Science and Mathematics Education Centre Students’ Understanding of Evidence in Science through Studying Paradoxes and the Principle of Falsification Steven C. Lockwood This thesis is presented as part of the requirement of the award of the Degree of Doctor of Philosophy of the Curtin University of Technology February 2014 Declaration This thesis does not contain material accepted, in any university, for the award of any other degree or diploma. To the best of my knowledge and belief this thesis contains no material previously published by any other person except where due acknowledgement has been made. Signature: Date: 2 Acknowledgements To my wife Sue, and my children, Morgan, Darcy and Alec, (born during the long and protracted process of thesis generation and writing) I owe a debt of gratitude not least for their preparedness to excuse my absences from fatherly duties but also for their acceptance of my often irritating logical semantics, one of the side-effects of the study of paradox. A particular ‘thank you’ goes to Dr Bevis Yaxley (dec.) and Dr Roya Pugh whose contributions to my well-being during times of challenge, not the least of which occurred when my wife Sue died from breast cancer, afforded me the courage to persist where I may have resolved to give up. To my students, past and present, without whom I would not have written this thesis, particularly those students described admirably by the writer Jorge Luis Borges in his book Labyrinths which I paraphrase. …although I could expect nothing from those students who passively accepted my doctrines, I could of those who, at times, would venture a reasonable contradiction. (Borges, 1964) To my fellow doctoral and masters students, the members of the aPIERon Academy, I thank you for your comradeship and engaging conversations. 3 Contents Declaration .......................................................................................................... 2 Acknowledgements ............................................................................................. 3 Abstract ............................................................................................................. 10 Chapter 1 – Theseus’ Journey ........................................................................... 12 The Story of Theseus .................................................................................... 12 The Theseus Metaphor .................................................................................. 13 The Paradox Hypothesis ............................................................................... 14 The Role of Formal Logic ............................................................................. 16 Emerging Questions ...................................................................................... 17 The Synthesis of an Idea ............................................................................... 18 My Teaching Environment ........................................................................... 20 Chapter 2 – Stark Raven Mad ........................................................................... 22 The Paradox of the Ravens ........................................................................... 22 Argument Forms ........................................................................................... 25 Resolving Paradoxes ..................................................................................... 26 Thought Experiments .................................................................................... 26 Solving Hempel’s Ravens ............................................................................. 28 My Early Arguments in Science ................................................................... 30 4 Hempel’s Ravens Place in the Science Classroom ....................................... 32 Chapter 3 – The Story of Erasto Mpemba – a case study ................................. 38 Finding Erasto ............................................................................................... 38 Paradox Resolution Strategies and the Mpemba Effect ................................ 41 Truthfulness .................................................................................................. 47 Chapter 4 – The Essence of Paradox................................................................. 50 Synonyms ...................................................................................................... 50 Lexical Definitions ........................................................................................ 52 Paradox and Common Sense ......................................................................... 57 Paradox and Literature .................................................................................. 67 Paradox and Induction................................................................................... 70 Paradox and Cognitive Conflict .................................................................... 76 My Stipulated Definition of Paradox ............................................................ 78 Conclusion .................................................................................................... 78 Chapter 5 – The Barber Paradox ....................................................................... 80 Russell’s Set Paradox .................................................................................... 80 The Principle of Comprehension .................................................................. 84 The Barber Paradox....................................................................................... 85 Phlogiston Theory Part 1 ............................................................................... 91 Paradox and Truth ......................................................................................... 94 More Thought Experiments .......................................................................... 96 5 The Tasmanian Tiger .................................................................................... 97 Chapter 6 – The Money Spider Hypothesis – a case study ............................. 100 The Gullibility Gene ................................................................................... 100 The Money Spider ....................................................................................... 101 Theory Confirmation ................................................................................... 102 Irrational Belief ........................................................................................... 104 Chapter 7 – Diabolical Internal Dialogues – my fictionalised story ............... 109 The Frailty of Inductive Logic .................................................................... 113 A Paradox of Confirmation ......................................................................... 116 The Ship of Theseus .................................................................................... 121 A Paradox of Self-Deception ...................................................................... 124 Reductio Arguments.................................................................................... 128 The Climax .................................................................................................. 133 Chapter 8 – Perception, Authority and Truth .................................................. 136 Perception .................................................................................................... 136 Student Misconceptions .............................................................................. 138 The Validity of Evidence ............................................................................ 142 Tectonic Theory – a case study ................................................................... 144 The Role of Authority and the Nature of Science ....................................... 149 Truth ............................................................................................................ 151 The Truthfulness of Science........................................................................ 153 6 The Moon Hoax .......................................................................................... 154 Falsificationism ........................................................................................... 155 The Role of Causal Mechanisms ................................................................ 156 Interviews with Students – the nature of evidence...................................... 159 Chapter 9 – The Left-handed Frog .................................................................. 186 Schrödinger’s Cat – a thought experiment .................................................. 187 Paradoxes of Nature .................................................................................... 187 The Fallibility of Confirmation ................................................................... 189 My Philosophical and Logical Tensions ..................................................... 193 The Paradox of the Ramp – a case study .................................................... 195 A Picture of the Universe – a case study of memic transfer ....................... 198 Phlogiston Theory Part 2 (see Part 1 in chapter 5)...................................... 199 The Lure of Certainty .................................................................................. 203 Capturing the novel relevant language .......................................................