The Fabric of Reality David Deutch

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.

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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
corroborated. 
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[3] — 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.

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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.

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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 holds?
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.
CRYPTO-INDUCTIVIST: I accept that.
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

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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-
falling 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

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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.
CRYPTO-INDUCTIVIST: 
What?
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

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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.

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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.
CRYPTO-INDUCTIVIST: Yes, I see.
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.
CRYPTO-INDUCTIVIST: …
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

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

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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,

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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?
CRYPTO-INDUCTIVIST: Er, yes.
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

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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’.
CRYPTO-INDUCTIVIST: Fire away.
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.
CRYPTO-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.
DAVID: 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.

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DAVID: Surely that is not called for. We Popperians believe in letting our
theories die in our place. Just throw 
inductivism overboard instead.
EX-INDUCTIVIST: I will, I will!
TERMINOLOGY
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.
Next, the fourth strand, the theory of evolution, which answers the question
‘what is life?’

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