMENTS OCTOBER 2017 Man possesses the capacity of constructing languages, in which every sense can be expressed, without having an idea how
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 information1.2. 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
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 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 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 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, Guwahati781017 SEMESTER: 1 PHILOSOPHY PAPER : 1 LOGIC: 1 BLOCK: 2 CONTENTS UNIT 6 : Modern analysis of proposition UNIT 7 : Square
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 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 informationLogic and Pragmatics: linear logic for inferential practice
Logic and Pragmatics: linear logic for inferential practice Daniele Porello danieleporello@gmail.com Institute for Logic, Language & Computation (ILLC) University of Amsterdam, Plantage Muidergracht 24
More informationPredicate 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. Firstorder logic. Question 1. Describe this discipline/subdiscipline, and some of its more
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 informationLogic & Proofs. Chapter 3 Content. Sentential Logic Semantics. Contents: Studying this chapter will enable you to:
Sentential Logic Semantics Contents: TruthValue Assignments and TruthFunctions TruthValue Assignments TruthFunctions Introduction to the TruthLab TruthDefinition Logical Notions TruthTrees Studying
More informationA Judgmental Formulation of Modal Logic
A Judgmental Formulation of Modal Logic Sungwoo Park Pohang University of Science and Technology South Korea Estonian Theory Days Jan 30, 2009 Outline Study of logic Model theory vs Proof theory Classical
More informationToday s Lecture 1/28/10
Chapter 7.1! Symbolizing English Arguments! 5 Important Logical Operators!The Main Logical Operator Today s Lecture 1/28/10 Quiz State from memory (closed book and notes) the five famous valid forms and
More informationHow Gödelian Ontological Arguments Fail
How Gödelian Ontological Arguments Fail Matthew W. Parker Abstract. Ontological arguments like those of Gödel (1995) and Pruss (2009; 2012) rely on premises that initially seem plausible, but on closer
More informationPhilosophy 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
More informationCircumscribing Inconsistency
Circumscribing Inconsistency Philippe Besnard IRISA Campus de Beaulieu F35042 Rennes Cedex Torsten H. Schaub* Institut fur Informatik Universitat Potsdam, Postfach 60 15 53 D14415 Potsdam Abstract We
More informationC. Exam #1 comments on difficult spots; if you have questions about this, please let me know. D. Discussion of extra credit opportunities
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
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 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 informationIntroduction to Logic. Instructor: Jason Sheley
Introduction to Logic Instructor: Jason Sheley In this section we will learn: What is the difference between Deduction and Induction? Why use different types of logic? What is a valid argument? Invalid?
More informationBonJour Against Materialism. Just an intellectual bandwagon?
BonJour Against Materialism Just an intellectual bandwagon? What is physicalism/materialism? materialist (or physicalist) views: views that hold that mental states are entirely material or physical in
More informationMr 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
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 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 information(Some More) Vagueness
(Some More) Vagueness Otávio Bueno Department of Philosophy University of Miami Coral Gables, FL 33124 Email: otaviobueno@mac.com Three features of vague predicates: (a) borderline cases It is common
More informationExercise Sets. KS Philosophical Logic: Modality, Conditionals Vagueness. Dirk Kindermann University of Graz July 2014
Exercise Sets KS Philosophical Logic: Modality, Conditionals Vagueness Dirk Kindermann University of Graz July 2014 1 Exercise Set 1 Propositional and Predicate Logic 1. Use Definition 1.1 (Handout I Propositional
More informationUC Berkeley, Philosophy 142, Spring 2016
Logical Consequence UC Berkeley, Philosophy 142, Spring 2016 John MacFarlane 1 Intuitive characterizations of consequence Modal: It is necessary (or apriori) that, if the premises are true, the conclusion
More informationUnit 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,
More informationTutorial A03: Patterns of Valid Arguments By: Jonathan Chan
A03.1 Introduction Tutorial A03: Patterns of Valid Arguments By: With valid arguments, it is impossible to have a false conclusion if the premises are all true. Obviously valid arguments play a very important
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) [3ab] Argument: Socrates is a maker of gods; so, Socrates corrupts the
More informationScott Soames: Understanding Truth
Philosophy and Phenomenological Research Vol. LXV, No. 2, September 2002 Scott Soames: Understanding Truth MAlTHEW MCGRATH Texas A & M University Scott Soames has written a valuable book. It is unmatched
More information1. Lukasiewicz s Logic
Bulletin of the Section of Logic Volume 29/3 (2000), pp. 115 124 Dale Jacquette AN INTERNAL DETERMINACY METATHEOREM FOR LUKASIEWICZ S AUSSAGENKALKÜLS Abstract An internal determinacy metatheorem is proved
More informationLogic: Deductive and Inductive by Carveth Read M.A. CHAPTER IX CHAPTER IX FORMAL CONDITIONS OF MEDIATE INFERENCE
CHAPTER IX CHAPTER IX FORMAL CONDITIONS OF MEDIATE INFERENCE Section 1. A Mediate Inference is a proposition that depends for proof upon two or more other propositions, so connected together by one or
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 information16. Universal derivation
16. Universal derivation 16.1 An example: the Meno In one of Plato s dialogues, the Meno, Socrates uses questions and prompts to direct a young slave boy to see that if we want to make a square that has
More informationComments 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
More informationArgument Mapping. Table of Contents. By James Wallace Gray 2/13/2012
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
More informationNegative Introspection Is Mysterious
Negative Introspection Is Mysterious Abstract. The paper provides a short argument that negative introspection cannot be algorithmic. This result with respect to a principle of belief fits to what we know
More informationCourses providing assessment data PHL 202. Semester/Year
1 Department/Program 20122016 Assessment Plan Department: Philosophy Directions: For each department/program student learning outcome, the department will provide an assessment plan, giving detailed information
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 information2. 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.
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 informationEthical 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
More informationClass 33: Quine and Ontological Commitment Fisher 5969
Philosophy 240: Symbolic Logic Fall 2008 Mondays, Wednesdays, Fridays: 9am  9:50am Hamilton College Russell Marcus rmarcus1@hamilton.edu Re HW: Don t copy from key, please! Quine and Quantification I.
More informationA R G U M E N T S I N A C T I O N
ARGUMENTS IN ACTION Descriptions: creates a textual/verbal account of what something is, was, or could be (shape, size, colour, etc.) Used to give you or your audience a mental picture of the world around
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 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 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 informationPortfolio Project. Phil 251A Logic Fall Due: Friday, December 7
Portfolio Project Phil 251A Logic Fall 2012 Due: Friday, December 7 1 Overview The portfolio is a semesterlong project that should display your logical prowess applied to realworld arguments. The arguments
More informationLogic type questions
Logic type questions [For use in the Philosophy Test and the Philosophy section of the MLAT] One of the questions on a test may take the form of a logic exercise, starting with the definition of a key
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 informationA Puzzle about Knowing Conditionals i. (final draft) Daniel Rothschild University College London. and. Levi Spectre The Open University of Israel
A Puzzle about Knowing Conditionals i (final draft) Daniel Rothschild University College London and Levi Spectre The Open University of Israel Abstract: We present a puzzle about knowledge, probability
More informationIn 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 wordplay, or
More informationArtificial Intelligence. Clause Form and The Resolution Rule. Prof. Deepak Khemani. Department of Computer Science and Engineering
Artificial Intelligence Clause Form and The Resolution Rule Prof. Deepak Khemani Department of Computer Science and Engineering Indian Institute of Technology, Madras Module 07 Lecture 03 Okay so we are
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 truthfunctional arguments.
More information