Contradictory Information Can Be Better than Nothing The Example of the Two Firemen
|
|
- Prosper Underwood
- 6 years ago
- Views:
Transcription
1 Contradictory Information Can Be Better than Nothing The Example of the Two Firemen J. Michael Dunn School of Informatics and Computing, and Department of Philosophy Indiana University-Bloomington Workshop on the Philosophy of Information: The Value of Information Info-Metrics Institute, American University April 26, 2013
2 This is a kind of dual sequel to my paper Contradictory Information: Too Much of a Good Thing, J. of Philosophical Logic (2010), pp I presented this at previous workshop on philosophy of information. Today s Example of the Two Firemen can be seen as motivating the formal apparatus of the earlier paper. I will argue that contradictory information can sometimes be Better Than Nothing. Rephrasing to match the theme of this workshop: Contradictory information can sometimes have value.
3 Bar-Hillel and Carnap (1953, p. 229)) wrote: "It might perhaps, at fi rst, seem strange that a self-contradictory sentence, hence one which no ideal receiver would accept, is regarded as carrying with it the most inclusive information.... A self-contradictory sentence asserts too much; it is too informative to be true."
4 Floridi (2011) wants a strong semantic theory of information" that avoids what he labels the Bar-Hillel Carnap Paradox (BCP). He says contradictions contain zero information, giving among other reasons that "inconsistent information is obviously of no use to a decision maker." My story of the Two Firemen is intended as a counterexample to the claim of uselessness of inconsistent Information.
5 The Two Firemen Suppose you are awakened in your hotel room by a fire alarm. You open the door. You see three possible ways out: left, right, straight Scenario 1. You see two firemen. One says the only safe route is to your left. The other says to your right. Contradictory information!
6 Scenario 1
7 Scenario 2. You find no one to give directions. Incomplete information!
8 Scenario 2
9 Question: Which scenario would you prefer? Obvious answer: A rational agent would prefer to be in Scenario 1. Contradictory information in this case is better than no information at all.
10 A More Homey Example The essence of the example of the two firemen can be duplicated over and over again. An instance very familiar to me goes like this: My wife Sally and I are leaving the house. I reach in my pocket and cannot find my car keys. I tell Sally I think they are in a jacket pocket in the closet. She tells me they are on the piano. Again, this is all useful information, and I will use it in my search. But it is contradictory.
11 Let us focus though on the firemen, and examine several ways out (pun intended). First a few abbreviations: L: Left is a way out. R: Right is a way out. S: Straight is a way out. O: There is just one way out.
12 First Way Out: This is not an explicit contradiction, like L & ~L. It is only a partial contradiction, (L & O) and (R & O) are only contraries. First Response: But contraries are only a stronger form of contradiction. (L & O) & (R & O) entails L & ~L.
13 Second Way Out: The firemen made separate statements contradicting each other. There is no contradiction until I conjoin them. Reject adjunction rule (Jaśkowski Discussive Logic). Second Response: But it is important to consider the two statements together, and if that is not conjunction then I don t know what conjunction means. If I had reason to believe one more than the other, I might just disregard that other, but in the situation I described I have equal reason to believe each. Also, it is only by my considering the two statements that I see that the two firemen agree on O.
14 Third Way Out: We are not dealing with a conjunction of L & O and R & O, but rather a disjunction. One fireman says L & O. The other says R & O. But suppose the first fireman then says: We can t both be right, but I am certain one of us is right. This makes perfect sense, retreating to what in correspondence David Makinson has described as: using their disjunction as a fall-back reading or integration of the conflicting inputs.
15 So even if neither of the firemen speaks up, I could reason more or less the same way. Both seem experts who have up-to-date info about the fire, and this is all the information I have readily (and safely) available. So probably at least one of them is right, i.e., (L & O) v (R & O). L & O entails ~ S, R & O entails ~ S, therefore ~ S.
16 Makinson is of course famous for the AGM (Alchourron, Gardenfors, Makinson) notion of belief revision. The key idea is that if one believes P, and then learns that ~ P, that one retreats to a consistent set of beliefs that includes ~ P (and hence excludes P). Makinson s response to The Two Firemen is in the same spirit.
17 Third Response: Suppose though that there is what Carl Hewitt calls a pervasively inconsistent background. Then unless one is going to fix everything at once, there is no consistent set of beliefs to drop back to.
18 To be a bit precise about this let s suppose that you are a dialethist (like Graham Priest who supposes there are true contradictions) and you were sitting in your room reflecting on the truth and beauty of the Russell Paradox (how the set of all sets not members of themselves is both a member of itself, and not a member of itself). Or suppose that you are a mere computer scientist reflecting on how the World Wide Web has made you a cyborg by extending your system of belief, with search replacing recall.
19 I really do not disagree with Makinson. I just think we have to somehow extend belief revision to accommodate pervasively inconsistent environments. Relevance logic could be a key component. Note that all the entailments so far mentioned in this talk are relevant implications within Anderson-Belnap s system of first-degree relevant entailments. Real trouble would raise its head if we allowed the irrelevant implication sometimes called Explosion : A & ~ A entails B.
20 Let s leave this topic for another day and get back to our two firemen. Scenario 1. Same as Scenario 1 (two firemen) but you can clearly see that you cannot safely go straight ahead. There are only two options, left and right. It now might seem that there is no reason to have a preference between Scenarios 1 and 2.
21
22 But wait, they still agree that there is a way out. So I can risk running left or right as opposed to staying in my room and preparing for my death.
23 Now suppose that a third fireman shows up and points right saying that this is the only safe way to go. Now I have some reason to run right.
24
25 WWW: Better Than Nothing? Suppose you want to find an answer to a certain yes/no question on the WWW. Which of the following scenarios do you prefer? A. You google and get no (relevant) response. B. You google and get multiple conflicting responses.
26 Perhaps such investigations will sort things out so that you have, in your mind at least, a definite answer as to yes or no. But in a worse case, where you do not have the mind, or time, to do that, at least you might assign a value within the Opinion Tetrahedron, if only based on your gut reaction.
27 I, and I expect you, would prefer to be in scenario B. In this circumstance you can at least try to sort the situation out, e.g.:
28 1) You can count the relative number of opinions on either side. 2) You can somehow assess the credentials (authority/motives) of the sources on either side. 3) You can look at the arguments, if any, provided by the sources. 4) You can try to find cited facts, try to reproduce cited experiments. Etc.
29 It is worth emphasizing that the utility of contradictions is due not just to their content but also to their pragmatic context. Some of the tools described on the previous slide might be taken as logical fallacies. E.g., counting the number of sources can be interpreted as an argument from repetition -- Fifty Million Frenchmen Can t Be Wrong. Anatole France responded: If fifty million people say a foolish thing, it is still a foolish thing. But the aim here is not to prove P by the number of sources that say it, but rather to take a vote to determine the subjective likelihood that P. An improvement would be to check for duplications (one source merely repeating another source), and to have trust weightings based on reliability (expertise, honesty, lack of bias, etc.).
30 Finally a quick overview of the formal background from my previous talk:
31 Subjective Logic A. Jøsang, Artificial Reasoning with Subjective Logic, Proceedings of the Second Australian Workshop on Commonsense Reasoning, Perth A. Jøsang, An Algebra for Assessing Trust in Certification Chains, Proceedings of the NDSS 99 Network and Distributed Systems Security Symposium, The Internet Society, San Diego From Wikipedia, the free encyclopedia Subjective logic is a type of probabilistic logic that explicitly takes uncertainty and belief ownership into account. In general, subjective logic is suitable for modeling and analysing situations involving uncertainty and incomplete knowledge[1][2]. For example, it can be used for modeling trust networks and for analysing Bayesian networks. Arguments in subjective logic are subjective opinions about propositions. A binomial opinion applies to a single proposition, and can be represented as a Beta distribution. A multinomial opinion applies to a collection of propositions, and can be represented as a Dirichlet distribution. Through the correspondence between opinions and Beta/Dirichlet distributions, subjective logic provides an algebra for these functions. Opinions are also related to the belief functions of Dempster-Shafer belief theory. A fundamental aspect of the human condition is that nobody can ever determine with absolute certainty whether a proposition about the world is true or false. In addition, whenever the truth of a proposition is expressed, it is always done by an individual, and it can never be considered to represent a general and objective belief.
32 w = (0.7, 0.1, 0.2) Ternary coordinates
33 DM4 Belnap-Dunn 4-valued Logic T(rue) {t} {t, f} { } B(oth) N(either) Logical (truth) Order {f} F(alse) Approximation (knowledge, information) Order
34 Two Kinds of Uncertainty: Too little information, too much information Uncertain = N Disbelief = F Belief = T Uncertain = B
35 Add a line and visualize it as an Opinion Tetrahedron! N F T B
36 Establish coordinates by dropping altitudes from each vertex to the center of the opposite side and by convention assign each the length 1.0 (measuring from 0 at the base to 1 at the vertex). They intersect at A point (b, d, u, c) in the Opinion Tetrahedron is to be understood as follows: b = degree of belief, d = degree of disbelief, u = degree of uncertainty (ignorance), c = degree of contradiction. 0 b, d, u, c 1.
37 Thank you.
38 Some references A. R. Anderson, N.D. Belnap, and J. M. Dunn, Entailment: The Logic of Relevance and Necessity, vol. 2,Princeton University Press, 775 pp. Belnap, N.D. (1977): How a computer should think, in: G. Ryle (ed.) Contemporary Aspects of Philosophy. Oriel Press, Stockfield, Belnap, N.D. (1977): A useful four-valued logic, in: J.M. Dunn, G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. Reidel, Dordrecht, J. M. Dunn (1967), "The Effective Equivalence of Certain Propositions About de Morgan Lattices," Journal of Symbolic Logic, 1967, pp J. M. Dunn (1976): "Intuitive Semantics for First-Degree Entailments and Coupled Trees," Philosophical Studies, 29, pp A. Jøsang (1997), Artificial Reasoning with Subjective Logic, Proceedings of the Second Australian Workshop on Commonsense Reasoning, Perth. A. Jøsang (1999), An Algebra for Assessing Trust in Certification Chains, Proceedings of the NDSS 99 Network and Distributed Systems Security Symposium, The Internet Society, San Diego.
ON PROMOTING THE DEAD CERTAIN: A REPLY TO BEHRENDS, DIPAOLO AND SHARADIN
DISCUSSION NOTE ON PROMOTING THE DEAD CERTAIN: A REPLY TO BEHRENDS, DIPAOLO AND SHARADIN BY STEFAN FISCHER JOURNAL OF ETHICS & SOCIAL PHILOSOPHY DISCUSSION NOTE APRIL 2017 URL: WWW.JESP.ORG COPYRIGHT STEFAN
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 informationTWO VERSIONS OF HUME S LAW
DISCUSSION NOTE BY CAMPBELL BROWN JOURNAL OF ETHICS & SOCIAL PHILOSOPHY DISCUSSION NOTE MAY 2015 URL: WWW.JESP.ORG COPYRIGHT CAMPBELL BROWN 2015 Two Versions of Hume s Law MORAL CONCLUSIONS CANNOT VALIDLY
More informationTruth At a World for Modal Propositions
Truth At a World for Modal Propositions 1 Introduction Existentialism is a thesis that concerns the ontological status of individual essences and singular propositions. Let us define an individual essence
More informationReasoning and Decision-Making under Uncertainty
Reasoning and Decision-Making under Uncertainty 3. Termin: Uncertainty, Degrees of Belief and Probabilities Prof. Dr.-Ing. Stefan Kopp Center of Excellence Cognitive Interaction Technology AG A Intelligent
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 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 informationIntroduction Questions to Ask in Judging Whether A Really Causes B
1 Introduction We live in an age when the boundaries between science and science fiction are becoming increasingly blurred. It sometimes seems that nothing is too strange to be true. How can we decide
More information2nd International Workshop on Argument for Agreement and Assurance (AAA 2015), Kanagawa Japan, November 2015
2nd International Workshop on Argument for Agreement and Assurance (AAA 2015), Kanagawa Japan, November 2015 On the Interpretation Of Assurance Case Arguments John Rushby Computer Science Laboratory SRI
More informationA Model of Decidable Introspective Reasoning with Quantifying-In
A Model of Decidable Introspective Reasoning with Quantifying-In Gerhard Lakemeyer* Institut fur Informatik III Universitat Bonn Romerstr. 164 W-5300 Bonn 1, Germany e-mail: gerhard@uran.informatik.uni-bonn,de
More informationTHE ROLE OF COHERENCE OF EVIDENCE IN THE NON- DYNAMIC MODEL OF CONFIRMATION TOMOJI SHOGENJI
Page 1 To appear in Erkenntnis THE ROLE OF COHERENCE OF EVIDENCE IN THE NON- DYNAMIC MODEL OF CONFIRMATION TOMOJI SHOGENJI ABSTRACT This paper examines the role of coherence of evidence in what I call
More informationON CAUSAL AND CONSTRUCTIVE MODELLING OF BELIEF CHANGE
ON CAUSAL AND CONSTRUCTIVE MODELLING OF BELIEF CHANGE A. V. RAVISHANKAR SARMA Our life in various phases can be construed as involving continuous belief revision activity with a bundle of accepted beliefs,
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 informationInstrumental reasoning* John Broome
Instrumental reasoning* John Broome For: Rationality, Rules and Structure, edited by Julian Nida-Rümelin and Wolfgang Spohn, Kluwer. * This paper was written while I was a visiting fellow at the Swedish
More informationWhat is a counterexample?
Lorentz Center 4 March 2013 What is a counterexample? Jan-Willem Romeijn, University of Groningen Joint work with Eric Pacuit, University of Maryland Paul Pedersen, Max Plank Institute Berlin Co-authors
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 informationIntroduction. I. Proof of the Minor Premise ( All reality is completely intelligible )
Philosophical Proof of God: Derived from Principles in Bernard Lonergan s Insight May 2014 Robert J. Spitzer, S.J., Ph.D. Magis Center of Reason and Faith Lonergan s proof may be stated as follows: Introduction
More informationLing 98a: The Meaning of Negation (Week 1)
Yimei Xiang yxiang@fas.harvard.edu 17 September 2013 1 What is negation? Negation in two-valued propositional logic Based on your understanding, select out the metaphors that best describe the meaning
More informationprohibition, moral commitment and other normative matters. Although often described as a branch
Logic, deontic. The study of principles of reasoning pertaining to obligation, permission, prohibition, moral commitment and other normative matters. Although often described as a branch of logic, deontic
More informationAutomated Reasoning Project. Research School of Information Sciences and Engineering. and Centre for Information Science Research
Technical Report TR-ARP-14-95 Automated Reasoning Project Research School of Information Sciences and Engineering and Centre for Information Science Research Australian National University August 10, 1995
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 informationReply to Robert Koons
632 Notre Dame Journal of Formal Logic Volume 35, Number 4, Fall 1994 Reply to Robert Koons ANIL GUPTA and NUEL BELNAP We are grateful to Professor Robert Koons for his excellent, and generous, review
More informationIn this paper I will critically discuss a theory known as conventionalism
Aporia vol. 22 no. 2 2012 Combating Metric Conventionalism Matthew Macdonald In this paper I will critically discuss a theory known as conventionalism about the metric of time. Simply put, conventionalists
More informationIs the Existence of the Best Possible World Logically Impossible?
Is the Existence of the Best Possible World Logically Impossible? Anders Kraal ABSTRACT: Since the 1960s an increasing number of philosophers have endorsed the thesis that there can be no such thing as
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 informationCircumscribing Inconsistency
Circumscribing Inconsistency Philippe Besnard IRISA Campus de Beaulieu F-35042 Rennes Cedex Torsten H. Schaub* Institut fur Informatik Universitat Potsdam, Postfach 60 15 53 D-14415 Potsdam Abstract We
More informationFormalizing a Deductively Open Belief Space
Formalizing a Deductively Open Belief Space CSE Technical Report 2000-02 Frances L. Johnson and Stuart C. Shapiro Department of Computer Science and Engineering, Center for Multisource Information Fusion,
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 informationEntailment, with nods to Lewy and Smiley
Entailment, with nods to Lewy and Smiley Peter Smith November 20, 2009 Last week, we talked a bit about the Anderson-Belnap logic of entailment, as discussed in Priest s Introduction to Non-Classical Logic.
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 information2 Lecture Summary Belief change concerns itself with modelling the way in which entities (or agents) maintain beliefs about their environment and how
Introduction to Belief Change Maurice Pagnucco Department of Computing Science Division of Information and Communication Sciences Macquarie University NSW 2109 E-mail: morri@ics.mq.edu.au WWW: http://www.comp.mq.edu.au/οmorri/
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 informationRamsey s belief > action > truth theory.
Ramsey s belief > action > truth theory. Monika Gruber University of Vienna 11.06.2016 Monika Gruber (University of Vienna) Ramsey s belief > action > truth theory. 11.06.2016 1 / 30 1 Truth and Probability
More informationPhilosophical Logic. LECTURE TWO MICHAELMAS 2017 Dr Maarten Steenhagen
Philosophical Logic LECTURE TWO MICHAELMAS 2017 Dr Maarten Steenhagen ms2416@cam.ac.uk Last Week Lecture 1: Necessity, Analyticity, and the A Priori Lecture 2: Reference, Description, and Rigid Designation
More informationCriticizing Arguments
Kareem Khalifa Criticizing Arguments 1 Criticizing Arguments Kareem Khalifa Department of Philosophy Middlebury College Written August, 2012 Table of Contents Introduction... 1 Step 1: Initial Evaluation
More informationThe Problem with Complete States: Freedom, Chance and the Luck Argument
The Problem with Complete States: Freedom, Chance and the Luck Argument Richard Johns Department of Philosophy University of British Columbia August 2006 Revised March 2009 The Luck Argument seems to show
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 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 informationLogical Omniscience in the Many Agent Case
Logical Omniscience in the Many Agent Case Rohit Parikh City University of New York July 25, 2007 Abstract: The problem of logical omniscience arises at two levels. One is the individual level, where an
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 informationPrompt: Explain van Inwagen s consequence argument. Describe what you think is the best response
Prompt: Explain van Inwagen s consequence argument. Describe what you think is the best response to this argument. Does this response succeed in saving compatibilism from the consequence argument? Why
More informationAkrasia and Uncertainty
Akrasia and Uncertainty RALPH WEDGWOOD School of Philosophy, University of Southern California, Los Angeles, CA 90089-0451, USA wedgwood@usc.edu ABSTRACT: According to John Broome, akrasia consists in
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 informationHow to Mistake a Trivial Fact About Probability For a. Substantive Fact About Justified Belief
How to Mistake a Trivial Fact About Probability For a Substantive Fact About Justified Belief Jonathan Sutton It is sometimes thought that the lottery paradox and the paradox of the preface demand a uniform
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 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 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 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 informationPostulates for conditional belief revision
Postulates for conditional belief revision Gabriele Kern-Isberner FernUniversitat Hagen Dept. of Computer Science, LG Prakt. Informatik VIII P.O. Box 940, D-58084 Hagen, Germany e-mail: gabriele.kern-isberner@fernuni-hagen.de
More information1 Chapter 6 (Part 2): Assessing Truth Claims
1 Chapter 6 (Part 2): Assessing Truth Claims In the previous tutorial we saw that the standard of acceptability of a statement (or premise) depends on the context. In certain contexts we may only require
More informationBayesian Probability
Bayesian Probability Patrick Maher September 4, 2008 ABSTRACT. Bayesian decision theory is here construed as explicating a particular concept of rational choice and Bayesian probability is taken to be
More informationFuture Contingents, Non-Contradiction and the Law of Excluded Middle Muddle
Future Contingents, Non-Contradiction 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 informationNICHOLAS J.J. SMITH. Let s begin with the storage hypothesis, which is introduced as follows: 1
DOUBTS ABOUT UNCERTAINTY WITHOUT ALL THE DOUBT NICHOLAS J.J. SMITH Norby s paper is divided into three main sections in which he introduces the storage hypothesis, gives reasons for rejecting it and then
More informationDetachment, Probability, and Maximum Likelihood
Detachment, Probability, and Maximum Likelihood GILBERT HARMAN PRINCETON UNIVERSITY When can we detach probability qualifications from our inductive conclusions? The following rule may seem plausible:
More informationPhilosophy 148 Announcements & Such. Inverse Probability and Bayes s Theorem II. Inverse Probability and Bayes s Theorem III
Branden Fitelson Philosophy 148 Lecture 1 Branden Fitelson Philosophy 148 Lecture 2 Philosophy 148 Announcements & Such Administrative Stuff I ll be using a straight grading scale for this course. Here
More informationLogic is the study of the quality of arguments. An argument consists of a set of
Logic: Inductive Logic is the study of the quality of arguments. An argument consists of a set of premises and a conclusion. The quality of an argument depends on at least two factors: the truth of the
More informationInductive inference is. Rules of Detachment? A Little Survey of Induction
HPS 1702 Junior/Senior Seminar for HPS Majors HPS 1703 Writing Workshop for HPS Majors A Little Survey of Inductive inference is (Overwhelming Majority view) Ampliative inference Evidence lends support
More informationEach copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission.
The Physical World Author(s): Barry Stroud Source: Proceedings of the Aristotelian Society, New Series, Vol. 87 (1986-1987), pp. 263-277 Published by: Blackwell Publishing on behalf of The Aristotelian
More informationPuzzles of attitude ascriptions
Puzzles of attitude ascriptions Jeff Speaks phil 43916 November 3, 2014 1 The puzzle of necessary consequence........................ 1 2 Structured intensions................................. 2 3 Frege
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 informationthen An Introduction to Logic
If...then An Introduction to Logic Kent Slinker February 18, 2014 Part I. Informal Logic 2 Contents I. Informal Logic 2 1. Introduction to Part One 4 2. Relations between statements 6 2.1. Entailment...................................
More informationA flaw in Kripke s modal argument? Kripke states his modal argument against the description theory of names at a number
A flaw in Kripke s modal argument? Kripke states his modal argument against the description theory of names at a number of places (1980: 53, 57, 61, and 74). A full statement in the original text of Naming
More informationEvidential Support and Instrumental Rationality
Evidential Support and Instrumental Rationality Peter Brössel, Anna-Maria A. Eder, and Franz Huber Formal Epistemology Research Group Zukunftskolleg and Department of Philosophy University of Konstanz
More information10 CERTAINTY G.E. MOORE: SELECTED WRITINGS
10 170 I am at present, as you can all see, in a room and not in the open air; I am standing up, and not either sitting or lying down; I have clothes on, and am not absolutely naked; I am speaking in a
More informationDegrees of Belief II
Degrees of Belief II HT2017 / Dr Teruji Thomas Website: users.ox.ac.uk/ mert2060/2017/degrees-of-belief 1 Conditionalisation Where we have got to: One reason to focus on credences instead of beliefs: response
More informationIntro Viewed from a certain angle, philosophy is about what, if anything, we ought to believe.
Overview Philosophy & logic 1.2 What is philosophy? 1.3 nature of philosophy Why philosophy Rules of engagement Punctuality and regularity is of the essence You should be active in class It is good to
More informationUnderstanding Truth Scott Soames Précis Philosophy and Phenomenological Research Volume LXV, No. 2, 2002
1 Symposium on Understanding Truth By Scott Soames Précis Philosophy and Phenomenological Research Volume LXV, No. 2, 2002 2 Precis of Understanding Truth Scott Soames Understanding Truth aims to illuminate
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 informationGödel's incompleteness theorems
Savaş Ali Tokmen Gödel's incompleteness theorems Page 1 / 5 In the twentieth century, mostly because of the different classes of infinity problem introduced by George Cantor (1845-1918), a crisis about
More informationDavid Hume, A Treatise of Human Nature ( ), Book I, Part III.
David Hume, A Treatise of Human Nature (1739 1740), Book I, Part III. N.B. This text is my selection from Jonathan Bennett s paraphrase of Hume s text. The full Bennett text is available at http://www.earlymoderntexts.com/.
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 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 informationWhat is the Frege/Russell Analysis of Quantification? Scott Soames
What is the Frege/Russell Analysis of Quantification? Scott Soames The Frege-Russell analysis of quantification was a fundamental advance in semantics and philosophical logic. Abstracting away from details
More informationCRITICAL THINKING (CT) MODEL PART 1 GENERAL CONCEPTS
Fall 2001 ENGLISH 20 Professor Tanaka CRITICAL THINKING (CT) MODEL PART 1 GENERAL CONCEPTS In this first handout, I would like to simply give you the basic outlines of our critical thinking model
More informationFinal Paper. May 13, 2015
24.221 Final Paper May 13, 2015 Determinism states the following: given the state of the universe at time t 0, denoted S 0, and the conjunction of the laws of nature, L, the state of the universe S at
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 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 informationSemantic Foundations for Deductive Methods
Semantic Foundations for Deductive Methods delineating the scope of deductive reason Roger Bishop Jones Abstract. The scope of deductive reason is considered. First a connection is discussed between the
More informationWittgenstein on the Fallacy of the Argument from Pretence. Abstract
Wittgenstein on the Fallacy of the Argument from Pretence Edoardo Zamuner Abstract This paper is concerned with the answer Wittgenstein gives to a specific version of the sceptical problem of other minds.
More informationIn general, the simplest of argument maps will take the form of something like this:
#6 Model Argument Maps 1 Argument Mapping 6: Model Argument Maps Most of the following discussion provides model or prototype argument maps that can be applied to any argument that takes a similar form.
More informationAm I free? Freedom vs. Fate
Am I free? Freedom vs. Fate We ve been discussing the free will defense as a response to the argument from evil. This response assumes something about us: that we have free will. But what does this mean?
More informationMcCLOSKEY ON RATIONAL ENDS: The Dilemma of Intuitionism
48 McCLOSKEY ON RATIONAL ENDS: The Dilemma of Intuitionism T om R egan In his book, Meta-Ethics and Normative Ethics,* Professor H. J. McCloskey sets forth an argument which he thinks shows that we know,
More informationEach copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission.
Tractatus 6.3751 Author(s): Edwin B. Allaire Source: Analysis, Vol. 19, No. 5 (Apr., 1959), pp. 100-105 Published by: Oxford University Press on behalf of The Analysis Committee Stable URL: http://www.jstor.org/stable/3326898
More informationCausation and Free Will
Causation and Free Will T L Hurst Revised: 17th August 2011 Abstract This paper looks at the main philosophic positions on free will. It suggests that the arguments for causal determinism being compatible
More informationA Solution to the Gettier Problem Keota Fields. the three traditional conditions for knowledge, have been discussed extensively in the
A Solution to the Gettier Problem Keota Fields Problem cases by Edmund Gettier 1 and others 2, intended to undermine the sufficiency of the three traditional conditions for knowledge, have been discussed
More informationMULTI-PEER DISAGREEMENT AND THE PREFACE PARADOX. Kenneth Boyce and Allan Hazlett
MULTI-PEER DISAGREEMENT AND THE PREFACE PARADOX Kenneth Boyce and Allan Hazlett Abstract The problem of multi-peer disagreement concerns the reasonable response to a situation in which you believe P1 Pn
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 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 informationIntroduction: Belief vs Degrees of Belief
Introduction: Belief vs Degrees of Belief Hannes Leitgeb LMU Munich October 2014 My three lectures will be devoted to answering this question: How does rational (all-or-nothing) belief relate to degrees
More informationNecessity and Truth Makers
JAN WOLEŃSKI Instytut Filozofii Uniwersytetu Jagiellońskiego ul. Gołębia 24 31-007 Kraków Poland Email: jan.wolenski@uj.edu.pl Web: http://www.filozofia.uj.edu.pl/jan-wolenski Keywords: Barry Smith, logic,
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 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 informationFaults and Mathematical Disagreement
45 Faults and Mathematical Disagreement María Ponte ILCLI. University of the Basque Country mariaponteazca@gmail.com Abstract: My aim in this paper is to analyse the notion of mathematical disagreements
More informationPhilosophy 240: Symbolic Logic
Philosophy 240: Symbolic Logic Russell Marcus Hamilton College Fall 2011 Class 27: October 28 Truth and Liars Marcus, Symbolic Logic, Fall 2011 Slide 1 Philosophers and Truth P Sex! P Lots of technical
More informationThe Development of Laws of Formal Logic of Aristotle
This paper is dedicated to my unforgettable friend Boris Isaevich Lamdon. The Development of Laws of Formal Logic of Aristotle The essence of formal logic The aim of every science is to discover the laws
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 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 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 informationResemblance Nominalism and counterparts
ANAL63-3 4/15/2003 2:40 PM Page 221 Resemblance Nominalism and counterparts Alexander Bird 1. Introduction In his (2002) Gonzalo Rodriguez-Pereyra provides a powerful articulation of the claim that Resemblance
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 information