03.04.20191
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PLEASE DO NOT QUOTE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 theorylicenses 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-miraclesargument. Second, I formulate a simple version of pessimistic meta-induction (simple PI, for short), and examine how it underminesthe 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 anti-realists 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 successundermining 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.
1ScientificRealism
1Definition 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 isthat 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.
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 thesethings 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 successfulat some point in time, just in case scientists have been able to compare sufficiently many consequencesof the theory with observationsuntil that time, and all of them have turned out to be correct.
2Comments 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 usbeyond 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, becauseI 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]
3The 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, 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.
2The pessimistic meta-induction
1The 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 examplesof 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 ultimately 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.
2Three 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, truthrestricted 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 PIsomewhat, 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.
**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 andmake 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 respectsand 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.
3The 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.