Cosmological Arguments for the Existence of God S. Clarke


 Joshua Tate
 1 years ago
 Views:
Transcription
1 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 start with a few background ideas. 2. Theoretical Entities: a. Sometimes we can infer the existence and nature of something that we cannot directly see by its effects. Such things are called theoretical entities. For example: i. We can infer electrons exist because of electricity We can infer the nature of the inside of the sun from its outside (e.g., cosmic rays) b. A number of the most famous arguments for the existence of God treat God this way. We infer His existence from his effects. c. But how can you do this? 3. Principle of Sufficient Reason a. This sort of inference turns on a basic principle that i. every phenomenon has an explanation, and that the explanation must explain every feature of the phenomenon. b. This is a tricky premise. I am not going to try to evaluate it beyond pointing out that it is very hard to see why it should be accepted. It is clear that many things do have explanations and causes. It is less clear that everything does. How can we know this? 4. Inference to the Best Explanation a. Of course, not all explanations are equally good. Some are better than others. b. We infer that electrons exist, and have certain properties such as being negatively charged, because, as far as we can tell right now, that is the best explanation of electrical phenomena such as lightning and so on. c. So the trick behind this sort of argument is to figure out what the best explanation for the relevant phenomenon is.
2 d. The idea behind several of the most famous argument for the existence of God is that God is the best explanation for many important phenomena. 5. Note several things about inference to the best explanation a. We do not necessarily want to accept something because it is the best explanation we can currently think of. For the best might be pretty bad! b. There is no universally accepted, general theory of what counts as a better explanation. There are some things that seem clear about it, but often scientists work on the fly, so to speak. Later, when we talk explicitly about science, we have to confront this issue more directly. 6. The Probabilistic and Falliblistic Character of Such Inferences a. Before continuing, it is important to recognize some crucial features of any argument to the best explanation, whether or not one about God. b. These are all inductive arguments and never certain. c. They are also open to revision. What seems like the best explanation of something today might not seem so tomorrow. d. In the context of God, this is interesting. In the past, lots of phenomena seemed to require a God to explain them but we now know they do not, e.g., lightning. 7. Simple Cosmological Argument a. The universe exists b. Everything that exists needs an explanation or cause c. An infinite series of causes backwards in time is not possible d. Therefore the universe has an explanation/cause: God [God as first cause. ] 8. Critique of this version of the Cosmological Argument a. Even if the argument works, it only gets that the universe has a creator. It does not get a God that is worthy of worship. Nor does it get anything like a traditional God save for the one feature: first cause. We do not know that this cause is allknowing, all good, or that it even continues to exist. Nor does it support any particular religion. Note, this does not refute the argument, but it does cast doubt on its ability to be useful to religion.
3 b. If everything needs a cause, than doesn t God? c. It is not clear why we should believe an infinite series of causes backwards in time is not possible. The proponent of this argument wants us to believe in a particular model of the universe, but consider several possibilities. i. The universe could have a start in time. i The universe could be infinite in time Time could loop somehow. Clarke s Complex Cosmological Argument 9. Clarkes version of the argument is designed to deal with at least some of the problems with the simpler version, a. the questionable premise that an infinite series of causes backwards in time is not possible. b. The issue of God s needing a cause. 10. Start with the Basic Distinction for Clarke a. He begins with a distinction between dependent beings and independent beings. i. A dependent being is one the existence of which is explained in terms of something else. Also called a contingent being. An independent being is one the existence of which is explained by its own nature. Also called a necessary or selfexistent being. 11. Independent Being: This is a very difficult to understand notion. Several points. a. In fact, we might not be able to understand it. After all, we do not usually bump up against any such beings. b. Still we do not want to just assume that we cannot get some grasp of this sort of thing, perhaps using mathematics or some other methods. c. And even if we cannot grasp it very well, it may be that we can only understand such a being negatively: it is not a dependent being. That is at least something. 12. Clarke s Conception of God and his Basic Thesis a. God is to be understood as an independent, necessary or self existent being.
4 b. There has always existed such a being. 13. The reductio ad absurdum : a. Clarke s argument is complex. I will put it into a somewhat simpler form that might make it easier to understand. b. But first we need a general point. Clarke s argument, as I will interpret it, is a reductio ad absurdum, or indirect proof. This is a general style of argument that can be employed anywhere, not just in the context of arguments about God. c. A reductio argument seeks to prove something by refuting its opposite. Its form is this. d. I wish to prove that P. To do it, I will assume, for reductio, notp. I will show that notp leads to an absurdity and is therefore false. Given that notp is false, it follows that P is true. i. Assume notp for reductio i iv. NotP leads to Q Q is false. Since notp lead to a falsehood, notp is itself false. v. Since NotP is false, P must be true. 14. Statement of Clarke s Argument: Pay attention to the complex structure of this argument. As I set it up, it has four premises, but premise (a) and (d) require support. So there are two subsidiary arguments, one for (a) and one for (d). a. Something has always existed. b. There are two possibilities i. There have always been dependent beings and no independent being. There has always been an independent being. c. The first is absurd. d. Therefore the second is true: there has always existed an independent being. 15. Clarification of Premise (b): Basically, (b) tells us that there are two possible picture of
5 the world. We need to choose between them. On one picture, all that has ever existed are dependent beings, that is, ordinary sorts of things like people, trees, planets, suns. On the other picture, along with those dependent beings, there is another special sort of being, an independent being. a. The first option, which excludes the independent being, includes that assumption that that there have always been dependent beings to that they go infinitely far backwards in time. b. But the second option does not assume this. The independent being is assumed to have always exist, but it is left open whether dependent beings have always existed along with it, or whether they came into existence at some time. That is not the important issue here. The important point is that on this picture of the universe, whether or not there have always been dependent beings, there has definitely always been an independent being. 16. Proof of Clarke s Premise (a) a. Suppose at some time nothing existed b. Something cannot come from nothing c. So, given (i) nothing would now exist d. But things do now exist. e. Therefore, 1 is false. 17. Proof of Clarke s Line (d) a. Suppose there has been an infinite series of dependent beings and no independent being. b. Everything has an explanation, so the existence of this series of dependent beings needs one. c. The explanation is either from within the series or from without it. d. The explanation cannot be from without since, by hypothesis, all that exists is the series. e. The explanation cannot be from within since the series is itself dependent. f. Therefore, this series has no explanation. g. But this contradicts premise a
6 h. Hence, our assumption leads to a contradiction and is therefore false. 18. This version of the cosmological argument is supposed to deal with several of the problems we saw in the original formulation of cosmological argument a. One of the problems with the original cosmological argument was this. It started from the premise that everything needs a cause. But if everything needs a cause, doesn t God? We now avoid this by not using that premise at all! It is not part of Clarke's argument. b. A second problem with the original cosmological argument was it turned on an assumption that the universe cannot go on forever backwards in time. That is not obvious. In fact, we looked at three possibilities: that the universe had a beginning, that it involved an infinite series backwards in time, and that it involved some sort of loop. Only the first leads to a first cause. But note, Clarke s argument does not turn on any such assumption. His argument works if the universe had a beginning, if the universe involved infinite time and had no beginning, and if time somehow loops back on itself. His point is that which ever of these three possibilities is correct, we need an explanation for the whole. And that requires an independent being. 19. Evaluation of the Argument a. If the argument works at all, it does not establish a traditional God or any one religion. i. Does not establish how many independent beings there are. Does not establish the power of God, his moral character, or virtually any of the other features we tend to think as central to God. b. The argument involves a very obscure notion, that of an independent being. And given that it is so obscure, we do not know that the universe can t be an independent being. c. The argument turns on a questionable assumption: the principle of sufficient reason. How do we know that everything has an explanation? That is not just obviously true, and it is hard to see how it could be proven. d. The argument involves a serious logical flaw. For we cannot transfer the properties of the parts to the whole. Clarke seems to assume that since the parts of the universe (e.g., trees, rocks, birds) are dependent beings, the whole is a dependent being. This is the classic fallacy of composition.
Last time we had arrived at the following provisional interpretation of Aquinas second way:
Aquinas Third Way Last time we had arrived at the following provisional interpretation of Aquinas second way: 1. 2. 3. 4. At least one thing has an efficient cause. Every causal chain must either be circular,
More informationDirect Proofs. CS 19: Discrete Mathematics. Direct Proof: Example. Indirect Proof: Example. Proofs by Contradiction and by Mathematical Induction
Direct Proofs CS 19: Discrete Mathematics Amit Chakrabarti Proofs by Contradiction and by Mathematical Induction At this point, we have seen a few examples of mathematical proofs. These have the following
More informationMAT2400 Analysis I. A brief introduction to proofs, sets, and functions
MAT2400 Analysis I A brief introduction to proofs, sets, and functions In Analysis I there is a lot of manipulations with sets and functions. It is probably also the first course where you have to take
More informationCOMP 250 Fall Mathematical induction Sept. 26, (n 1) + n = n + (n 1)
COMP 50 Fall 016 9  Mathematical induction Sept 6, 016 You will see many examples in this course and upcoming courses of algorithms for solving various problems It many cases, it will be obvious that
More informationAd hominem: An argument directed at an opponent in a disagreement, not at the topic under discussion.
Glossary of Key Terms Ad hominem: An argument directed at an opponent in a disagreement, not at the topic under discussion. Agent: One who acts and is held responsible for those actions. Analytic judgment:
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 informationHandout #1: Mathematical Reasoning
Math 101 Rumbos Spring 2010 1 Handout #1: Mathematical Reasoning 1 Propositional Logic A proposition is a mathematical statement that it is either true or false; that is, a statement whose certainty or
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 informationThe argument from evil
The argument from evil Our topic today is the argument from evil. This is by far the most important argument for the conclusion that God does not exist. The aim of at least the simplest form of this argument
More informationDivine command theory
Today we will be discussing divine command theory. But first I will give a (very) brief overview of the semester, and the discipline of philosophy. Why do this? One of the functions of an introductory
More informationTh e ontological argument distinguishes itself from the cosmological
Aporia vol. 18 no. 1 2008 Charles Hartshorne and the Ontological Argument Joshua Ernst Th e ontological argument distinguishes itself from the cosmological and teleological arguments for God s existence
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 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 informationThe ontological argument: Comment: What does ontological mean? What is the ontological argument?
Phil. 1000 Notes #7: The Ontological Argument To Discuss Today: Background points for arguing about God. St. Anselm s Ontological Argument. Objections to the argument. Preliminary points about God Traditional
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 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 informationElementary Number Theory and Methods of Proof. CSE 215, Foundations of Computer Science Stony Brook University http://www.cs.stonybrook.
Elementary Number Theory and Methods of Proof CSE 215, Foundations of Computer Science Stony Brook University http://www.cs.stonybrook.edu/~cse215 1 Number theory Properties: 2 Properties of integers (whole
More informationPHLA The Problem of Induction
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
More informationDEVELOPING HYPOTHESIS AND
Shalini Prasad Ajith Rao Eeshoo Rehani DEVELOPING 500 METHODS SEPTEMBER 18 TH 2001 DEVELOPING HYPOTHESIS AND Introduction Processes involved before formulating the hypotheses. Definition Nature of Hypothesis
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 informationIn this essay I will discuss the ongoing controversy on the subject of teaching Intelligent
An essay concerning the controversy In this essay I will discuss the ongoing controversy on the subject of teaching Intelligent Design (ID) in high school science classes. The objection against teaching
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 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 informationScientific Method & Statistical Reasoning
Scientific Method & Statistical Reasoning Paul Gribble http://www.gribblelab.org/stats/ Winter, 2016 MD Chapters 1 & 2 The idea of pure science Philosophical stances on science Historical review Gets you
More information1.3 Induction and Other Proof Techniques
4CHAPTER 1. INTRODUCTORY MATERIAL: SETS, FUNCTIONS AND MATHEMATICAL INDU 1.3 Induction and Other Proof Techniques The purpose of this section is to study the proof technique known as mathematical induction.
More informationThe Way of Gd Class #6
The Way of Gd Class #6 A world that is getting older has to have a starting point. by Rabbi Moshe Zeldman 2007 JewishPathways.com 1 So far in our investigation of the logical basis for an infinite existence,
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 informationLesson 2. The Existence of God Cause & Effect. Apologetics Press Introductory Christian Evidences Correspondence Course
Lesson 2 The Existence of God Cause & Effect Apologetics Press Introductory Christian Evidences Correspondence Course THE EXISTENCE OF GOD CAUSE & EFFECT One of the most basic issues that the human mind
More informationreductio ad absurdum null hypothesis, alternate hypothesis
Chapter 10 s Using a Single Sample 10.1: Hypotheses & Test Procedures Basics: In statistics, a hypothesis is a statement about a population characteristic. s are based on an reductio ad absurdum form of
More informationWRITING A CRITICAL ARTICLE REVIEW
WRITING A CRITICAL ARTICLE REVIEW A critical article review briefly describes the content of an article and, more importantly, provides an indepth analysis and evaluation of its ideas and purpose. The
More informationInduction. Margaret M. Fleck. 10 October These notes cover mathematical induction and recursive definition
Induction Margaret M. Fleck 10 October 011 These notes cover mathematical induction and recursive definition 1 Introduction to induction At the start of the term, we saw the following formula for computing
More information6.080 / 6.089 Great Ideas in Theoretical Computer Science Spring 2008
MIT OpenCourseWare http://ocw.mit.edu 6.080 / 6.089 Great Ideas in Theoretical Computer Science Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
More informationIntroduction to Metaphysics
1 Reading Questions Metaphysics The Philosophy of Religion Arguments for God s Existence Arguments against God s Existence In Case of a Tie Summary Reading Questions Introduction to Metaphysics 1. What
More informationLogic and Proofs. Chapter 1
Section 1.0 1.0.1 Chapter 1 Logic and Proofs 1.1 Propositional Logic 1.2 Propositional Equivalences 1.3 Predicates and Quantifiers 1.4 Nested Quantifiers 1.5 Rules of Inference 1.6 Introduction to Proofs
More informationMathematical Induction. Mary Barnes Sue Gordon
Mathematics Learning Centre Mathematical Induction Mary Barnes Sue Gordon c 1987 University of Sydney Contents 1 Mathematical Induction 1 1.1 Why do we need proof by induction?.... 1 1. What is proof by
More information1/8. Descartes 4: The Fifth Meditation
1/8 Descartes 4: The Fifth Meditation Recap: last time we found that Descartes in the 3 rd Meditation set out to provide some grounds for thinking that God exists, grounds that would answer the charge
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 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 informationComputer Science 211 Data Structures Mount Holyoke College Fall Topic Notes: Recursion and Mathematical Induction
Computer Science 11 Data Structures Mount Holyoke College Fall 009 Topic Notes: Recursion and Mathematical Induction Recursion An important tool when trying to solve a problem is the ability to break the
More informationIntroduction to mathematical arguments
Introduction to mathematical arguments (background handout for courses requiring proofs) by Michael Hutchings A mathematical proof is an argument which convinces other people that something is true. Math
More information2. Methods of Proof Types of Proofs. Suppose we wish to prove an implication p q. Here are some strategies we have available to try.
2. METHODS OF PROOF 69 2. Methods of Proof 2.1. Types of Proofs. Suppose we wish to prove an implication p q. Here are some strategies we have available to try. Trivial Proof: If we know q is true then
More informationAn Innocent Investigation
An Innocent Investigation D. Joyce, Clark University January 2006 The beginning. Have you ever wondered why every number is either even or odd? I don t mean to ask if you ever wondered whether every number
More informationYou will by now not be surprised that a version of the teleological argument can be found in the writings of Thomas Aquinas.
The design argument The different versions of the cosmological argument we discussed over the last few weeks were arguments for the existence of God based on extremely abstract and general features of
More information31 is a prime number is a mathematical statement (which happens to be true).
Chapter 1 Mathematical Logic In its most basic form, Mathematics is the practice of assigning truth to welldefined statements. In this course, we will develop the skills to use known true statements to
More informationExcerpts from Debating 101 Logic Fallacies
Excerpts from Debating 101 Logic Fallacies The following definition of a fallacy and all the other materials in this document are excerpts from the notes for a course entitled Debating 101 Logic Fallacies.
More informationMathematical induction: variants and subtleties
Mathematical induction: variants and subtleties October 29, 2010 Mathematical induction is one of the most useful techniques for solving problems in mathematics. I m assuming you re familiar with the basic
More informationWRITING PROOFS. Christopher Heil Georgia Institute of Technology
WRITING PROOFS Christopher Heil Georgia Institute of Technology A theorem is just a statement of fact A proof of the theorem is a logical explanation of why the theorem is true Many theorems have this
More informationHow do we know that Christianity is true? How do we show that Christianity is true?
How do we know that Christianity is true? How do we show that Christianity is true? I know that Christianity is true because of the testimony of the Holy Spirit. My relationship with God isn t dependent
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 informationLOGICAL INFERENCE & PROOFs. Debdeep Mukhopadhyay Dept of CSE, IIT Madras
LOGICAL INFERENCE & PROOFs Debdeep Mukhopadhyay Dept of CSE, IIT Madras Defn A theorem is a mathematical assertion which can be shown to be true. A proof is an argument which establishes the truth of a
More informationMathematical Induction
Mathematical Induction MAT30 Discrete Mathematics Fall 016 MAT30 (Discrete Math) Mathematical Induction Fall 016 1 / 19 Outline 1 Mathematical Induction Strong Mathematical Induction MAT30 (Discrete Math)
More informationArtificial Intelligence Automated Reasoning
Artificial Intelligence Automated Reasoning Andrea Torsello Automated Reasoning Very important area of AI research Reasoning usually means deductive reasoning New facts are deduced logically from old ones
More informationPhilosophy 1100: Introduction to Ethics
Philosophy 1100: Introduction to Ethics WRITING A GOOD ETHICS ESSAY The writing of essays in which you argue in support of a position on some moral issue is not something that is intrinsically difficult.
More informationMathematical Induction. Lecture 1011
Mathematical Induction Lecture 1011 Menu Mathematical Induction Strong Induction Recursive Definitions Structural Induction Climbing an Infinite Ladder Suppose we have an infinite ladder: 1. We can reach
More informationSection 3 Sequences and Limits
Section 3 Sequences and Limits Definition A sequence of real numbers is an infinite ordered list a, a 2, a 3, a 4,... where, for each n N, a n is a real number. We call a n the nth term of the sequence.
More informationEvidential Arguments from Evil
24.00: Problems of Philosophy Prof. Sally Haslanger September 26, 200 I. Reasons: Inductive and Deductive Evidential Arguments from Evil We ve been considering whether it is rational to believe that an
More informationLikewise, we have contradictions: formulas that can only be false, e.g. (p p).
CHAPTER 4. STATEMENT LOGIC 59 The rightmost column of this truth table contains instances of T and instances of F. Notice that there are no degrees of contingency. If both values are possible, the formula
More informationThe Cosmological Argument for the Existence of God Gerry J Hughes
The Cosmological Argument for the Existence of God What is one trying to prove? Traditionally, the cosmological argument was intended to prove that there exists a being which is distinct from the universe,
More informationClimbing an Infinite Ladder
Section 5.1 Climbing an Infinite Ladder Suppose we have an infinite ladder and the following capabilities: 1. We can reach the first rung of the ladder. 2. If we can reach a particular rung of the ladder,
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 informationON WHITCOMB S GROUNDING ARGUMENT FOR ATHEISM Joshua Rasmussen Andrew Cullison Daniel HowardSnyder
ON WHITCOMB S GROUNDING ARGUMENT FOR ATHEISM Joshua Rasmussen Andrew Cullison Daniel HowardSnyder Abstract: Dennis Whitcomb argues that there is no God on the grounds that (i) God is omniscient, yet (ii)
More informationPerception and MindDependence Lecture 4
Perception and MindDependence Lecture 4 1 Last Week The Argument from Illusion relies on the Phenomenal Principle. The Phenomenal Principle is motivated by its ability to explain the sensuous character
More informationChapter 1 LOGIC AND PROOF
Chapter 1 LOGIC AND PROOF To be able to understand mathematics and mathematical arguments, it is necessary to have a solid understanding of logic and the way in which known facts can be combined to prove
More informationMATHEMATICAL INDUCTION. Mathematical Induction. This is a powerful method to prove properties of positive integers.
MATHEMATICAL INDUCTION MIGUEL A LERMA (Last updated: February 8, 003) Mathematical Induction This is a powerful method to prove properties of positive integers Principle of Mathematical Induction Let P
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 informationThe Problem of Evil not If God exists, she'd be OOG. If an OOG being exists, there would be no evil. God exists.
24.00: Problems of Philosophy Prof. Sally Haslanger September 14, 2005 The Problem of Evil Last time we considered the ontological argument for the existence of God. If the argument is cogent, then we
More informationThis section demonstrates some different techniques of proving some general statements.
Section 4. Number Theory 4.. Introduction This section demonstrates some different techniques of proving some general statements. Examples: Prove that the sum of any two odd numbers is even. Firstly you
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 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 informationHow to write proofs: a quick guide
How to write proofs: a quick guide Eugenia Cheng Department of Mathematics, University of Chicago Email: eugenia@math.uchicago.edu Web: http://www.math.uchicago.edu/ eugenia October 2004 A proof is like
More informationChapter Eight: Cause and
Chapter Eight: Cause and Effect Reasoning What is Causality? When examining events, people naturally seek to explain why things happened. This search often results in cause and effect reasoning, which
More informationDIVINE CONTINGENCY Einar Duenger Bohn IFIKK, University of Oslo
DIVINE CONTINGENCY Einar Duenger Bohn IFIKK, University of Oslo Brian Leftow s God and Necessity is interesting, full of details, bold and ambitious. Roughly, the main question at hand is: assuming there
More informationGould, James A. and Robert J. Mulvaney, eds. Classic Philosophical Questions, Eleventh Ed. Upper Saddle River, New Jersey Pearson Prentice Hall: 2004
From: Gould, James A and Robert J Mulvaney, eds Classic Philosophical Questions, Eleventh Ed Upper Saddle River, New Jersey Pearson Prentice Hall: 2004 PART 6: Philosophy of Religion: Can We Prove God
More informationStudents in their first advanced mathematics classes are often surprised
CHAPTER 8 Proofs Involving Sets Students in their first advanced mathematics classes are often surprised by the extensive role that sets play and by the fact that most of the proofs they encounter are
More informationA Critical Discussion of William Hatcher s Proof of God
A Critical Discussion of William Hatcher s Proof of God 1 Introduction Hatcher has recently described a logical proof of the existence of God based on three simple postulates. 1 The proof is based on a
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 information13 Infinite Sets. 13.1 Injections, Surjections, and Bijections. mcsftl 2010/9/8 0:40 page 379 #385
mcsftl 2010/9/8 0:40 page 379 #385 13 Infinite Sets So you might be wondering how much is there to say about an infinite set other than, well, it has an infinite number of elements. Of course, an infinite
More information(Refer Slide Time: 1:41)
Discrete Mathematical Structures Dr. Kamala Krithivasan Department of Computer Science and Engineering Indian Institute of Technology, Madras Lecture # 10 Sets Today we shall learn about sets. You must
More informationFormal Logic Lecture 2
Faculty of Philosophy Formal Logic Lecture 2 Peter Smith Peter Smith: Formal Logic, Lecture 2 1 Outline Validity again Systematicity and formality Modality and the invalidity principle The counterexample
More informationThe Ontological Argument by St. Anselm
The Ontological Argument by St. Anselm Canterbury Cathedral, Library of Congress, Detroit Publishing About the author.... St. Anselm (10331109), a member of the Benedictine Order and Bishop of Canterbury,
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 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 informationCSE373: Data Structures and Algorithms Lecture 2: Proof by Induction. Linda Shapiro Winter 2015
CSE373: Data Structures and Algorithms Lecture 2: Proof by Induction Linda Shapiro Winter 2015 Background on Induction Type of mathematical proof Typically used to establish a given statement for all natural
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 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 informationThis puzzle is based on the following anecdote concerning a Hungarian sociologist and his observations of circles of friends among children.
0.1 Friend Trends This puzzle is based on the following anecdote concerning a Hungarian sociologist and his observations of circles of friends among children. In the 1950s, a Hungarian sociologist S. Szalai
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 informationLogic, Sets, and Proofs
Logic, Sets, and Proofs David A. Cox and Catherine C. McGeoch Amherst College 1 Logic Logical Statements. A logical statement is a mathematical statement that is either true or false. Here we denote logical
More informationLESSON 1 PRIME NUMBERS AND FACTORISATION
LESSON 1 PRIME NUMBERS AND FACTORISATION 1.1 FACTORS: The natural numbers are the numbers 1,, 3, 4,. The integers are the naturals numbers together with 0 and the negative integers. That is the integers
More informationDescartes rationalism
Michael Lacewing Descartes rationalism Descartes Meditations provide an extended study in establishing knowledge through rational intuition and deduction. We focus in this handout on three central claims:
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 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 informationMathematical Induction
MCS236: Graph Theory Handout #A5 San Skulrattanakulchai Gustavus Adolphus College Sep 15, 2010 Mathematical Induction The following three principles governing N are equivalent. Ordinary Induction Principle.
More informationDescartes : The Epistemological Argument for MindBody Distinctness. (Margaret Wilson)
Descartes : The Epistemological Argument for MindBody Distinctness Detailed Argument Introduction Despite Descartes mindbody dualism being the most cited aspect of Descartes philosophy in recent philosophical
More informationCritical Terminology for Theory of Knowledge
Critical Terminology for Theory of Knowledge The following glossary offers preliminary definitions for some key terms that arise frequently in the literature of the theory of knowledge. Keep in mind that
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 informationwell as explain Dennett s position on the arguments of Turing and Searle.
Perspectives on Computer Intelligence Can computers think? In attempt to make sense of this question Alan Turing, John Searle and Daniel Dennett put fourth varying arguments in the discussion surrounding
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 informationScience & Engineering Practices in Next Generation Science Standards
Science & Engineering Practices in Next Generation Science Standards Asking Questions and Defining Problems: A practice of science is to ask and refine questions that lead to descriptions and explanations
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 information