Deutsch’s Explanations …

The Beginning of Infinity: Explanations that Transform the World Allen Lane 2011.

Deutsch’s ‘big idea’ is that easy to vary explanations are not good explanations, and that we should seek hard to vary explanations. He explains his thinking to some extent, but leads on to advocate a principle of optimism, whose explanation I find wanting and whose conclusions I suspect.

Under Construction.


[All] progress … has resulted from … the quest for what I call good explanations. …

The Reach of Explanations

[Inductivism] purports to explain how science obtains predictions about experiences. But most of our theoretical knowledge simply does not take that form. …

The second fundamental misconception in inductivism is that scientific theories predict that ‘the future will resemble the past’, and the unseen resembles the unseen, and so on. (Or that it ‘probably’ will.)

But science often enables novelty, such as the first nuclear bomb.

Fallibilism, the recognition that no belief about external reality can ever be known to be absolutely true, is ‘essential for the initiation of unlimited knowledge growth’. (In particular, one should always have some degree of doubt about any scientific knowledge.)

[A] scientific theory must be testable … That is … , the theory must make predictions which, if the theory were false, could be contradicted by the outcome of some possible observation.

(Thus: If X is a theory (scientific or not) and Y is the theory that X will tend to fail some statistical test under certain sufficiently objective conditions, then Y is a scientific theory. But:)

   The essence of experimental testing is that there are at least two apparently viable theories known about the issue in question, making conflicting predictions that can be distinguished by the experiment.

[When] theories are easily variable … experimental testing is almost useless for correcting their errors. I call such theories bad explanations.

[A] common way in which an explanation can be bad is by containing superfluous features or arbitrariness, and sometimes removing these leaves a good explanation. This has given rise to a misconception known as ‘Occam’s razor’ … [But] there are many simple explanations that are nevertheless easily variable .. .

[Testable] explanations that have passed stringent tests become extremely good explanations, which in turn is why the maxim of testability promotes the growth of knowledge in science.

Deutsch gives the example of the axis-tilt explanation of the seasons, which predicts different seasons for foreign parts. If one doubted this, it would be very hard to ‘fix’ the theory to give more uniform seasons. This makes it a good theory.

[The] reach of an explanation is neither an additional assumption nor a detachable one. It is determined by the content of the explanation itself.

The Spark

[All] regularities in nature have explanations [and] the explanation of that regularity would itself be a law of nature, or a consequence of one.

The Reality of Abstractions

[There] is a class of high-level phenomena – including the liquidity of water … – that can be well explained in terms of each other, with no direct reference to anything [at the lower level – their parts]. … [The] whole class of high-level phenomena is quasi-autonomous – almost self-contained. This resolution into explicability at a higher, quasi-autonomous levels known a emergence.

There is often a moral undertone to reductionism (science should be essentially reductive).

[Success] entails a commitment to all sorts of values … tolerance, integrity and openness of debate.

Since the universe is explicable, it must be that morally right values are connected  in this way with true factual theories, and morally wrong values with false theories.

[Utilitarianism] played much the same role as empiricism did in the philosophy of science: it acted as a liberating focus for the rebellion against traditional dogmas, while its own positive content contained little truth.

The Jump to Universalism

[A] computer is [a universal simulator], so expecting it to be able to do whatever neurons can is not [just] a metaphor: it is a known and proven property of the laws of physics as w know them.

Digital computers are held to be universal with respect to all possible forms of computation (not just ‘definite methods’.

Artificial Creativity

Alan Turing’s work is linked to the notion that ‘thinking’ can be expressed as a ‘definite method’. Typical AI programs, including evolutionary programs, are criticised in that they merely seek optimum values for parameters, without being creative. Emergent phenomena require changes in language to be understood or influenced.

A Window on Infinity

Deutsch discusses mathematical notions of undecidability. He claims:

[There] is nothing mathematically special about the undecidable questions, the non-computable functions, the unprovable propositions. They are distinguished by physics only.

Our knowledge of whether a proposition is true or false always depends on knowledge about how physical objects behave.

Whether a mathematical proposition is true or not is indeed independent of physics. But the proof of such a propositions is a matter of physics only. There is not such thing as abstractly proving something , just as there is no such thing as abstractly knowing something. [All]knowledge is generated by physical processes, and its scope and limitations are conditioned by the laws of nature. [A theory] of abstract ‘computation’ has no bearing on what can or cannot be computed in reality.

Consequently, the reliability of our knowledge of mathematics remains forever subsidiary to that of our knowledge of physical reality. Every mathematical proof depends absolutely for its validity on our being right about the rules that govern the behaviour of some physical object, like computers, or ink and paper, or brains. .. proof theory is a science, it is computer science.

[Proof] is merely universal in the physics that governs our world. …

So there is something special – infinitely special, it seems – about the laws of physics as we actually find them, something exceptionally computation-friendly, prediction-friendly and explanation-friendly.

[I] conjecture that, in mathematics as well as in science and philosophy, if the question is interesting then the question is soluble.

Summary: … Proof is a physical process … .


    No good explanation can predict the outcome, or the probability of an outcome, of a phenomenon whose outcome whose course is going to be significantly affected by the creation of new knowledge. This is a fundamental limitation on the reach of scientific prediction, and, when planning for the future, it is vital to come to terms with it. Following Popper, I shall use the term prediction for conclusions about future events that follow from good explanations, and prophecy for anything that purports to know what is not yet knowable. Trying to know the unknowable leads inexorably to error and self-deception.

What is the rational approach to the unknowable … ?

Popper’s criterion [of being able to get rid of bad governments without violence] can be met only by societies that expect their knowledge to grow – and to grow unpredictably. And further, they are expecting that if it did grow, that would help.
This expectation is what I call optimism, and I can state it, in its most general form, thus:

The Principle of Optimism
All evils are caused by insufficient knowledge.

[Either] the laws of physics forbid eliminating [an evil] in a given time with the available resources or there is a way of eliminating it in the time and with these resources.

Summary: … Problems are soluble. … An optimistic civilization is open and not afraid to innovate, and is based on traditions of criticisms. Its institutions keep improving, and the most important knowledge that they employ is knowledge of how to detect and eliminate errors. There have been many short-lived enlightenments in history. Ours has been uniquely long-lived.

A Dream of Socrates

What has happened to the ‘difficulty of communication’ … ?

If it is a good theory … then it is exceeding hard to vary while still remaining a viable explanation. So the learners, through criticism of their initial [interpretations] and with the help of their books, teachers and colleagues, seeking a viable explanation, will arrive at the same theory as the originator. …
Slowly, and with many setbacks, the same is becoming true in non-scientific fields. The way to converge with each other is to converge upon the truth.

The Multiverse

Deutsch describes fungibility in terms of bank accounts. It may be that one has $100, but one does not have 100 specific dollars. It may be that $10 are paid in and then later $10 are paid out, but there is no sense in which they can be the same dollars. A bank is not at all like a piggy-bank. Multiverses have ‘measures’, from which subjective probabilities are derived (somewhat like Popper’s propensities).

[Common] sense and classical physics contain the parochial error that only one error exists. This error, built into our language and conceptual framework, makes it sound odd to say that an event can be one sense extremely unlikely and in another certain to happen. But there is nothing odd about it in reality.

[Every] object carries within it information about which instances of it could interact with which instances of other objects … it is known as entanglement information.

When two or more variables of a physical variable have differently affected something in the rest of the world, knock-on effects typically continue indefinitely … entangling more and more objects. if the differential effects can all be undone, then interference between those possible values becomes possible again; but … undoing them requires fine control of all the affected objects, and that rapidly becomes infeasible.

[For] any fungible collection of instances of a physical object, some of their attributes must be diverse.

We are channels of information flow [‘what affects what’]. Since the growth of knowledge is a process of error-correction, and since there are many more ways of being wrong than being right, knowledge=creating entities rapidly become more alike in different histories than other entities. As far as is known, knowledge-creating processes are unique in both these respects: all other effects diminish with distance in space, and become increasingly different, in the long-run.

What if there is something other than information flow that can cause coherent, emergent phenomena in the universe? What if knowledge, or something other than knowledge, could emerge from that, and begin to have purposes of its own, and to conform the multiverse to those purposes, as we do?

A Physicist’s History of Bad Philosophy

Deutsch has previously presented the Mach-Zehnder interferometer, where a photon stream is split by a half-silvered mirror and then the two paths are re-combined with another half-silvered mirror, to give a single stream. Thus:

[The] path that was not taken affects the one that was.

Deutsch claims that this shows that there are multiple universes. Deutsch is generally a follower of Popper. He denigrates positivism, which he describes as requiring that science should be ‘derived from observation’, and logical positivism, which he describes as supposing that ‘statements not verifiable by observation are not only worthless but meaningless.’

[Creating] a good explanation is hard … because there is an objective reality that does not meet anyone’s prior expectations … . [The] method of seeking good explanations creates an engagement with reality … .

Deutsch, in effect, criticises the use of statistics to generate Bayesian probabilities that were then used as if they were propensities. For example, good looks might haver a strong genetic component – but fashions and hence the perception of ‘good looks’ may change.

A theory that predicts how happy people will (probably) be cannot possibly take account of the effects of knowledge creation.

[Explanationless] science … really means science with unstated, uncriticized explanations … .

[As] soon as scientists allow themselves to stop demanding good explanations and consider only whether a prediction is accurate or inaccurate, they are liable to make fools of themselves.


Deutsch considers paradoxes of allocation and choice, including Arrow’s theorem. He notes that if ‘weight of evidence’ were analogous to opinions, then one would have similar paradoxes of personal choice. But:

[Rational] decision-making consists not of weighing evidence but of explaining it, in the course of explaining the world. … It is in the nature of good explanations – being hard to vary – that there is only one of them. … [Alternatives] have been not outweighed, but out-argued, refuted and abandoned. … [Typically,] one is struggling to create even one good explanation, and, having succeeded, one is glad to be rid of the rest.

[If] your conception of justice conflicts with the demands of logic or rationality then it is unjust. If your concept of rationality conflicts with a mathematical theorem … then your concept of rationality is irrational.

Deutsch compares first-past-the-post and proportional at length and claims that first-past-the-past is better at removing bad governments and policies’. He does not consider voting in isolation, but considers the impact of the system on the formation of parties and policies.

Successful truth-seeking system works its way towards broad consensus or near-unanimity  … . So convergence in the broad consensus over time is made possible by the fact that all concerned are gradually eliminating errors in their positions and converging on objective truths. Facilitating that process … is more important than which of two contending factions with near-equal support gets its way in  a particular election.

The purpose of deferring to the majority in democratic systems should be to approach unanimity in the future, by giving all concerned the incentive to abandon bad ideas and to conjecture better ones.

If those institutions do, as they seem to, fulfil the hope that it is possible for changes to be for the better, on balance, then human life can improve without limit as we advance from misconception to even better misconception.

Why are Flowers Beautiful?

Why are good explanations often ‘beautiful’? Is it purely cultural? Are all cultures and points of view equally valid? According to some cultures:

[When] analysed in sufficient detail, everything is mechanical. … Yet one cannot explain what a mathematician does … without referring to the objective truths of mathematics.

But if mathematics operates in a world outside of the laws of physics, it mat be that art does so too. Deutsch discusses co-evolution between flowers and insects.

[Both] the criterion [the insect’s requirements and tastes] and the means of meeting it [the flower’s attributes] had to be hard to vary.

Deutsch considers being ‘hard to vary’ a critical aspect of ‘beauty’, in art, mathematics and science.

The Evolution of Culture

Culture consists of memes, ‘sticky’ ideas, rational or anti-rational. Rational memes have some benefit to those who act upon them, and hence embody some kind of ‘truth’. Anti-rational memes are harmful, but typically come as part of a culture that protects its memes from challenge, and so stabilises societies.

The primary [means of propagating irrational cultures] is always to disable the source of new ideas, namely human creativity.


Static societies … are not perfectly unchanging. They are static on the trimescale that humans can notice; but memes cannot prevent changes that are slower than that.

[Rational] memes evolve towards deep truths, anti-rational memes evolve away from them.

Nations beyond the West today … must either become ‘Western’ in their mode of operation or lose all their knowledge and thus seek to exists … .
Even in the West, the Enlightenment today is nowhere near complete. It is relatively advanced in a few, vital areas: the physical sciences and Western political and economic institutions are prime examples … ideas are fairly open to criticism and experimentation, and to choice and change. But in many other areas memes are still replicated in the old manner, by means that suppress the recipients’ critical faculties and ignore their preferences. [This] is a difficult fact for us to accept.

[In] regard to academic knowledge … [without] a critical, discriminating approach to what they are learning, most [students] are not effectively replicating the memes of science and reason into their minds.

[Whenever] we find ourselves enacting a complex or narrowly defined behaviour that has been accurately repeated from one holder to the next, we should be suspicious. If we find that enacting this behaviour thwarts our efforts to attain our personal objectives, or is faithfully continued when the ostensible justification for it disappears, we should become more suspicious. If we then find ourselves explaining our own bad behaviour with bad explanations, we should become still more suspicious.

Another thing that should make us suspicious is the presence of conditions for anti-rational meme evolution, such as deference to authority, static subcultures and so on.

The Evolution of Creativity

[Paradoxically] it requires creativity to thrive in a static society – creativity that enables one top be less innovative than other people. {That] is how … societies [that] existed only by supressing innovation, constituted environments that strongly favoured the evolution of an ever greater ability to innovate.


Deutsch interprets ‘sustainability’ as follows:

[Suppose that] your way of life [is such that, whatever you do,] you can continue to live afterwards exactly as you did before. That is sustainable. But if your way of life leads you to invent a more efficient method of farming, and to cure a disease that has been killing many children, that is unsustainable.

But then he states:

[The] laws of nature cannot possibly impose any bound on progress … . In other words, progress is sustainable, indefinitely. But only by people who engage in a particular kind of thinking and behaviour – the problem solving and problem – creating kind of characteristic of the Enlightenment. And that requires the optimism of a dynamic society.

And on the other hand:

    A solution may be problem-free for a period, and in a parochial application, but there is no way of identifying in advance which problems will have such a solution. Hence there is no way, short of stasis, to avoid unforeseen problems arising from new solutions. But stasis itself is unsustainable, as witness every static society in history.

[There] are ideas that reliably cause disasters, and one of them is, notoriously, the idea that the future can be scientifically planned. The only rational policy … is to judge institutions, plans and ways of life according to how good they are a correcting mistakes: removing bad policies and leaders, superseding bad explanations, and recovering from disasters.

Prevention and delaying tactics are useful, but they can be no more than a minor part of a viable strategy for the future. Problems are inevitable, and sooner or later survival will depend on being able to cope when prevention and delaying tactics have failed. Obviously we need to work towards cures. But we can do that only for diseases that we already know about. So we need the capacity to deal with unforeseen, unforeseeable failures. For this we need a large and vibrant research community, interested in explanation and problem-solving. We need the wealth to fund it, and the technological capacity to implement what it discovers.

In connection with climate change, Deutsch opines:

[The aspiration for a ‘sustainable’ lifestyle] is dangerous. For what would we be aspiring to? To forcing the future world into our image, endlessly reproducing our lifestyle, our misconceptions and our mistakes. But if we choose instead to embark on an open-ended journey of creation and exploration whose every step is unsustainable until it is redeemed by the next – if this becomes the prevailing ethic and aspiration of our society – then then ascent of man, will have become, if not secure, then at least sustainable.

Strategies to prevent foreseeable disasters are bound to fail eventually, and cannot even address the unforeseeable. To prepare for these, we need rapid progress in science and technology and as much wealth as possible.

The Beginning

[A] persistent assumption remains that our existing theories are at or fairly close to the limit of what is knowable .. .

[The] most fundamental discoveries have always, and will always, not only consist of new explanations, but use new modes of explanation.

Everything physically possible will eventually be revealed: watches that came into existence spontaneously … .

Deutsch notes that all the laws of physics are expressed in terms of analytic functions. Hence anything that exists must have a non-zero probability, and hence must have a non-zero probability almost always, and hence must happen infinitely often. On the other hand, if we relate our knowledge to simulations, Deutsch questions the link between multiplicity of [simulated] universes and (prior) probability.

[We] should really understand all our predictions as implicitly including the proviso ‘unless the creation of new knowledge intervenes’.

What lies ahead of us in any case is infinity. All we can choose is whether it is an infinity of ignorance or of knowledge, wrong or right, death or life.


Deutsch is well respected and quite succinct. Popper says much the same, but people tend to focus on his headline criterion of falsifiability. In so far as Deutsch goes beyond Popper I find him unconvincing.

Optimism and Sustainability

Deutsch concludes that if only we invest enough in science and technology, we will be able to overcome all the problems , such as global warming, that the use of science and technology have thrown up. He is very scathing about sustainability, which he represents in an extreme version.

Even if one accepts his principle of optimism, it is not clear that ‘science and technology’ is the only source of relevant knowledge. Is designing a voting system a science, for example? Is the ‘Arab Spring’ only to be viewed through the lens of science?

I also find the principle itself vague and hence easy to vary, and hence not a good explanation for his conclusion. Does it mean that there are no dead-ends, where the thoughtless application of science and technology could lead us to inevitable extinction, no matter what we discovered subsequently? No evidence in support of such a belief has been given. But if this is not what is being claimed, then Deutsch’s conclusion does not follow.

If one takes the financial crisis of 2007/8, it seems to me that the best accepted science and technology was being applied (in so far as economics is a kind of science) and that this contributed to the crash. Politicians realised what was happening before there were mass lay-offs, but too late to do anything about it. Deutsch may argue that economics is not yet sufficiently scientific, but it seems to me that the difficulty of experimentation prevents economics from ever being a science of the kind that Deutsch considers. It also seems to me that the dominant economic theory was ‘hard to vary’. It has a lot of widely taught and believed propositions that all tend to support themselves, such that to question one you have to question many of them. Moreover, economics seems well crafted to provide politicians and others with the kind of answers that they seek, when a real science of economies might incorporate inevitable uncertainties. It seems to me that physics has not yet developed a satisfactory alternative to classical physics: quantum physics appears to be smoke and mirrors, and similarly it may be that there is not acceptable economic theory that accords with ‘the facts’. So the notion of ‘hard to vary’ seems to me to need developing further.


Deutsch’s notion of reach seems important, but not so well explained. What I think he means is that one seeks general rather than particular applications. Ordinary science does identify laws with reach, which one expects to be the same almost everywhere, almost all the time. But politics, economics, sociology, psychology and – arguably – biology and ecology are not like this: they depend on geography and cultures that vary with place and time, which are far richer than the parameters of physics. It seems to me, then, that these areas are of a different kind form ‘ordinary’ science. Thus, while one still needs a scientific ‘attitude’, one  should be careful about adopting the methods of the ‘hard’ sciences.

Abstractions and Emergence

Deutsch’s discussion of abstractions refers to ’emergence’ without explicitly acknowledging much related work that I would have thought relevant. (It was underpinned by mathematics that informed the development of economics.) According to this view, cultures can have their own laws, not derived from laws of nature, and not universal. It seems to me that science still struggles with this type of knowledge, and that it would be unsafe simply to assume that the traditional practices of science are adequate.

Infinity, Mathematics and Proof

Deutsch says some odd things about mathematics and proof, but this may be a question of terminology.

He regards mathematical statements as ideals, independent of physics. Later this leads him to recognize the possibility of other aspects of life, independent of physics. But at the end he seems to suppose that the problems thrown up by the application of science and technology can be solved by science and technology alone. But are these other aspects of life ‘independent’ in this sense? It seems to me that (as for concepts of ’emergence’) mathematics may need to be used to solve the problems thrown up by the use of science of technology, and hence – by analogy – so might other areas of knowledge.

I find Deutsch’s statements about proof extremely odd. To me a proof is a mathematical statement that justifies a conclusion in terms of axioms previously proven theorems. As a mathematical statement Deutsch would seem to regard it as an ideal, independent of physics. But he says that he regards proof as dependent on physics.

What humans and machines are capable of proving is dependent on physics, so I conjecture that by ‘proof’ Deutsch means what I would call ‘proof discovery’ or ‘proving’. For fully explicated proofs, proof checking should be straightforward. It seems to me that there exists an idealised ‘proof checking’ that is independent of physics, while our ability to construct a proof checking machine depends on physics.

Perhaps more seriously, Deutsch seems to misconstrue Turing’s work. Turing showed that a universal computer could emulate any ‘definite method’. But his work on morphogenesis showed how emergent properties can arise from processes that cannot be produced by any definite method. This is not to say that computers cannot simulate emergent properties, just that one the conceptual base that Deutsch refers to is technically inadequate.


Suppose that an airplane has crashed, that we believe it to be due to a software bug. All aircraft of that type are grounded. It will be disastrous if we do not find the bug within 48 hours. According to the principle of optimism:

[Either] the laws of physics forbid [finding the bug in time] with the available resources or there is a way of eliminating it in the time and with these resources.

According to Turing’s halting problem theorem, we cannot always know in advance how to find the bug in a given time. We can try to find the bug. We can make estimates of how long it will take, but we cannot be sure. The first point is that Deutsch’s principle isn’t as helpful as it seems. The second is that mathematical or other constraints that are not laws of physics may apply, so Deutsch’s principle seems to be

Either there is some reason (which you may not know) why you cannot eliminate an evil in a given time with the available resources or there is a way of eliminating it in the time and with these resources, although there may be no way to know what it is.

For example, consider:

Either the laws of physics forbid the UN of eliminating conflict in the middle east within a year or there is a way of eliminating it in the time and with these resources.


Either the UN will eliminate conflict in the middle east, or something will prevent it.

Dream of Socrates

Deutsch seems to suppose that science has already reached a kind of ‘critical mass’ where the key ideas are effectively promulgated. This may be true in some specific areas, but it seems to me that the use of science and technology can lead to problems that transcend these boundaries and that, for example, the ‘science’ of global warming has not (yet?) reached the stage where we should assume anything much about its adequacy or future development.

A key part of Deutsch’s dream is that ‘science and technology will always provide, given enough funding’. It seems to me that this is not common to all respectable scientists, and in this sense there is no single ‘dream’ that is being successfully promulgated.

Multiverses and Probability

I am something of a fan of Deutsch’s physics in this area, but this seems like a distraction from the main argument. From an evolutionary or relativistic perspective, things respond to what they know, and in particular to what might be the case, not just what is the case. Talking about other universes here seems to be just a language game.

In his physics, Deutsch employs conventional probabilistic models within universes, and links failure of such models to the existence of multiverses. As he says here, new knowledge is injected into the situation, which breaks the probabilistic model. It seems to me that this is a very helpful insight. For example, a culture or economy may be relatively stable and hence we may have a good probabilistic model, but if we come into contact with other cultures or economies we may find that our models fail.


If I had to select one quote, it would be:

[If] your conception of justice conflicts with the demands of logic or rationality then it is unjust. If your concept of rationality conflicts with a mathematical theorem … then your concept of rationality is irrational.

On the other hand, it seems to me that many people, including Deutsch, claim that logic and rationality apply to our actions in ways that are quite spurious. It is quite possible that the harm done in the name of logic and rationality is much greater than the benefits that might be gained by applying them properly, as long as one had sound debate.

Deutsch supposes that sound debate would lead to consensus. It seems to me that we are a long way from this, and I fail to see why it should be true in the long-run. If we were reaching a consensus, I suspect group-think, a failure of critical thinking and irresilience. It is almost as if either Deutsch or I had completely misunderstood the previous discussion on explanations and emergence. ‘Deferring to the majority’ is not always a good idea. Where would we be if all economists, financiers and politicians had genuinely deferred to the majority in 2006?

Cultures and memes

A key part of Deutsch’s discussions is an explanation of why evolution favours specific things, rather than arbitrary variations. Thus one tends to have behaviours that are locally optimal, without always being globally optimal. Thus, whereas under ‘choice’ he opines that certain mechanisms will favour convergence to single solutions, more generally this is not the case. Thus we cannot assume that are local culture, institutions or economics are the best, or that globalisation will necessarily lead to an optimal solution.

Deutsch notes that memes may be hard to vary either because they punish deviance or because variants are naturally less useful. Thus one should ask, are ideas about free-trade and capitalism successful because they are optimal, or because interested parties influence academic funding and the media? How would we know? Where would the debate take place?

Deutsch argues that memes are of one type or the other. But is seems to me that memes can act in conceptual ‘spaces’ that have multiple dimensions, or – to put it another way – memes can come in self-supporting clusters. It seems to me that these memes can be of different types in different dimensions, and that this can even be beneficial. For example, religious beliefs can promote trust relationships than then enable the development of freer markets and other good things.

Deutsch offers some good advice on spotting bad memes. I am applying ti in these comments.

The Beginning

I obviously do not ‘buy’ the conclusion. But the rather gratuitous argument from probability particularly annoys me.

Firstly, under ‘bad philosophy’ he seems to recognize the limits of probabilistic reasoning. But even if one applies probability theory uncritically, his argument is essentially that ‘x exists here’, so P(x) > 0, hence x exists infinitely many times, since the universe is infinite. But if there are infinitely many universes it could be that P(x)=0.


The key issue seems to be one which Keynes discusses in his mathematical Treatise. Some people suppose that regularity is natural, and it is irregularity that demands an explanation. Thus where a regularity is observed, they assume – ‘pragmatically’ – that it will continue, unless there is a specific reason why not. For example, in economics it has been assumed that trends can be extrapolate without considering the underlying situation. The alternative, with Keynes and Deutsch advocate, is to suppose that regularities are the result of some ‘systems’, and that one can only rely on extrapolations if there is reason to think that the systems will be maintained. This in economics one only relies on trends continuing when the relevant agencies (e.g. central banks) have the ability and will to sustain their preconditions.


Deutsch presents a view of the world somewhat like Whitehead’s, in which one has law-like epochs, with changes in ‘the rules’ between, but ends up, like Popper, advocating that one does one’s best in the epoch that you are in, and trust to your ability to cope should things change. But, for the reasons that Deutsch gives in the first part of his book, this isn’t the whole story. When the rules change, not everything changes. Some things stay the same. It is helpful (at least in my experience) to have a view about how robust the different rules of the current epoch are, so that one can more quickly modify one’s theories when necessary. Thus, it seems to me, one needs to have critiqued the existing theories in advance, and particularly their explanations, to judge which aspects are well founded and which are ad-hoc. It seems to me that the theories of physics are very bad exemplar for this. At best they offers us a theory with an explanation in terms experiments that, for the reasons that Deutsch gives, is simplistic. The practice of physics, with its on-going debates, offers us a better model, but only in its ‘live’ areas. My own view is that the area would be improved by more logical reasoning, acknowledging and describing the inevitable uncertainties in the theories.


Thought-provoking. Some useful insights. But I prefer my optimism more humble and forward-looking. Where Deutsch offers a dichotomy that is analogous to trust or distrust, I prefer ‘trust but verify’. Where he offers a choice between jump or don’t jump, I prefer ‘look before you leap’. Where he looks to science and technology, I would look to a broader mix.

In Whitehead’s terms, one needs to differentiate between the various ‘levels’ in considering the rules, and characterise risk and uncertainty.

If we think of risk in terms of sailing around a headland into the unknown, the Deutsch offers the choice between venturing around or not. But there may be more to it. Perhaps we can have a back-up fleet anchored in safety, wait for a strong head-wind and then row around the headland, poised to sail back to our colleagues most rapidly, at the first sign of trouble.

See Also

David Deutsch’s TED talk : A new way to explain explanation.

My notes on science and, more generally, on rationality and uncertainty.

Dave Marsay

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