Alexander Bird PHILOSOPHY OF SCIENCE Fundamentals of Philosophy Series Editor:John Shand Also available as a printed book see title verso for ISBN details
Fundamentals of Philosophy Series editor:John Shand This series presents an up-to-date set of engrossing,accurate,and lively introductions to all the core areas of philosophy.Each volume is written by an enthusiastic and knowledgeable teacher of the area in question.Care has been taken to produce works that while evenhanded are not mere bland expositions,and as such are original pieces of philosophy in their own right.The reader should not only be well informed by the series, but also experience the intellectual excitement of being engaged in philosophical debate itself.The volumes serve as an essential basis for the undergraduate courses to which they relate,as well as being accessible and absorbing for the general reader.Together they comprise an indispensable library of living philosophy. Published: Piers Benn Ethics Alexander Bird Philosophy of Science Colin Lyas Aesthetics Alexander Miller Philosophy of Language Forthcoming: Stephen Burwood,Paul Gilbert,Kathleen Lennon Philosophy of Mind Richard Francks Modern Philosophy Dudley Knowles Political Philosophy Harry Lesser Ancient Philosophy
Fundamentals of Philosophy Series editor: John Shand This series presents an up-to-date set of engrossing, accurate, and lively introductions to all the core areas of philosophy. Each volume is written by an enthusiastic and knowledgeable teacher of the area in question. Care has been taken to produce works that while evenhanded are not mere bland expositions, and as such are original pieces of philosophy in their own right. The reader should not only be well informed by the series, but also experience the intellectual excitement of being engaged in philosophical debate itself. The volumes serve as an essential basis for the undergraduate courses to which they relate, as well as being accessible and absorbing for the general reader. Together they comprise an indispensable library of living philosophy. Published: Piers Benn Ethics Alexander Bird Philosophy of Science Colin Lyas Aesthetics Alexander Miller Philosophy of Language Forthcoming: Stephen Burwood, Paul Gilbert, Kathleen Lennon Philosophy of Mind Richard Francks Modern Philosophy Dudley Knowles Political Philosophy Harry Lesser Ancient Philosophy
Philosophy of science Alexander Bird University of Edinburgh ROUTLEDG ROUTLEDGE 。 Taylot Francis Group
Philosophy of science Alexander Bird University of Edinburgh
First published 1998 by UCL Press Routledge is an imprint of the Taylor Francis Group This edition published in the Taylor Francis e-Library,2006. "To purchase your own copy of this or any of Taylor Francis or Routledge's collection of thousands of eBooks please go to http://www.ebookstore.tandf.co.uk/." ○1998 Alexander Bird All rights reserved.No part of this book may be reprinted or reproduced or utilised in any form or by any electronic,mechanical,or other mean,now known or hereafter invented,including photocopying and recording,or in any information storage or retrieval system,without permission in writing from the publishers. British Library Cataloguing in Publication Data.A catalogue record for this book is available from the British Library. ISBN 0-203-13397-8 Master e-book ISBN ISBN 0-203-17709-6(Adobe e-Reader Format) ISBN:1-85728-681-2 (Print Edition)HB 1-85728-504-2 (Print Edition)PB
First published 1998 by UCL Press Routledge is an imprint of the Taylor & Francis Group This edition published in the Taylor & Francis e-Library, 2006. “To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to http://www.ebookstore.tandf.co.uk/.” © 1998 Alexander Bird All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other mean, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cataloguing in Publication Data. A catalogue record for this book is available from the British Library. ISBN 0-203-13397-8 Master e-book ISBN ISBN 0-203-17709-6 (Adobe e-Reader Format) ISBN: 1-85728-681-2 (Print Edition) HB 1-85728-504-2 (Print Edition) PB
For Michael Bird
For Michael Bird
Contents Preface Introduction:the nature of science 1 Part I Representation 1 Laws of nature 17 2 Explanation 41 3 Natural kinds 63 4 Realism 80 PartⅡReason 5 Inductive scepticism 109 6 Probability and scientific inference 123 7 Inductive knowledge 141 8 Method and progress 156 Glossary 191 Notes 196 Bibliography 200 Index 204
Contents Preface viii Introduction: the nature of science 1 Part I Representation 1 Laws of nature 17 2 Explanation 41 3 Natural kinds 63 4 Realism 80 Part II Reason 5 Inductive scepticism 109 6 Probability and scientific inference 123 7 Inductive knowledge 141 8 Method and progress 156 Glossary 191 Notes 196 Bibliography 200 Index 204
Preface This book aims to be an introduction to the philosophy of science.While I expect students of philosophy to form the majority of its readers,I hope that it will also find favour among students of science subjects and indeed anyone else who is interested in conceptual questions surrounding the nature of the world and our scientific investigation of it.Conceptions of what the philosophy of science is have changed markedly over the years.For a long time positivist concerns were at the fore,for instance establishing the observational given from which scientific reasoning starts(the problem of the empirical basis),or constructing an inductivist logic or theory of confirmation which would take us from the empirical basis to generalized scientific knowledge.The positivist and related programmes did not succeed.There ensued a reaction in which this failure was taken to demonstrate the hopelessness of any objective conception of scientific knowledge and progress.Instead the appropriate task for philosophers of science was to provide support for more historical and indeed sociological approaches to science.This road was fruitful in many ways.But,especially by associating itself with relativism about knowledge and progress,it divorced itself from work being done in the mainstream of philosophy, especially in metaphysics and epistemology. My impression is that the philosophy of science is swinging back the other way.But not to where it began.Philosophers of science are now much more historically sensitive. They are not likely to put inductive logics or the problem of the empirical basis at the centre of their concerns.Nonetheless,their interests have moved closer to those of philosophers in other fields.This book is intended both to contribute to as well as to describe that shift.Thus the first part of the book is primarily metaphysical,seeking to give a philosophical account of the most general sorts of thing scientists aim to represent-laws of nature,explanations,natural kinds.The second half moves into epistemological territory and sets out to show how an externalist,moderately naturalized epistemology can show how scientific knowledge is possible.This leads to a view about the scientific method (that there is no such unique thing)and progress(it is possible)into which I weave a discussion of the historical approach. The ideas of many philosophers,colleagues,and friends have gone into making this book possible.The suggestions for further reading,the notes,and the bibliography give some partial but incomplete indication of my debt to other philosophers working in this area.What I owe to friends and acquaintances with whom I have exchanged thoughts is even less well indicated.Nonetheless,I would like to thank in particular those who have read parts of earlier drafts and thereby enabled me to complete this work:Helen Beebee, Rebecca Bryant,Timothy Chan,Penn Dodson,Richard Foggo,Will Hubbard,Scott Jacobs,Mary MacLeod,Hugh Mellor,Lucasta Miller,Peter Milne,Jim Moor,John Pellettieri,John Shand,Walter Sinnott-Armstrong,Lucy Wayman,Denis Walsh, Timothy Williamson,and Ben Young
Preface This book aims to be an introduction to the philosophy of science. While I expect students of philosophy to form the majority of its readers, I hope that it will also find favour among students of science subjects and indeed anyone else who is interested in conceptual questions surrounding the nature of the world and our scientific investigation of it. Conceptions of what the philosophy of science is have changed markedly over the years. For a long time positivist concerns were at the fore, for instance establishing the observational given from which scientific reasoning starts (the problem of the empirical basis), or constructing an inductivist logic or theory of confirmation which would take us from the empirical basis to generalized scientific knowledge. The positivist and related programmes did not succeed. There ensued a reaction in which this failure was taken to demonstrate the hopelessness of any objective conception of scientific knowledge and progress. Instead the appropriate task for philosophers of science was to provide support for more historical and indeed sociological approaches to science. This road was fruitful in many ways. But, especially by associating itself with relativism about knowledge and progress, it divorced itself from work being done in the mainstream of philosophy, especially in metaphysics and epistemology. My impression is that the philosophy of science is swinging back the other way. But not to where it began. Philosophers of science are now much more historically sensitive. They are not likely to put inductive logics or the problem of the empirical basis at the centre of their concerns. Nonetheless, their interests have moved closer to those of philosophers in other fields. This book is intended both to contribute to as well as to describe that shift. Thus the first part of the book is primarily metaphysical, seeking to give a philosophical account of the most general sorts of thing scientists aim to represent—laws of nature, explanations, natural kinds. The second half moves into epistemological territory and sets out to show how an externalist, moderately naturalized epistemology can show how scientific knowledge is possible. This leads to a view about the scientific method (that there is no such unique thing) and progress (it is possible) into which I weave a discussion of the historical approach. The ideas of many philosophers, colleagues, and friends have gone into making this book possible. The suggestions for further reading, the notes, and the bibliography give some partial but incomplete indication of my debt to other philosophers working in this area. What I owe to friends and acquaintances with whom I have exchanged thoughts is even less well indicated. Nonetheless, I would like to thank in particular those who have read parts of earlier drafts and thereby enabled me to complete this work: Helen Beebee, Rebecca Bryant, Timothy Chan, Penn Dodson, Richard Foggo, Will Hubbard, Scott Jacobs, Mary MacLeod, Hugh Mellor, Lucasta Miller, Peter Milne, Jim Moor, John Pellettieri, John Shand, Walter Sinnott-Armstrong, Lucy Wayman, Denis Walsh, Timothy Williamson, and Ben Young
Introduction The nature of science Our starting point is the question What is science?In the first part of this chapter we will see what an American judge had to say when the question came before his court.He had to rule on whether what is called "creation science"really is science.This is useful,first because it shows that the question is a live and important one,and secondly because the answer is revealing.Although the judge did not give a complete and systematic answer (as a philosopher may have attempted to do),he did identify several of the key issues. These are the subject matter for much of the rest of this book.The judge was interested in questions like What is science about?and What is a scientific theory?He did not, however,ask How do we know when a theory is true?,mainly because he was not concerned with the truth of creation science,but with whether creationism is science or not.For a theory can be false yet still be scientific (e.g.Priestley's phlogiston theory of combustion),and a claim can be true without being scientific (e.g.the claim that Brazil won the 1994 World Cup).Nonetheless,the nature of scientific knowledge is clearly important and this chapter ends with two puzzles concerning it. What is science? First,the background.In recent years an interesting phenomenon has appeared in American political,religious,and educational circles.For instance,in 1995 and 1996 new laws were proposed in the legislatures of five American states that required schools to give equal attention to evolution and to creation science in state school science classes. Creation science originates with a literal reading of the Bible,in particular the book of Genesis.It claims,however,not to be religious in content;rather,it says,the relevant propositions,for instance that the universe,the solar system,and life were suddenly created,that currently living animals and plants have existed since creation,that this creation was relatively recent (i.e.some thousands of years ago),that man and apes have a separate ancestry,and that the geological features of the Earth are to be explained by large-scale sudden catastrophes (e.g.a flood)are all scientific hypotheses for which there is strong scientific evidence. Why was the Genesis story turned into science in this way?For centuries scientists have regarded the universe and its laws as the manifestations of the will and nature of its Creator.And it is natural enough to seek in it signs of those events that the Bible records as His work.More recently,however,creation science has gained a political purpose.The constitution of the USA provides for the separation of church and state,and for this reason religious doctrine may not be taught in state schools.Nonetheless,for many years some states have prohibited the teaching of those scientific theories that would be antithetical to the prevailing fundamentalist version of Christianity.It is for this reason that the famous "monkey"trial of John Scopes took place,in Dayton,Tennessee,in 1925. Scopes was accused,and found guilty,of violating a Tennessee law forbidding the teaching of evolution.Such laws no longer exist.(It may have been the fear of
Introduction The nature of science Our starting point is the question What is science? In the first part of this chapter we will see what an American judge had to say when the question came before his court. He had to rule on whether what is called “creation science” really is science. This is useful, first because it shows that the question is a live and important one, and secondly because the answer is revealing. Although the judge did not give a complete and systematic answer (as a philosopher may have attempted to do), he did identify several of the key issues. These are the subject matter for much of the rest of this book. The judge was interested in questions like What is science about? and What is a scientific theory? He did not, however, ask How do we know when a theory is true?, mainly because he was not concerned with the truth of creation science, but with whether creationism is science or not. For a theory can be false yet still be scientific (e.g. Priestley’s phlogiston theory of combustion), and a claim can be true without being scientific (e.g. the claim that Brazil won the 1994 World Cup). Nonetheless, the nature of scientific knowledge is clearly important and this chapter ends with two puzzles concerning it. What is science? First, the background. In recent years an interesting phenomenon has appeared in American political, religious, and educational circles. For instance, in 1995 and 1996 new laws were proposed in the legislatures of five American states that required schools to give equal attention to evolution and to creation science in state school science classes. Creation science originates with a literal reading of the Bible, in particular the book of Genesis. It claims, however, not to be religious in content; rather, it says, the relevant propositions, for instance that the universe, the solar system, and life were suddenly created, that currently living animals and plants have existed since creation, that this creation was relatively recent (i.e. some thousands of years ago), that man and apes have a separate ancestry, and that the geological features of the Earth are to be explained by large-scale sudden catastrophes (e.g. a flood) are all scientific hypotheses for which there is strong scientific evidence.1 Why was the Genesis story turned into science in this way? For centuries scientists have regarded the universe and its laws as the manifestations of the will and nature of its Creator. And it is natural enough to seek in it signs of those events that the Bible records as His work. More recently, however, creation science has gained a political purpose. The constitution of the USA provides for the separation of church and state, and for this reason religious doctrine may not be taught in state schools. Nonetheless, for many years some states have prohibited the teaching of those scientific theories that would be antithetical to the prevailing fundamentalist version of Christianity. It is for this reason that the famous “monkey” trial of John Scopes took place, in Dayton, Tennessee, in 1925. Scopes was accused, and found guilty, of violating a Tennessee law forbidding the teaching of evolution. Such laws no longer exist. (It may have been the fear of
Philosophy of science 2 communism that brought the teaching of evolution to those schools where it had been ignored.The launch of Sputnik in 1957,the first artificial satellite,raised the spectre of the USSR stealing a march on the USA in science and technology,and thereby led to a revival in science education,although Tennessee's Butler Act forbidding the teaching of evolution remained on the statute books until 1967.) Since the end of the Cold War,Christian fundamentalists,allied with elements of the political right wing (a coalition known as the Religious Right),have sought to regain their position in American education.But the educational and political climate has changed so much that there could be no return to an outright ban on evolutionist teaching. The next best thing for the Religious Right would be the introduction,on equal terms,of the creationist alternative into the syllabus.Even so,as creationism is a religious doctrine, teaching it in state schools would clearly violate the First Amendment of the Constitution regarding separation of church and state.So,in order to get creationism introduced into schools,and,better,into the same classes in which evolution is taught,supporters of creationism have sought to pass it off as a purely scientific doctrine devoid of religious content.In their words "the creation model is at least as scientific as the evolution model. and is at least as nonreligious as the evolution model."2 Indeed,the state of Arkansas passed a law that required equal treatment of evolution and creationism.Scientists and churchmen immediately challenged the constitutionality of the new law in the courts.They argued that,despite the rhetoric and the appearance of scientific respectability,creation science simply is not science but religion dressed up as science.What is at issue is not science versus religion (many religious people reject creationism),or the question of whether creationism is true or even reasonable.The debate focuses on the claims of creation science to be scientific.So the court had to ask: what is science?When is a claim scientific?How do we distinguish science from non- science or pseudo-science?These are all philosophical questions,and the court had the benefit of the testimony of philosophers as well as scientists in its deliberations.The opinion of the judge.William R.Overton,is interesting in this respect,because he summed up the criteria he used in deciding whether creationism is scientific.3 He said that a scientific theory has the following features: (a)It is guided by natural law. (b)It has to be explanatory by reference to natural law. (c)It is testable against the empirical world. (d)Its conclusions are tentative,i.e.are not necessarily the final word. (e)It is falsifiable What did Overton mean by these criteria?The creationist claims about the origins of the world,in order to be science rather than mere assertion,must be claims (a)about what the laws of nature are,or (b)about facts which themselves have explanations in terms of natural law.(I will tend to use the term "law of nature"for what Overton calls "natural law").What are laws of nature?This is a question for the next chapter,but roughly speaking they are the very general relations among things that explain their behaviour- the sort of things that we call the laws of physics,chemistry,and so on.Newton's laws of motion,Ohm's law of resistance,Hooke's law of elasticity,and So on are things we think or have thought are laws,(c)The claims must be made in such a way as to be testable,i.e. be sufficiently detailed as to have observable consequences or testable predictions that
communism that brought the teaching of evolution to those schools where it had been ignored. The launch of Sputnik in 1957, the first artificial satellite, raised the spectre of the USSR stealing a march on the USA in science and technology, and thereby led to a revival in science education, although Tennessee’s Butler Act forbidding the teaching of evolution remained on the statute books until 1967.) Since the end of the Cold War, Christian fundamentalists, allied with elements of the political right wing (a coalition known as the Religious Right), have sought to regain their position in American education. But the educational and political climate has changed so much that there could be no return to an outright ban on evolutionist teaching. The next best thing for the Religious Right would be the introduction, on equal terms, of the creationist alternative into the syllabus. Even so, as creationism is a religious doctrine, teaching it in state schools would clearly violate the First Amendment of the Constitution regarding separation of church and state. So, in order to get creationism introduced into schools, and, better, into the same classes in which evolution is taught, supporters of creationism have sought to pass it off as a purely scientific doctrine devoid of religious content. In their words “the creation model is at least as scientific as the evolution model, and is at least as nonreligious as the evolution model.”2 Indeed, the state of Arkansas passed a law that required equal treatment of evolution and creationism. Scientists and churchmen immediately challenged the constitutionality of the new law in the courts. They argued that, despite the rhetoric and the appearance of scientific respectability, creation science simply is not science but religion dressed up as science. What is at issue is not science versus religion (many religious people reject creationism), or the question of whether creationism is true or even reasonable. The debate focuses on the claims of creation science to be scientific. So the court had to ask: what is science? When is a claim scientific? How do we distinguish science from nonscience or pseudo-science? These are all philosophical questions, and the court had the benefit of the testimony of philosophers as well as scientists in its deliberations. The opinion of the judge, William R.Overton, is interesting in this respect, because he summed up the criteria he used in deciding whether creationism is scientific.3 He said that a scientific theory has the following features: (a) It is guided by natural law. (b) It has to be explanatory by reference to natural law. (c) It is testable against the empirical world. (d) Its conclusions are tentative, i.e. are not necessarily the final word. (e) It is falsifiable. What did Overton mean by these criteria? The creationist claims about the origins of the world, in order to be science rather than mere assertion, must be claims (a) about what the laws of nature are, or (b) about facts which themselves have explanations in terms of natural law. (I will tend to use the term “law of nature” for what Overton calls “natural law”). What are laws of nature? This is a question for the next chapter, but roughly speaking they are the very general relations among things that explain their behaviour— the sort of things that we call the laws of physics, chemistry, and so on. Newton’s laws of motion, Ohm’s law of resistance, Hooke’s law of elasticity, and So on are things we think or have thought are laws, (c) The claims must be made in such a way as to be testable, i.e. be sufficiently detailed as to have observable consequences or testable predictions that Philosophy of science 2
Introduction:the nature of science 3 can be verified,(e)In particular,if these testable claims are found to be refuted by experience,then this should count as powerful evidence against the theory,which may amount to showing the theory to be false.Our belief in the theory should be proportional to the strength of the evidence in its favour (which means considering it in relation to its rivals),(d)Even if the evidence is very favourable,experience shows that sophisticated well-confirmed theories can be overturned by falsifying evidence found later or challenged by new competing theories that themselves are supported by the evidence in the way that the original theory is not.A scientific attitude requires being open to this possibility. Let us look at some examples.The creationist says that the Earth's geological features are explained in terms of catastrophic events,primarily a large-scale flood.By contrast, standard geology explains them in terms of forces that work over extended periods of time-erosion,glaciation,plate tectonics.The latter can all be understood as phenomena that obey the laws of physics.For instance,tidal motion is a result of the Moon's gravitational pull,and so is a manifestation of the law of gravity.Even if a massive flood could explain the Earth's geology,why did the flood occur in the first place?While disastrous floods do still happen today,they are restricted in scope and can to some extent be explained by reference to local weather conditions such as hurricanes.But a global flood is a different matter.What sort of weather conditions could bring about such a calamity?If the whole Earth was covered in water,where did it all come from?And where did it go to thereafter?No laws or law-governed phenomena are invoked-or could be-to answer such questions.The reason why is clear.A flood,Noah's,is referred to in the book of Genesis.This flood was the work of divine intervention.While God's actions may indeed be the correct explanation of an event,such an explanation fails to be scientific by Judge Overton's criteria.God's will is not subject to natural law.And for precisely that reason this hypothesis is not testable either.God does not submit to experimentation. Of course all explanations end somewhere,even orthodox ones.The difference here is that the orthodox scientist seeks to extend the chain of explanations as far as possible and is limited only by ignorance,while the creationist is happy to terminate the chain of explanations much earlier,in accordance with biblical constraints,and at that point to use supernatural explanations. Another reason creationists have for adopting catastrophism is that they are committed to a young Earth-six to ten thousand years old-too young for the long-term effects of traditional geological processes.The nineteenth century physicist Lord Kelvin (whose name was given to the scale of temperature)made careful calculations concerning the rate of cooling of the Earth and Sun.These suggest that the solar system could not have been around long enough for life to have evolved.His arguments are still quoted by creationists.Kelvin's calculations were quite right-if one assumes no heat source in the Earth and that the Sun's energy comes from combustion.In both cases there are energy sources he ignored,viz.nuclear processes,fusion in the Sun,and radioactive decay in the Earth.Lord Kelvin can be forgiven for not knowing about something discovered only after he made his calculations;a contemporary writer cannot.Again the best explanation of the creationists'stance is not the evidence and arguments that they present,but a prior commitment to biblical historiography (from which the date of Adam's creation and so the creation of everything can be calculated)
can be verified, (e) In particular, if these testable claims are found to be refuted by experience, then this should count as powerful evidence against the theory, which may amount to showing the theory to be false. Our belief in the theory should be proportional to the strength of the evidence in its favour (which means considering it in relation to its rivals), (d) Even if the evidence is very favourable, experience shows that sophisticated well-confirmed theories can be overturned by falsifying evidence found later or challenged by new competing theories that themselves are supported by the evidence in the way that the original theory is not. A scientific attitude requires being open to this possibility. Let us look at some examples. The creationist says that the Earth’s geological features are explained in terms of catastrophic events, primarily a large-scale flood. By contrast, standard geology explains them in terms of forces that work over extended periods of time—erosion, glaciation, plate tectonics. The latter can all be understood as phenomena that obey the laws of physics. For instance, tidal motion is a result of the Moon’s gravitational pull, and so is a manifestation of the law of gravity. Even if a massive flood could explain the Earth’s geology, why did the flood occur in the first place? While disastrous floods do still happen today, they are restricted in scope and can to some extent be explained by reference to local weather conditions such as hurricanes. But a global flood is a different matter. What sort of weather conditions could bring about such a calamity? If the whole Earth was covered in water, where did it all come from? And where did it go to thereafter? No laws or law-governed phenomena are invoked—or could be—to answer such questions. The reason why is clear. A flood, Noah’s, is referred to in the book of Genesis. This flood was the work of divine intervention. While God’s actions may indeed be the correct explanation of an event, such an explanation fails to be scientific by Judge Overton’s criteria. God’s will is not subject to natural law. And for precisely that reason this hypothesis is not testable either. God does not submit to experimentation. Of course all explanations end somewhere, even orthodox ones. The difference here is that the orthodox scientist seeks to extend the chain of explanations as far as possible and is limited only by ignorance, while the creationist is happy to terminate the chain of explanations much earlier, in accordance with biblical constraints, and at that point to use supernatural explanations. Another reason creationists have for adopting catastrophism is that they are committed to a young Earth—six to ten thousand years old—too young for the long-term effects of traditional geological processes. The nineteenth century physicist Lord Kelvin (whose name was given to the scale of temperature) made careful calculations concerning the rate of cooling of the Earth and Sun. These suggest that the solar system could not have been around long enough for life to have evolved. His arguments are still quoted by creationists. Kelvin’s calculations were quite right—if one assumes no heat source in the Earth and that the Sun’s energy comes from combustion. In both cases there are energy sources he ignored, viz. nuclear processes, fusion in the Sun, and radioactive decay in the Earth. Lord Kelvin can be forgiven for not knowing about something discovered only after he made his calculations; a contemporary writer cannot. Again the best explanation of the creationists’ stance is not the evidence and arguments that they present, but a prior commitment to biblical historiography (from which the date of Adam’s creation and so the creation of everything can be calculated). Introduction: the nature of science 3