PHLA The Problem of Induction


 Mervyn Manning
 1 years ago
 Views:
Transcription
1
2 Knowledge versus mere justified belief Knowledge implies truth Justified belief does not imply truth Knowledge implies the impossibility of error Justified belief does not imply impossibility of error Justified belief comes in grades of more or less You are more justified in believing you will lose the 649 lottery than in believing this coin will come up heads We often express this gradation in terms of probability The concept of evidence can be expressed in terms of probability too P is evidence in favour of Q = P raises the probability of Q Learning you rolled an even number is (some) evidence in favour of you having rolled a six
3 Ordinary skepticism attacks knowledge Claims that we have no (or almost no) knowledge Does not deny that some beliefs are more reasonable than others... Does not deny that some beliefs are evidence for others (e.g. raises their probability) Justified belief skepticism attacks rationality Claims that we have no reason to think that any belief is either more or less probable than any other Denies we have any good reason to think that any belief is evidence in favour of (or against) any other possible belief (A priori beliefs/probabilities may be an exception)
4 Review: what is induction A method of amplifying or adding knowledge (or at least adding to our stock of beliefs) Unlike in a valid deductive argument, the conclusion of an inductive argument is not guaranteed to be true, even if the premises are true example: (1) Most dogs are pets (2) Fido is a dog (3) therefore, Fido is a pet Recall what makes a good inductive argument good sample size good sample distribution (sample must be representative of total) These requirements assume there are better or worse evidential relations
5 Two (closely related) forms of induction (1) Generalization (GEN) example: All observed mammals have hair; therefore all mammals have hair. (2) Prediction (PRED) example: All observed reptiles are cold blooded; therefore the next reptile to be observed will be cold blooded. Obviously (GEN) and (PRED) are not deductively valid argument forms. But it seems intuitively obvious that the premises give us a good reason to believe the conclusion Hume argues that this intuition is unsupportable and wrong
6 Hume s version Hume believed that all inductive arguments involved one crucial assumption: the Principle of the Uniformity of Nature (PUN). PUN = nature will continue to behave in the future as it has in the past / nature will generally be similar to the way it is around here David Hume ( )
7 How does PUN fit into inductive arguments? Instead of All thus far observed mammals have hair, so the next mammal we meet will have hair We have All thus far observed mammals have hair and PUN, so the next mammal we meet will have hair Does PUN turn an inductive argument into a deductive argument? Perhaps it is meant to. But what kind of proposition is PUN? A priori (can be deductively proven)? A posteriori (can only be inductively proven)?
8 Is PUN a priori? Can we give a deductive proof of PUN? Is it possible that nature should not be uniform? It seems possible Therefore, PUN is not a priori Therefore, PUN is a posteriori So it must be proven either by observation or induction We cannot observe PUN (because it is about the future) So we must give an inductive argument for PUN Whatever this argument might look like it will be an inductive argument. Therefore, the argument will contain an assumption The assumption according to Hume will be PUN This is circular reasoning and cannot show PUN
9 Example argument: In the past, PUN has always been true Therefore (inductively) PUN is true Hume notes that this argument depends on the assumption that nature will continue to obey PUN So the argument ought to be: In the past, PUN has always been true PUN Therefore, PUN is true This argument fails because it blatantly assumes what it wants to prove!
10 Hume s attitude towards induction Hume thought we should reason inductively even though we have no rational reason to do so He thought we (and many other animals) are naturally structured to believe in and use induction Example: Pavlov s dogs Hume sometimes called this habit He also noticed instincts which are built in by nature and carry information about how organisms expect the world to work Hume wondered how instincts arose and came somewhat close to a concept of evolution But rationality cannot support the beliefs expressed in instinct or by the habit of inductive inference
11 But is PUN needed for inductive arguments or the attack on induction? What, exactly, is the content of PUN? Is nature always uniform? Do the seasons of the year show uniformity or diversity? Is the death of animals a feature of natural uniformity or a sudden disuniformity in an animal s life It seems impossible to state PUN in any nontrivial way But PUN is not needed to create the problem of induction
12 Induction and reliability We want our inductive knowledge to be secure Let s say that a reliable method of inference is one that usually leads to the truth usually can be thought of as a scale, from the not very reliable to the highly reliable examples: prediction of solar eclipses (highly reliable) to weather prediction (not highly rel.) This scale can be expressed in terms of probability The probability of an eclipse given what we know about Sun, Earth and Moon is virtually 1 The probability of rain next week given our current knowledge is slightly more than ½ Sober s version of the problem of induction How do we know that induction in general is a reliable way to get knowledge?
13 Sober s new version of the problem of induction How do we know that induction in general is a reliable way to get knowledge? Now we replay Hume s point Either we can deductively prove that induction is a reliable way to get knowledge, or We have to inductively prove it is reliable There is no way to prove deductively that induction is reliable (because we can consistently imagine induction failing) But to prove that induction is reliable inductively is to argue in a circle PUN plays no part in this argument
14 Sober s version of the problem of induction Think about what this means We have zero reason to think that induction is reliable This implies that we have no reason to believe what is inductively reasonable versus the opposite Example: we have zero reason to believe that the Sun will rise tomorrow it is exactly as reasonable to believe it will not rise as that it will?! How can that be right? Can we save induction?
15 Strawson s attempt to save induction Maybe it is an analytic truth that induction is a rational way to amplify knowledge (Recall what an analytic truth is) Strawson seems to be claiming that the idea that induction is a good way to reason is part of the concept of rationality Suppose that is true Would this prove that induction is reliable? It would seem not Sir Peter Strawson ( )
16 Black s attempt to save induction Recall the argument in favour of induction: Induction has been successful in the past, so it will be successful in the future Is the argument in favour of induction really circular? Note the difference between a premise of an argument and a rule of inference Black argues that an argument is circular just in case the conclusion appears (maybe only implicitly) among the premises On that understanding, the inductive argument in favour of induction is not circular it just uses the inductive rule of inference Max Black ( )
17 Black s attempt to save induction Is Black s notion of circularity right? Or is there something wrong with an argument that defends a form of argument which you can accept only if you already accept that form of argument? We could also ask Black: even if we could give this inductive proof of induction, would that show that induction is reliable? No, because counterinduction (CI) is equally supported by a counterinductive argument CI = if X has happened in the past, expect notx example: gambler s fallacy The CI argument in favour of CI CI has failed in the past, so expect it to succeed in the future This is a good CI argument!
18 Sober s Trip Beyond Foundationalism Note how Sober divides knowledge claims into 3 levels Indubitable beliefs (a priori / introspectible) Present and past observations Predictions and generalizations Descartes had problems getting from 1 to 2 Hume adds problems getting from 2 to 3 Sober thinks there is no way to Move deductively from a level to a higher level Even use lower level stuff as evidence as higher level That is, IF one is restricted to the lower level This is because something is evidence only relative to additional background beliefs Example: phantom limb pain...
19 The relativity of evidence Suppose we have this evidence: we have examined 10,000 emeralds and they are all green Is this evidence for: all emeralds are green Not if we also believe X: There are many emeralds and they are 99% green OR all emeralds are green but there are very few emeralds in the world Notice that X is not a level 2 statement Sober s thesis: no strictly level n statements justify any level n+1 statements Why? Because of the relativity of evidence What if we had no level n+1 beliefs? Then we could say nothing about level n+1 based only on level n evidence (except for trivial or a priori truths) Is that true?
20 Antifoundationalism about justification Is rational justification strictly about interlevel justification? If so, Sober thinks it s impossible to achieve Or is there a sense of rational justification that takes into account our current epistemic position? That is, could we say something like Given our current epistemic situation (what we believe now) evidence E would justify belief P This assumes an idea of shared epistemic situation Neurath s Boat
General Philosophy. Dr Peter Millican, Hertford College. Lecture 3: Induction
General Philosophy Dr Peter Millican, Hertford College Lecture 3: Induction Hume s s Fork 2 Enquiry IV starts with a vital distinction between types of proposition: Relations of ideas can be known a priori
More informationOne natural response would be to cite evidence of past mornings, and give something like the following argument:
Hume on induction Suppose you were asked to give your reasons for believing that the sun will come up tomorrow, in the form of an argument for the claim that the sun will come up tomorrow. One natural
More informationDescartes Meditations Module 3 AQA. Meditation I Things which can be called into Doubt
Descartes Meditations Module 3 AQA Meditation I Things which can be called into Doubt Descartes rejects all his beliefs about the external world because they are doubtful and he wants to find a foundation
More informationCHAPTER 3. Methods of Proofs. 1. Logical Arguments and Formal Proofs
CHAPTER 3 Methods of Proofs 1. Logical Arguments and Formal Proofs 1.1. Basic Terminology. An axiom is a statement that is given to be true. A rule of inference is a logical rule that is used to deduce
More informationPlato gives another argument for this claiming, relating to the nature of knowledge, which we will return to in the next section.
Michael Lacewing Plato s theor y of Forms FROM SENSE EXPERIENCE TO THE FORMS In Book V (476f.) of The Republic, Plato argues that all objects we experience through our senses are particular things. We
More informationQuine on truth by convention
Quine on truth by convention March 8, 2005 1 Linguistic explanations of necessity and the a priori.............. 1 2 Relative and absolute truth by definition.................... 2 3 Is logic true by convention?...........................
More informationA Few Basics of Probability
A Few Basics of Probability Philosophy 57 Spring, 2004 1 Introduction This handout distinguishes between inductive and deductive logic, and then introduces probability, a concept essential to the study
More informationCosmological Arguments for the Existence of God S. Clarke
Cosmological Arguments for the Existence of God S. Clarke [Modified Fall 2009] 1. Large class of arguments. Sometimes they get very complex, as in Clarke s argument, but the basic idea is simple. Lets
More informationRead this syllabus very carefully. If there are any reasons why you cannot comply with what I am requiring, then talk with me about this at once.
LOGIC AND CRITICAL THINKING PHIL 2020 Maymester Term, 2010 Daily, 9:3012:15 Peabody Hall, room 105 Text: LOGIC AND RATIONAL THOUGHT by Frank R. Harrison, III Professor: Frank R. Harrison, III Office:
More informationThis is because the quality of extension is part of the essence of material objects.
UNIT 1: RATIONALISM HANDOUT 5: DESCARTES MEDITATIONS, MEDITATION FIVE 1: CONCEPTS AND ESSENCES In the Second Meditation Descartes found that what we know most clearly and distinctly about material objects
More information3. Mathematical Induction
3. MATHEMATICAL INDUCTION 83 3. Mathematical Induction 3.1. First Principle of Mathematical Induction. Let P (n) be a predicate with domain of discourse (over) the natural numbers N = {0, 1,,...}. If (1)
More informationInternal Critique: A Logic is not a Theory of Reasoning and a Theory of Reasoning is not a Logic
Internal Critique: A Logic is not a Theory of Reasoning and a Theory of Reasoning is not a Logic Gilbert Harman Princeton University In order to understand the relations between reasoning and logic, it
More informationInductive Reasoning Page 1 of 7. Inductive Reasoning
Inductive Reasoning Page 1 of 7 Inductive Reasoning We learned that valid deductive thinking begins with at least one universal premise and leads to a conclusion that is believed to be contained in the
More informationST ANSELM S VERSION OF THE ONTOLOGICAL ARGUMENT Anselm s argument relies on conceivability :
Michael Lacewing The ontological argument St Anselm and Descartes both famously presented an ontological argument for the existence of God. (The word ontological comes from ontology, the study of (ology)
More informationAnselm s Ontological Argument for the Existence of God
Anselm s Ontological Argument for the Existence of God Anselm s argument is an a priori argument; that is, it is an argument that is independent of experience and based solely on concepts and logical relations,
More informationTHE KNOWLEDGE ARGUMENT
Michael Lacewing Descartes arguments for distinguishing mind and body THE KNOWLEDGE ARGUMENT In Meditation II, having argued that he knows he thinks, Descartes then asks what kind of thing he is. Discussions
More informationPhilosophical argument
Michael Lacewing Philosophical argument At the heart of philosophy is philosophical argument. Arguments are different from assertions. Assertions are simply stated; arguments always involve giving reasons.
More informationScience and Scientific Reasoning. Critical Thinking
Science and Scientific Reasoning Critical Thinking Some Common Myths About Science Science: What it is and what it is not Science and Technology Science is not the same as technology The goal of science
More informationKant s deontological ethics
Michael Lacewing Kant s deontological ethics DEONTOLOGY Deontologists believe that morality is a matter of duty. We have moral duties to do things which it is right to do and moral duties not to do things
More informationLecture 7.1 Descartes Meditation 2, 3.
TOPIC: Lecture 7.1 Descartes Meditation 2, 3. Descartes Rationalism; Wax argument; Argument for the Existence of God. KEY TERMS/ GOALS: Rationalism and Empiricism Cogito ergo sum. Wax argument. Argument
More informationSorensen on Unknowable Obligations
Sorensen on Unknowable Obligations Theodore Sider Utilitas 7 (1995): 273 9 1. Access principles Vagueness in the phrase can know aside, the principle of Access An act is obligatory only if its agent can
More informationReality in the Eyes of Descartes and Berkeley. By: Nada Shokry 5/21/2013 AUC  Philosophy
Reality in the Eyes of Descartes and Berkeley By: Nada Shokry 5/21/2013 AUC  Philosophy Shokry, 2 One person's craziness is another person's reality. Tim Burton This quote best describes what one finds
More informationPascal is here expressing a kind of skepticism about the ability of human reason to deliver an answer to this question.
Pascal s wager So far we have discussed a number of arguments for or against the existence of God. In the reading for today, Pascal asks not Does God exist? but Should we believe in God? What is distinctive
More informationLecture 8 The Subjective Theory of Betting on Theories
Lecture 8 The Subjective Theory of Betting on Theories Patrick Maher Philosophy 517 Spring 2007 Introduction The subjective theory of probability holds that the laws of probability are laws that rational
More information1/10. Descartes 2: The Cogito and the Mind
1/10 Descartes 2: The Cogito and the Mind Recap: last week we undertook to follow Descartes path of radical doubt in order to attempt to discover what, if anything, can be known for certain. This path
More informationKilling And Letting Die
[This essay originally appeared in the Encyclopedia of Ethics, 2nd edition, ed. Lawrence Becker and Charlotte Becker (New York: Routledge, 2001), vol. 2, pp. 94750.] Killing And Letting Die Is it worse
More informationMathematical Induction
Mathematical Induction (Handout March 8, 01) The Principle of Mathematical Induction provides a means to prove infinitely many statements all at once The principle is logical rather than strictly mathematical,
More informationDivine Command Theory
Divine Command Theory 1. Divine Command Theory: This is the view that rightness stems from God s commands: That is, an action is right if God commands it, and wrong if He forbids it. On this view, morality
More informationLecture Notes, October 30. 0. Introduction to the philosophy of mind
Philosophy 110W  3: Introduction to Philosophy, Hamilton College, Fall 2007 Russell Marcus, Instructor email: rmarcus1@hamilton.edu website: http://thatmarcusfamily.org/philosophy/intro_f07/course_home.htm
More informationChapter 4. Descartes, Third Meditation. 4.1 Homework
Chapter 4 Descartes, Third Meditation 4.1 Homework Readings :  Descartes, Meditation III  Objections and Replies: a) Third O and R: CSM II, 132; 1278. b) Fifth O and R: CSM II, 19597, 251. c) First
More information6.3 Conditional Probability and Independence
222 CHAPTER 6. PROBABILITY 6.3 Conditional Probability and Independence Conditional Probability Two cubical dice each have a triangle painted on one side, a circle painted on two sides and a square painted
More informationREASONS FOR HOLDING THIS VIEW
Michael Lacewing Substance dualism A substance is traditionally understood as an entity, a thing, that does not depend on another entity in order to exist. Substance dualism holds that there are two fundamentally
More informationChapter 5: Fallacies. 23 February 2015
Chapter 5: Fallacies 23 February 2015 Plan for today Talk a bit more about arguments notice that the function of arguments explains why there are lots of bad arguments Turn to the concept of fallacy and
More informationSkepticism about the external world & the problem of other minds
Skepticism about the external world & the problem of other minds So far in this course we have, broadly speaking, discussed two different sorts of issues: issues connected with the nature of persons (a
More informationFrege s theory of sense
Frege s theory of sense Jeff Speaks August 25, 2011 1. Three arguments that there must be more to meaning than reference... 1 1.1. Frege s puzzle about identity sentences 1.2. Understanding and knowledge
More informationDescartes Meditations II & III. Phil 100, Intro to Philosophy Benjamin Visscher Hole IV
Descartes Meditations II & III Phil 100, Intro to Philosophy Benjamin Visscher Hole IV SUMMARY OF MEDITATION ONE 1. Knowledge is either a priori or it is a posteriori. 2. If it is a posteriori, we do not
More informationSession 8 Smith, Is There A Prima Facie Obligation to Obey the Law?
Session 8 Smith, Is There A Prima Facie Obligation to Obey the Law? Identifying the Question Not: Does the fact that some act is against the law provide us with a reason to believe (i.e. evidence) that
More informationDeductive reasoning is the kind of reasoning in which, roughly, the truth of the input
Forthcoming in The Encyclopedia of the Mind, edited by Hal Pashler, SAGE Publishing. Editorial Board: Tim Crane, Fernanda Ferreira, Marcel Kinsbourne, and Rich Zemel. Deductive Reasoning Joshua Schechter
More informationDescartes Handout #2. Meditation II and III
Descartes Handout #2 Meditation II and III I. Meditation II: The Cogito and Certainty A. I think, therefore I am cogito ergo sum In Meditation II Descartes proposes a truth that cannot be undermined by
More information8. Inductive Arguments
8. Inductive Arguments 1 Inductive Reasoning In general, inductive reasoning is reasoning in which we extrapolate from observed experience (e.g., past experience) to some conclusion (e.g., about present
More informationLecture 6.1 Descartes Meditations I. Descartes Foundationalism, Method of Doubt, and his famous Evil Demon thought experiment.
TOPIC: Lecture 6.1 Descartes Meditations I Descartes Foundationalism, Method of Doubt, and his famous Evil Demon thought experiment. KEY TERMS/ GOALS: Skepticism A priori and Empirical Justification Empiricists
More informationDEDUCTIVE & INDUCTIVE REASONING
DEDUCTIVE & INDUCTIVE REASONING Expectations 1. Take notes on inductive and deductive reasoning. 2. This is an information based presentation  I simply want you to be able to apply this information to
More informationThe Foundations: Logic and Proofs. Chapter 1, Part III: Proofs
The Foundations: Logic and Proofs Chapter 1, Part III: Proofs Rules of Inference Section 1.6 Section Summary Valid Arguments Inference Rules for Propositional Logic Using Rules of Inference to Build Arguments
More informationThe MarketClearing Model
Chapter 5 The MarketClearing Model Most of the models that we use in this book build on two common assumptions. First, we assume that there exist markets for all goods present in the economy, and that
More informationWe now explore a third method of proof: proof by contradiction.
CHAPTER 6 Proof by Contradiction We now explore a third method of proof: proof by contradiction. This method is not limited to proving just conditional statements it can be used to prove any kind of statement
More informationWhat Is Probability?
1 What Is Probability? The idea: Uncertainty can often be "quantified" i.e., we can talk about degrees of certainty or uncertainty. This is the idea of probability: a higher probability expresses a higher
More informationDiscrete Mathematics and Probability Theory Fall 2009 Satish Rao, David Tse Note 2
CS 70 Discrete Mathematics and Probability Theory Fall 2009 Satish Rao, David Tse Note 2 Proofs Intuitively, the concept of proof should already be familiar We all like to assert things, and few of us
More informationThe Cosmological Argument
Cosmological Argument Page 1 of 5 The Cosmological Argument (A) Discuss the key features of the Cosmological Argument. The Cosmological Argument has several forms, but is fundamentally a proof for the
More informationDescartes Fourth Meditation On human error
Descartes Fourth Meditation On human error Descartes begins the fourth Meditation with a review of what he has learned so far. He began his search for certainty by questioning the veracity of his own senses.
More informationCultural Relativism. 1. What is Cultural Relativism? 2. Is Cultural Relativism true? 3. What can we learn from Cultural Relativism?
1. What is Cultural Relativism? 2. Is Cultural Relativism true? 3. What can we learn from Cultural Relativism? What is it? Rough idea: There is no universal truth in ethics. There are only customary practices
More informationMathematical Induction
Mathematical Induction In logic, we often want to prove that every member of an infinite set has some feature. E.g., we would like to show: N 1 : is a number 1 : has the feature Φ ( x)(n 1 x! 1 x) How
More information1/9. Locke 1: Critique of Innate Ideas
1/9 Locke 1: Critique of Innate Ideas This week we are going to begin looking at a new area by turning our attention to the work of John Locke, who is probably the most famous English philosopher of all
More information6.207/14.15: Networks Lecture 15: Repeated Games and Cooperation
6.207/14.15: Networks Lecture 15: Repeated Games and Cooperation Daron Acemoglu and Asu Ozdaglar MIT November 2, 2009 1 Introduction Outline The problem of cooperation Finitelyrepeated prisoner s dilemma
More informationReview. Bayesianism and Reliability. Today s Class
Review Bayesianism and Reliability Models and Simulations in Philosophy April 14th, 2014 Last Class: Difference between individual and social epistemology Why simulations are particularly useful for social
More informationFallacies are deceptive errors of thinking.
Fallacies are deceptive errors of thinking. A good argument should: 1. be deductively valid (or inductively strong) and have all true premises; 2. have its validity and truthofpremises be as evident
More informationPerfect being theology and modal truth
Perfect being theology and modal truth Jeff Speaks February 9, 2016 Perfect being theology is the attempt to use the principle that God is the greatest possible being to derive claims about the divine
More informationExample 1. Consider the following two portfolios: 2. Buy one c(s(t), 20, τ, r) and sell one c(s(t), 10, τ, r).
Chapter 4 PutCall Parity 1 Bull and Bear Financial analysts use words such as bull and bear to describe the trend in stock markets. Generally speaking, a bull market is characterized by rising prices.
More informationThe last three chapters introduced three major proof techniques: direct,
CHAPTER 7 Proving NonConditional Statements The last three chapters introduced three major proof techniques: direct, contrapositive and contradiction. These three techniques are used to prove statements
More informationEPISTEMOLOGY: Foundationalism
Gábor Forgács, Tihamér Margitay, Zsolt Ziegler Dept. of Philosophy and the History of Science 1111 Budapest, Egry J. st. 1. E 610. forgacsg@gmail.com, margitay@filozofia.bme.hu, batajba@gmail.com www.filozofia.bme.hu
More informationINCIDENCEBETWEENNESS GEOMETRY
INCIDENCEBETWEENNESS GEOMETRY MATH 410, CSUSM. SPRING 2008. PROFESSOR AITKEN This document covers the geometry that can be developed with just the axioms related to incidence and betweenness. The full
More informationWEAK DOMINANCE: A MYSTERY CRACKED
WEAK DOMINANCE: A MYSTERY CRACKED JOHN HILLAS AND DOV SAMET Abstract. What strategy profiles can be played when it is common knowledge that weakly dominated strategies are not played? A comparison to the
More informationLecture 9 Maher on Inductive Probability
Lecture 9 Maher on Inductive Probability Patrick Maher Scientific Thought II Spring 2010 Two concepts of probability Example You know that a coin is either twoheaded or twotailed but you have no information
More informationKant on Time. Diana Mertz Hsieh (diana@dianahsieh.com) Kant (Phil 5010, Hanna) 28 September 2004
Kant on Time Diana Mertz Hsieh (diana@dianahsieh.com) Kant (Phil 5010, Hanna) 28 September 2004 In the Transcendental Aesthetic of his Critique of Pure Reason, Immanuel Kant offers a series of dense arguments
More informationDraft Copy: Do Not Cite Without Author s Permission
WHAT S WRONG WITH THE FUTURE OF VALUE ARGUMENT (1/8/2015) A. WHAT THE FUTURE OF VALUE ARGUMENT IS According to the future of value argument, what makes it wrong to kill those postnatal human beings we
More informationScientific Reasoning: A Solution to the Problem of Induction
International Journal of Basic & Applied Sciences IJBASIJENS Vol:10 No:03 49 Scientific Reasoning: A Solution to the Problem of Induction Wilayat Khan and Habib Ullah COMSATS Institute of Information
More informationKnowledgeClosure and Skepticism (J)
KnowledgeClosure and Skepticism (J) Uncovering difficulties in the details of particular formulations of [the closure principle] will not weaken the principle s intuitive appeal; such quibbling will seem
More informationStyle Guide For Writing Mathematical Proofs
Style Guide For Writing Mathematical Proofs Adapted by Lindsey Shorser from materials by Adrian Butscher and Charles Shepherd A solution to a math problem is an argument. Therefore, it should be phrased
More informationor conventional implicature [1]. If the implication is only pragmatic, explicating logical truth, and, thus, also consequence and inconsistency.
44 ANALYSIS explicating logical truth, and, thus, also consequence and inconsistency. Let C1 and C2 be distinct moral codes formulated in English. Let C1 contain a norm N and C2 its negation. The moral
More informationCS 441 Discrete Mathematics for CS Lecture 5. Predicate logic. CS 441 Discrete mathematics for CS. Negation of quantifiers
CS 441 Discrete Mathematics for CS Lecture 5 Predicate logic Milos Hauskrecht milos@cs.pitt.edu 5329 Sennott Square Negation of quantifiers English statement: Nothing is perfect. Translation: x Perfect(x)
More informationPractical Jealousy Management
Florida Poly Retreat 2006 Practical Jealousy Management Part 1: On the Nature of Jealousy Jealousy is an unusual emotion in that it is an emotion rooted in other emotions. Often, the root of jealousy lies
More informationCRITICAL THINKING REASONS FOR BELIEF AND DOUBT (VAUGHN CH. 4)
CRITICAL THINKING REASONS FOR BELIEF AND DOUBT (VAUGHN CH. 4) LECTURE PROFESSOR JULIE YOO Claims Without Arguments When Claims Conflict Conflicting Claims Conflict With Your Background Information Experts
More informationStrictly speaking, all our knowledge outside mathematics consists of conjectures.
1 Strictly speaking, all our knowledge outside mathematics consists of conjectures. There are, of course, conjectures and conjectures. There are highly respectable and reliable conjectures as those expressed
More informationLocating the Line Between Acceptable Performance Enhancement and Cheating. Alberto Salazar
Locating the Line Between Acceptable Performance Enhancement and Cheating Alberto Salazar Regulating authorities in the sports world and the public need to recognize what all athletes striving to be their
More informationUnderstanding Options: Calls and Puts
2 Understanding Options: Calls and Puts Important: in their simplest forms, options trades sound like, and are, very high risk investments. If reading about options makes you think they are too risky for
More informationDescartes. Philosophy and Good Sense
Perspectives in Philosophy Rene Descartes Descartes Philosophy is the search for certainty the search to know, for yourself, what is really true and really false to know which beliefs are reliable. However,
More informationGod and Reality. Arman Hovhannisyan
God and Reality Arman Hovhannisyan Metaphysics has done everything to involve God in the world of being. However, in case of considering Reality as being and nothingness, naturally, the metaphysical approach
More informationMath 4310 Handout  Quotient Vector Spaces
Math 4310 Handout  Quotient Vector Spaces Dan Collins The textbook defines a subspace of a vector space in Chapter 4, but it avoids ever discussing the notion of a quotient space. This is understandable
More information8 Divisibility and prime numbers
8 Divisibility and prime numbers 8.1 Divisibility In this short section we extend the concept of a multiple from the natural numbers to the integers. We also summarize several other terms that express
More informationON EXTERNAL OBJECTS By Immanuel Kant From Critique of Pure Reason (1781)
ON EXTERNAL OBJECTS By Immanuel Kant From Critique of Pure Reason (1781) General Observations on The Transcendental Aesthetic To avoid all misapprehension, it is necessary to explain, as clearly as possible,
More informationDiscrete Mathematics and Probability Theory Fall 2009 Satish Rao,David Tse Note 11
CS 70 Discrete Mathematics and Probability Theory Fall 2009 Satish Rao,David Tse Note Conditional Probability A pharmaceutical company is marketing a new test for a certain medical condition. According
More informationLogic and Reasoning Practice Final Exam Spring 2015. Section Number
Logic and Reasoning Practice Final Exam Spring 2015 Name Section Number The final examination is worth 100 points. 1. (5 points) What is an argument? Explain what is meant when one says that logic is the
More informationHow should we think about the testimony of others? Is it reducible to other kinds of evidence?
Subject: Title: Word count: Epistemology How should we think about the testimony of others? Is it reducible to other kinds of evidence? 2,707 1 How should we think about the testimony of others? Is it
More informationExplain and critically assess the Singer Solution to Global Poverty
1 Explain and critically assess the Singer Solution to Global Poverty Introduction In this essay, I will summarise Singer's solution to world poverty, and then consider some of the objections that may
More informationBinomial Sampling and the Binomial Distribution
Binomial Sampling and the Binomial Distribution Characterized by two mutually exclusive events." Examples: GENERAL: {success or failure} {on or off} {head or tail} {zero or one} BIOLOGY: {dead or alive}
More informationit is no surprise that God, in creating me, should have placed this idea in me to be, as it were, the mark of the craftsman stamped on his work.
THIRD MEDITATION The existence of God So far Descartes sceptical arguments have threatened all knowledge but the knowledge of self provided in the cogito. But instead of turning now to the question of
More informationEPISTEMOLOGY. PHILOSOPHY FOR AS.indb 23 16/07/2014 16:10
EPISTEMOLOGY 2 What can we know? And how do we know what we know? These questions are central to the branch of philosophy called epistemology. At its heart are two very important, very interesting questions
More informationNegative Automatic Thoughts
The Problem Negative Automatic Thoughts People who are depressed tend to think about themselves, the world and the future in a negative way. These negative thoughts are: AUTOMATIC DISTORTED UNHELPFUL PLAUSIBLE
More informationThe Refutation of Relativism
The Refutation of Relativism There are many different versions of relativism: ethical relativism conceptual relativism, and epistemic relativism are three. In this paper, I will be concerned with only
More informationTastes and Indifference Curves
C H A P T E R 4 Tastes and Indifference Curves This chapter begins a 2chapter treatment of tastes or what we also call preferences. In the first of these chapters, we simply investigate the basic logic
More informationWriting Thesis Defense Papers
Writing Thesis Defense Papers The point of these papers is for you to explain and defend a thesis of your own critically analyzing the reasoning offered in support of a claim made by one of the philosophers
More informationRSR Episode #11 Ontological Argument
RSR Episode #11 Ontological Argument The Ontological Argument for God s existence was developed in the Middle Ages by St. Anselm. It claims that reflection on God s nature as the greatest conceivable being
More informationOmnipotence & prayer
Omnipotence & prayer Today, we ll be discussing two theological paradoxes: paradoxes arising from the idea of an omnipotent being, and paradoxes arising from the religious practice of prayer. So far, in
More informationIs there ethics in algorithms? Searching for ethics in contemporary technology. Martin Peterson
Is there ethics in algorithms? Searching for ethics in contemporary technology Martin Peterson www.martinpeterson.org m.peterson@tue.nl What is an algorithm? An algorithm is a finite it sequence of welldefined
More informationInvalidity in Predicate Logic
Invalidity in Predicate Logic So far we ve got a method for establishing that a predicate logic argument is valid: do a derivation. But we ve got no method for establishing invalidity. In propositional
More informationProblem Set I: Preferences, W.A.R.P., consumer choice
Problem Set I: Preferences, W.A.R.P., consumer choice Paolo Crosetto paolo.crosetto@unimi.it Exercises solved in class on 18th January 2009 Recap:,, Definition 1. The strict preference relation is x y
More informationMessage: Faith & Science  Part 1
The Light Shines Outside the Box www.jesusfamilies.org Message: Faith & Science  Part 1 This message is not for people who believe that God exists. Most people on the earth believe that some God exists,
More informationContinuous Functions, Smooth Functions and the Derivative
UCSC AMS/ECON 11A Supplemental Notes # 4 Continuous Functions, Smooth Functions and the Derivative c 2004 Yonatan Katznelson 1. Continuous functions One of the things that economists like to do with mathematical
More informationGames of Incomplete Information
Games of Incomplete Information Jonathan Levin February 00 Introduction We now start to explore models of incomplete information. Informally, a game of incomplete information is a game where the players
More informationPhilosophy 203 History of Modern Western Philosophy. Russell Marcus Hamilton College Spring 2010
Philosophy 203 History of Modern Western Philosophy Russell Marcus Hamilton College Spring 2010 Class 2  Meditation One Marcus, Modern Philosophy, Spring 2010, Slide 1 Five dogmas undermined by the new
More informationDIFFERENTIABILITY OF COMPLEX FUNCTIONS. Contents
DIFFERENTIABILITY OF COMPLEX FUNCTIONS Contents 1. Limit definition of a derivative 1 2. Holomorphic functions, the CauchyRiemann equations 3 3. Differentiability of real functions 5 4. A sufficient condition
More information