What are TruthTables and What Are They For?


 Eustace Norton
 6 years ago
 Views:
Transcription
1 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 4pm. Please see separate sheet with the problem set. Please read Tomassi, 2.1 & Office Hours this week changed from Thursday 12 to Friday 34. Regular OH Monday Review  Upper case letters (P, Q and R) are sentential constants, or sentence letters.  When translating a sentence from English to Propositional Logic, we require a key.  There are five logical connectives in Propositional Logic: Negation (~), Conjunction (&), Disjunction (v), Conditional ( ), and Biconditional ( ).  Negation is a unary (oneplace) connective, the others are all binary (twoplace).  Logical connectives connect either atomic or compound formulas.  Brackets (parentheses) are used to specify the scope of a connective. 2. Truth and Falsity  Arguments can be valid or invalid, sound or unsound.  Sentences, on the other hand, are either true or false. As logicians say, there are two truthvalues: true and false.  This is known as the Principle of Bivalence, which states: every sentence is either true or false but not both and not neither. 3. Scope Every connective has a specific scope. The scope of the tilda (~) is the formula that is being negated. In the simplest case this will be a simple atomic proposition, but in other cases it will be some more complex wff (wellformed formula). To determine the scope of a tilda, then, we simply ask: exactly what is being negated here? Consider these examples: ~P scope of negation (what is being negated): P ~ (P & Q) scope of negatation: (P & Q) ~(P & Q) R scope of negation: (P & Q) ~((P & Q) R) scope of negation: ((P & Q) R) For a two place connective, the scope of the connective are the TWO wffs that are being connected. In the following examples I have used underlining to indicate the scope of the ampersands. P & Q P & ~Q (P v Q) & (~P Q) 4. Exercise: Using underlining, show the scope of the indicated connective. Indicate the scope of the tilda ~(P v ~P) Indicate the scope of the arrow P (P & Q) Indicate the scope of the second arrow ~(((P Q) (Q R)) & ~(P R))
2 5. SKILL: Find the Main Connective The main connective in a formula of propositional calculus is the connective whose scope encompasses the whole formula. The main connective tells us what kind of compound formula we are dealing with: whether a negation, a conjunction, a disjunction, a conditional, or a biconditional. The simplest compound formulae have only a single connective, which accordingly serves as the main connective. Hence the ampersand is the main connective in (P&Q); the whole formula is accordingly a conjunction. A crucial skill in interpreting the propositional calculus is the skill of finding the main connective in moderately complex formulae. This is a bit like finding the main verb in an English sentence that has various subordinate and relative clauses. Read the following formulae (aloud if you can) and find the main connective. Specify what kind of formula is being expressed: a) P (P & Q) b) P & ~P c) ~(P v ~P) d) P (Q P) e) (P & Q) (Q & P) f) ((P Q) (Q R)) (P R) g) ~(((P Q) (Q R)) & ~(P R)) h) (P Q) v (Q P) 6. Truth Functions and Truth Tables A truth table is a logical calculating device. In order to understand its distinctive utility, we need to start by recalling some crucial background. 1.. In the formal symbolic language of the propositional calculus, a sentence is called a formula (or a wellformed formula a WFF). 2. As we have seen, there are two classes of formulae in the propositional calculus: atomic and compound. An atomic formula is represented by a single sentential constant (e.g., P ) and represents a simple declarative sentence such as Socrates is wise. A compound formula is formed by combining atomic formulae using the logical connectives (~, &, v,, ). Hence the sentence If Socrates is not wise then Plato was a fool can be expressed as a compound formula of the propositional calculus: (~P Q), where P represents the proposition that Socrates is wise and Q represents the proposition that Plato is a fool. 3. Now here is a key point: the truth or falsity of a compound formula is a function of the truth value of the atomic formulae that figure in it. Don t be put off by the abstract talk of functions here. The point is really as simple as this: Suppose I want to know whether the following claim is true or false: Today is Monday and the weather is fine. In order to figure out whether this is true I need to know whether each of its constituent claims is true. That is, Is today Monday? And is the weather fine? Once I know the answers to these questions, and the meaning of the logical term and I can determine the truth value of the compound sentence. That is: the truth value of the compound formula is a function of the truth value is its atomic sentences. 2
3 4. Now truth tables are nothing more than a device for spelling this out exactly and in full detail. A truth table is divided into two sides, left and right. On the left hand side is a specification of all the possible combinations of truth values for the atomic propositions that figure in a compound formulae. The right side specifies the truth value of the compound formula as a function of the truth values of the atomic formulae. Hence for instance the truth table for conjunction shows under what circumstances the compound formula is true and under what circumstances false. P Q P&Q Starting from the left side and reading one row at a time, we can see the following: If both atomic propositions are true then the conjunction is true. (That is the first row of under the horizontal line.) But for any other combination of truth values, the conjunction is false. (That is represented in the last three rows of the table.) USING TRUTH TABLES OK, so what is the point of this? What is a truth table for? As we shall see, truth tables turn out to be quite a powerful (if also somewhat clumsy) tool for a number of interrelated tasks in logic. Let s consider them one at a time. A. Using Truth Tables to Define the Logical Connectives. Logical languages depend on perfect clarity and the absence of ambiguity. While the logical connectives all have natural language correlates, they cannot be defined by appeal to natural language without importing the ambiguities of natural language into the symbolic systems. We have already seen one example of this with the ambiguity of the English word, or, which can be used either inclusively or exclusively. Similar ambiguity infects the English word and. If someone says I got the money at the bank and I went to buy the car, that would typically mean that they first got the money at the bank and then went to buy the car. In short, the word and sometimes conveys temporal information. But it need not. If I say that I have a bike and a scooter, I am not saying anything about which I got first. In order to provide proper definitions of the logical connectives, therefore, we need a way of defining them more exactly than is possible by simply providing natural language correlates. Truth tables provide the tool for this purpose. In logic, the logical connectives are defined as truthfunctions. (P&Q) is defined as the formula which is true if and only if both of its constituent propositions are true. (PvQ) is defined as the formula which is false if and only if both of its constituent propositions are false. The truth tables for each connective spell out these definitions exactly, and without circularity. That is, they specify the truth value of the compound formula given any possible combination of truth value of its constituents. After all, that is exactly what truth tables do. a) Negation  The truth functional nature of each of the logical connectives is represented by a truthtable.  The truthtable for negation is written as follows: P ~P T F F T  Negation is a truthfunction that reverses truth values. b) Conjunction  The truthtable for conjunction is written as follows: P Q P&Q  A conjunction is true only when both conjuncts are true. The sense of temporal direction that exists 3
4 in the English and is not present in &. c) Disjunction  The truthtable for disjunction is as follows: P Q PvQ T F T F T T  A disjunction is true when either or both of the disjuncts are true. It is false only when both are false.  Disjunction in Propositional Logic is inclusive (it is true when both disjuncts are true), rather than the exclusive or that we often find in natural language. d) Conditional  The truthtable for conditional is written as follows: P Q P Q F T T F F T  There only way in which a conditional comes out false is if its antecedent is true and its consequent is false.  The conditional is, intuitively, the least close to its natural language equivalent if then. e) Biconditional  The truthtable for biconditional is written as follows: P Q P Q F F T  A biconditional is true when both sides have the same truth value. B. Using Truth Tables to Interpret Complex Compound Formulae. Once we have truthfunctional definitions of the five connectives, we can put truth tables to work for other purposes. As an example, consider this fairly simple compound formula: P v ~(P v R) For the logician, an interpretation of this compound formulae must tell us its truth value (that is, whether it is true or false) for every combination of the truth values of its constituent atomic propositions. But that is exactly the job for which truth tables are designed. P Q P v ~ (P v Q) T F T T F T T F T F F T T T F mc What this truth table shows is that this compound formula is false only in the case where P is false and Q is true (that is the second row from the bottom of the table). It is true in every other case. 4
5 EXERCISES Construct truth tables for the following formula P & (Q P) (P & Q) R ((P v Q) & ~P) Q C. Using Truth Tables to Sort Formulae into Tautologies, Contingencies, and Inconsistencies (Contradictions): A fourth use of Truth Tables will be particularly important for establishing a further set of tools of proof in the propositional calculus. We can use truth tables to sort formulae into three different groups. E. Exercise: Tautologies are formulae that are always true, no matter what the truth value of their constituent atomic propositions. If today is Thursday then today is Thursday is a simple tautology. But other tautologies are more interesting and will provide us with a set of logical transformation rules. An example is ((P v Q) & ~Q P). A compound formula is a tautology if and only if the compound formula comes out as true in every row of its truth table. Contradictions (or Inconsistencies) are compound formulae that are never true, no matter what the assignment of truth values to the atomic propositions that comprise them. An example of a primitive contradiction is (P & ~P). A compound formula is a contradiction if and only if the compound formula comes out as false in every row of its truth table. Contingent formulae are all the rest. In order to know whether a contingent proposition is true or false you need to know more than its logical form; you need to know the actual truth value of its constituent atomic propositions. An example of a contingent proposition is Tomorrow is Friday and I am going down to the pub. A compound formula is contingent if and only if the compound formula comes out as false in some rows of its truth table and true in others. Consider the following propositions. Without constructing a truth table, try to determine whether each one is a tautology, a contradiction or a contingent proposition. After placing your bets we can split up the list and use truth tables for each one. a) (P Q) & ~(P Q) b) (P v Q) & Q c) (P Q) & (~Q ~P) d) ~P (P Q) 5
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 truthvalue of a given truthfunctional compound proposition depends
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 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 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 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 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: 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 informationG. H. von Wright Deontic Logic
G. H. von Wright Deontic Logic Kian MintzWoo University of Amsterdam January 9, 2009 January 9, 2009 Logic of Norms 2010 1/17 INTRODUCTION In von Wright s 1951 formulation, deontic logic is intended to
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 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 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. 431432 Part C (125) Predicate Logic Consider the argument: All
More informationCan Negation be Defined in Terms of Incompatibility?
Can Negation be Defined in Terms of Incompatibility? Nils Kurbis 1 Abstract Every theory needs primitives. A primitive is a term that is not defined any further, but is used to define others. Thus primitives
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 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 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 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 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 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 informationExposition of Symbolic Logic with KalishMontague derivations
An Exposition of Symbolic Logic with KalishMontague derivations Copyright 200613 by Terence Parsons all rights reserved Aug 2013 Preface The system of logic used here is essentially that of Kalish &
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 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 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 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 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. 110 and do "You Try It" (to use Submit); Read 1929 for lecture. C. Anthony Anderson (caanders@philosophy.ucsb.edu)
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 informationChapter 6. Fate. (F) Fatalism is the belief that whatever happens is unavoidable. (55)
Chapter 6. Fate (F) Fatalism is the belief that whatever happens is unavoidable. (55) The first, and most important thing, to note about Taylor s characterization of fatalism is that it is in modal terms,
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 informationTruthFunctional Propositional Logic
by Sidney Felder Truthfunctional propositional logic is the simplest and expressively weakest member of the class of deductive systems designed to capture the various valid arguments and patterns of reasoning
More informationIntroduction 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
More informationVerificationism. PHIL September 27, 2011
Verificationism PHIL 83104 September 27, 2011 1. The critique of metaphysics... 1 2. Observation statements... 2 3. In principle verifiability... 3 4. Strong verifiability... 3 4.1. Conclusive verifiability
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 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 informationRussell: On Denoting
Russell: On Denoting DENOTING PHRASES Russell includes all kinds of quantified subject phrases ( a man, every man, some man etc.) but his main interest is in definite descriptions: the present King of
More informationAyer 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...............................
More informationCan Negation be Defined in Terms of Incompatibility?
Can Negation be Defined in Terms of Incompatibility? Nils Kurbis 1 Introduction Every theory needs primitives. A primitive is a term that is not defined any further, but is used to define others. Thus
More informationAppeared in: AlMukhatabat. A Trilingual Journal For Logic, Epistemology and Analytical Philosophy, Issue 6: April 2013.
Appeared in: AlMukhatabat. A Trilingual Journal For Logic, Epistemology and Analytical Philosophy, Issue 6: April 2013. Panu Raatikainen Intuitionistic Logic and Its Philosophy Formally, intuitionistic
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 informationIntersubstitutivity Principles and the Generalization Function of Truth. Anil Gupta University of Pittsburgh. Shawn Standefer University of Melbourne
Intersubstitutivity Principles and the Generalization Function of Truth Anil Gupta University of Pittsburgh Shawn Standefer University of Melbourne Abstract We offer a defense of one aspect of Paul Horwich
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 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 informationMethods of Proof for Boolean Logic
Chapter 5 Methods of Proof for Boolean Logic limitations of truth table methods Truth tables give us powerful techniques for investigating the logic of the Boolean operators. But they are by no means the
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 mindbody problem. The discussion here brings to bear many of the results
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 informationElements of Science (cont.); Conditional Statements. Phil 12: Logic and Decision Making Fall 2010 UC San Diego 9/29/2010
Elements of Science (cont.); Conditional Statements Phil 12: Logic and Decision Making Fall 2010 UC San Diego 9/29/2010 1 Why cover statements and arguments Decision making (whether in science or elsewhere)
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 informationConstructive Logic, Truth and Warranted Assertibility
Constructive Logic, Truth and Warranted Assertibility Greg Restall Department of Philosophy Macquarie University Version of May 20, 2000....................................................................
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 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 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 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 informationpart one MACROSTRUCTURE Cambridge University Press X  A Theory of Argument Mark Vorobej Excerpt More information
part one MACROSTRUCTURE 1 Arguments 1.1 Authors and Audiences An argument is a social activity, the goal of which is interpersonal rational persuasion. More precisely, we ll say that an argument occurs
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 informationTautological Necessity and Tautological Validity With Quantifiers
Some sentences containing quantifiers are truth table necessary. Tautological Necessity and Tautological Validity With Quantifiers Mark Criley IWU 25 October 2017 That is, they are forced to be true just
More informationFoundations of Logic, Language, and Mathematics
Chapter 1 Foundations of Logic, Language, and Mathematics l. Overview 2. The Language of Logic and Mathematics 3. Sense, Reference, Compositionality, and Hierarchy 4. Frege s Logic 5. Frege s Philosophy
More informationWhat is the Nature of Logic? Judy Pelham Philosophy, York University, Canada July 16, 2013 PanHellenic Logic Symposium Athens, Greece
What is the Nature of Logic? Judy Pelham Philosophy, York University, Canada July 16, 2013 PanHellenic Logic Symposium Athens, Greece Outline of this Talk 1. What is the nature of logic? Some history
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 information(Refer Slide Time 03:00)
Artificial Intelligence Prof. Anupam Basu Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur Lecture  15 Resolution in FOPL In the last lecture we had discussed about
More informationFuture Contingents, NonContradiction and the Law of Excluded Middle Muddle
Future Contingents, NonContradiction and the Law of Excluded Middle Muddle For whatever reason, we might think that contingent statements about the future have no determinate truth value. Aristotle, in
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 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 informationBased on the translation by E. M. Edghill, with minor emendations by Daniel Kolak.
On Interpretation By Aristotle Based on the translation by E. M. Edghill, with minor emendations by Daniel Kolak. First we must define the terms 'noun' and 'verb', then the terms 'denial' and 'affirmation',
More informationAn alternative understanding of interpretations: Incompatibility Semantics
An alternative understanding of interpretations: Incompatibility Semantics 1. In traditional (truththeoretic) semantics, interpretations serve to specify when statements are true and when they are false.
More informationThe paradox we re discussing today is not a single argument, but a family of arguments. Here s an example of this sort of argument:!
The Sorites Paradox The paradox we re discussing today is not a single argument, but a family of arguments. Here s an example of this sort of argument:! Height Sorites 1) Someone who is 7 feet in height
More informationI. In the ongoing debate on the meaning of logical connectives 1, two families of
What does & mean? Axel Arturo Barceló Aspeitia abarcelo@filosoficas.unam.mx Instituto de Investigaciones Filosóficas, UNAM México Proceedings of the TwentyFirst World Congress of Philosophy, Vol. 5, 2007.
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 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 informationIn more precise language, we have both conditional statements and biconditional statements.
MATD 0385. Day 5. Feb. 3, 2010 Last updated Feb. 3, 2010 Logic. Sections 34, 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 informationRecall. Validity: If the premises are true the conclusion must be true. Soundness. Valid; and. Premises are true
Recall Validity: If the premises are true the conclusion must be true Soundness Valid; and Premises are true Validity In order to determine if an argument is valid, we must evaluate all of the sets of
More informationA CONCISE INTRODUCTION TO LOGIC
A CONCISE INTRODUCTION TO LOGIC Craig DeLancey Professor of Philosophy State University of New York at Oswego (29 July 2015 draft) TABLE OF CONTENTS 0. Introduction Part I. Propositional Logic. 1. Developing
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 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. nplace Conjunctions and Disjunctions 15 3.2. Neither nor, Not both
More informationTheories of propositions
Theories of propositions phil 93515 Jeff Speaks January 16, 2007 1 Commitment to propositions.......................... 1 2 A Fregean theory of reference.......................... 2 3 Three theories of
More informationWilliams on Supervaluationism and Logical Revisionism
Williams on Supervaluationism and Logical Revisionism Nicholas K. Jones Noncitable draft: 26 02 2010. Final version appeared in: The Journal of Philosophy (2011) 108: 11: 633641 Central to discussion
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 InferenceIndicators and the Logical Structure of an Argument 1. The Idea
More informationLogic: Deductive and Inductive by Carveth Read M.A. CHAPTER VI CONDITIONS OF IMMEDIATE INFERENCE
CHAPTER VI CONDITIONS OF IMMEDIATE INFERENCE Section 1. The word Inference is used in two different senses, which are often confused but should be carefully distinguished. In the first sense, it means
More informationMCQ 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 .
More informationAquinas' Third Way Modalized
Philosophy of Religion Aquinas' Third Way Modalized Robert E. Maydole Davidson College bomaydole@davidson.edu ABSTRACT: The Third Way is the most interesting and insightful of Aquinas' five arguments for
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 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 informationPhilosophy 220. Truth Functional Properties Expressed in terms of Consistency
Philosophy 220 Truth Functional Properties Expressed in terms of Consistency The concepts of truthfunctional logic: Truthfunctional: Truth Falsity Indeterminacy Entailment Validity Equivalence Consistency
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 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 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 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 informationTOWARDS A PHILOSOPHICAL UNDERSTANDING OF THE LOGICS OF FORMAL INCONSISTENCY
CDD: 160 http://dx.doi.org/10.1590/01006045.2015.v38n2.wcear TOWARDS A PHILOSOPHICAL UNDERSTANDING OF THE LOGICS OF FORMAL INCONSISTENCY WALTER CARNIELLI 1, ABÍLIO RODRIGUES 2 1 CLE and Department of
More information