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The Pessimistic Meta-Induction
and the Exponential Growth of Science
Ludwig Fahrbach
PLEASE DO NOT QUOTE
Abschnitte und Absätze, die fürs Seminar nicht wichtig sind, sind mit zwei Sternen ** gekennzeichnet.
I aim to defend scientific realism against the argument of pessimistic meta-induction. I start
form a preliminary definition of scientific realism according to which empirical success of a scientific
theory licenses an inference to its approximate truth. Pessimistic meta-induction, then, is the argument
that this inference is undermined by numerous counterexamples, i.e., by theories from the history of
science that were successful, but false. To counter pessimistic meta-induction I argue that the realist
should refine his position by using a graded notion of empirical success. I then examine the history of
science and formulate some claims about the pattern of how the degrees of success of the best theories
have developed over the history of science.
I proceed as follows. First, I define scientific realism, and present the No-miracles argument.
Second, I formulate a simple version of pessimistic meta-induction (simple PI, for short), and examine
how it undermines the realist’s position. Third, I sketch a counterstrategy for realists against this version of PI. This counterstrategy relies on the notion of degrees of success of scientific theories. It
states that in the history of science degrees of success have been continuously growing, and that our
current best theories have higher degrees of success then any of their predecessors. In response antirealists may present what I call the sophisticated PI. The sophisticated PI states that the growth of degrees success of theories has been continually accompanied by theory changes, therefore we should
extrapolate the existence of refuted theories to current degrees of success undermining the inference to
truth. In the second half of the paper, I argue that the case for the sophisticated PI has not been made.
At the centre of my counterargument will be the observation that the increase in degrees of success
over the history of science has by no means been uniform, quite the opposite, most of its increase occurred in very recent times.
1 Scientific Realism
1 Definition of scientific realism and definition of success
In this paper, I start from the definition of scientific realism as the position that the following inductive principle which I call the success-to-truth principle is correct: Empirically successful theories
are probably approximately true. Another formulation of this principle that I will use is that the empirical success of a scientific theory is a good indicator of the approximate truth of the theory. Later this
definition will be refined. Examples for successful theories that realists have in mind here are theories
such as the atomic theory of matter, the theory of evolution or claims about the role of viruses and
bacteria in infectious diseases.
The success-to-truth principle is not meant to be a full-blown account of confirmation or induction; it is only meant to capture the common core relevant for the realism debate as discussed in this
paper of all those inductive principles or accounts of theory confirmation, such as inference to the best
explanation, hypothetico-deductivism, etc., that realists typically offer to formulate their respective
variants of scientific realism.
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I adhere to the following conventions. Because it plays only a minor role in this paper, I generally omit the term “approximately” in “approximately true” and simply use “true”.1 Furthermore, I use
the term “theory” in a rather generous sense so that it also denotes laws of nature, theoretical statements, sets of theoretical statements and even classification systems such as the Periodic Table of Elements the reason being that realists usually want to endorse the truth of the statements involved in
these things as well. For example, the term “Periodic Table of Elements” is meant to refer to the
statements involved in that classification system.
We need to define the notion of empirical success. I will start here with a simple definition of
success, which will be refined in some ways over the course of the paper. The definition employs entirely standard ideas of how theories are tested by observation. Thus, a theory is empirically successful
(or simply successful) at some point in time, just in case its known observational consequences fit with
all the data gathered until that time, i.e., the theory describes correctly, as far as scientists know at that
time, all observations and experimental results gathered by scientists until that time, and there are sufficiently many such cases of fit. In other words, a theory is successful at some point in time, just in
case scientists have been able to compare sufficiently many consequences of the theory with observations until that time, and all of them have turned out to be correct.
2 Comments on the definitions
I defined scientific realism as a position which endorses a certain inductive principle, so my definition of realism is a purely epistemic one. Many definitions of realism offered in the literature involve, in addition, semantic, pragmatic and other conditions, but in this paper I focus on epistemic
topics. 2 Put in general terms, the question at issue is how far inductive inference can take us beyond
all observations that scientists have gathered so far, or, in other word, which forms of inductive inferences are reliable and which are not. Realists are typically optimistic about the reach of inductive inference, and therefore endorse the success-to-truth principle or similar principles of induction. In contrast, anti-realists typically doubt in different ways and to different degrees that inductive inference can
take us very far beyond observation, and therefore normally reject the success-to-truth principle and all
the realist principles of inference, of which it is the common core. They maintain, for example, that it
is nothing but the fallacy of affirming the consequent (e.g., Laudan 1981, Alan Musgrave 1988, 230).
There are many different forms of anti-realism, of course, but in this paper I will understand the
position of anti-realism entirely negatively as the rejection of the success-to-truth principle, because I
only want to discuss realism, and arguments for and against realism, and none of the different forms of
anti-realism. So, anti-realists only occur as people who oppose scientific realism and offer counterarguments and other challenges to realism.3
3 The No-miracles Argument
The most important argument offered by realists to support the success-to-truth principle and
similar principles is the no-miracles argument (NMA for short) (Putnam 1978, Smart 1960). The simplest version consists in pointing out the inherent plausibility of the success-to-truth principle: “Given
that a theory enjoys empirical success wouldn’t it be a miracle if it nevertheless were false? Wouldn’t
it be miracle, if infectious diseases behaved all the time, as if they are caused by viruses and bacteria,
but there are no viruses and bacteria.” This argument appeals directly to our confirmational intuitions.
For what follows, we need not engage in a detailed examination of the different versions of the NMA,
1
Realists usually admit that a general explication of the notion of approximate truth has not yet been devised and may even
be impossible to devise, but they think that our intuitive grasp of that notion and scientists’ successful application of it in
many specific situations suffice to justify its use for defining realism. An obstacle for devising a general explication of the
notion of approximate truth is identified in Alexander Bird (2007).
2 For recent book length treatments of the scientific realism debate see Jarrett Leplin (1997), André Kukla (1998), Stathis
Psillos (1999), Jaako Niiniluoto (1999), and Kyle Stanford (2006).
3 For a comparison of different forms of anti-realism with regard to the pessimistic meta-induction see Fahrbach (2009a,
2009b).
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all we need to note is that, in the end, they are all based on confirmational intuitions, which are by and
large shared by most realists. Let us call those intuitions the “shared realist intuitions”.4
As anti-realists reject the success-to-truth principle and all the confirmational principles of
which it is the common core they also reject whatever arguments realists offer in support of these
principles, that is they reject all versions of the NMA. For example, they reject inference to the best
explanation. Thus, realists and anti-realists are engaged in an ongoing dispute over the success-to-truth
principle, the principles of which it is the common core, and the possibility of their justification, in
which no side can convince the other side, and which goes on without any signs of a resolution. Their
disagreement can be traced back to a clash of intuitions, where the “shared realist intuitions” on which
the different versions of the NMA are ultimately based are rejected by anti-realists, who simply do not
share them.
2 The pessimistic meta-induction
1 The simple PI
But now, the anti-realist thinks she can offer an independent argument – independent of her rejection of the NMA, inference to the best explanation, the realist’s confirmational intuitions, etc. –
which undermines the success-to-truth principle. This argument is the simple PI. The simple PI moves
from the premise that the history of science is full of theories that were once successful and accepted
by scientists as true, but later refuted and abandoned. Let’s assume for the time being that this premise
is correct. Then these successful, but false theories constitute counterinstances to the inference from
success to truth. In other words, the success-to-truth principle has had a really bad track-record, which
counts strongly against its being valid. This is the simple PI.5
The premise of the simple PI about the widespread occurrence of successful but false theories in
the history of science requires evidence. Thus, antirealists present long lists of examples of such theories. Larry Laudan (1981) famously presents the following list of theories, all of which were once successful, and all of which are now considered to have been refuted:
•
•
•
•
•
•
•
•
•
•
•
•
The crystalline spheres of ancient and medieval astronomy
The humoral theory of medicine
The effluvial theory of static electricity
’Catastrophist’ geology (including Noah’s deluge)
The phlogiston theory of chemistry
The caloric theory of heat
The vibratory theory of heat
The vital force theories of physiology
Electromagnetic ether
Optical ether
The theory of circular inertia
Theories of spontaneous generation.
The anti-realist then argues that, even if judged from the perspective of the realist, i.e., starting
from the confirmational views and intuitions of the realist (his optimism about the reach of inductive
inference, the NMA, the shared realist intuitions) and disregarding the confirmational views and intuitions of the anti-realist, the success-to-truth principle has to be given up. From this perspective two
arguments concerning the success-to-truth principle have to be considered, the NMA and the simple
PI. The NMA supports the success-to-truth principle, the simple PI undermines it. The two arguments
have to be balancee against each other. The anti-realist maintains that the result of the balancing is that
the simple PI is much stronger than the NMA. Whereas the NMA is apriori and theoretical, and ulti4
The nature of the intuitions, whether they are a apriori or somehow rooted in experience, need not concern us here.
Compare, among others, Psillos (1999, ch. 5), Psillos (2000), Peter Lewis (2001), Michael Devitt (2005), Kitcher (2001),
??? Lyons and Juha Saatsis (2004).
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mately based on intuitions, the premise of the simple PI is based on empirical evidence from the history of science, and provides many concrete counterexamples against the inference from success to
truth.6 What better case against an inference than counterexamples can you provide? Hence, the success-to-truth principle’s support by the NMA is trumped by its negative track record, the wide-spread
incidence of successful, but false theories in the past. The anti-realist concludes that even if one endorses the realist’s confirmational views and intuitions, one has to change one’s view about the success-to-truth principle, and admit that is undermined by the past of science.
What follows for our current successful theories which are so dear to the realist’s heart? The anti-realist can offer what he might call the No-indicators argument: Empirical success is the only promising indicator of truth in empirical science. It is neutralized by the history of science. No other indicator of truth is available to justify our belief in our current successful theories. Therefore, belief in the
truth of those theories is not justified.
2 Three Counterstrategies
**The counterstrategies realists have devised to defend their position against the simple PI fall
roughly into three kinds. Consider the success-to-truth principle: If a theory is successful, then it is
true. Counterstrategies of the first kind restrict the consequent, i.e., restrict what can be inferred from
success; counterstrategies of the second kind restrict the antecedent, i.e., restrict from what truth can
be inferred; counterstrategies of the third kind are combinations of the first and second counterstrategy.
**Counterstrategies of the first kind restrict the consequent of the success-to-truth principle:
They weaken it to an inference from success to some diminished form of truth, such as reference, truth
restricted to some sub-domain of the original domain of the theory, or partial truth (truth about structure, about classification, or about other parts that contributed to the success of the theory). To defend
the inference to diminished truth, proponents of this counterstrategy aim to show that the theory
changes of the past were mostly not as deep as might have seemed at first sight, that the successful
refuted theories of the past, although strictly speaking false, were – judged from today – not entirely
false, but had terms that referred, were approximately true in restricted domains, had parts that were
true, etc. In pursuit of such strategies, realists have developed elaborate accounts of reference, partial
truth, and so on.7 If any of these accounts work, the position of the realist (the success-to-truth principle) is weakened somewhat, but we can still infer some diminished form of truth for our current successful theories. I will later (mis-)use this kind of strategy in my defence of the “shared realist intuitions”.
**The counterstrategies of the second kind restrict what truth can be inferred from by working
on the notion of empirical success. The simplest version consists in noting that several theories on
Laudan’s list enjoyed very little success. For example, Kitcher writes “Laudan’s list includes such
things as the humoral theory of medicine, catastrophist geology, and theories of spontaneous generation. In none of these examples does it seem right to hail the theory as successful…”.8 This reduces the
inductive base of the simple PI somewhat, and therefore weakens it somewhat, but it leaves many
counterexamples untouched, so this reply cannot help much. Other versions of the second counterstrategy, also meant to decrease the number of counterexamples, consist in raising the standards for
counting a theory as successful. The most prominent version of this strategy relies on the demand that
a theory only count as successful, if it has made novel predictions. Unfortunately there remain important cases of refuted theories which produced true novel predictions before being refuted, such as
theories of light and the caloric theory of heat (see Lyons). What is more, the value of novel predictions is quite contested (Hempel, Hull). Therefore, this attempt also succeeds only partially, at best.
6
See also Ladyman/Ross 200??, p. 83
There is a lot of literature on these approaches. See, for example, McMullin (1984, p. 18), Kitcher (1993), Leplin (1997),
Psillos (1999), John Worall (19??), Martin Carrier (2004), Gerhard Schurz (2004, 2009), Nola, Theo Kuipers, Ladyman/Ross (2007??), and so on.
8 Kitcher (2001, footnote 31); likewise McMullin (1984??), McAllister (1993), Kukla (1998), Psillos (1999, Ch. 5), Devitt
(2005, 772).
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**Finally, counterstrategies of the third kind combine the first and the second counterstrategy.
For example, they refine the success-to-truth principle so that it asserts that an increase in success
leads to an increase in truth-likeness. This is the popular idea that increase in success leads to convergence to truth.
In this paper, I want to develop a version of the second counterstrategy. It relies on grading the
notion of success. Let us begin with the following simple, standard account of theory testing. In order
to test a theory, scientists derive observable consequences, i.e., predictions, from the theory and make
observations. A particular test of a theory consists in comparing some prediction of the theory with
some observation. I use the notion of a test in a rather broad sense here to cover all cases in which
scientists are aware of the theory coming into contact with experience so that it is possible for the theory to fail.9 Also I use the term “prediction of a theory” in a broad sense to denote any observable consequence of the theory scientists are aware of.10 The reason to do so will become apparent later. If
prediction and observation agree, the theory enjoys some measure of success. As a theory passes more
and more tests its degree of success increases. Hence, different theories can differ with respect to the
degree of success they enjoy at some point in time, and the same theory can enjoy different levels of
success at different points in time. As we will see later, these differences can be quite large.
If prediction and observation don’t agree, the theory suffers from an anomaly. As long as the
anomaly is not significant or the anomalies do not accumulate, they can be tolerated. If the anomaly is
significant or the anomalies do accumulate, the theory counts as refuted. In that case scientists have to
look for alternative theories, and a theory change may take place. Of course, this account of theory
testing and empirical success is rather minimal in several respects and could be made more precise in
many ways, but it is all we will need at the moment. Later on, I will refine it further in several respects.
3 The modified success-to-truth inference
Given the grading of success, the assertion is very plausible that the degrees of success of the
theories accepted by scientists in the history of science have by and large grown steadily over time.
They have grown both during theory changes and between theory changes. During theory changes,
successor theories have usually incorporated the successes of their predecessors, and were moreover
successful where the predecessors failed, for the simple reason that they have typically been designed
to take over the successes of their predecessors and to avoid the failures of their predecessors. As for
the times in between theory changes, theories have usually become more successful while they were
accepted (before possibly significant anomalies showed up or anomalies began to pile up), because the
amount and diversity of data, the precision of measurements, the precision of the predictions, etc.,
have been growing all the time in the history of science.
Realists can then offer the following idea of a counterargument to the simple PI: Because degrees of success have increased during the history of science our current best, i.e., most successful,
theories enjoy higher degrees of success than past theories; therefore, we are warranted to infer their
probable truth; in contrast theories of the past were not sufficiently successful to warrant an inference
to their probable truth (as the theory changes of the past show). Hence, according to this idea realists
modify the success-to-truth principle so that it allows the inference to truth for current levels of success only. This idea to counter the simple PI belongs to the counterstrategies of the second kind in that
it does something with the notion of success. To support the modified success-to-truth principle realists invoke, as before, the NMA (in whatever version), although modified so that it only supports the
revised success-to-truth principle. Remember that we are only concerned with defending and restoring
Kitcher’s (2001) notion of success includes practical success in our dealings with the world to reach our practical goals. I
don’t include practical success in my definition, because to every case of practical success which somehow depends on a
theory corresponds a true consequence of the theory, so that my notion of success captures all practical successes of theories
as well. The practical success of science and technology, especially over the last 100-200 years, is nevertheless a good indicator of success in my sense, and could be used alongside the other indicators of success I discuss below.
10 One kind of observational consequence has to be excluded, though, namely irrelevant consequences of a theory which, if
true, offer no support for the theory at all. For example, T implies TO, where O is any true observation sentence, but T is
usually not confirmed by TO. For further discussion of this problem and an account of irrelevant consequences see Schurz
(1991).
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the realist position, hence we assume that realists are allowed to call upon their confirmational views
and intuitions, and disregard the intuitions of anti-realists. The “shared realist intuitions”, then, feed
into the modified version of the NMA so that it supports the modified position that only current levels
of success indicate truth. If this counterargument works, the realist position is not incompatible with
the history of science, and is saved from the attack by the simple PI.11 As we will see this idea is on
the right track. But it is seriously underdeveloped and certainly looks rather ad hoc so far. It is open to
objections from the anti-realist. Let us look at the objections.
4 Three objections**
The anti-realist can raise three objections. The first objection reiterates the argument from earlier
that the realist applied the NMA to past successful theories some of which were refuted showing that
the „shared realist intuitions” on which it is based are not trustworthy. Hence, the realist can no longer
use them to support anything at all, specifically not the inference to truth for current levels of success.
The realist may respond that a realist in 1800 or 1900, for example, should not have made the inference to truth and should not have supported it by the NMA, because, if he had really possessed shared
realist intuitions and had carefully attended to them, he would have recognized that those levels of
success were actually not high enough to indicate truth; if we listen carefully to shared realist intuitions we recognize that they tell us that only current levels of success suffice to indicate truth.
This response of my realist is certainly not satisfactory. We may wonder whether instead of past
realists not carefully attending to shared realist intuitions, it is my realist who is not carefully attending
to them and only hears from them what he wants to hear, namely that they differentially support the
success-to-truth inference for present, but not for past levels of success. In any case the realist intended
the shared realist intuitions to accord with the intuitions of the working scientists. But the scientists
themselves accepted the theories of the past that were later refuted. Therefore, the shared realist intuitions are such that they did back the inference to truth for past levels of success. The realist cannot
simply change his intuitions as it suits him. Thus, he is still faced with a conflict between the conclusion of the NMA, applied to the theories of the past, and the historical track record, which still throws
the trustworthiness of the shared realist intuitions into doubt.
For the second objection the anti-realist grants that the first objection can be met somehow, that
the shared realist intuitions are not discredited by their application via the NMA to past refuted theories. The second objection starts with the observation that in his defence the realist uses a simple distinction between past and present science. This distinction is based on a distorted view of the relative
weights of past, present and future times. Science has been a human endeavor for at least some centuries now, and will probably go on for some more centuries (or so we can assume). The present is only
a small part of this whole time period. The objection then is that the realist’s preference for the present
looks entirely arbitrary and ad hoc. Why should we believe that it is precisely now, instead of at some
future time, some decades or centuries from now, that a level of success sufficient for truth is reached?
The realist invokes the NMA, but that only pushes the problem back one step: If it is granted that the
NMA does not apply to past levels of success, why does it support the inference from success to truth
for current theories, and not just for theories of some future time? What is special about the present
levels of success? The anti-realist submits that my realist’s whole defence looks as if he adjusted his
position a bit too flexibly to the history of science.
5 The sophisticated PI
The third objection of the anti-realist is as follows. The anti-realist objects that a realist in 1900,
for example, could have reasoned in exactly the same way as my realist just did: “Success of scientific
theories has generally been growing until now. All our current best theories enjoy higher degrees of
success today than any of the refuted theories of the past. Consequently we can infer the truth of our
current best theories from their success, (where that inference is supported by the NMA), whereas their
predecessors’ lower degrees of success in the past didn’t suffice for an inference to their truth.” This
reasoning of a realist of 1900 would have been futile, says the anti-realist, because many of the best
11
Leplin (1997, p. 141), Kyle Stanford (BJPS??, Buch??), Psillos and Gerard Doppelt (2007), among others, mention or
discusses variants of this argument.
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theories of 1900 were refuted after 1900. In general, at any point in the history of science, whether
1700 or 1800 or 1900, realists could have reasoned in exactly the same way as the realist just did
(namely that the levels of success of their respective successful theories had risen and now sufficed to
indicate truth), but all these realists would have been refuted by later theory changes. The anti-realist
asks: What is different about current levels of success that they – all at once – suffice to indicate truth,
whereas past levels of success did not suffice to indicate truth? This rhetorical question means, of
course, that nothing is different today, and that we should expect that our current best theories will
suffer the same fate that befell the theories of the past.
The realist will immediately reply that there does exist a relevant difference between past and
present, namely precisely the degrees of success of the respective best theories; they have increased
between the past and the present. So, the epistemic situation of a realist in 1900 and the epistemic situation of a contemporary realist are actually not similar. To this the anti-realist replies that the very
same dissimilarity, namely a difference in degrees of success, also existed for a realist in 1900, namely
with respect to a realist in 1800, say, but after 1900 refutations did occur, showing that the difference
did not save the realist of 1900 from being refuted. So, what is going on here? I take it that the third
objection is meant to be the following piece of reasoning: In the history of science, degrees of success
have been growing continuously for several centuries, and all the time right to the present while they
have been growing, theories enjoying those degrees of success kept being refuted. We should extrapolate the incidence of false theories from past levels of success to current levels of success.12 Such an
extrapolation along degrees of success does justice to what is similar and what is not similar between
the epistemic situations of the different times. It supports that many of our current best theories will
also be refuted at some future time. It is another version of the PI. I will call it “the sophisticated PI”.
The sophisticated PI is an argument in support of the claim that there exist many counterexamples to
the inference from success to truth for current levels of success, and thereby undermines that inference. If it is correct the defence of the realist presented above does not work.13
**Like the second objection the third objection is independent from the first objection; hence the
third objection may work, even if the first does not. (I will later provide an independent reply to the
first objection.) Thus, for the third objection it can be granted that the NMA still has force. This means
that we have to balance two arguments once again, in this case the sophisticated PI with the NMA.
The result of the balancing is less clear than in the first case of balancing, the simple PI with the NMA,
but I will simply assume that the sophisticated PI trumps the NMA also in this case. An additional
reason to do so is that the sophisticated PI can be strengthened somewhat. It is not plausible that the
increase in levels of success has been uniform for all successful theories across all scientific fields.
Instead, it is quite clear that among our current best theories those of some fields have reached higher
levels of success earlier than those of other fields, and have differing levels of success today. In general, the distribution of levels of success across scientific fields at all points in time is far from uniform, even if we only consider the best theories of some time. Therefore, the anti-realist could claim
that it is plausible that some of the refuted theories already enjoyed degrees of success that are typical
of our current best theories; these cases can be used to undermine the success-to-truth inference for
current levels of success directly without invoking an extrapolation. This strengthens the third objection. Anyway, I will ignore these complications (balancing and non-uniformity) from now on.
It is clear that the arguments and objections presented so far assume quite some degree of simplification of the history of science. However this makes the arguments and objections clearer, and it
can, as we will now see, be tolerated. I will now tackle the third objection. This will be the main part
of the paper. It will also provide a response to the second objection. Afterwards I will tackle the first
objection.
12
See also Stanford (2006, Ch. 1.2), Gerald Doppelt (2007), Bird (2007, Section 4.1).
A similar extrapolation threatens to refute a counterargument by Devitt against the PI. Devitt wants to argue against the PI
by invoking the improvement of scientific methods (see Devitt 1991, p. 163, and Psillos 1999, p. 104). His suggestion can be
challenged by an argument similar to the sophisticated PI: In the last few centuries, scientific methods have improved all the
time, and while they have improved, the theories accepted by scientists kept being refuted, therefore, we should extrapolate
this pattern of failures to current levels of quality of scientific methods.
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3 The Growth of Success
1 Problems for the sophisticated PI
How good an argument against the success-to-truth inference is the sophisticated PI? It has the
premise that “all the time right to the present theories have been refuted”. So far this premise is just a
claim. What is its support from the history of science? The anti-realist will probably assert that it is
supported by the same data from the history of science that supported the simple PI, namely the refuted theories on Laudan’s list and other such examples offered in the philosophical literature. But is that
really so? Let has have another look at those examples. If we do so we notice that all the theories on
Laudan’s list are actually rather old, namely more than 100 years old. The same holds for practically
all examples of theory changes offered in the philosophical literature.14 Kyle Stanford (2006) extensively discusses three further examples, but they are older than 100 years as well. So far anti-realists
have not shown that theory changes occurred “right to the present”, i.e., they have not offered sufficient support for the sophisticated PI so far.
Anti-realists could react by trying to show that despite the difference in time between the refuted
theories and our current best theories, the difference in degrees of success is not that big, so it is still
true that we should extrapolate the occurrence of false theories to current levels of success. At this
point I could stop. The burden of proof is clearly on the side of anti-realists to show that this reply can
be made to work. As long as he has not shown this there is no attack on realism.15 But I won’t stop
here. Instead I want to show that the prospects for anti-realists to succeed with this task are not good at
all. To do so I will now aim to compare the degrees of success of the refuted theories with those of our
current best theories.
In preparation of the comparison, let me present some further examples of what I consider to be
our current best theories. Here is a list meant to be representative of our current best theories (remember that the realist endorses the approximate truth of those theories):
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








the Periodic Table of Elements16
the theory of evolution17
“Stars are like our sun.”
the conservation of mass-energy
the germ theory of disease
the kinetic gas theory
“All organisms on Earth consist of cells.“
E = mc2
“The oceans of the Earth have large-scale systems of rotating ocean currents.”
And so on18
The list does not include any theories which are simple generalizations from just one kind of observation such as “all pieces of copper expand when heated”. The abandonment of such low-level empirical generalizations is sometimes called “Kuhn-loss”. There seems to be wide agreement that Kuhnlosses are rare in the history of science, i.e., such low-level empirical generalizations have rarely been
abandoned. Therefore, we need not take them into account. Consequently, all theories on my list are
more than just low-level empirical generalizations: They have a certain measure of unifying power
14
As is often the case in philosophy, the same examples are discussed again and again. Here the most discussed examples by
far are the cases of phlogiston, caloric, and ether, all of which are older than 100 years. Examples that are also discussed a lot
are the cases of Newtonian mechanics, QM and GTR, but I want to exclude them from my discussion, because theories in
fundamental physics seem to me to represent a special case with respect to the success-to-truth inference, and should therefore be examined separately.
15 The anti-realist may also try to search for examples of refuted theories which enjoyed degrees of success typical of our
current best theories from the recent history of science. I will later examine this second possible reply by the anti-realist.
16 As remarked at the beginning of the paper, I use the term “theory” in a rather broad sense.
17 The theory of evolution may be taken to consist of two claims, that all organisms on earth are related by common ancestors, and that natural selection is an important force for change.
18 The list does not contains any theories from fundamental physics such as Quantum Theory and the Special Theory of Relativity, because, as just remarked, I think that theories from fundamental physics represent a special case.
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(generalize over several distinct domains), or are about unobservables, or are about facts that are otherwise not easily accessible, etc.
In order to compare the degrees of success of current best theories with the successful, but refuted theories of the past I want to employ five “indicators of success”. I call them “indicators of success”, because they are positively correlated with the degrees of success of theories. The first indicator
is the amount of scientific word done by scientists until some time. The second, third, and fourth indicator are the amount, diversity and precision of scientific data and observations gathered by scientists
until some time. The fifth indicator is the amount of computing power available to scientists at some
time. I will examine the growth of these indicators over the history of science. From their growth I will
draw an inference to the degrees of success of both the refuted theories of the past and our current best
theories. This inference will constitute the main argument of this paper. Before turning to discuss the
indicators I have to warn the reader. He will now be showered by a great deal of figures.
2 First indicator: the exponential growth of scientific work
The first indicator of success I want to examine is the amount of scientific work done by scientists in some period of time. Here, “scientific work” means such things as making observations, performing experiments, constructing and testing theories, etc. The amount of scientific work done by
scientists in some period of time can be measured with the help of various quantities. Two such quantities are especially pertinent: the number of journal articles published in the respective period of time
and the number of scientists working in the respective period of time. Because we are only interested
in very rough estimates of the amount of scientific work done in different periods of time, both quantities are plausible ways to measure over-all scientific work during those times. 19 Consider the number
of journal articles published by scientists every year. Over the last few centuries, this number has
grown in an exponential manner. The doubling rate of the number of journal articles published every
year has been 15 – 20 years over the last 300 years. Before 1700, there were, of course, even less publications per year than anytime after 1700. Roughly the same growth rates hold for the number of scientists over the last 300 years (although we can assert this with less confidence for times before the
20th century, because for those times not much good data is available). 20
1900
1950
1970
1990
2010
-∞
Figure 1. The time-line weighted in such a way that the length of any interval is proportional to
the amount of scientific work done in that interval.
Growing with a doubling rate of 15-20 years is a very strong sort of growth. It means that half
of all scientific work ever done was done in the last 15-20 years, while the other half was done in all
the time before; and three quarters of all scientific work ever done was done in the last 30-40 years,
while one quarter was done in all the time before. Figure 1 provides an idea of this sort of growth.
Scientific work is connected with success of theories in the following way. Our definition of degrees of success implies that a theory gains in degree of success, if it passes more tests,
where a test of a theory occurs whenever scientists compare a consequence of the theory with some
piece of data. Hence in the testing of theories two kinds of scientific activities are involved: gathering
data and deriving consequences from theories. Scientists need to gather data, i.e., make observations
and perform experiments. This is certainly an important kind of scientific work for which scientists
often have to invest considerable effort and time. But in addition scientists need to make calculations
19
There are also other ways of measuring scientific work such as government and industry expenditures on research, the
number of scientific journals (rather than scientific journal articles), the number of universities and the number of doctorates.
Where data is available it shows that all these ways of measuring the amount of scientific work yield essentially the same
results.
20 For more details and references see Fahrbach (2009a).
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and derivations to arrive at consequences from the theories they want to test. The latter is often not
easy to do either. In most physical sciences and increasingly in many other natural sciences, theories
are formulated using mathematical equations, for example differential equations, therefore scientists
can only arrive at predictions from the theories by solving those equations. But developing and applying such methods is often hard work and may require a great effort on the part of the scientists.
The increase in amount of scientific work done over some time is then linked with the increase
in degrees of success of theories over that time via three steps: (1) the increase in amount of scientific
work leads to an increase in both the amount and the quality of both observations and calculations. (2)
An increase in the amount and quality of both observations and calculations leads to an increase in
both the number and quality of tests of theories. (3) If the number and quality of tests of theories increases, and the tests are passed, then the degrees of success of the tested theories increases, see Figure
2.
More scientific work → more and better observations/calculations
→ more and better tests
→ more success
Figure 2.
3 First part of main argument
Using the link between scientific work and degrees of success, we can now formulate the first
part of the main argument (where the main argument is the inference from the indicators of success to
the degrees of success of the two classes of theories we want to compare). It’s only the first part, because it relies only on the first indicator of success. The rest of the main argument will then be developed over the next few sections.
The first part of the main argument proceeds as follows. As we just saw, by far most of the
growth of scientific work has occurred in the recent past, i.e., in the last 50 to 80 years. Our current
best theories have profited from this increase via the three steps: The increase in scientific work has
meant a huge increase in relevant observations and computations; this has resulted in a huge increase
in tests of those theories; that all these theories have been approximately stable in the last 50 years
(and often much longer) shows that practically all these tests were passed; finally, the high amount of
passed tests has resulted in a huge increase in degrees of success for these theories. So, our current
best theories have received a big boost in degrees of success in the recent past, an increase that is far
greater than any increase in success for any theories of earlier times. In contrast, the refuted theories
discussed by philosophers were all held prior to the big boost of success, therefore they could not partake in it. Therefore, their degrees of success were quite modest. Figure 1 can be used to represent the
big boost of success by reinterpreting the x-axis as depicting the degrees of success of the respective
best theories at different points in time. The conclusion of the main argument is the main thesis of this
paper: Our current best theories enjoy far higher degrees of success than any of the successful, but
refuted theories of the past, which enjoyed only quite modest degrees of success. The main thesis provides us with the sought comparison between current best and refuted past theories.
An objection to the first part of the main argument may be that in many scientific fields more
scientific work has obviously not lead to more successful theories. There are many domains of reality
such as the economy and human society where a lot of efforts by scientists investigating those domains has lead to quite moderately successful theories at best. The same holds for many theories in the
natural sciences such as theories about the origin of life on earth, the future weather or the fundamental constitution of everything. Generally speaking there are, quite obviously, still a lot of large gaps in
our knowledge of the world, despite the exponential growth of scientific work. Indeed, most hypotheses considered at the “research frontier” of science are further examples. So, the two quantities, scientific work and degree of success, seem to be fairly independent from each other.
In reply it has to be conceded that the relationship between scientific work and success is not as
straightforward as the three steps may suggest. Instead, it is a complex and contingent one and varies
with the part of reality scientists are dealing with. Certainly an increase in amount of scientific activity
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in a scientific field does not automatically lead to an increase in empirical success of the theories in
that field. However, it is quite implausible that the enormous increase in scientific work had no or little
effect on the degrees of success of all theories of all scientific fields. It would be very surprising, if no
theory profited substantially from all the efforts of scientists in the last few decades and centuries. And
it is, of course, the theories that did profit that realists want to focus on. And these theories are precisely our current best theories.
Still, the first part of the main argument relies solely on the connection between amount of scientific work and degrees of success, and this connection is of a rather indirect sort, as just conceded.
We need to develop the main argument further. I will do so by first looking at what I call core theories.
This will serve to further develop the first part of the main argument. Afterwards I look at the growth
of the other four indicators of success. This will serve to further develop the rest of the main argument.
4 Core theories, weak confirmation, and confirmation en passant
In order to further develop the first part of the main argument we need a couple of further notions. For one kind of theory it is especially plausible that they profited from the huge increase in scientific work, namely those of our current best theories that are highly unifying in the sense that they
are involved in much of what is going on in their respective scientific disciplines. For example, the
periodic Table of Elements plays a role in practically everything chemists do and think. Also, the theory of evolution is involved in much of what is going on in biology.21 A third example: the conversation
of mass-energy plays a role in very many situations in physics, chemistry, engineering, etc. Finally,
plate tectonics is connected with or explains much of the topography of the Earth (location of mountains, shape of seafloor, etc.), locations of earthquakes and volcanoes, magnetic stripes on the seafloor, etc. I call theories that are highly unifying in this sense “core theories” of their respective scientific discipline, and every situation in which a core theory plays a role an “application” of the core
theory.
Even though many of the applications of a core theory don’t constitute tests of the core theory, a
large number of them do. However, almost all of the latter applications are not “severe” tests of the
core theory in any way, but only tests of a weak or moderate kind. Based on the core theory scientists
have expectations about the application (about observations and outcomes of experiments), but these
expectations are typically not of a strong sort. For example, on the basis of the periodic Table of Elements chemists expect that every new substance has a chemical structure in terms of the 92 elements,
and every chemical reactions is describable in terms of the 92 elements. Likewise, based on the theory
of evolution, biologists form expectations about the features of organisms, fossils, genomes, species,
etc. Lets call such tests of a theory “gentle tests” of the theory. If the theory fulfils the respective expectations, i.e., passes the gentle test, it only receives a small or moderate increase in its success. If it
fails a gentle test, it only suffers from a non-significant anomaly, i.e., an anomaly which only means
some kind of trouble for the theory, which, in Bayesian terms, may lower its probability somewhat,
but does usually not lead to its refutation, or only leads to its refutation, if the theories already suffers
from a lot of other anomalies. Thus, as long as theory and observation come into contact in the application somehow, so that it is possible for the application to become an anomaly for the theory that
scientists can notice22, the application counts as a gentle test of the theory.
The term “prediction of a theory” will also be used in a rather broad sense. It will denote any observable statement which scientists arrive at by deriving it from the theory. This includes any expectations scientists form on the basis of the theory. In particular, this includes two things. First, predictions
need not be “novel” in the sense of Worall (1989), i.e., need not be about new kinds of phenomena,
but rather include all consequences derived from the theory even if they are about the same kind of
observations as the observable statements used in the theory‘s construction. Second, if the derivation
As Theodosius Dobzhansky famously said (exaggerating somewhat) “Nothing in biology makes sense except in the light
of evolution”.
22 Kuhn thought that scientists engaged in normal science don’t test their paradigm, and when anomalies arise usually don’t
blame the paradigm. Hence, he depicts scientists engaged in normal science as uncritical and close-minded. I think this is a
misrepresentation. Anyway according to Hoyningen-Huene, Kuhn also thought that scientists “trained in normal science …
are … extraordinarily suited to diagnosing” anomalies of theories (1993, p. 227).
21
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from the theory is only approximate, then the prediction is the result of this approximate derivation. In
that case the prediction is not strictly a logical consequence of the theory.23
When scientist consider a core theory to be well-confirmed and accept it, they usually don’t devote their time and energy to further testing of the theory. Therefore, when an application of a core
theory is a test of it, testing it is usually not the scientist’s main aim in the scientific project of which
the application is a part, and mostly not even any one of her aims for that project at all. Instead she
may pursue other aims in the project, such as explaining some phenomenon with the help of the theory, filling in details in the theory, or testing some other entirely different theories. For example, when
scientists study malaria bacteria they don’t intend to test once again that malaria is caused by bacteria,
nevertheless, a lot of studies about the (rather complicated) behaviour of the malaria bacterium are
also (usually rather weak) tests of the germ theory of disease for the case of malaria. Likewise, when
palaeontologists look for fossils nowadays, they generally don’t have the aim of testing the theory of
evolution once more, nevertheless, any fossil they find is also a (usually very weak) test of the theory
of evolution, because some of its features may turn out to contradict or undermine the theory of evolution, e.g., may suggest really big jumps in the fossil record, which would not accord well with the byand-large gradual nature of evolution. When an application of a theory is a test of the theory, but testing the theory is not among the main purposes of the scientists in applying the theory, and the test is
passed, I will call the resulting kind of confirmation of the theory “confirmation en passant”.
5 The main argument again
We can now develop the first part of the main argument further, as follows. Consider those theories among our current best theories that are core theories in their respective scientific disciplines.
Most of their applications have only been gentle tests. So, in most of them they have received only a
small or moderate increase in degree of success. However as the very strong growth of scientific work
shows, the number of applications has increased enormously. In almost all of them, the expectations
were met, and the gentle tests were passed. Some applications may not have been successful, but in
those cases there was almost never a reason to blame the core theory, otherwise it would not have been
as stable as we observe it to have been. Hence, the small or moderate successes have accumulated to a
very high overall amount of increase in degrees of success for the core theory. In this way, weaker
kinds of confirmation of core theories have contributed strongly to the increase in their degrees of
success. I will now present an example for this reasoning, and then strengthen the main argument by
examining the other four indicators of success.
The core theory of chemistry is the periodic Table of Elements. Like in the rest of science, manpower and publications in chemistry have risen exponentially. Jochen Schummer observes that “[o]nly
during the past 15 years [i.e., until 1999] we saw more chemistry publications than had been written
ever before… [T]his year chemists will publish a hundred times as many papers as in 1901, when
van’t Hoff received the first chemistry Nobel prize.“ (1999) Schummer shows that during the past 200
years the growth of scientific work in chemistry meant that the number of newly discovered or produced chemical substances has risen exponentially with a growth rate of around 13 years. “During the
whole period the total curve corresponds quite well to a stable exponential growth … with an annual
rate of 5.5% and doubling time of 12.9 years.” (1997, p. 111)24
As remarked above the Periodic Table of Elements implies constraints about, for example, the
features of any chemical substance and what can happen in any chemical reaction. Hence, every new
substance provides an occasion for a gentle test of the Periodic Table of Elements. That the Periodic
Table of Elements has been entirely stable for many decades shows that the gentle tests have always
been passed. Mostly they have only provided a weak increase of degree of success. But because the
number of such gentle tests has been huge – as witnessed by the number of new substances that have
been found or produced over the last 150 years, all of them different from each other – the over-all
23
Of course, a theory rarely implies an observational statement all by its own, but needs boundary conditions, auxiliary theories, etc., to do so. I ignore such complications here.
24 A growth rate of 12.9 years seems to be higher than that of scientific manpower or journal articles. Schummer provides a
plausible explanation for this discrepancy. He observes that the number of reported new substances per article, and also the
number of reported new substances per chemist has been growing over time, i.e., the productivity of chemists has increased
over time. (Schummer 1997b, p. 118)
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increase in degrees of success of the Periodic Table of Elements has been huge. Note that nowadays
and in the more recent past testing the periodic Table of Elements has clearly not been a purpose of
chemists on any of these applications, as chemists have accepted it for a long time now, so these applications are all cases of confirmation en passant.
4 The other four indicators of success
1 Amount of data
The second indicator of success is the amount of data gathered by scientists until some time.
Here, we observe that in many scientific disciplines the amount of data has grown at a very strong rate.
First, in some disciplines such as palaeontology or chemistry, it is often still the scientists themselves
who gather or produce the data, e.g., searching for fossils or synthesizing chemical substances. For
such kinds of data, it is often plausible that the amount of data gathered or produced by scientists has
grown very roughly proportional to the number of scientists in the field. As we saw earlier manpower
has increased with a doubling rate of 15-20 years over the last few centuries. A doubling time of 20
years means that today there are around 30 times as many scientists as in 1900, around 1.000 times as
many scientists as in 1800, and around 30.000 times as many scientists as in 1700.25 Therefore, in such
disciplines the amount of data has often risen in a similar fashion. For example, figure 3 depicts the
growth of the number of a certain type of fossil over the last two centuries, where this kind of growth
is entirely typical for the growth of the fossil record in general.26
Secondly and more importantly, in many scientific disciplines the growth of amount of data has
been far stronger than the growth of scientific man power due to better instruments and computer
technology.27 In many disciplines, data are nowadays gathered automatically.28 During the last six
years the Sloan Digital Sky Survey, the “most ambitious astronomical survey project ever undertaken
… measured precise brightnesses and positions for hundreds of millions of galaxies, stars and quasars…. it mapped in detail one-quarter of the entire sky. … The total quantity of information produced, about 15 terabytes (trillion bytes), rivals the information content of the Library of Congress.”29
By comparison, the most ambitious such project at the beginning of the 20th century, a survey of the
sky conducted at Harvard and completed in 1908, measured and cataloged the brightnesses and positions of 45 000 stars.30 The future has even more in stock: The “Large Synoptic Survey Telescope,
scheduled for completion atop Chile’s Cerro Pachon in 2015, will gather that much data [as did the
Sloan Digital Sky Survey over the last six years] in one night”.31
25
A doubling rate of 15 years means that today there are around 100 times as many scientists as in 1900, around 10.000 as
many scientists as in 1800, and around 1.000.000 as many scientists as in 1700. Here are the calculations: For a doubling rate
of 20 years we get 25  30, 210  1000, and 215  30.000; for a doubling rate of 15 years we get 13 doublings in 195 years,
hence a factor of 213  8.000, or around 10.000 in 200 years.
26 Timothy Rowe (2005), Book Review of Mammals From the Age of Dinosaurs: Origins, Evolution, and Structure by Zofia
Kielan-Jaworowska, Richard L. Cifelli and Zhe-Xi Luo. Nature 438, 426 (24 November 2005). For similar numbers about
the growth of dinosaur fossils, see New Scientist, (21 May 2005, pp. 36, 38).
27 See also the fourth indicator which concerns computing power.
28 See also Humphreys (2004, pp. 6-8)
29 http://www.sdss.org/. See also Robert Kennicutt (2007).
30 Jones and Boyd, (1971, p. 202). Cited from Johnson (2005)
31 Nature (2009), vol. 460, no. 7255, p. 551. This represents an increase of time efficiency by a factor of around 2000, namely
5 times 365. The Large Synoptic Survey Telescope is just one of several large astronomical projects planned for the next 10
years.
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Figure 3 The growth of the fossil record of mammals from the age of dinosaurs (245 – 66 million years ago). From Kielan-Jaworowska, Cifelli, Luo, 2005, S.7
Another example is provided by the sequencing of DNA. Here, over the last 20 years the overall number of decoded DNA sequences has grown with a fairly stable doubling rate of 18 months.32
This means a growth by a factor of 100 every 10 years from 1984 (around 4000 sequences) to 2004
(around 40 000 000 sequences). Again, this is not possible without automation. To illustrate, “geneticists spent more than a decade getting their first complete reading of the 3 billion base pairs of the
human genome, which they finally published in 2003. But today’s rapid sequencing machines can run
through that much DNA in a week.”33 The costs for sequencing the first human genome was probably
at least $500 million, whereas the costs for sequencing the eighth human genome in 2009 was around
$50,000. In the next few years, the costs are expected to decrease by a factor of two each year (Nicholas Wade 2009).
As a final example consider the Argo system which was installed in the years 2005 to 2009 and
which consists of a network of 3000 robotic probes floating in the Earth’s oceans. The probes continuously measure and record salinity and temperature of the upper 2000m of the ocean, surfacing once
every 10 days to transmit the collected data via satellite to some stations on land. In these and many
other fields, the automatic gathering of data has lead to truly gigantic amounts of data. 34 Relating my
examples from palaeontology, astronomy, genetics, and oceanography of increase of data with the
respective entries on my list of our current best theories supports the main thesis that those theories
enjoy far higher degrees of success than any theories some decades ago.
2 The worry of diminishing returns and the diversity of data
At this point the following worry might arise. Even if in the examples above the amount of data
has increased enormously, still every new pieces of data may be rather similar to data gathered previously, and, as is well known, if new data is of the same kind as old data its confirmational value converges to zero very quickly. For an extreme example, the results of the same kind of experiment repeated again and again only varying times or locations or other irrelevant characteristics quickly loose
32
See http://www.ncbi.nlm.nih.gov/Genbank/genbankstats.html.
Nature (2009), vol. 460, no. 7255, p. 551
34 Sazlay and Gray (2006, pp. 413-4), in a report about a Microsoft workshop on the future of science, claim that the amount
of scientific data is doubling every year.
33
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any confirmational value. This is the worry of diminishing returns.35 If the worry were correct, the
increase in amount of data would not mean that there was a big boost in degrees of success in the recent past. In reply note the following: It is surely the case for the above sets of data (fossils, stars, etc.)
that for every piece of data gathered nowadays there are almost always many pieces of data gathered
earlier that look rather similar to it. But this way of viewing the confirmational situation is misleading.
We need to adopt a global perspective, and determine for each whole set of data whether it exhibits
high diversity or not.
So, how much diversity do the data sets presented above (data from fossils, chemical elements,
oceans, astronomical objects) possess? Surely they are not such that all the pieces of data are of the
same narrow kind. It is not the case that palaeontologists examine the same features of the same fossil
again and again, or that all fossils they find are of the same species and the same age. Such deeds
would correspond to repeating the same sort of experiment again and again varying only insignificant
properties such as time or location. Instead palaeontologists look for fossils from different locations
and strata, and what they find are mostly different species. Thus, in Figure 3 the y-axis depicts the
number of genera of mammalian fossils. (Genera are a more general classification grouping than species). Although some important parts of the fossil record are missing, especially from earlier times,
e.g., from the beginning of life on earth, we possess fossils for many important parts of the tree of life,
enough to have a rough outline of it.36 Also it is not the case that chemists examine the same features
of the same substance again and again; instead they create, as we saw, new substances incessantly. The
millions of chemical substances that have been synthesized so far clearly represent an extremely high
variety of evidence. Likewise it is not the case that all probes of ARGO were released at the very same
location in the same ocean, but instead were, of course, distributed widely over many different locations in the oceans of the earth so as to maximize the worth of the data produced. Finally, astronomical
projects such as the Sloan Digital Sky Survey don’t record the same star again and again, but record
features of hundreds of millions of different stars and galaxies.
The rise in the diversity of data manifests itself also in the very strong rise in the number of
kinds of instruments and kinds of measurement techniques in many scientific disciplines, especially in
the last few decades. While 100 years ago, we just had light microscopes, after World War II many
new kinds of microscopes have been developed: many types of light microscopes (polarization, fluorescence, phase contrast, etc., etc.), many types of electron microscopes, scanning probe microscopes
and acoustic microscopes.37 Similarly in astronomy: Until some decades ago, we had only light telescopes, while today, astronomers have many different kinds of instruments which not only cover most
of the electromagnetic spectrum, from radio-telescopes to gamma-ray telescopes, but also detect neutrinos, muons, Oh-My-God particles, and so on. To get an impression of the diversity of microscopes,
telescopes and other measurement techniques, have a look at the respective entries in Wikipedia, e.g.
at the entries of “measuring instruments” and “non-destructive testing”.
Finally, we can point to a further feature of science that supports that the evidence gathered by
scientists show a huge and ever growing variety and breadth. This feature is the ever increasing specialization in science. In practically all scientific disciplines we see an ever increasing number of approaches, techniques, instruments, problems, etc. All the time we see fields splitting into sub-fields. It
is very plausible that if there is a core theory in the respective scientific disciplines specialization often
results in more diversity of evidence for the core theory.
A particular salient indication of the specialisation is the problem of communication between
scientists. Scientists of different scientific disciplines, and even scientists of the same discipline, but
different sub-disciplines or sub-sub-discipline, have an ever harder time to communicate the particulars of their work with each other. This can easily be witnessed at scientific conferences. (Just go to
any talk of any conference and ask any member of the audience how much he really understood of the
talk.) In general, communication is possible for the basics of the respective field, the general aims,
35
This worry was first suggested to me by Rachel Cooper. See Hempel XXX
The fossil record as evidence for the theory of evolution has only a limited diversity. However, fossils are just one kind of
evidence among very many very different kinds of evidence from very different sources such as biogeography, genetics,
embryology, molecular biology, etc. To get an impression of the diversity of evidence for the theory of evolution compare
such sites as www.talkorigins.org, or any textbook on evolution such as Douglas Futuyama (2009).
37 See Ian Hacking’s “Do We See Through a Microscope”, in particular the section titled “A Plethora of Microscopes”. Microscopy is nowadays being developed in many different sometimes surprising directions, see Alison Abbott (2009).
36
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theories and problems of the respective scientific field. In contrast, communication about the specifics
of the daily work in the field, the particular techniques, data, instruments, particular problems and
special theories is mostly not possible without being provided a lot of special background information.
Compare this situation with the situation 100 years (or even 200 years ago), when it was far easier for
scientists to keep up with developments in their own discipline and even in other scientific disciplines.
The omnipresent difficulties of communication between scientists of different fields show just
how specialized science has become. And the ever higher specialisation is a clear indication of the
ever growing diversity of approaches, techniques, instruments, etc, and hence of the ever growing
diversity of evidence for the core theories. As with growing scientific work in general the growing
specialization does not automatically lead to more diversity of evidence. It is only an indicator of diversity. Surely, there are many scientific fields in which the large increase in specialization has not
lead to much more diversity of evidence for the theories in that field that result in a very degree of
high success for any of the theories. But, as with the increase of scientific work in general, it is also
implausible that no scientific theories profited in this way. Especially for the core theories of the respective disciplines such as the theory of evolution or the periodic Table of Elements it is highly plausible that they profited in this way.
3 The final definition of success
Before turning to the fourth and fifth indicator of success, I want to improve the notion of success one last time. To do so I will once more use confirmational ideas that are entirely standard (compare, e.g., Hempel 1966). So, here is the final characterization of success. It is still a partial characterization in that it only specifies some factors on which the degree of success of a scientific theory depends. First, as was noted earlier the degree of success of a theory at a given time depends on the total
number and diversity of all the tests that the theory has passed until that time. In every test a prediction38 of the theory and a piece of data are compared, hence the degree of success of a theory at a given
time depends on both the total number and variety of the predictions and the total number and variety
of the data involved in all the passed tests.
Second, individual tests differ with respect to their quality. I will here consider only one aspect
of the quality of tests, namely the precision (or specificity) of the data and predictions involved in
tests. The notion of precision applies to data of both a qualitative and a quantitative sort. If the data is
of a quantitative sort, then obviously its level of precision may vary, but the same is true for data of a
qualitative sort: It can vary in its precision from rather unspecific to very specific. For example, the
precise description of all features of a fossil can constitute a quite precise piece of data. Likewise for
the predictions derived by scientists from the given theory: they may be of a qualitative or a quantitative sort, and in both cases their precision may vary. For example, when scientists have to solve equations to derive predictions from a theory, they often have to use approximations and simplifications
which usually reduce the precision of the predictions.
In general, if the data is of higher precision than the prediction, then the quality of the test is determined by the precision of the prediction, and if the data is of lower precision than the prediction,
then the quality of the test is determined by the data precision of the data. If in a test either data or
predictions are of low or modest precision, we have a gentle test of the theory. Such a test, if passed,
can only result in a weak or modest increase in degrees of success for the theory. Confirmation en
passant is typically of this sort.
My partial characterization of the notion of success is of a rather basic sort. It could surely be refined in many ways, e.g., with the help of probabilistic means. Some ways of refining it are not necessary for our purposes here, quite the opposite some measure of generality is welcome having the advantage of making the arguments of this paper compatible with a large range of realist theories of confirmation. However other ways of refining the notion would be important to consider. It should be
taken into account that confirmation is holistic (that theories are not tested singly, but in bundles). The
same holds for the distinction between data and phenomena (Bogen/Woodward 198XX). Also relationships such as mutual support of theories at different levels of generality and between neighbouring
38
As noted earlier the notion of a prediction of a theory is used in a rather broad sense: Any observation statement which
scientists have derived from the theory counts as a prediction.
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scientific areas have to be examined. And so on. Taking all these complications into account has to be
left for several other occasions.
We can discern two extreme ways of how a theory can acquire very high degrees of success.
The two extreme ways form the two end points of a continuum. At one end we find theories that have
passed only gentle tests – all the data or predictions of the tests have had a low or moderate precision –
, but there are a very large number and variety of such tests. At the other end are theories that have not
passed very many tests, but passed tests of a very precise sort. In between the two ends of the continuum are a lot of possible mixtures of the two extreme ways. The support for our current best theories
are typically mixtures. A plausible conjuncture would be that for the best theories of the physical sciences we find both high precision and strong diversity of evidence. By contrast, the current best theories from other sciences, such as the theory of evolution or the periodic table of elements, profited less
from tests with very high precision, and more from a very high diversity of evidence.
4 Precision
The fourth indicator of success is the precision of data. Data becomes more precise, when scientists improve already existing kinds of instruments and measurement techniques, or develop new kinds
of instruments and measurement techniques. This happens all the time, of course, and has lead to constant improvement in the precision of data over the last few centuries, and especially the last few decades. Often the improvements were by great leaps. Examples abound. Let me just mention three especially interesting ones.
The first example concerns the measurement of distances between places on the surface of the
earth for the purpose of determining details about the movement of tectonic plates. The kinds of measurement available until the 1980s required years to produce meaningful data. In the 1980s this
changed dramatically through the advent of GPS. The precision increased 100fold. In consequence
determining the movements of tectonic plates became rather easy and very reliable.39 In this case we
have a substantial increase in the precision of the data which exhibits at the same time a large variety,
namely from thousands of GPS stations from many different places on the earth. This example is interesting, because it concerns the only interesting theory change discussed in the philosophical literature of recent times: In the 1960s geologists changed their view from the belief that the earth crust
does not move to the theory of moving tectonic plates. The example also illustrates the notion of confirmation en passant. Clearly, the purpose of the measurements is not to confirm once again that plate
tectonics is true, but instead to determine details of the tectonic plates such as their precise borders,
direction and velocity of their movements, etc., nevertheless plate tectonics is reconfirmed all the time
by these measurements.
The second example is the increase in precision of time measurement. Figure 4 offers a rough
idea of the immense increase in precision of time measurement over the last 400 years. Note that the yaxis has a logarithmic scale so that the increase is actually hyper-exponential. Furthermore, since the
1950s the precision of the best clocks has increased by at least one digit per decade (Sullivan, 2001, p.
6). Today the best clocks, so-called optical clocks, reach a precision of 1 in 1017. They are, of course,
expected to become still better soon (T. Rosenband, et al 2008). Needless to say precise measurements
of time are vital in very many different scientific fields (for example for GPS), and have led to a strong
increase in success for many of our current best theories over last few decades.
The third example is a very specific one, namely a test of Einstein’s equation E = mc2 in the year
2005. Using “improved crystal Bragg spectrometers” and a “Penning trap” (whatever those are), E =
mc2 was reconfirmed with an accuracy of at least 0.00004%.40 This accuracy is 55 times higher than
the accuracy of the previous best test from 1991, which, by the way, used an entirely different method.
39
GPS became available much earlier for scientists than for the general public. Incidentally, GPS works only, because several relativistic effects are taken into account (Neil Ashby 2003). So, every time you use GPS successfully, you reconfirm en
passant the approximate truth of general relativity, although only a tiny little bit.
40 NATURE, Vol. 438, (22/29 December 2005, pp. 1096-7). See New Scientist (4 March 2006, pp. 42-43) for the story
behind this recent validation of E = mc2 in which two teams, one in the US and the other in France made their respective
measurements entirely independently from each other until they deemed them stable, before simultaneously faxing the results
to each other.
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The last example shows that even for some of our best theories scientists don’t stop intentionally
testing them. As remarked earlier, reconfirmation of our best theories mainly occurs as a side-effect of
scientific projects, as “confirmation en passant”. But the last example shows that scientific projects in
which scientists make a deliberate effort to recheck a well-established theory, so that rechecking of the
theory is the main purpose or one of the main purposes of the project, do exist. While such intentional
tests are not considered to provide great advances, and are rarely in the limelight of the scientific
community (precisely because the theories are considered to be already sufficiently confirmed), still,
those tests are performed when the occasion to do so arises (which they do time and again, because of
new instruments and techniques), and their results are noticed and acknowledged. 41 It is simply interesting (and also satisfying) to see that a theory you already accept passes further more stringent tests.
And it is always at least possible that the theory does not pass a further test, in which case, if you can
really establish that this is so, you will become a candidate for the Nobel prize. Nevertheless, this does
not happen, and every such passed test constitutes a further boost for the success of the respective theory.
Figure 4: Improvement in the quality of artificial clocks and comparison with the clock provided
by terrestrial rotation (from XX)
5 Computing power
The fifth indicator of success is computing power. As I use the term here, the computing power
of the scientists at some time has two components, the software known to the scientists at that time
and the hardware available to the scientists at that time. The software comprises the methods and algorithms known to scientists to solve equations (and, more generally, methods to derive predictions from
theories). The hardware comprises the devices on which software are implemented such as abacuses,
logarithmic tables, computers, and the human brain. The computing power – software and hardware –
available to scientists at some time determines three things: the kinds of equations scientists of that
Another example is the recent test of Newton’s law of gravitation gravitational forces between masses separated by 55m
(“Gravity passes a little test“, NATURE Vol 446, 1 March 2007, pp. 31-32). This test also served to rule out some versions of
string theory, so testing Newton’s law of gravitation was not the only purpose of the project.
41
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time can solve, the precision of the solutions, and the amount of time needed to obtain the solutions
(efficiency).
So, let us look how computing power has developed over the last few centuries. First, software.
Mathematics and the other disciplines responsible for finding methods and algorithms to solve equations have, like the rest of science, gone through exponential growth during the history of science.
Hence, the number and efficiency of methods and algorithms to solve mathematical equations has
certainly been growing very strongly. However, it is difficult to quantify this growth in any meaningful way on a global level. Describing the growth of hardware over the history of science is far easier.
Until 50 years ago computations were done by humans, therefore overall human computing power
rose at least at the rate of the number of scientists, and actually considerably more due to instruments
like abacuses, logarithmic tables, slide rules, etc. Furthermore, for the last 50 years hardware power of
computers certainly rose exponentially: As is well know, hardware power of computers doubled
roughly every two years over the last 50 years. This growth is, of course, much stronger than the
growth of the number of scientists and journal articles.
6 The benefits of the increase in computing power
The increase in computing power is then connected with increase in success of theories in
straightforward ways. New and better software, i.e., new and better methods for solving equations, can
provide solutions for kinds of equations which were not solvable before, and it can lead to solutions of
already solvable equations, but with higher efficiency (i.e., consuming less time and other resources);
both kinds of improvement can then result in a higher number of predictions, which can thereby exhibit more diversity. Similarly, new and better software can lead to more precise solutions of already
solvable equations, hence to more precise predictions. The same holds for hardware: more and better
hardware leads to a higher number and diversity of predictions, and to more precise predictions.
Note an important difference between computing power and data. Every piece of data is taken to
have a specific content, i.e., is taken to carry information about a specific object or phenomenon such
as some star, some stretch of DNA, or some fossil. Therefore every piece of data is confirmationally
relevant for a very narrow set of theories only, mostly in just one scientific area. By contrast, neither
software nor hardware are taken to have a specific content.42 A method to solve some kind of equation
can, of course, be used in every scientific field in which such equations of that kind arise. And very
many methods for solving equations are in fact used in many different scientific areas.43 Even more so
for hardware. The same piece of hardware can usually implement a large number of different kinds of
software. This is certainly true for the human brain and for electronic computers.
All of this makes it highly plausible that the growth of software and hardware has contributed
strongly to the increase in degrees of success of our current best theories. Paul Humphreys remarks
that “much of the success of the modern physical sciences is due to calculation” (2004, especially Ch.
3). He observes that our knowledge of the numerical methods needed to solve equations numerically
have made big advances.44 Thus, he writes:
… [B]ehind a great deal of physical science lies this principle: It is the invention and deployment of tractable mathematics that drives much progress
in the physical sciences. Whenever you have a sudden increase in usable
42
Here are the correspondences between the elements on the prediction side of testing and the elements on the observation
side of testing: Software corresponds to observational and measurement techniques, hardware (including the human brain)
corresponds to measuring instruments (including the human perceptual apparatus). On both sides we can draw the distinction
between process and product. Making a calculation means running some piece of software on some piece of hardware. This is
a process the product of which is some computational result. Likewise, making an observation or measurement means employing a measuring device. This is a process the product of which is some piece of data. Finally, comparing the results of
calculations with the data constitutes a test of the respective theory. – Needless to say, I chose to examine those elements on
the two sides of testing for which some kind of quantitative statement is meaningful and for which I could find numerical
information.
43 See Paul Humphrey (2004, Ch ??)
44 The vast majority of equations are nowadays solved numerically. For example, the equations of Quantum Mechanics are
almost exclusively solved numerically today (Humphreys 2004, p. 60).
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mathematics, there will be a sudden, concomitant increase in scientific progress in the areas affected. And what has always been true of the physical
sciences is increasingly true of the other sciences. Biology, sociology, anthropology, economics, and other areas now have available, or are developing for themselves, computational mathematics that provide a previously unavailable dimension to their work. (p. 55, emphasis in original)
Humphreys provides ample evidence for the huge difference increase in computing power has
made for the empirical success of theories.
An important use of computing power in both physical and non-physical sciences is the construction of computer models and computer simulations as an intermediary between theory and observation. When constructing computer models scientists often have to make strong approximations and
idealizations. If so, their confidence that the predictions of the models are actually the predictions of
the theory cannot be that high. In case data is available for comparison with the predictions of the
model, i.e., in case we have a test of the respective theory, this test is a gentle test at best. Therefore, if
the predictions of the model accord with the respective observations or experimental results, the
amount of success the respective theory enjoys is limited. Still, if the theory is a core theory that is
profitably used in very many such models, and if the cases where the predictions are wrong are rare or
the fault can be traced to other culprits, such models of the theory can strongly contribute to the rise in
its degree of success. What is more, because computing power has increased so strongly, especially
over the last 50 years, the approximations have become ever better and the necessary idealizations
ever weaker, leading in many scientific fields to ever more precise models, which therefore constitute
increasingly stringent tests of the respective theories and have contributed ever more strongly to an
increase in their degrees of success.
5 Saving Realism
1 Completing the main argument
Let us complete the main argument. The main argument is an inference from statements about
the five indicators of success to statements about the degrees of success of the two classes of theories
we want to compare. As we saw, the indicators of success have enjoyed an enormous increase over the
last few decades. Before that almost all of them were quite low, today they are very high. From this we
can infer the degrees of success of both our current best theories and the refuted theories of the past.
On the one hand, we can infer that our current best theories profited from the enormous increase in the
indicators in the recent past and therefore received a big boost in their degrees of success in the recent
past, an increase that is far greater than any increase in success of any theories of earlier times. So they
enjoy very high degrees of success today. This inference proceeds on a general level, but we could
also show directly for a number of specific theories, e.g., some core theories, that their degrees of success profited from the increase of the indicators. On the other hand, the refuted theories of the past
discussed by philosophers were all refuted before the big boost of success took place. At those times
practically all indicators were quite low. Therefore, the degrees of success of the refuted theories were
quite modest. This completes the main argument. The conclusion of the main argument is the main
thesis of the paper: All our current best theories enjoy far higher degrees of success than any of the
successful, but refuted theories of the past, which enjoyed only quite modest degrees of success.
2 Reply to sophisticated PI
We can now reply to the sophisticated PI. The sophisticated PI is the argument that right to the
present theories kept being refuted, therefore we should extrapolate the incidence of false theories
from past degrees of success to current degrees of success. The target of the sophisticated PI is the
modified success-to-truth principle which restricts the inference from success to truth to current degrees of success, and which threatens to be undermined by the extrapolation of false theories. But the
sophisticated PI is challenged by the main thesis. The main thesis states that there is a large difference
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in degrees of success between the refuted theories of the past and our current best theories. It implies
that the claim of the sophisticated PI that theories kept being refuted as success kept growing is simply
not true. Quite the opposite is true: theory change among theories stopped at rather low levels of success. Therefore, the extrapolation of the existence of false theories from past degrees of success to
current degrees of success is not plausible. This rebuts the sophisticated PI, and saves the modified
success-to-truth principle.
3 How Realism is saved
Because the modified success-to-truth principle is not threatened by the existence of counterexamples, the realist can modify his position so that it consists in the endorsement of the modified success-to-truth principle. This modified form of realism is save from the sophisticated PI. It is a version
of realism which is compatible with the history of science.
The realist wants to support his position, i.e., the modified success-to-truth principle, with the
NMA, but the NMA and the intuitions behind it were attacked in the first objection. In a moment I will
offer a reply to the first objection. I want to show that the NMA and the intuitions behind it appear
slightly scathed, yet basically intact from the confrontation with the history of science. Assuming I can
show this, the realist can, after all, use the NMA to support the modified success-to-truth principle.
Finally, he can apply the modified success-to-truth principle to our current best theories, and infer that
they are approximately true.
6 Restoring the Intuitions**
1 The weak success-to-truth principle**
Let us now deal with the first objection. The first objection aims to undermine what I called the
shared realist intuitions by pointing out that they support via the NMA an inference to truth for the
levels of success enjoyed by the refuted theories of the past, so that the shared realist intuitions are at
odds with the historic track record. In this conflict, the intuitions lose, rendering them untrustworthy
and no longer able to support anything at all, in particular not the inference from success to truth for
current levels of success.
To restore the integrity of the shared realist intuitions, I want to consider what I will call the
weak success-to-truth principle. This principle states what we can infer for theories with moderate
degrees of success, as typically possessed by the successful, but refuted theories of the past. The principle is a conjunctions of two statements. First, we can infer that such a theory is partly true45 in the
sense that important components of such a theory are probably correct. The correct components may
be part of its ontology (some of its central terms refer), or part of its classification system, or they may
be structural claims such as its equations. Scientist accepting such a theory may not be able to determine which of its components are the correct ones, but rather know only in hindsight. 46 Also the theory may be true or partially true not in the whole domain of application as it was initially intended, but
only in a sizeable part of it, where this part may also be known in hindsight only. Second, the weak
success-to-truth principle states that there is a substantial probability (to fix ideas arbitrarily, between
20% and 80% say) that the theory is not just partially true, but actually fully true. A person is warranted to have some, though not that high level of confidence in its full truth, e.g., an attitude of tentative
belief may not be altogether unreasonable.
To show that realists can hold on to the weak success-to-truth principle I have to show two
things: that it is by and large in line with shared realist intuitions, and that it is not undermined by the
historical track record. First, we need to show that it is by and large in line with shared realist intuitions. When Smart and Putnam presented the NMA the levels of success they had in mind were, of
course, the present ones. I showed above that by far most of the growth in success of the respective
As before, “true” always means “approximately true”.
Kitcher compares this situation of not knowing which components are the correct ones with the preface paradox (2001,
170-71).
45
46
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best theories occurred in the recent past, that levels of success of the refuted theories of the more distant past were much lower than that of our current best theories. Also it is clearly the case that the lower the degree of success of some theory, the weaker the shared realist intuitions’ support for its truth
via the NMA. For these two reasons, the claim is plausible that the shared realist’s intuitions are such
that they don’t offer that much support for a NMA in support of the success-to-truth inference for the
refuted theories of the past. A realist 100 or 200 years ago, for example, if he had inferred the truth of
some successful theory of those times, should have been aware that he could have done so only rather
tentatively, and that anti-realism was a real option for many of the best theories at that time. When
some theories with so much lower amounts of success turned out to be wrong, it should not have been
such a big surprise for him, far less a miracle. Thus, for past refuted theories the common realist intuitions seem to support at most a watered-down NMA (which may therefore not really deserve its name
in this case).
Having said this it must be admitted that it is difficult to determine the shared realist intuitions
with any precision. It must also be admitted that current realists often seem to identify with past realists and realist-minded scientists, and may think that, at least in some cases, success of past refuted
theories already sufficed to have greater confidence in their truth than the weak success-to-truth principle recommends. Therefore, this principle may not be entirely in line with common realist intuitions.
Still, I think we can say that it is by and large in line with them.
2 The weak success-to-truth principle and the history of science**
We further have to show that the weak success-to-truth principle is not undermined by the history of science, but on the whole accords with it. So, let us examine the history of science and therein
the theories with moderate levels of success. What we then can do is use the first counterstrategy
against the PI mentioned earlier. That counterstrategy consists in showing that judged from today the
successful refuted theories of the past, although strictly speaking false, had parts that were true, e.g.,
had terms that referred, got the structure right, etc., or were approximately true in restricted domains.
Many philosophers have develop versions of this counterstrategy and have provided convincing historical evidence for its viability. Therefore I can be brief here. Thus, for example, important claims of the
phlogiston theory of combustion are still accepted today. Likewise many central claims of the caloric
theory of heat are true (in many situations heat behaves like a substance).47 Another example is the
sequence of theories of light since Maxwell: All its members agree on the structure of light, i.e., on
Maxwell’s equations.48 Furthermore, the ontologies of many of the successful abandoned theories of
the past overlap to a considerable extent with the ontologies of the theories we accept today, e.g. theories about the electron (Nola 19XX, Norton 19XX in Nola eds). Finally, some theories can only be
considered approximately true, if their domain of application is significantly restricted. Newtonian
mechanics is approximately true in a very large domain including the domains of most engineering
sciences. Hence, the first part of the weak success-to-truth principle, according to which theories with
moderate success usually have important components that are correct, is in accord with the history of
science.
In order to assess the second part of the weak success-to-truth principle, we not only have to
look at the incidence of false theories among theories with moderate degrees of success, but also at the
theories that were not refuted; we have to determine the ratio of the number of non-refuted theories to
the number of refuted theories. The weak principle is only compatible with the history of science if
that ratio has been not much lower than one, i.e., if among theories with moderate success the number
of refuted theories has at most the same order of magnitude as the number of non-refuted theories. Of
course, to show this is once again an ambitious thing to do, with numerous problems, such as how
theories are individuated, what levels of success precisely count as moderate, how degrees of success
are to be determined in the first place, etc. Hence, the following (all to brief) observations from the
history of science can only provide a crude estimation of that ratio. Still, I think they are already suffi47
Martin Carrier (2004) defends the claim that phlogiston theory and the caloric theory of heat already got significant statements about classification, i.e., natural kinds, right. This idea is further developed into a formal proof showing that under
certain conditions the successor theory in a theory has to retain some elements of the abandoned theory, see Schurz (2004,
2009). See also, among others, Ladyman (2009, §5).
48 Worall (1989), French and Ladyman (19XX). Many more examples are provided by Ladyman 1998XX.
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ciently good to show that the realist’s case is promising. As my aim is only to defend realism, the burden of proof that the ratio is considerably lower than one is once again on the side of the antirealist, as
he wants to attack the intuitions, therefore it suffices for the realist to throw sufficient doubt on the
anti-realist’s attack on the intuitions.
So, let us examine the moderately successful theories of the history of science. Here are four observations. First, inspecting the set of abandoned theories, for instance those on Laudan’s list or the
other cases offered in the philosophical literature, we observe that most of the successor theories of
the abandoned theories are still held today. Judged from today, many of the abandoned theories, especially the most interesting and most frequently discussed ones, were already “finalists” or, at the very
least, “semi-finalists” in the “theory contests” of the respective scientific fields. For example, the theory of phlogiston, the caloric theory of heat and the geocentric system were finalists (or semi-finalists,
depending inter alia on how theories are individuated and which theories count as versions of each
other) in their respective fields.
Second observation. As a more recent set of examples consider the field of clinical studies. In a
recent meta-study, 49 highly cited (i.e., cited more than 1000 times) original clinical studies claiming
that a drug or other treatment worked were examined. We can classify the results of these studies as
cases of moderate success, because they were usually supported by just one study and did not enjoy
strong support from independent evidence. It then turned out that subsequent studies of comparable or
larger sample size and with similarly or better-controlled designs contradicted the results of 16% of
the earlier studies and reported weaker results for another 16%. (For example, the refuted studies had
seemingly shown that hormone pills protect menopausal women from heart disease and that vitamin A
supplements reduce the risk of breast cancer.) This means that nearly two-thirds of the original results
held up.49
Third, there are only very few scientific fields which experienced more than one or two theory
changes among successful theories. The three to five changes of theories of light are quite an exception in this regard. Very few scientific fields exhibit such a large number of theory changes. Because
of the low number of such fields, their contribution to the ratio of non-refuted to refuted theories is
rather small, and barely lowers it.
Fourth, there are some fields in which the first really successful theories scientists hit on were
already the theories we still accept today. Examples of such theories are provided by discoveries of
entities and phenomena to which scientists had no access before, e.g., the discovery of X-rays, the
double helix, or double stars. If such discoveries were based on at least moderate evidence, they mostly have survived until today, hence in these cases there were sometimes no theory changes at all.
Hence, these cases either increase or, at least, do not lower the ratio of non-refuted to refuted theories.
Putting these four observations together (which, of course, have to be checked more thoroughly
than I can do here), we arrive at the (admittedly preliminary) estimation of the ratio of non-refuted to
refuted theories among moderately successful theories of very roughly one. It follows that scientists
could be reasonably confident that the moderate success of those theories sufficed to eliminate all but
two or three theories, that the two or three known and seriously entertained theories of their times
probably included the true theory, or, in other words, that the respective small disjunction of those
theories was probably true. For example, Priestly and Lavoisier could both be reasonably confident
that one of them was right. So, although Priestly, for example, was not right to have a strong conviction in phlogiston theory, he was not only justified to believe that important parts of his theory were
true, but also a tentative acceptance of his theory as a whole would not have been entirely unreasonable for him. Hence, the first part of the weak success-to-truth principle which allows an attitude of
tentative belief towards theories with a moderate amount of success is compatible with the history of
science.
From this and my conclusion above about the first part of the weak success-to-truth principle, it
follows that, although the common realist’s intuitions may not escape entirely unscathed from the confrontation with the past of science, they are not invalidated by the confrontation either, and can still be
used by the realist as reasons for supporting the full (as well as the weak) success-to-truth principle.
49
Paraphrased from John Ioannidis (2005) and Lindey Tanner (2005). Ironically whereas I use the results of this meta-study
to support realism, its real import is that it shows that clinical studies are not as reliable as commonly thought.
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7 Five objections
(…)
(…)
8 Conclusion
(…)
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