Cosmological Arguments for the Existence of God S. Clarke
|
|
- Joshua Tate
- 7 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 self-existent 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, not-p. I will show that not-p leads to an absurdity and is therefore false. Given that not-p is false, it follows that P is true. i. Assume not-p for reductio i iv. Not-P leads to Q Q is false. Since not-p lead to a falsehood, not-p is itself false. v. Since Not-P 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 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 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 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 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 in-depth analysis and evaluation of its ideas and purpose. The
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 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 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 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 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 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 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 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 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 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 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 informationON WHITCOMB S GROUNDING ARGUMENT FOR ATHEISM Joshua Rasmussen Andrew Cullison Daniel Howard-Snyder
ON WHITCOMB S GROUNDING ARGUMENT FOR ATHEISM Joshua Rasmussen Andrew Cullison Daniel Howard-Snyder Abstract: Dennis Whitcomb argues that there is no God on the grounds that (i) God is omniscient, yet (ii)
More informationMathematical Induction. Lecture 10-11
Mathematical Induction Lecture 10-11 Menu Mathematical Induction Strong Induction Recursive Definitions Structural Induction Climbing an Infinite Ladder Suppose we have an infinite ladder: 1. We can reach
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 informationBackground Biology and Biochemistry Notes A
Background Biology and Biochemistry Notes A Vocabulary dependent variable evidence experiment hypothesis independent variable model observation prediction science scientific investigation scientific law
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 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 informationArguments and Dialogues
ONE Arguments and Dialogues The three goals of critical argumentation are to identify, analyze, and evaluate arguments. The term argument is used in a special sense, referring to the giving of reasons
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 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 informationHow to write proofs: a quick guide
How to write proofs: a quick guide Eugenia Cheng Department of Mathematics, University of Chicago E-mail: eugenia@math.uchicago.edu Web: http://www.math.uchicago.edu/ eugenia October 2004 A proof is like
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 informationCS 3719 (Theory of Computation and Algorithms) Lecture 4
CS 3719 (Theory of Computation and Algorithms) Lecture 4 Antonina Kolokolova January 18, 2012 1 Undecidable languages 1.1 Church-Turing thesis Let s recap how it all started. In 1990, Hilbert stated a
More informationKenken For Teachers. Tom Davis tomrdavis@earthlink.net http://www.geometer.org/mathcircles June 27, 2010. Abstract
Kenken For Teachers Tom Davis tomrdavis@earthlink.net http://www.geometer.org/mathcircles June 7, 00 Abstract Kenken is a puzzle whose solution requires a combination of logic and simple arithmetic skills.
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 informationBook Review of Rosenhouse, The Monty Hall Problem. Leslie Burkholder 1
Book Review of Rosenhouse, The Monty Hall Problem Leslie Burkholder 1 The Monty Hall Problem, Jason Rosenhouse, New York, Oxford University Press, 2009, xii, 195 pp, US $24.95, ISBN 978-0-19-5#6789-8 (Source
More informationINCIDENCE-BETWEENNESS GEOMETRY
INCIDENCE-BETWEENNESS 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 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 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 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
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 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 informationSet Theory Basic Concepts and Definitions
Set Theory Basic Concepts and Definitions The Importance of Set Theory One striking feature of humans is their inherent need and ability to group objects according to specific criteria. Our prehistoric
More informationChapter 11 Number Theory
Chapter 11 Number Theory Number theory is one of the oldest branches of mathematics. For many years people who studied number theory delighted in its pure nature because there were few practical applications
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 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 informationBuilding a Better Argument
Building a Better Argument Summary Whether it s an ad for burger chains, the closing scene of a Law & Order spinoff, a discussion with the parents about your social life or a coach disputing a close call,
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 informationIF The customer should receive priority service THEN Call within 4 hours PCAI 16.4
Back to Basics Backward Chaining: Expert System Fundamentals By Dustin Huntington Introduction Backward chaining is an incredibly powerful yet widely misunderstood concept, yet it is key to building many
More informationBasic Proof Techniques
Basic Proof Techniques David Ferry dsf43@truman.edu September 13, 010 1 Four Fundamental Proof Techniques When one wishes to prove the statement P Q there are four fundamental approaches. This document
More informationPeter: I think it's ridiculous. Almost as ridiculous as believing in the Tooth Fairy, or the Easter Bunny, or Santa Claus.
The following dialogue is partially edited/modified to reduce length. The material is from Peter Kreeft s (1984) The Best Things in Life. Socrates: Are you looking for me, Peter? Peter: As a matter of
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 information6.080/6.089 GITCS Feb 12, 2008. Lecture 3
6.8/6.89 GITCS Feb 2, 28 Lecturer: Scott Aaronson Lecture 3 Scribe: Adam Rogal Administrivia. Scribe notes The purpose of scribe notes is to transcribe our lectures. Although I have formal notes of my
More informationScience and Religion
1 Science and Religion Scripture: Colossians 1:15-20 By Pastor John H. Noordhof Williamsburg Christian Reformed Church October 21, 2012 Morning Service People of God: Today we will deal with the troubling
More informationLecture 2. What is the Normative Role of Logic?
Lecture 2. What is the Normative Role of Logic? What is the connection between (deductive) logic and rationality? One extreme: Frege. A law of logic is a law of rational thought. Seems problematic, if
More informationThe fundamental question in economics is 2. Consumer Preferences
A Theory of Consumer Behavior Preliminaries 1. Introduction The fundamental question in economics is 2. Consumer Preferences Given limited resources, how are goods and service allocated? 1 3. Indifference
More information~SHARING MY PERSONAL PERSPECTIVE~
April 2012 ~SHARING MY PERSONAL PERSPECTIVE~ Dear Friends, It is a certainty that shared values encourage cooperative relationships. I don t know who first said this, but I certainly believe it to be true.
More informationCONCEPTUAL CONTINGENCY AND ABSTRACT EXISTENCE
87 CONCEPTUAL CONTINGENCY AND ABSTRACT EXISTENCE BY MARK COLYVAN Mathematical statements such as There are infinitely many prime numbers and 2 ℵ 0 > ℵ 0 are usually thought to be necessarily true. Not
More informationThe Prime Numbers. Definition. A prime number is a positive integer with exactly two positive divisors.
The Prime Numbers Before starting our study of primes, we record the following important lemma. Recall that integers a, b are said to be relatively prime if gcd(a, b) = 1. Lemma (Euclid s Lemma). If gcd(a,
More informationArgument Mapping 2: Claims and Reasons
#2 Claims and Reasons 1 Argument Mapping 2: Claims and Reasons We ll start with the very basics here, so be patient. It becomes far more challenging when we apply these basic rules to real arguments, as
More informationResponding to Arguments against the Existence of God Based on Evil
Responding to Arguments against the Existence of God Based on Evil By INTRODUCTION Throughout the history of western thought, numerous philosophers and great thinkers have struggled with what is known
More informationINTELLECTUAL APPROACHES
Michael Lacewing Can social science explain away religion? The view of religion taken by social scientists has changed considerably over the last 150 years. (A helpful review of the first 100 years is
More informationAN INTRODUCTION TO SOCIOLOGICAL THEORIES
An Introduction to Sociological Theories 1 1 AN INTRODUCTION TO SOCIOLOGICAL THEORIES Introduction Humans are social beings. Whether we like it or not, nearly everything we do in our lives takes place
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 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 informationTHE DIMENSION OF A VECTOR SPACE
THE DIMENSION OF A VECTOR SPACE KEITH CONRAD This handout is a supplementary discussion leading up to the definition of dimension and some of its basic properties. Let V be a vector space over a field
More informationHow to Get Your Prayers Answered. By Dr. Roger Sapp
How to Get Your Prayers Answered By Dr. Roger Sapp There are many good Christians who pray daily with diligence and with discipline but seem to struggle to get their prayers answered by the Father. On
More informationLinear Programming Notes VII Sensitivity Analysis
Linear Programming Notes VII Sensitivity Analysis 1 Introduction When you use a mathematical model to describe reality you must make approximations. The world is more complicated than the kinds of optimization
More informationCONSTRUCTING A LOGICAL ARGUMENT
Sloan Communication Program Teaching Note CONSTRUCTING A LOGICAL ARGUMENT The purpose of most business writing is to recommend some course of action ("we should open a branch office in Duluth"; "management
More informationDigitalCommons@University of Nebraska - Lincoln
University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln MAT Exam Expository Papers Math in the Middle Institute Partnership 7-1-007 Pythagorean Triples Diane Swartzlander University
More information1 SCIENCE AND NATURAL PHILOSOPHY BEFORE THE 17 TH CENTURY
1 SCIENCE AND NATURAL PHILOSOPHY BEFORE THE 17 TH CENTURY FOR TEACHERS Lesson Title: Science and Natural Philosophy Before the Seventeenth Century Area of Learning: chronology, states of affairs Aims.
More informationFull and Complete Binary Trees
Full and Complete Binary Trees Binary Tree Theorems 1 Here are two important types of binary trees. Note that the definitions, while similar, are logically independent. Definition: a binary tree T is full
More information1. Current situation Describe the problem or opportunity (the need for your proposal).
Generic Grant Outline Always check with the sponsor for specific proposal guidelines (and follow them closely), but also become familiar with the generic proposal structure to better understand what information
More informationStatistical tests for SPSS
Statistical tests for SPSS Paolo Coletti A.Y. 2010/11 Free University of Bolzano Bozen Premise This book is a very quick, rough and fast description of statistical tests and their usage. It is explicitly
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, 9:30-12:15 Peabody Hall, room 105 Text: LOGIC AND RATIONAL THOUGHT by Frank R. Harrison, III Professor: Frank R. Harrison, III Office:
More informations = 1 + 2 +... + 49 + 50 s = 50 + 49 +... + 2 + 1 2s = 51 + 51 +... + 51 + 51 50 51. 2
1. Use Euler s trick to find the sum 1 + 2 + 3 + 4 + + 49 + 50. s = 1 + 2 +... + 49 + 50 s = 50 + 49 +... + 2 + 1 2s = 51 + 51 +... + 51 + 51 Thus, 2s = 50 51. Therefore, s = 50 51. 2 2. Consider the sequence
More informationCHAPTER 7 GENERAL PROOF SYSTEMS
CHAPTER 7 GENERAL PROOF SYSTEMS 1 Introduction Proof systems are built to prove statements. They can be thought as an inference machine with special statements, called provable statements, or sometimes
More informationDescartes Meditations. ? God exists I exist (as a thinking thing)
Descartes Meditations Descartes Structure of Belief What does he know with absolute certainty?? God exists I exist (as a thinking thing) Why try to prove God exists? Intellectual interest. : Are any of
More informationTopic #6: Hypothesis. Usage
Topic #6: Hypothesis A hypothesis is a suggested explanation of a phenomenon or reasoned proposal suggesting a possible correlation between multiple phenomena. The term derives from the ancient Greek,
More informationBook of over 45 Spells and magic spells that actually work, include love spells, health spells, wealth spells and learning spells and spells for life
Book of over 45 Spells and magic spells that actually work, include love spells, health spells, wealth spells and learning spells and spells for life Stop Chasing Happiness, Make it Find You! Here's how
More informationA Short Course in Logic Example 8
A Short ourse in Logic xample 8 I) Recognizing Arguments III) valuating Arguments II) Analyzing Arguments valuating Arguments with More than one Line of Reasoning valuating If then Premises Independent
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 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 informationLocke s psychological theory of personal identity
Locke s psychological theory of personal identity phil 20208 Jeff Speaks October 3, 2006 1 Identity, diversity, and kinds............................. 1 2 Personal identity...................................
More informationCS104: Data Structures and Object-Oriented Design (Fall 2013) October 24, 2013: Priority Queues Scribes: CS 104 Teaching Team
CS104: Data Structures and Object-Oriented Design (Fall 2013) October 24, 2013: Priority Queues Scribes: CS 104 Teaching Team Lecture Summary In this lecture, we learned about the ADT Priority Queue. A
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 informationScientific Reasoning: A Solution to the Problem of Induction
International Journal of Basic & Applied Sciences IJBAS-IJENS Vol:10 No:03 49 Scientific Reasoning: A Solution to the Problem of Induction Wilayat Khan and Habib Ullah COMSATS Institute of Information
More informationWhat Is Circular Reasoning?
What Is Circular Reasoning? Logical fallacies are a type of error in reasoning, errors which may be recognized and corrected by observant thinkers. There are a large number of informal fallacies that are
More informationECON 459 Game Theory. Lecture Notes Auctions. Luca Anderlini Spring 2015
ECON 459 Game Theory Lecture Notes Auctions Luca Anderlini Spring 2015 These notes have been used before. If you can still spot any errors or have any suggestions for improvement, please let me know. 1
More informationThe Sherlock Cycle. A Theory of Natural Climate Cycles
The Sherlock Cycle Does the Earth have a natural climate cycle of the kind that could account for events like the Medieval Warm Period and the large global temperature increase that has been observed since
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 informationdef: An axiom is a statement that is assumed to be true, or in the case of a mathematical system, is used to specify the system.
Section 1.5 Methods of Proof 1.5.1 1.5 METHODS OF PROOF Some forms of argument ( valid ) never lead from correct statements to an incorrect. Some other forms of argument ( fallacies ) can lead from true
More informationHow to Get Your Prayers Answered By Dr. Roger Sapp
How to Get Your Prayers Answered By Dr. Roger Sapp There are many good Christians who pray daily with diligence and with discipline but seem to struggle to get their prayers answered by the Father. On
More informationSYMBOL AND MEANING IN MATHEMATICS
,,. SYMBOL AND MEANING IN MATHEMATICS ALICE M. DEAN Mathematics and Computer Science Department Skidmore College May 26,1995 There is perhaps no other field of study that uses symbols as plentifully and
More informationScientific Method Worksheet
Scientific Method Worksheet Anyone who has ever read a mystery novel or seen a whodunit on TV, has seen the scientific method in action. Anyone who has ever tried to figure out what happens to the refrigerator
More informationSCIENCE PROJECT & RESEARCH PAPER TIMELINE FOR PARTICIPANTS OUTSIDE THE SCHOOL BODY
Geneva Academy has an invested interest in giving God glory as it teaches and prepares students to experience the joys of scientific discovery unraveling the way God created everything and how it works
More informationCHAPTER II THE LIMIT OF A SEQUENCE OF NUMBERS DEFINITION OF THE NUMBER e.
CHAPTER II THE LIMIT OF A SEQUENCE OF NUMBERS DEFINITION OF THE NUMBER e. This chapter contains the beginnings of the most important, and probably the most subtle, notion in mathematical analysis, i.e.,
More informationWhere is Fundamental Physics Heading? Nathan Seiberg IAS Apr. 30, 2014
Where is Fundamental Physics Heading? Nathan Seiberg IAS Apr. 30, 2014 Disclaimer We do not know what will be discovered. This is the reason we perform experiments. This is the reason scientific research
More informationThe Top 3 Common Mistakes Men Make That Blow All Their Chances of Getting Their Ex-Girlfriend Back Which of these mistakes are you making?
The Top 3 Common Mistakes Men Make That Blow All Their Chances of Getting Their Ex-Girlfriend Back Which of these mistakes are you making? By George Karanastasis, M.D. COPYRIGHT NOTICE THIS ELECTRONIC
More informationPlanning a Class Session
Planning a Class Session A Guide for New Teachers by Diane M. Enerson Kathryn M. Plank R. Neill Johnson The Pennsylvania State University 301 Rider Building II University Park, PA 16802 www.schreyerinstitute.psu.edu
More informationYr11 Philosophy and Ethics Religious Studies B (OCR) GCSE. Science and Religion B602
Name:. Form:. Yr11 Philosophy and Ethics Religious Studies B (OCR) GCSE Science and Religion B602 ACTIVITY: Scientific ideas about the origins of the world and humanity In the frame below there are six
More informationClick on the links below to jump directly to the relevant section
Click on the links below to jump directly to the relevant section What is algebra? Operations with algebraic terms Mathematical properties of real numbers Order of operations What is Algebra? Algebra is
More informationc 2008 Je rey A. Miron We have described the constraints that a consumer faces, i.e., discussed the budget constraint.
Lecture 2b: Utility c 2008 Je rey A. Miron Outline: 1. Introduction 2. Utility: A De nition 3. Monotonic Transformations 4. Cardinal Utility 5. Constructing a Utility Function 6. Examples of Utility Functions
More informationG C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
Performance Assessment Task Circle and Squares Grade 10 This task challenges a student to analyze characteristics of 2 dimensional shapes to develop mathematical arguments about geometric relationships.
More information