Abstract
Let us begin by reviewing the main results of the previous chapter. It was argued that, provided certain conditions are met, we can construct a purely probabilistic inference to some scientific realist claims. To recap, it was argued that we are justified in adopting realism with respect to some theory T if:
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Notes
- 1.
See Wright Science and the Theory of Rationality (Avebury, 1991) and Explaining Science’s Success: Understanding How Scientific Knowledge Works (Acumen, 2013).
- 2.
- 3.
For a discussion of the impressive degree of accuracy of Ptolemy’s system, see “Contra-Copernicus: A Critical Re-estimation of the Mathematical Planetary Theory of Ptolemy, Copernicus and Kepler” by Derek J. de S. Price in Critical Problems in the History of Science edited by Marshall Claggett, (University of Wisconsin Press, 1959), pp. 197–218.
- 4.
It is again perhaps worth stressing that this account is not offered as serious history of science. But its aim is not to provide an accurate account of an episode from the history of science. The aim, rather, is to use some familiar concepts from the history of science to illustrate a conceptual point.
It would, of course, have been desirable if there had been some episode from the history of science that illustrated the conceptual points in a way that could be stated very briefly. Unfortunately, however, I have not been able to find any such episodes. The example of the Ptolemy versus Kepler is the nearest I have been able to come to something that illustrates the conceptual points reasonably simply.
I have elsewhere argued that a number of episodes from the history of science do exemplify the concepts illustrated here. These episodes are: Newton’s argument for universal gravitation, the transition from the phlogiston theory of combustion to the oxygen theory of combustion, Einstein’s development of the Special Theory of Relativity and Mendel’s development of genetics.
It might perhaps be suggested that the absence of any examples in the history science that simply and briefly exemplify the concepts is a sign that these concepts are not really those used by scientists in evaluating theories. However, it seems to me that this conclusion does not necessarily follow. The real world is often extremely complex. A leaf being blown the street might not obviously be conforming to Newton’s laws of motion at all, but to a very high degree of approximation, it is. It has been argued that in the examples cited above, scientists really do prefer those theories that maximize the independence of theory from data, but showing how they do often involves a lot of detail. One reason for this is because the chains of reasoning used by scientists are often very complex. I have argued that each individual (ampliative, non-deductive) step in their reasoning involves choosing the most independent theory, but since there are many such steps in their reasoning, the overall picture can be quite complex.
- 5.
See the author’s Science and the Theory of Rationality (Avebury, 1991) and Explaining Science’s Success: Understanding How Scientific Knowledge Works (Routledge, 2013).
- 6.
- 7.
We will not here attempt to explicate the notion of “all possible observations” precisely, but a rough way of doing it is as follows. What we are after, in our example, is the set of all possible true values of the observable property P at different times. Let us represent any such a statement as a triple <P, t, n>. This tells us that at t property P has value n. Now, let W be the set of possible states of the world in which the laws of nature are the same as they are in the actual world, but in which the “initial conditions” may vary. We will say that a <P, t, n> is a possible observation if and only if there exists a world in W in which <P, t, n> is true. And the set of all possible observations is just the set of all such true-in-some-member-of-W possible observations.
- 8.
Explaining Science’s Success, Chap. 4, pp. 57–94.
- 9.
See Jarrett Leplin “Book Review: Explaining Science’s Success” in Analysis, v 74, (2014), pp. 184–185.
- 10.
For more detail, Explaining Science’s Success, p. 68.
- 11.
See Explaining Science’s Success, pp. 70–81.
- 12.
See Matthias Egg “Book Review: Explaining Science’s Success” in Dialectica, v. 67 (2013), pp. 367–372.
- 13.
See Mario Alai “Book Review: Explaining Science’s Success” in Metascience, v. 23 (2014), pp. 125–130.
- 14.
These remarks presuppose that there is a distinction between the “observational level” and the “theoretical level”. Such a distinction has of course proved difficult to precisely define. However, it is skepticism about scientific realism that is surely based on the assumption that some such distinction exists, even if it is “fuzzy”. A skeptic about scientific realism will presumably advance theses such as: “Some claims are clearly less observational than others, as claims become less observational their epistemic status becomes more dubious, and many of the statements of contemporary science are so far removed from the observational level, and have such a low epistemic status, it is not rational to believe them.” It is the last of these claims, it will here be assumed, that scientific realists are out to refute.
- 15.
Popper uses the term “boldness” to describe what he regards as the central desirable quality of scientific theories in The Logic of Scientific Discovery (Routledge, London, 2002), p. 280. The similarity between Popper’s view and the notion of the independence of theory from data is noted in Brad K. Wray’s review of Wright (2014) Australasian Journal of Philosophy.
- 16.
See for example Popper, Karl Conjectures and Refutations (Routledge, London, 1963), p. 315.
- 17.
See Wright, J Science and the Theory of Rationality (Avebury, 1991) and Explaining Science’s Success: Understanding How Scientific Knowledge Works (Acumen, 2013), esp. pp. 66.
It is worth looking a little more closely at just what it is the argument aims to establish. The conclusion of the argument, as presented here is: “(4): The more independent a theory is from the data, the more likely it is the data would conform to that theory if the data were to be obtained from other (including future) locations.” It is claimed that the argument that has been given for (4) makes (4) epistemically probable.
Objections have been raised against the adequacy of saying that (4) is (merely) epistemically probable. (See, for example, K. Brad Wray’s review in Australasian Journal of Philosophy 91 (4), pp. 833–834. (2013). In Explaining Science’s Success I offered the notion of the independence of theory from data as a way of explaining certain types of novel predictive success in science. Moreover, I acknowledge that, at least on the face of it, appealing to purely epistemic probabilities to explain certain events, such as empirical successes, might seem to be problematic. But here the episemic probability of (4) is not used to explain any subsequent events. It is rather used to show what makes a belief rationally acceptable, or rationally preferable to others.
However, is it really the case that it is not legitimate to use (4) to explain the success of science? It will be argued that actually it is perfectly legitimate. This will become clear, it will be argued, if we attend to the distinction between an explanans having an epistemic probability, and an explanans being the assertion of an epistemic probability.
Let us begin with a simple example. Suppose a dice is tossed a large number of times, and it is observed to come up “six” about half the time. Then, we will surely be inclined to say that the dice is probably unfair, or weighted. Assume that, on the basis of our observations, we conclude:
-
The propensity for a six to come up is about one half.________________(PS)
Although PS is an ascription of a propensity, it will itself also have a certain degree of epistemic probability. Since PS is supported by our observations, and seems to be a reasonable thing to believe on the basis of those observations, PS will presumably have some degree of epistemic probability.
Now, let us suppose we continue to toss the dice, and find that “six” continues to come up about half the time. How are we to explain this? It is, as far as I can see, reasonable to explain it by saying the dice is weighted, or by saying that there is a propensity for “six” to come up that is about a half. PS can surely play an explanatory role. And the fact that PS has an epistemic probability does not prevent it from being able to play an explanatory role. On contrary – although PS would still be the type of statement that was capable of playing an explanatory role even if it had an epistemic probability of zero, it is surely rational for us to assert or believe PS as an explanation of the subsequent behaviour of the dice only if it does have some reasonably high epistemic probability.
Let us now consider again proposition: “(4) The more independent a theory is from the data the more likely it is that the data would conform to the theory if the data were to be obtained from other, including future, locations”. The evidence for the truth of this proposition (4), it has been argued, is a priori. That is, (4) has some degree of epistemic probability. The degree of epistemic probability of (4) depends on the merit, or otherwise, of the a priori argument for it. We will not here go in to the merits or otherwise of the argument: I have done so elsewhere. But let us, for the sake of the argument, accept that (4) has some epistemic probability. Now, let us assume that T is some theory with a high degree of independence from the data. So, we will accept:
-
T has a high degree of independence from the data._________(2)
It follows from (2), and the claim that (4) has a good level of epistemic probability, that:
-
It is epistemically probable that it is likely that future data will conform to T. _____(3)
But now, (3) makes it reasonable to assert:
-
It is likely future data will conform to T.______________(5)
Now, the sense of “likely” that appears in (5) is not epistemic probability but propensity. I have elsewhere argued that the more independent a theory is from the data, the more (epistemically) likely it is that there exists a propensity for the data to conform to the theory. So, at least if the argument for the preferability of independent theories is a good one, we may take (5) to be equivalent to:
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There exists a propensity for the data to conform to T._______(6)
It is (6) which, on the view I have defended elsewhere, does the explaining. More specifically, it has been argued that it explains the novel predictive success of science. No claim is made that epistemic probability explains anything. All that epistemic probability does is justify our acceptance of claims such as (5) and (6). But the only type of probability that is asserted to actually explain anything is propensity.
-
- 18.
See Science and the Theory of Rationality and Explaining Science’s Success.
- 19.
This is discussed in more detail in my Explaining Science’s Success, pp. 78–86.
- 20.
As noted in the main text, this is only a very broad-brush account. More detailed accounts are given in Wright (1991, 2013). In Wright (1991) an account is given which includes both causal claims and existential claims as explanatory components of theories.Mario Alai, op cit, objects that the account of independence given in Wright (2013) only applies to laws and not to theories. The main focus of his objection seems to be that the account of independence only applies to generalisations, and not to existential and causal claims. While this is true of Wright (2013), these matters were treated in Wright (1991). (They were not included in the later work for reasons of space.)
- 21.
This suggests that there might be something to be said for offering a slightly different definition of independence. It may for certain purposes be more appropriate to define independence as follows:
$$ \mathrm{Independence}\ \mathrm{of}\ \mathrm{T}=\frac{\mathrm{Number}\ \mathrm{of}\ \mathrm{CODS}\ \mathrm{explained}\ by\ \mathrm{T}}{\mathrm{Number}\ \mathrm{of}\ \mathrm{DECs}\ \mathrm{of}\ \mathrm{T}}-1 $$On this definition, a “theory” that is nothing more than a description of the regularities to be found in the data will have a degree of independence of zero. A theory that is even more complex than the data it purports to explain will have a negative degree of independence. A theory only starts to be a good one once its degree of independence has some positive, greater than zero value.
- 22.
A more detailed account of the individuation of dependent explanatory components of theory (DECs) and components of data (CODs) can be found in the author’s Science and the Theory of Rationality (Avebury, 1991) and Explaining Science’s Success: Understanding How Scientific Knowledge Works (Acumen Publishing, 2013)
- 23.
See Explaining Science’s Success, Chap. 6.
- 24.
This is argued for in Science and the Theory of Rationality (Avebury, 1991), Chap. 6.
- 25.
Explaining Science’s Success, Chap. 7.
- 26.
Explaining Science’s Success, Chap. 8.
- 27.
Science and the Theory of Rationality, Chap. 5.
Bibliography
Wright, J. (1991). Science and the theory of rationality. Aldershot: Avebury.
Wright, J. (2013). Explaining science’s success: Understanding how scientific knowledge works. Durham: Acumen Publishing Company.
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Wright, J. (2018). Underdetermination and Theory Preference. In: An Epistemic Foundation for Scientific Realism. Synthese Library, vol 402. Springer, Cham. https://doi.org/10.1007/978-3-030-02218-1_6
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