Philosophy of science made simple - or am I too simple!

I initially came up with the idea of writing this particular essay after I wrote my critical essay on the topic of rt-PA for acute stroke ("Brain attacks" - just do the right thing!) - because I personally felt that too many aspects of the NINDS study-saga were not reflective of "good" science. What do we mean when we use the term "good" science (in contrast to "bad" science)? Before we can answer that important question, we first have to understand how science actually works and we also have to understand how scientific beliefs are actually established and verified!

So, let's start at the very beginning! How do we actually define a scientific belief and how does it differ from a metaphysical (religious) belief? Most educated people could easily answer that question - it is our ability to subject a personal belief to scientific testing (experimentation) that distinguishes a scientific belief from a metaphysical (religious) belief. The simple element of 'testability' is obviously the most crucial distinguishing element and any scientific belief has to be testable. If we cannot test the belief, then it cannot be regarded as scientific. But how does a person think scientifically and how do scientific beliefs actually arise?

I have found that many people presume that scientific beliefs are established when a person (scientist) makes theoretical generalisations following a series of observations (or experiments), and they believe that fundamental laws of nature are discovered (or uncovered) when a series of observations follow a predictable (and repeatable) pattern. They feel that the laws of nature are fixed and immutable and that the laws of nature acquire an "absolute" scientific quality once they have been determined to be scientifically true. This process of making observations and then generalising the results of the observations to create a theory, and then testing the theory by making more observations, is the inductivist principle of science. Consider a good example of this type of inductive thinking -  picture a scene where a person is obliged to explain to a child why an apple, that falls from the tree, always strikes the ground. The person, who is obliged to explain that event to a child, would probably explain that simple event as being a natural phenomenon that is due to the 'law of gravity', and he would probably tell the child that the 'law of gravity' is a theoretical scientific generalisation that was elucidated by a very wise person (Newton) following a series of careful observations.

That simple explanation of how science works could give a child the distinct impression that scientific theories are derived from the careful observation of nature (or through the conduct of experiments involving the physical world). The child would presume that the following sequence-of-events occurs:- a person performs an experiment or makes a series of observations => he observes the results =>  he comes to certain conclusions based on the preponderance of the observational evidence => he then establishes a 'scientific truth' if his theoretical conclusion can consistently and accuratedly predict the same sequence-of-events in the future. Consider a simple example of that sequence-of-events by noting what happens when a person tries to determine at what absolute temperature water boils. The experimenter would start his experiment by placing a thermometer in a pot of water => he would then heat the water => he would then determine the temperature at which the water started to boil => he would record the results => he would then come to the conclusion that it must be a scientific law of nature "that water boils at an absolute temperature of 100 degrees celsius" if he determined that water always started to boil at a temperature of 100 degrees celcius whenever the experiment was repeated. In other words, it would seem to an observing child that the validity of that particular law of nature was ascertained from the consistent repeatability (and consistent predictability) of the experiment. The child would seemingly have been taught a fundamental lesson about how science really works. But is that how science really works?

Consider the essential elements of the scientific statement:- "water boils at 100 degrees celcius." Notice that the scientific statement has two elements - it has an informational (factual) element and it has an element of testability. All scientific statements have to have those two elements to be regarded as scientifically valid. By definition, a scientific statement has to be testable. Why? If a statement is not testable it would be regarded as a metaphysical statement (rather than a scientific statement) - and the accuracy of a non-testable statement requires an 'act of faith' (and not scientific testing). It is not possible to convince another person of the accuracy of a non-scientific (metaphysical) statement if the person does not have 'faith' in the accuracy of the statement. By contrast, scientific statements seem to acquire their 'convincing-power' because of the element of testability. People tend to believe that a scientific statement is true if it is consistently and repeatedly true on repeated testing. It almost seems intuitively natural that this is how science really works! How would you convince an obdurate child, who refused to believe that water boils at 100 degrees celsius, of the scientific validity of that fact. The most likely response would be to subject the child to repeated observations of the same experiment with the hope that the consistent (and repeated) confirmation of the same results would eventually convince even the most stubborn child of this "true" scientific fact. This belief that scientific facts become more "true" if the same fact is repeatedly and consistently confirmed is a commonly held belief and it forms the fundamental framework that underpins many an individual's concept of scientific validity. But do scientific facts become more "true" if they are repeatedly confirmed?

Take for instance, the statement:- "all swans are white". Is that statement a scientific statement and is that statement scientifically true? It is obviously a scientific statement because it has the two essential elements required of a scientific statement - it has an informational content and it can be experimentally tested. How would you test the statement? Obviously - by frequently observing swans. How many white swans would you need to see before you were convinced that "all swans are white"? 100? 1,000? 100,000?  In other words, if you really believe that a scientific statement becomes "true" if it is consistently repeatable - how many repeated events are required to confirm a scientific truth as being scientifically justified? Hmm! Now, this is where things get slightly more complex!

The entire inductivist scheme of explaining how science works is based on this inductivist justification. However, you don't have to be 'rocket scientist' to see that there is no real endpoint (solution) to this way of thinking! There is no perfect way to ensure that two scientists can agree on how many consistent predictions are necessary before they mutually accept that some scientific fact is really "true". Another problem with inductivist thinking is that a theory (that merely makes generalised predictions) is not really an useful scientific theory if it does not exist within an explanatory framework. What do I mean by explanatory framework? Let's go back to the very basic foundations of the scientific process! Why do we perform scientific experiments in the first place? We usually perform scientific experiments to solve problems. In other words, we need an explanation (theory) to help us start the problem-solving process - the explanation forms the basis of the theoretical hypothesis that is to be tested through observation (experimentation). This is a critical point - it is very important to understand that explanations (and not observations) form the basic framework of science and that science is really a problem-solving game - a game where explanations are subjected to critical analysis (experimental testing) to determine whether they win-or-lose the game!

Let me explain (in another way) why inductivist thinking and explanatory thinking are incompatible. Consider Bertrand Russell's story about the farmer and the farmyard chicken. Each day, the farmer scatters feed in front of the chicken. What does the chicken conclude from the farmer's behaviour? Using inductivist thinking, the chicken concludes from the repeated and consistent daily feeding that "the farmer is a benevolent, animal-loving creature that is going to feed him everlastingly". Then one day, the farmer wrings the chicken's neck and puts him in a pot and cooks him for dinner! The chicken's explanation (theory or hypothesis) of the farmer's behaviour was obviously flawed. The farmer was really feeding the chicken in order to fatten him up for a future dinner. In other words, there were at least two diametrically opposite explanations (theories) that could explain the farmer's behaviour. Both theories were extrapolated from the same observational evidence and it was not initially possible to determine which theory was the accurate theory based on the same observational evidence. How can one then scientifically determine, from constantly observing the farmer's pattern of behaviour, which of the two theories is correct? Is the farmer a benevolent, animal-loving creature that just likes to feed chickens, or is the farmer feeding the chicken for an alternative reason - to fatten him up for dinner? How does science determine (or predict) from repeated observations of the farmer's behaviour which final explanation is really true?

Science determines which one of the two competing explanations (theories) is "true" via the process of scientific testing, but it is important to realise that scientific testing is merely a process, and that science only solves the problem when observational data (scientific testing) shows that one of the competing theories is false. The farmyard chicken's theory about the benevolent farmer was eventually shown to be false when his neck was wrung and he ended up in a dinner pot! Up to that point in time, the chicken's theory that the farmer was feeding him for purely benevolent reasons could have been true - it only became false when his neck was wrung. This story shows that even 'bad' explanations can be true (compatible with the observational data) for awhile, and that it may take further (or different) observational data to show that a particular explanation is false. The story also demonstrates that science actually works best when it falsifies theories (explanations) - rather than when it confirms theories. The conclusion that science really works best when it falsifies explanations may seem to be counterintuitive - so I will expand my argument about this point. How should a clever scientist prove his pet theory that "all swans  are white"? The scientist could spend the rest of his life seeking white swans, but he would be no more sure of the "truth" of his theory after he found 1,000,000 white swans than after he found 100,000 white swans. He could still not be absolutely certain that there was not one swan out-there that was not white. What the clever scientist should do to expedite his experiment is try to disprove his hypothesis! This may seem crazy at first glance - why should a scientist try to disprove his own pet theory? Think about it - if the scientist found just one black swan, then that single finding would falsify his hypothesis that "all swans are white". That would allow the scientist to get on with his life and work on a new problem. The late Karl Popper was the first philosopher of science to come up with the idea that science works best by first starting with a hypothesis and then devising experiments to falsify (rather than confirm) the hypothesis. He called this scientific principle the falsification principle. He also stated that science progresses by a series of conjectures and refutations, which is an elegant way of expressing the same principle.

It may seem strange to think of a scientist deliberately doing experiments to falsify his own hypothesis. However, let me explain why scientific progress is enhanced when a scientist's thought-processes are dominated by 'falsification principle' thinking (rather than being clouded by inductivist thinking). Consider the scientific hypothesis that "water boils at 100 degrees celcius". How should a dedicated scientist prove that his scientific hypothesis is "true"? As I have explained previously, the scientist could boil water a 1,000,000x and he would still be no more certain that his theory was really "true" than after he had performed the boiling water experiment 1,000x. The dedicated scientist could test his theory more efficiently if he took the opposite approach and deliberatedly tried to falsify his theory -  by specifically altering the experimental methodology! In fact, the scientist could quickly falsify his theory by a simple maneuver - he could perform his experiment on top of a high mountain, and he would soon discover that water does not always boil at 100 degrees celcius. What advantage is gained by the scientist falsifying his own theory? The answer:- it actually allows the scientist to develop a better theory eg. the theory "that water boils at 100 degrees celcius at sea level". Why is that new theory better than the original theory? The answer:- the amended theory is better than the original theory because its informative content has been expanded and refined, and also because it is more difficult to falsify the amended theory!  In other words, the scientific statement has been made more encompassing, more precise and less falsifiable! But is the amended theory now "true" and how many modifications will be required to make it "true"? This is where things get really interesting!

It is important to realise that scientific theories are really only explanations that are designed to solve particular problems, and that science is not really trying to determine the absolute "truth". In fact, science can never determine the absolute "truth" - because the possibility always exists that somebody will dream up a newer theory that has even more informative content than the current "best" theory and that is even less falsifiable than the current "best" theory. That is precisely how science advances. Einstein's theory of relativity has supplanted Newton's theory of gravity because it was as predictively accurate (as unfalsifiable) as Newton's theory, but its informative content was greater (it could explain much more and solve more problems). A scientific theory is obviously more useful when it has better problem-solving power!

How do scientific theories actually get started? The process may start by some serendipitious event - a theory that is not based on any previous versions of a similar theory (eg. the theory that peptic ulcer disease is due to a bacterial infection), or it could simply be an improvement of a previously inadequate theory (eg. the slow, but progressive, evolution of the old prevailing theory of what actually caused heart attacks). The important point to remember is that science first starts with a problem, and that the existing theories are the scientific world's 'presently-best' theories of how to optimally solve that particular problem (eg. the problem of developing an effective therapy for acute ischemic stroke). The problem-solving process can be described as follows:-  Problem => conjectured solutions => criticism (specifically including experimental tests) => replacement of erroneous theories => new problem. Note that the scientific process always starts with a conjectured solution to an existing problem (a new theory, or a modification of an older or a defunct theory). Note that the second part of the process is a critical examination of the coherence (sensibility) of the prevailing theories to determine which theories offers the best explanations (explanations that are likely to be widely encompassing, precisely defined and least likely to be falsified). The best theories are then subjected to intellectual analysis and experimental testing, and any conjectured theory that is likely to be falsified (or which is experimentally falsified, or which cannot be accuratedly tested) should be abandoned. The 'new best' theory then replaces the 'previous best' theory. Note that the process does not end with a conclusion (the "truth"). The process actually ends with a 'new' problem - because no explanation can even begin to predict the content or quality of its own future rivals. Any successfull theory merely spawns new opportunities for other scientists to refine the theory and expand its problem-solving power! In other words, all scientific endeavour is an endless continuum of trying to develop better-and-better explanations. That is what science is all about - developing better explanations to solve more-and-more problems!

Key points about the scientific testing of explanatory theories (that you always need to keep in mind) include:-

It is very important that you always keep those points clearly in mind if you want to be able to critically evaluate the quality of "good" science.

Before I continue with a discussion of what constitutes "good" scientific practice, I would like you to read the following essay by David Deutsch. The essay is called "A conversation about justification". The essay goes over the same ground that I have just covered, but David Deutsch does it much more eloquently and more elegantly.

The essay is not really an essay - it is the entire chapter 7 from David Deutsch's book "The Fabric of Reality". In that book David Deutsch attempts to offer a new understanding of reality. I personally don't think that he succeeds in his endeavour - and therefore I wouldn't recommend that you read his book - but chapter 7 is a masterfully executed "conversation about scientific justification" and you can learn much more from his artfully-created conversation between a Crypto-inductivist and David (a Popperian philosopher) than you could possibly have learnt from my previous intellectual ramblings.

A Conversation About Justification

(or 'David and the Crypto-inductivist) 

I think that I have solved a major philosophical problem: the problem of induction.  Karl Popper 

As I explained in the Preface, this book is not primarily a defence of the fundamental theories of the four main strands; it is an investigation of what those theories say, and what sort of reality they describe. That is why I do not address opposing theories in any depth. However, there is one opposing theory - namely, common sense - which reason requires me to refute in detail wherever it seems to conflict with what I am asserting. Hence in.Chapter 2 I presented a root-and-branch refutation of the common-sense idea that there is only one universe. In Chapter 11 I shall do the same for the common-sense idea that time 'flows', or that our consciousness 'moves' through time. In Chapter 3 I criticized inductivism, the common-sense idea that we form theories about the physical world by generalizing the results of observations, and that we justify our theories by repeating those observations. I explained that inductive generalization from observations is impossible, and that inductive justification is invalid. I explained that inductivism rests upon a mistaken idea of science as seeking predictions on the basis of observations, rather than as seeking explanations in response to problems. I also explained (following Popper) how science does make progress, by conjecturing new explanations and then choosing between the best ones by experiment. All this is largely accepted by scientists and philosophers of science. What is not accepted by most philosophers is that this process is justified. Let me explain.

Science seeks better explanations. A scientific explanation accounts for our observations by postulating something about what reality is like and how it works. We deem an explanation to be better if it leaves fewer loose ends (such as entities whose properties are themselves unexplained), requires fewer and simpler postulates, is more general, meshes more easily with good explanations in other fields and so on. But why should a better explanation be what we always assume it to be in practice, namely the token of a truer theory? Why, for that matter, should a downright bad explanation (one that has none of the above attributes, say) necessarily be false? There is indeed no logically necessary connection between truth and explanatory power. A bad explanation (such as solipsism) may be true. Even the best and truest available theory may make a false prediction in particular cases, and those might be the very cases in which we rely on the theory. No valid form of reasoning can logically rule out such possibilities, or even prove them unlikely. But in that case, what justifies our relying on our best explanations as guides to practical decision-making? More generally, whatever criteria we used to judge scientific theories, how could the fact that a theory satisfied those criteria today possibly imply anything about what will happen if we rely on the theory tomorrow?

This is the modern form of the 'problem of induction'. Most philosophers are now content with Popper's contention that new theories are not inferred from anything, but are merely hypotheses. They also accept that scientific progress is made through conjectures and refutations (as described in Chapter 3), and that theories are accepted when all their rivals are refuted, and not by virtue of numerous confirming instances. They accept that the knowledge obtained in this way tends, in the event, to be reliable. The problem is that they do not see why it should be. Traditional inductivists tried to formulate a 'principle of induction', which said that confirming instances made a theory more likely, or that 'the future will resemble the past', or some such statement. They also tried to formulate an inductive scientific methodology, laying down rules for what sort of inferences one could validly draw from 'data'. They all failed, for the reasons I have explained. But even if they had succeeded, in the sense of constructing a scheme that could be followed successfully to create scientific knowledge, this would not have solved the problem of induction as it is nowadays understood. For in that case 'induction' would simply be another possible way of choosing theories, and the problem would remain of why those theories should be a reliable basis for action. In other words, philosophers who worry about this 'problem of induction' are not inductivists in the old-fashioned sense. They do not try to obtain or justify any theories inductively. They do not expect the sky to fall in, but they do not know how to justify that expectation.

Philosophers today yearn for this missing justification. They no longer believe that induction would provide it, yet they have an induction-shaped gap in their scheme of things, just as religious people who have lost their faith suffer from a 'God-shaped gap' in their scheme of things. But in my opinion there is little difference between having an X-shaped gap in one's scheme of things and believing in X. Hence to fit in with the more sophisticated conception of the problem of induction, I wish to redefine the term 'inductivist' to mean someone who believes that the invalidity of inductive justification is a problem for the foundations of science. In other words, an inductivist believes that there is a gap which must be filled, if not by a principle of induction then by something else. Some inductivists do not mind being so designated. Others do, so I shall call them crypto-inductivists.

Most contemporary philosophers are crypto-inductivists. What makes matters worse is that (like many scientists) they grossly underrate the role of explanation in the scientific process. So do most Popperian anti-inductivists, who are thereby led to deny that there is any such thing as justification (even tentative justification). This opens up a new explanatory gap in their scheme of things. The philosopher John Worrall has dramatized the problem as he sees it in an imaginary dialogue between Popper and several other philosophers, entitled 'Why Both Popper and Watkins Fail to Solve the Problem of Induction'. The setting is the top of the Eiffel Tower. One of the participants - the 'Floater' - decides to descend by jumping over the side instead of using the lift in the usual way. The others try to persuade the Floater that jumping off means certain death. They use the best available scientific and philosophical arguments. But the infuriating Floater still expects to float down safely, and keeps pointing out that no rival expectation can logically be proved to be preferable on the basis of past experience.

I believe that we can justify our expectation that the Floater would be killed. The justification (always tentative, of course) comes from the explanations provided by the relevant scientific theories. To the extent that those explanations are good, it is rationally justified to rely on the predictions of corresponding theories. So, in reply to Worrall, I now present a dialogue of my own, set in the same place. 

DAVID: Since I read what Popper has to say about induction, I have believed that he did indeed, as he claimed, solve the problem of induction. But few philosophers agree. Why?

CRYPTO-INDUCTIVIST: Because Popper never addressed the problem of induction as we understand it. What he did was present a critique of inductivism. Inductivism said that there is an 'inductive' form of reasoning which can derive, and justify the use of, general theories about the future, given evidence in the form of individual observations made in the past. it held that there was a principle of nature, the principle of induction, which said something like 'observations made in the future are likely to resemble observations made under similar circumstances in the past'. Attempts were made to formulate this in such a way that it would indeed allow one to derive, or justify, general theories from individual observations. They all failed. Popper's critique, though influential among scientists (especially in conjunction with his other work, elucidating the methodology of science), was hardly original. The unsoundness of inductivism had been known almost since it was invented, and certainly since David Hume's critique of it in the early eighteenth century. The problem of induction is not how to justify or refute the principle of induction, but rather, taking for granted that it is invalid, how to justify any conclusion about the future from past evidence. And before you say that one doesn't need to ... 

DAVID: One doesn't need to. 

CRYPTO-INDUCTIVIST: But one does. This is what is so irritating about you Popperians: you deny the obvious. Obviously the reason why you are not even now leaping over this railing is, in part, that you consider it justified to rely on our best theory of gravity and unjustified to rely on certain other theories. (Of course, by 'our best theory of gravity' in this case I mean more than just general relativity. I am also referring to a complex set of theories about such things as air resistance, human physiology, the elasticity of concrete and the availability of mid-air rescue devices.) 

DAVID: Yes, I would consider it justified to rely on that theory. According to Popperian methodology, one should in these cases rely on the best-corroborated theory - that is, the one that has been subjected to the most stringent tests and has survived them while its rivals have been refuted. 

CRYPTO-INDUCTIVIST: You say 'one should' rely on the best- corroborated theory, but why, exactly? Presumably because, according to Popper, the process of corroboration has justified the theory, in the sense that its predictions are more likely to be true than the predictions of other theories. 

DAVID: Well, not more likely than all other theories, because no doubt one day we'll have even better theories of gravity ... 

CRYPTO-INDUCTIVIST: Now look. Please let's agree not to trip each other up with quibbles that do not bear on the substance of what we are discussing. Of course there may be a better theory of gravity one day, but you have to decide whether to jump now, now. And given the evidence available to you now, you have chosen a certain theory to act upon. And you have chosen it according to Popperian criteria because you believe that those criteria are the ones most likely to select theories which make true predictions. 

DAVID: Yes. 

CRYPTO-INDUCTIVIST: So to summarize, you believe that the evidence currently available to you justifies the prediction that you would be killed if you leapt over the railing. 

DAVID: No, it doesn't. 

CRYPTO-INDUCTIVIST: But dammit, you are contradicting yourself. Just now you said that that prediction is justified. 

DAVID: It is justified. But it was not justified by the evidence, if by 'the evidence' you mean all the experiments whose outcomes the theory correctly predicted in the past. As we all know, that evidence is consistent with an infinity of theories, including theories predicting every logically possible outcome of my jumping over the railing. 

CRYPTO-INDUCTIVIST: So in view of that, I repeat, the whole problem is to find what does justify the prediction. That is the problem of induction. 

DAVID: Well, that is the problem that Popper solved. 

CRPYPTO-INDUCTIVIST: That's news to me, and I've studied Popper extensively. But anyway, what is the solution? I'm eager to.. hear it. What justifies the prediction, if it isn't the evidence? 

DAVID: Argument. 


DAVID: Only argument ever justifies anything - tentatively, of course. All theorizing is subject to error, and all that. But still, argument can sometimes justify theories. That is what argument is for. 

CRYPTO-INDUCTIVIST: I think this is another of your quibbles. You can't mean that the theory was justified by pure argument, like a mathematical theorem. The evidence played some role, surely. 

DAVID: Of course. This is an empirical theory, so, according to Popperian scientific methodology, crucial experiments play a pivotal role in deciding between it and its rivals. The rivals were refuted; it survived. 

CRYPTO-INDUCTIVIST. And in consequence of that refuting and surviving, all of which happened in the past, the practical use of the theory to predict the future is now justified. 

DAVID: I suppose so, though it seems misleading to say 'in consequence of' when we are not talking about a logical deduction. 

CRYPTO-INDUCTIVIST: 'Well that's the whole point again: what sort of consequence was it? Let me try to pin you down here. You admit that it was both argument and the outcomes of experiments that justified the theory. If the experiments had gone differently, the argument would have justified a different theory. So do you accept that in that sense - yes, via the argument, but I don't want to keep repeating that proviso - the outcomes of past experiments did justify the prediction? 

DAVID: Yes. 

CRYPTO- INDUCTIVIST: So what exactly was it about those actual past outcomes that justified the prediction, as opposed to other possible past outcomes which might well have justified the contrary prediction? 

DAVID: It was that the actual outcomes refuted all the rival theories, and corroborated the theory that now prevails. 

CRYPTO-INDUCTIVIST: Good. Now listen carefully, because you have just said something which is not only provably untrue, but which you yourself conceded was untrue only moments ago. You say that the outcomes of experiments 'refuted all the rival theories'. But you know very well that no set of outcomes of experiments can refute all possible rivals to a general theory. You said yourself that any set of past outcomes is (I quote) 'consistent with an infinity of theories, including theories predicting every logically possible outcome of my jumping over the railing'. It follows inexorably that the prediction you favour was not justified by the experimental outcomes, because there are infinitely many other rivals to your theory, also unrefuted as yet, which make the opposite prediction. 

DAVID: I'm glad I listened carefully, as you asked, for now I see that at least part of the difference between us has been caused by a misunderstanding over terminology. When Popper speaks of 'rival theories' to a given theory, he does not mean the set of all logically possible rivals: he means only the actual rivals, those proposed in the course of a rational controversy. (That includes theories 'proposed' purely mentally, by one person, in the course of a 'controversy' within one mind.) 

CRYPTO-INDUCTIVIST: I see. Well, I'll accept your terminology. But incidentally (I don't think it matters, for present purposes, but I'm curious), isn't it a strange assertion you are attributing to Popper, that the reliability of a theory depends on the accident of what other theories - false theories - people have proposed in the past, rather than just on the content of the theory in question, and on the experimental evidence? 

DAVID. Not really. Even you inductivists speak of ... 

CRYPTO-INDUCTIVIST: I am not an inductivist! 

DAVID: Yes you are. 

CRYPTO-INDUCTIVIST: Hmph! Once again, I shall accept your terminology if you insist. But you may as well call me a porcupine. It really is perverse to call a person an 'inductivist' if that person's whole thesis is that the invalidity of inductive reasoning presents us with an unsolved philosophical problem. 

DAVID: I don't think so. I think that that thesis is what defines, and always has defined, an inductivist. But I see that Popper has at least achieved one thing: 'inductivist' has become a term of abuse! Anyway, I was explaining why it's not so strange that the reliability of a theory should depend on what false theories people have proposed in the past. Even inductivists speak of a theory being reliable or not, given certain 'evidence'. Well, Popperians might speak of a theory being the best available for use in practice, given a certain problem-situation. And the most important features of a problem-situation are: what theories and explanations are in contention, what arguments have been advanced, and what theories have been refuted. 'Corroboration' is not just the confirmation of the winning theory. It requires the experimental refutation of rival theories. Confirming instances in themselves have no significance. 

CRYPTO-INDUCTIVIST: Very interesting. I now understand the role of a theory's refuted rivals in the justification of its predictions. Under inductivism, observation was supposed to be primary. One imagined a mass of past observations from which the theory was supposed to be induced, and observations also constituted the evidence which somehow justified the theory. In the Popperian picture of scientific progress, it is not observations but problems, controversies, theories and criticism that are primary. Experiments are designed and performed only to resolve controversies. Therefore only experimental results that actually do refute a theory - and not just any theory, it must have been a genuine contender in a rational controversy - constitute 'corroboration'. And so it is only those experiments that provide evidence for the reliability of the winning theory. 

DAVID: Correct. And even then, the 'reliability' that corroboration confers is not absolute but only relative to the other contending theories. That is, we expect the strategy of relying on corroborated theories to select the best theories from those that are proposed. That is a sufficient basis for action. 'We do not need (and could not validly get) any assurance about how good even the best proposed course of action will be. Furthermore, we may always be mistaken, but so what? We cannot use theories that have yet to be proposed; nor can we correct errors that we cannot yet see. 

CRYPTO-INDUCTIVIST: Quite so. I am glad to have learned something about scientific methodology. But now - and I hope you don't think me impolite - I must draw your attention yet again to the question I have been asking all along. Suppose that a theory has passed through this whole process. Once upon a time it had rivals. Then experiments were performed and all the rivals were refuted. But it itself was not refuted. Thus it was corrobor- ated. What is it about its being corroborated that justifies our relying on it in the future?

DAVID: Since all its rivals have been refuted, they are no longer rationally tenable. The corroborated theory is the only rationally tenable theory remaining. 

CRYPTO-INDUCTIVIST: But that only shifts the focus from the future import of past corroboration to the future import of past refutation. The same problem remains. Why, exactly, is an experimentally refuted theory 'not rationally tenable'? Is it that having even one false consequence implies that it cannot be true? 

DAVID: Yes. 

CRYPTO-INDUCTIVIST: But surely, as regards the future applicability of the theory, that is not a logically relevant criticism. Admittedly, a refuted theory cannot be true universally - in particular, it cannot have been true in the past, when it was tested. But it could still have many true consequences, and in particular it could be universally true in the future. 

DAVID: This 'true in the past' and 'true in the future' terminology is misleading. Each specific prediction of a theory is either true or false; that cannot change. What you really mean is that though the refuted theory is strictly false, because it makes some false predictions, all its predictions about the future might nevertheless be true. In other words, a different theory, which makes the same predictions about the future but different predictions about the past, might be true. 

CRYPTO-INDUCTIVIST: If you like. So instead of asking why a refuted theory is not rationally tenable, I should, strictly speaking, have asked this: why does the refutation of a theory also render untenable every variant of the theory that agrees with it about the future - even a variant that has not been refuted? 

DAVID: It is not that refutation renders such theories untenable. It is just that sometimes they already are untenable, by virtue of being bad explanations. And that is when science can make progress. For a theory to win an argument, all its rivals must be untenable, and that includes all the variants of the rivals which anyone has thought of. But remember, it is only the rivals which anyone has thought of that need be untenable. For example, in the case of gravity no one has ever proposed a tenable theory that agrees with the prevailing one in all its tested predictions, but differs in its predictions about future experiments. I am sure that such theories are possible - for instance, the successor to the prevailing theory will presumably be one of them. But if no one has yet thought of such a theory, how can anyone act upon it? 

CRYPTO-INDUCTIVIST: What do you mean, 'no one has yet thought of such a theory'? I could easily think of one right now. 

DAVID: I very much doubt that you can. 

CRYPTO-INDUCTIVIST: Of course I can. Here it is. 'Whenever you, David, jump from high places in ways that would, according to the prevailing theory, kill you, you float instead. Apart from that, the prevailing theory holds universally.' I put it to you that every past test of your theory was also necessarily a test of mine, since all the predictions of your theory and mine regarding past experiments are identical. Therefore your theory's refuted rivals were also my theory's refuted rivals. And therefore my new theory is exactly as corroborated as your prevailing theory. How, then, can my theory be 'untenable'? What faults could it possibly have that are not shared by your theory? 

DAVID: Just about every fault in the Popperian book! Your theory is constructed from the prevailing one by appending an unexplained qualification about me floating. That qualification is, in effect, a new theory, but you have given no argument either against the prevailing theory of my gravitational properties, or in favour of the new one. You have subjected your new theory to no criticism (other than what I am giving it now) and no experimental testing. It does not solve - or even purport to solve - any current problem, nor have you suggested a new, interesting problem that it could solve. Worst of all, your qualification explains nothing, but spoils the explanation of gravity that is the basis of the prevailing theory. It is this explanation that justifies our relying on the prevailing theory and not on yours. Thus by all rational criteria your proposed qualification can be summarily rejected.

CRYPTO-INDUCTIVIST: Couldn't I say exactly the same thing about your theory? Your theory differs from mine only by the same minor qualification, but in reverse. You think I ought to have explained my qualification. But why are our positions not symmetrical? 

DAVID: Because your theory does not come with an explanation of its predictions, and mine does. 

CRYPTO-INDUCTIVIST: But if my theory had been proposed first, it would have been your theory that appeared to contain an unexplained qualification, and it would be your theory that would be 'summarily rejected'. 

DAVID: That is simply untrue. Any rational person who was comparing your theory with the prevailing one, even if yours had been proposed first, would immediately reject your theory in favour of the prevailing one. For the fact that your theory is an unexplained modification of another theory is manifest in your very statement of it.

CRYPTO-INDUCTIVIST: You mean that my theory has the form 'such-and-such a theory holds universally, except in such-and-such a situation', but I don't explain why the exception hold's? 

DAVID: Exactly.

CRYPTO-INDUCTIVIST: Aha! Well, I think I can prove you wrong here (with the help of the philosopher Nelson Goodman). Consider a variant of the English language that has no verb 'to fall'. Instead it has a verb 'to x-fall' which means 'to fall' except when applied to you, in which case it means 'to float'. Similarly, 'to x-float' means 'to float' except when applied to you, in which case it means 'to fall'. In this new language I could express my theory as the unqualified assertion 'all objects x-fall if unsupported'. But the prevailing theory (which in English says 'all objects fall if unsupported') would, in the new language, have to be qualified: 'all objects x-fall when unsupported, except David, who x-floats'. So which of these two theories is qualified depends on the language they are expressed in, doesn't it? 

DAVID: In form, yes. But that is a triviality. Your theory contains, in substance, an unexplained assertion, qualifying the prevailing theory. The prevailing theory is, in substance, your theory stripped of an unexplained qualification. No matter how you slice it, that is an objective fact, independent of language. 

CRYPTO-INDUCTIVIST: I don't see why. You yourself used the form of my theory to spot the 'unnecessary qualification'. You said that it was 'manifest' as an additional clause in my very statement of the theory - in English. But when the theory is translated into my language, no qualification is manifest; and on the contrary, a manifest qualification appears in the very statement of the prevailing theory. 

DAVID: So it does. But not all languages are equal. Languages are theories. In their vocabulary and grammar, they embody substantial assertions about the world. Whenever we state a theory, only a small part of its content is explicit: the rest is carried by the language. Like all theories, languages are invented and selected for their ability to solve certain problems. In this case the problems are those of expressing other theories in forms in which it is convenient to apply them, and to compare and criticize them. One of the most important ways in which languages solve these problems is to embody, implicitly, theories that are uncontroversial and taken for granted, while allowing things that need to be stated or argued about to be expressed succinctly and cleanly. 


DAVID: Thus it is no accident when a language chooses to cover the conceptual ground with one set of concepts rather than another. It reflects the current state of the speakers' problem-situation. That is why the form of your theory, in English, is a good indication of its status vis a' vis the current problem-situation - whether it solves problems or exacerbates them. But it is not the form of your theory I am complaining about. It is the substance. My complaint is that your theory solves nothing and only exacerbates the problem-situation. This defect is manifest when the theory is expressed in English, and implicit when it is expressed in your language. But it is no less severe for that. I could state my complaint equally well in English, or in scientific jargon, or in your proposed language or in any language capable of expressing the discussion we have been having. (It is a Popperian maxim that one should always be willing to carry on the discussion in the opponent's terminology.) 

CRYPTO-INDUCTIVIST: You may have a point there. But could you elaborate? In what way does my theory exacerbate the problem-situation, and why would this be obvious even to a native speaker of my hypothetical language? 

DAVID: Your theory asserts the existence of a physical anomaly which is not present according to the prevailing theory. The anomaly is my alleged immunity from gravity. Certainly, you can invent a language which expresses this anomaly implicitly, so that statements of your theory of gravity need not refer to it explicitly. But refer to it they do. A rose by any other name would smell as sweet. Suppose that you - indeed suppose that everyone - were a native speaker of your language, and believed your theory of gravity to be true. Suppose that we all took it entirely for granted, and thought it so natural that we used the same word 'x-fall' to describe what you or I would do if we jumped over the railing. None of that alters in the slightest degree the obvious difference there would be between my response to gravity and everything else's. If you fell over the railing, you might well envy me on the way down. You might well think, 'if only I could respond to gravity as David does, rather than in this entirely different way that I do!' 

CRYPTO-INDUCTIVIST: That's true. Just because the same word 'x-falling' describes your response to gravity and mine, I wouldn't think that the actual response is the same. On the contrary, being a fluent speaker of this supposed language, I'd know very well that 'x-falling' was physically different for you and for me, just as a native English speaker knows that the words 'being drunk' mean something physically different for a person and for a glass of water. I wouldn't think, 'if this had happened to David, he'd be x-failing just as I am'. I'd think, 'if this had happened to David, he'd x-fall and survive, while I shall x-fall and die.' 

DAVID: Moreover, despite your being sure that I would float, you wouldn't understand why. Knowing is not the same as understanding. You would be curious as to the explanation of this 'well-known' anomaly. So would everyone else. Physicists would congregate from all over the world to study my anomalous gravitational properties. In fact, if your language were really the prevailing one, and your theory were really taken for granted by everyone, the scientific world would presumably have been impatiently awaiting my very birth, and would be queuing for the privilege of dropping me out of aircraft! But of course, the premise of all this, namely that your theory is taken for granted and embodied in the prevailing language, is preposterous. Theory or no theory, language or no language, in reality no rational person would entertain the possibility of such a glaring physical anomaly without there being a very powerful explanation in its favour. Therefore, just as your theory would be summarily rejected, your language would be rejected too, for it is just another way of stating your theory. 

CRYPTO-INDUCTIVIST: Could it be that there is a solution of the problem of induction lurking here after all? Let me see. How does this insight about language change things? My argument relied upon an apparent symmetry between your position and mine. We both adopted theories that were consistent with existing experimental results, and whose rivals (except each other) had been refuted. You said that I was being irrational because my theory involved an unexplained assertion, but I countered by saying that in a different language it would be your theory that contained such an assertion, so the symmetry was still there. But now you have pointed out that languages are theories, and that the combination of my proposed language and theory assert the existence of an objective, physical anomaly, as compared with what the combination of the English language and the prevailing theory assert. This is where the symmetry between our positions, and the argument I was putting forward, break down hopelessly. 

DAVID: Indeed they do.

CRYPTO-INDUCTIVIST: Let me see if I can clarify this a little further. Are you saying that it is a principle of rationality that a theory which asserts the existence of an objective, physical anomaly is, other things being equal, less likely to make true predictions than one that doesn't? 

DAVID: Not quite. Theories postulating anomalies without explaining them are less likely than their rivals to make true predictions. More generally, it is a principle of rationality that theories are postulated in order to solve problems. Therefore any postulate which solves no problem is to be rejected. That is because a good explanation qualified by such a postulate becomes a bad explanation. 

CRYPTO-INDUCTIVIST: Now that I understand that there really is an objective difference between theories which make unexplained predictions and theories which don't, I must admit that this does look promising as a solution of the problem of induction. You seem to have discovered a way of justifying your future reliance on the theory of gravity, given only the past problem-situation (including past observational evidence) and the distinction between a good explanation and a bad one. You do not have to make any assumption such as 'the future is likely to resemble the past'. 

DAVID: It was not I who discovered this.

CRYPTO-INDUCTIVIST: 'Well, I don't think Popper did either. For one thing, Popper did not think that scientific theories could be justified at all. You make a careful distinction between theories being justified by observations (as inductivists think) and being justified by argument. But Popper made no such distinction. And in regard to the problem of induction, he actually said that although future predictions of a theory cannot be justified, we should act as though they were! 

DAVID.- I don't think he said that, exactly. If he did, he didn't really mean it. 


DAVID: Or if he did mean it, he was mistaken. Why are you so upset? It is perfectly possible for a person to discover a new theory (in this case Popperian epistemology) but nevertheless to continue to hold beliefs that contradict it. The more profound the theory is, the more likely this is to happen. 

CRYPTO-INDUCTIVIST: Are you claiming to understand Popper's theory better than he did himself? 

DAVID: I neither know nor care. The reverence that philosophers show for the historical sources of ideas is very perverse, you know. In science we do not consider the discoverer of a theory to have any special insight into it. On the contrary, we hardly ever consult original sources. They invariably become obsolete, as the problem-situations that prompted them are transformed by the discoveries themselves. For example, most relativity theorists today understand Einstein's theory better than he did. The founders of quantum theory made a complete mess of understanding their own theory. Such shaky beginnings are to be expected; and when we stand upon the shoulders of giants, it may not be all that hard to see further than they did. But in any case, surely it is more interesting to argue about what the truth is, than about what some particular thinker, however great, did or did not think. 

CRYPTO-INDUCTIVIST: All right, I agree. But wait a moment, I think I spoke too soon when I said that you were not postulating any sort of principle of induction. Look: you have justified a theory about the future (the prevailing theory of gravity) as being more reliable than another theory (the one I proposed), even though they are both consistent with all currently known observations. Since the prevailing theory applies both to the future and to the past, you have justified the proposition that, as regards gravity, the future resembles the past. And the same would hold whenever you justify a theory as reliable on the grounds that it is corroborated. Now, in order to go from 'corroborated' to 'reliable', you examined the theories' explanatory power. So what you have shown is that what we might call the 'principle of seeking better explanations', together with some observations - yes, and arguments - imply that the future will, in many respects, resemble the past. And that is a principle of induction! If your 'explanation principle' implies a principle of induction, then, logically, it is a principle of induction. So inductivism is true after all, and a principle of induction does indeed have to be postulated, explicitly or implicitly, before we can predict the future. 

DAVID: Oh dear! This inductivism really is a virulent disease. Having gone into remission for only a few seconds, it now returns more violently than before. 

CRYPTO-INDUCTIVIST: Does Popperian rationalism justify ad hominem arguments as well? I ask for information only. 

DAVID: I apologize. Let me go straight to the substance of what you said. Yes, I have justified an assertion about the future. You say this implies that 'the future resembles the past'. Well, vacuously, yes, inasmuch as any theory about the future would assert that it resembled the past in some sense. But this inference that the future resembles the past is not the sought-for principle of induction, for we could neither derive nor justify any theory or prediction about the future from it. For example, we could not use it to distinguish your theory of gravity from the prevailing one, for they both say, in their own way, that the future resembles the past. 

CRYPTO-INDUCTIVIST: Couldn't we derive, from the 'explanation principle', a form of the principle of induction that could be used to select theories? What about: 'if an unexplained anomaly does not happen in the past, then it is unlikely in the future'? 

DAVID: No. Our justification does not depend on whether a particular anomaly happens in the past. It has to do with whether there is an explanation for the existence of that anomaly. 

CRYPTO-INDUCTIVIST: All right then, let me formulate it more carefully: 'if, in the present, there is no explanatory theory predicting that a particular anomaly will happen in the future, then that anomaly is unlikely to happen in the future'. 

DAVID: That may well be true. I for one, believe that it is. However, it is not of the form 'the future is likely to resemble the past'. Moreover, in trying to make it look as much like that as possible, you have specialized it to cases 'in the present', 'in the future', and to the case of an 'anomaly'. But it is just as true without these specializations. It is just a general statement about the efficacy of argument. In short, if there is no argument in favour of a postulate, then it is not reliable. Past, present or future. Anomaly or no anomaly. Period. 


DAVID: Nothing in the concepts of 'rational argument' or 'explanation' relates the future to the past in any special way. Nothing is postulated about anything 'resembling' anything. Nothing of that sort would help if it were postulated. In the vacuous sense in which the very concept of 'explanation' implies that the future 'resembles the past', it nevertheless implies nothing specific about the future, so it is not a principle of induction. There is no principle of induction. There is no process of induction. No one ever uses them or anything like them. And there is no longer a problem of induction. Is that clear now? 

CRYPTO-INDUCTIVIST: Yes. Please excuse me for a few moments while I adjust my entire world-view. 

DAVID: To assist you in that exercise, I think you should consider your alternative 'theory of gravity' more closely. 


DAVID: As we have agreed, your theory consists objectively of a theory of gravity (the prevailing theory), qualified by an unexplained prediction about me. It says that I would float, unsupported. 'Unsupported' means 'without any upward force acting' on me, so the suggestion is that I would be immune to the 'force' of gravity which would otherwise pull me down. But according to the general theory of relativity, gravity is not a force but a manifestation of the curvature of spacetime. This curvature explains why unsupported objects, like myself and the Earth, move closer together with time. Therefore, in the light of modern physics your theory is presumably saying that there is an upward force on me, as required to hold me at a constant distance from the Earth. But where does that force come from, and how does it behave? For example, what is a 'constant distance'? If the Earth were to move downwards, would I respond instantaneously to maintain the same height (which would allow communication faster than the speed of light, contrary to another principle of relativity), or would the information about where the Earth is have to reach me at the speed of light first? If so, what carries this information? Is it a new sort of wave emitted by the Earth - in which case what equations does it obey? Does it carry energy? What is its quantum-mechanical behaviour? Or is it that I respond in a special way to existing waves, such as light? In that case, would the anomaly disappear if an opaque barrier were placed between me and the Earth? Isn't the Earth mostly opaque anyway? Where does 'the Earth' begin: what defines the surface above which I am supposed to 'float'? 


DAVID: For that matter, what defines where I begin? If I hold on to a heavy weight, does it float too? If so, then the aircraft in which I have flown could have switched off their engines without mishap. What counts as 'holding on'? Would the aircraft then drop if I let go of the arm rest? And if the effect does not apply to things I am holding on to, what about my clothes? Will they weigh me down and cause me to be killed after all, if I jump over the railing? What about my last meal? 


DAVID: I could go on like this ad infinitum. The point is, the more we consider the implications of your proposed anomaly, the more unanswered questions we find. This is not just a matter of your theory being incomplete. These questions are dilemmas. Whichever way they are answered, they create fresh problems by spoiling satisfactory explanations of other phenomena. 


DAVID: So your additional postulate is not just superfluous, it is positively bad. In general, perverse but unrefuted theories which one can propose off the cuff fall roughly into two categories. There are theories that postulate unobservable entities, such as particles that do not interact with any other matter. They can be rejected for solving nothing ('Occam's razor', if you like). And there are theories, like yours, that predict unexplained observable anomalies. They can be rejected for solving nothing and spoiling existing solutions. It is not, I hasten to add, that they conflict with existing observations. It is that they remove the explanatory power from existing theories by asserting that the predictions of those theories have exceptions, but not explaining how. You can't just say 'spacetime geometry brings unsupported objects together, unless one of them is David, in which case it leaves them alone'. Either the explanation of gravity is spacetime curvature or it isn't. just compare your theory with the perfectly legitimate assertion that a feather would float down slowly because there would indeed be a sufficient upward force on it from the air. That assertion is a consequence of our existing explanatory theory of what air is, so it raises no new problem, as your theory does. 

CRYPTO-INDUCTIVIST: I see that. Now, will you give me some help in adjusting my world-view? 

DAVID: Well, have you read my book, The Fabric of Reatity?

CRYPTO-INDUCTIVIST: I certainly plan to, but for the moment the help that I was asking for concerns a very specific difficulty. 

DAVID: Go ahead. 

CRYPTO-INDUCTIVIST: The difficulty is this. When I rehearse the discussion,we have been having, I am entirely convinced that your prediction of what would happen if you or I jumped off this tower was not derived from any inductive hypothesis such as 'the future resembles the past'. But when I step back and consider the overall logic of the situation, I fear I still cannot understand how that can be. Consider the raw materials for the argument. Initially, I assumed that past observations and deductive logic are our only raw material. Then I admitted that the current problem-situation is relevant too, because we need justify our theory only as being more reliable than existing rivals. And then I had to take into account that vast classes of theories can be ruled out by argument alone, because they are bad explanations, and that the principles of rationality can be included in our raw material. What I cannot understand is where in that raw material - past observations, the present problem-situation and timeless principles of logic and rationality, none of which justifies inferences from the past to the future - the justification of future predictions has come from. There seems to be a logical gap. Are we making a hidden assumption somewhere?

DAVID: No, there is no logical gap. What you call our 'raw material' does indeed include assertions about the future. The best existing theories, which cannot be abandoned lightly because they are the solutions of problems, contain predictions about the future. And these predictions cannot be severed from the theories' other content, as you tried to do, because that would spoil the theories' explanatory power. Any new theory we propose must therefore either be consistent with these existing theories, which has implications for what the new theory can say about the future, or contradict some existing theories but address the problems thereby raised, giving alternative explanations, which again constrains what they can say about the future. 

CRYPTO-INDUCTIVIST: So we have no principle of reasoning which says that the future will resemble the past, but we do have actual theories which say that. So do we have actual theories which imply a limited form of inductive principle? 

DAVID: No. Our theories simply assert something about the future. Vacuously, any theory about the future implies that the future will 'resemble the past' in some ways. But we only find out in what respects the theory says that the future will resemble the past after we have the theory. You might as well say that since our theories hold certain features of reality to be the same throughout space, they imply a 'spatial principle of induction' to the effect that 'the near resembles the distant'. Let me point out that, in any practical sense of the word 'resemble', our present theories say that the future will not resemble the past. The cosmological 'Big Crunch', for instance (the recollapse of the universe to a single point), is an event that some cosmologists predict, but which is just about as unlike the present epoch, in every physical sense, as it could possibly be. The very laws from which we predict its occurrence will not apply to it. 

CRYPTO-INDUCTIVIST: I am convinced on that point. Let me try one last argument. We have seen that future predictions can be justified by appeal to the principles of rationality. But what justifies those? They are not, after all, truths of pure logic. So there are two possibilities: either they are unjustified, in which case conclusions drawn from them are unjustified too; or they are justified by some as yet unknown means. In either case there is a missing justification. I no longer suspect that this is the problem of induction in disguise. Nevertheless, having exploded the problem of induction, have we not revealed another fundamental problem, also concerning missing justification, beneath? 

DAVID: What justifies the principles of rationality? Argument, as usual. What, for instance, justifies our relying on the laws of deduction, despite the fact that any attempt to justify them logically must lead either to circularity or to an infinite regress? They are justified because no explanation is improved by replacing a law of deduction.

CRYPTO-INDUCTIVIST: That doesn't seem a very secure foundation for pure logic. 

DAVID: It is not perfectly secure. Nor should we expect it to be, for logical reasoning is no less a physical process than scientific reasoning is, and it is inherently fallible. The laws of logic are not self-evident. There are people, the mathematical 'intuitionists', who disagree with the conventional laws of deduction (the logical 'rules of inference'). I discuss their strange world-view in Chapter 10 of The Fabric of Reality. They cannot be proved wrong, but I shall argue that they are wrong, and I am sure you will agree that my argument justifies this conclusion. 

CRYPTO-INDUCTIVIST: So you don't think that there is a 'problem of deduction', then? 

DAVID: No. I don't think that there is a problem with any of the usual ways of justifying conclusions in science, philosophy or mathematics. However, it is an interesting fact that the physical universe admits processes that create knowledge about itself, and about other things too. We may reasonably try to explain this fact in the same way as we explain other physical facts, namely through explanatory theories. You will see in Chapter 6 of The Fabric of Reality that I think that the Turing principle is the appropriate theory in this case. It says that it is possible to build a virtual-reality generator whose repertoire includes every physically possible environment. If the Turing principle is a law of physics, as I have argued that it is, then we should not be surprised to find that we can form accurate theories about reality, because that is just virtual reality in action. just as the fact that steam engines are possible is a direct expression of the principles of thermodynamics, so the fact that the human brain is capable of creating knowledge is a direct expression of the Turing principle. 

CRYPTO-INDUCTIVIST: But how do we know that the Turing principle is true

DAVID: We don't, of course ... But you are afraid, aren't you, that if we can't justify the Turing principle, then we shall once again have lost our justification for relying on scientific predictions? 


DAVID: But we have now moved on to a completely different question! We are now discussing an apparent fact about physical reality, namely that it can make reliable predictions about itself. We are trying to explain that fact, to place it within the same framework as other facts we know. I suggested that there may be a certain law of physics involved. But if I were wrong about that, indeed even if we were entirely unable to explain this remarkable property of reality, that would not detract one jot from the justification of any scientific theory. For it would not make the explanations in such a theory one jot worse. 

CRYPTO-INDUCTIVIST: Now my arguments are exhausted. Intellectually, I am convinced. Yet I must confess that I still feel what I can only describe as an 'emotional doubt'. 

DAVID: Perhaps it will help if I make one last comment, not about any of the specific arguments you have raised, but about a misconception that seems to underlie many of them. You know that it is a misconception; yet you may not yet have incorporated the ramifications of that into your world-view. Perhaps that is the source of your 'emotional doubt'. 


DAVID: The misconception is about the very nature of argument and explanation. You seem to be assuming that arguments and explanations, such as those that justify acting on a particular theory, have the form of mathematical proofs, proceeding from assumptions to conclusions. You look for the 'raw material' (axioms) from which our conclusions (theorems) are derived. Now, there is indeed a logical structure of this type associated with every successful argument or explanation. But the process of argument does not begin with the 'axioms' and end with the 'conclusion'. Rather, it starts in the middle, with a version that is riddled with inconsistencies, gaps, ambiguities and irrelevancies. All these faults are criticized. Attempts are made to replace faulty theories. The theories that are criticized and replaced usually include some of the 'axioms'. That is why it is a mistake to assume that an argument begins with, or is justified by, the theories that eventually serve as its 'axioms'. The argument ends - tentatively - when it seems to have shown that the associated explanation is satisfactory. The 'axioms' adopted are not ultimate, unchallengeable beliefs. They are tentative, explanatory theories. 

CRYPTO-INDUCTIVIST'. I see. Argument is not the same species of thing as deduction, or the non-existent induction. It is not based on anything or justified by anything. And it doesn't have to be, because its purpose is to solve problems - to show that a given problem is solved by a given explanation., 

DAVID: Welcome to the club.

EX-INDUCTIVIST: All these years I have felt so secure in my great Problem. I felt so superior both to the ancient inductivists, and to the upstart Popper. And all the time, without even knowing it, I was a crypto-inductivist myself! Inductivism is indeed a disease. It makes one blind. 

D A V I D: Don't be too hard on yourself. You are cured now. If only your fellow-sufferers were as amenable to being cured by mere argument! 

EX-INDUCTIVIST: But how could I have been so blind? To think that I once nominated Popper for the Derrida Prize for Ridiculous Pronouncements, while all the time he had solved the problem of induction! O mea culpa! God save us, for we have burned a saint! I feel so ashamed. I see no way out but to throw myself over this railing. 

DAVID: Surely that is not called for. We Popperians believe in letting our theories die in our place. just throw inductivism overboard instead. 



crypto-inductivist   Someone who believes that the invalidity of inductive reasoning raises a serious philosophical problem, namely the problem of how to justify relying on scientific theories. 

Well, are you confused or enlightened? Do you remain an inductivist thinker, or did David (and I) convince you that the "best" scientific thinking is based on Popperian principles?

Let me briefly summarise the Popperian view of science before I finally conclude this essay with my personal views about what constitutes 'good' science. Karl Popper proposed that the essential element in science is the explanation (and not the observation). He also felt that all explanations had to be subjected to rigorous critical analysis and rigorous experimental testing. He felt that science progresses by 'conjectures and refutations' and that the falsification of an explanation by experimental testing eliminated that particular explanation from contention. He also thought that the corroboration of an explanatory theory is not just the confirmation of a particular 'winning' explanatory theory, but the simultaneous experimental refutation of its genuine contending rival theories. He also indicated that corroboration of a theory is never absolute, and that it is only relative to 'present-day' contending rival theories. He also felt that because all explanatory theories are only relatively true, that even the 'presently-best' corroborated theory could eventually be superceded by a 'better' theory. Finally, he felt that science does not attempt to determine any absolute truth - rather, he felt that science is merely the process by which experimental testing is used to improve the problem-solving quality of 'ever-evolving' explanatory theories.

If you agree with Karl Popper's philosophy of science, then you may agree with some of my ideas of what represents 'good' scientific practice.

'Good' scientific practice consists of the following attitudes/behaviourisms by a practicing scientist:-

1) A scientist should always cultivate an "open-minded" attitude - an attitude that readily accepts criticism and experimental refutation, and a scientist should resist becoming 'emotionally-attached' to any particular explanatory theory

2) A scientist should realise that repeated confirmation of his 'pet' explanatory theory does not increase its scientific legitimacy and that repeated affirmations are neutral in effect

3) A scientist should resist the tendency to think inductively - in other words, the scientist should resist any tendency to draw general conclusions from a series of experimental observations (other than the specific conclusion as to whether the observational data supports or contradicts his primary hypothesis); other general conclusions that are not directly connected to the primary hypothesis can be posited in the form of another (seperate) explanatory theory that may be suitable for future experimental testing

4) A scientist should readily encourage criticism of his explanatory theory (and/or criticism of his experimental methodology), because it is only through the refutation and re-formulation of an explanatory theory that science really progresses

5) A scientist should share his data freely with the general scientific community, because widespread data sharing increases the chance of refutation, and a refuted theory spawns further scientific endeavour and the possibility of even more refined theories

6) A scientist should resist any tendency to perform 'data-torturing' - post hoc re-analysis of the scientific data in order to obtain positive confirming results from equivocal, or semi-contradictory, experimental evidence - because he may then become entrapped in a tangled web of inductivist thinking or inductivist behaviourisms

7) A scientist should realise that a 'bad' explanation may sometimes be true, and that there is no certain logical connection between an experiment's test results and the explanatory power of his theory => a scientist should therefore constantly ensure that there is no critical intellectual 'disconnect' between his explanatory theory and the observational data

8) A scientist should structure his explanatory theory in a scientifically articulate manner - so that the avenues available for confirmation or refutation of his theory are clearly delineated => this will lessen the likelihood of there being an intellectual 'disconnect' between his explanatory theory and the observational data

9) A scientist should realise that even if his explanatory theory is experimentally confirmed by very stringent scientific testing (eg. randomised, double-blind, placebo-controlled trial) that his explanatory theory must still be shown to be intellectually coherent and logically consistent, and it must also mesh seamlessly with other 'good' explanatory theories in the same field

10) A scientist should realise that his explanatory theory has to be un-falsifiable if he wants it to become the current 'winning' theory, and the scientist should therefore actively promote rigorous experimental challenges to demonstrate that his explanatory theory cannot be falsified

11) A scientist should -------. Tell me! What do you think a scientist should do to ensure that he is practicing 'good' science?

(Note that I have flagrantly plagiarised part of this essay's material from David Deutsch's book - The Fabric of Reality - and that I have greatly simplified the presentation of his material so that it would not be an overly tedious read)

Commentary, criticism and controversy:

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