Abstract
There are three main accounts of scientific progress: (1) the epistemic account, according to which an episode in science constitutes progress when there is an increase in knowledge; (2) the semantic account, according to which progress is made when the number of truths increases; (3) the problem-solving account, according to which progress is made when the number of problems that we are able to solve increases. Each of these accounts has received several criticisms in the last decades. Nevertheless, some authors think that the epistemic account is to be preferred if one takes a realist stance. Recently, Dellsén proposed the noetic account, according to which an episode in science constitutes progress when scientists achieve increased understanding of a phenomenon. Dellsén claims that the noetic account is a more adequate realist account of scientific progress than the epistemic account. This paper aims precisely at assessing whether the noetic account is a more adequate realist account of progress than the epistemic account.
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Notes
- 1.
Cf. e.g. Niiniluoto (2015b, Sect. 3.5): “many past theories were not approximately true or truthlike. Ptolemy’s geocentric theory was rejected in the Copernican revolution, not retained in the form ‘approximately Ptolemy’. Indeed, the progressive steps from Ptolemy to Copernicus or from Newton to Einstein are not only matters of improved precision but involve changes in theoretical postulates and laws.”
- 2.
Claiming that the debate over scientific realism is about what is the aim of science is just one of the many possible ways to define such debate that have been proposed so far (Chakravartty 2015), and it is used here just for illustrative purpose. Which characterization of scientific realism is the most adequate one does not impinge on the present article, since for any possible characterization of the debate over scientific realism, it is possible to define how this debate and the debate over scientific progress intersect each other in a way similar to the one presented here. For similar reasons, it is not relevant here to survey the different proposals that have been advanced on what is the aim of science.
- 3.
- 4.
On the reason why Dellsén named his view ‘noetic’, cf. Dellsén (2016, p. 72, fn. 2): “‘Noetic’ as in the Greek ‘nous’, which is often translated into English as ‘understanding’.”
- 5.
Bird’s presentation of the problem-solving account does not do justice to the theoretical richness of this approach. For reasons of space, we follow Bird. For some recent works that innovate the problem-solving view, see Cellucci (2013), Ippoliti (2014), Ippoliti and Cellucci (2016), who advocate the heuristic view, according to which knowledge increases when, to solve a problem, a hypothesis “is produced that is a sufficient condition for solving it. The hypothesis is obtained from the problem, and possibly other data already available, by some non-deductive rule, and must be plausible […]. But the hypothesis is in its turn a problem that must be solved, and is solved in the same way” (Cellucci 2013, p. 55).
- 6.
For a survey on the issue of understanding, see Baumberger et al. (2017) and de Regt et al. (2009). On the related issue of the value of knowledge, see Pritchard and Turri (2014) for a survey. With regard to the debate over understanding in epistemology, see Elgin (2007, 2009), Kvanvig (2003), Zagzebski (2001); with regard to the debate over understanding in philosophy of science, see de Regt (2009, 2015), de Regt and Gijsbers (2017), Mizrahi (2012), Khalifa (2011) and Grimm (2006).
- 7.
On what spurious correlations are, cf. Dellsén (2016a, p. 78): “Suppose we have two variables V1 and V2 that are known on independent grounds to be unrelated, causally and nomologically. Let us further suppose that we learn, i.e. come to know, that there is some specific statistical correlation between V1 and V2—e.g. such that a greater value for V1 is correlated with a greater value for V2.” This correlation represents an instance of spurious correlation, i.e. a correlation between two variables which is not due to any real relation between them. In these cases, such a correlation does not convey any information on the correlated variables, nor on some other relevant aspect of the world, so it is useless, irrelevant, or worse, it may lead us astray, if we do not identify it as spurious.
- 8.
In this case (i.e. c = 2), if we have k = 3, then γ = 8. To see this, consider the following sequence of binary digits of length 8: 01100110. This string contains no arithmetic progression of length 3, because the positions 1, 4, 5, 8 (which are all ‘0’) and 2, 3, 6, 7 (which are all ‘1’) do not contain an arithmetic progression of length 3. However, if we add just one bit more to that string (i.e. if we add either ‘1’ or ‘0’), we obtain the following two strings: 011001100 and 011001101. Both these strings contain a monochromatic arithmetic progression of length 3. Consider 011001100: positions 1, 5, 9 are all ‘0’. Consider 011001101: positions 3, 6, 9 are all ‘1’. More generally, it can be proved that if a string contains more than 8 digits, it will contain a monochromatic arithmetic progression of length 3. And in fact, all the 512 possible binary strings of length 9 contain a monochromatic arithmetic progression of length 3.
- 9.
It is important to stress that the nature of the correlation function is irrelevant: it can be completely arbitrary, i.e. in no way related to the nature of the data stored in the database.
- 10.
Cf. Calude and Longo (2016, p. 6): “it is exactly the size of the data that allows our result: the more data, the more arbitrary, meaningless and useless (for future action) correlations will be found in them.” It may be interesting to note that, in order to derive their result, Calude and Longo define “spurious” in a more restrictive way than Dellsén. According to them, “a correlation is spurious if it appears in a ‘randomly’ generated database” (p. 13). Details can be found in Calude and Longo (2016). In any case, this does not impinge on the considerations that follow.
- 11.
Think of the increase in the understanding of some phenomenon X that may be derived by the findings of relevant (i.e. not-spurious) correlations among X and other phenomena Y and Z: if the number of spurious correlations increases, the number of correlations that we have to discard before finding the relevant ones increases too. Thus, increasing the understanding becomes more difficult when the number of spurious correlations increases.
- 12.
On a similar point, see Rancourt (2015).
- 13.
Cf. Dellsén (2016, p. 73, fn. 6): “the noetic account amounts to a moderately realist view of the aim of science.”
- 14.
Several very different views have been advanced on the requirements that have to be fulfilled in order to have understanding (see for a survey Baumberger et al. 2017). The main distinction is between those authors who think that understanding is just a species of knowledge (and so there is not a real distinction between these two concepts, see Grimm 2006), and those who, on the contrary, think that understanding is not just a species of knowledge (see Dellsén 2016b). Those who belong to this latter group have different ideas on how exactly understanding differs from knowledge. They usually claim that understanding lacks one or more of the traditional knowledge requirements, i.e. truth, justification, and some anti-luck condition. Here we will follow Dellsén’s characterization of understanding, and assume, at least for the sake of the argument, that understanding is not just a species of knowledge.
- 15.
The idea that empirical success is a good indicator of truth is a pillar of scientific realism (see e.g. Wray 2013). Thus, a realist view of scientific progress cannot completely sever the link between the empirical success of a theory and its truth.
- 16.
See e.g. Kvanvig (2003), who maintains that the truth requirement is necessary for understanding; Elgin (2007), who maintains that we may have understanding even through falsities; Rancourt (2015), who maintains that, in certain circumstances, an increase in truth-content may even lead to a decrease in understanding.
- 17.
- 18.
Many authors argue that knowledge is a factive propositional attitude. To say that a propositional attitude is factive is to say that “it is impossible for you to have that attitude towards anything other than a true proposition” (Pritchard and Turri 2014), where “true” has to be intended in the sense of “corresponding to facts”. Williamson (2000) argues that knowledge is the most general factive propositional attitude. For a radically different view on knowledge, see Cellucci (2017).
- 19.
The main criticism to the quasi-factive view of understanding is the one developed by Elgin (2007, 2009), who shows how in many cases idealizations and other ‘untrue’ elements of a scientific theory are “central terms” of that theory, not peripheral. They are “essential elements of a theory” that cannot be replaced, nor are expected to be replaced in the future by scientists.
- 20.
It is worth noticing that this argument does not rest on a sort of pessimistic induction over past science (Laudan 1981), as many anti-realist arguments do. And so it does not display the weakness that is usually thought to afflict that kind of arguments, i.e. their inductive character (Barrett 2003). Indeed, the argument we are dealing with here is based on the theoretical impossibility of reconciling the images of the world provided by our current most powerful scientific theories.
- 21.
There are some additional difficulties for Dellsén’s account worth being pointed out: the first is that it is true that if QM and GTR are incompatible, at least one of them cannot be true. But we cannot exclude that neither is. How would the noetic view account for the possibility that, in light of future science, the essential elements of both QM and GTR will be deemed untrue? Shall we then claim that neither QM nor GTR were cases of progress when they were formulated and applied? In the same vein: even if we concede that future confirmation will allow us to determine that one theory between QM and GTR really increases our understanding because of the truth of its essential elements, there will still be the difficulty for the supporter of the noetic account to explain the empirical success enjoyed by the other radically ‘false’ theory, given that it is uncontroversial that both QM and GTR are extremely successful in dealing with the world, and that the noetic account claims to be a realist account of progress.
- 22.
Cf. Barrett (2003, p. 1216): “While we do have a vague commitment that our future physical theories will somehow be better than our current physical theories, we do not now know how they will be better. If we did, we would immediately incorporate this insight into our current physical theories.”
- 23.
Cf. Barrett (2003, p. 1216): “insofar as we expect surprising innovations in the construction of future theories […], we cannot now know even what the structure of the space of possible options for refining our current theories will prove to be.” This point cannot be developed here, but it is worth underlining that this line of reasoning is analogous to the unconceived alternatives argument developed by Stanford (2006), who elaborates on Sklar (1981).
- 24.
- 25.
Some work would be necessary to generalize Rice’s proposal and make it suitable to account for the case of the incompatibility between QM and GTR, since Rice (2016) refers just to some kinds of models, and especially focuses on some optimality models used in biology, while QM and GTR are theories. This point cannot be developed here, but a promising route may be to adopt the semantic view of theories, according to which a theory is the class of its models.
- 26.
- 27.
The adoption of possible-worlds modal realism amounts to assuming that there is something “like a realm of metaphysical possibility and necessity that outstrips the possibility and necessity that science deals with, but this is exactly what naturalists should not be willing to concede” (Morganti 2016, p. 87).
- 28.
On the consequences of Gödel’s results for how mathematical knowledge should be conceived, see Cellucci (2013, 2017). On how modalism construes the analogy between modality and mathematics, cf. Bueno and Shalkowski (2004, pp. 97–98): “If the analogy with mathematics is taken seriously, it may actually provide a reason to doubt that we have any knowledge of modality. One of the main challenges for platonism about mathematics comes from the epistemological front, given that we have no access to mathematical entities—and so it’s difficult to explain the reliability of our mathematical beliefs. The same difficulty emerges for modal realism, of course. After all, despite the fact that, on Lewis’ account, possible worlds are concrete objects, rather than abstract ones, we have no access to them. Reasons to be skeptical about a priori knowledge regarding mathematics can be easily ‘transferred’ to the modal case, in the sense that difficulties we may have to establish a given mathematical statement may have a counterpart in establishing certain modal claims. For example, how can we know that a mathematical theory, say ZFC, is consistent? Well, we can’t know that in general; we have, at best, relative consistency proofs. And the consistency of the set theories in which such proofs are carried out is far more controversial than the consistency of ZCF itself, given that such theories need to postulate the existence of inaccessible cardinals and other objects of this sort.”
- 29.
There is no space here to adequately argue for this claim, but we think that the noetic account may well be construed in anti-realist terms, and that a promising way for developing this conception is relying on the notion of ‘effectiveness’ proposed by de Regt and Gijsbers (2017). They propose to replace the usual truth requirement for understanding with an effectiveness condition on understanding, according to which understanding requires representational devices that are scientifically effective, where being ‘scientifically effective’ means being able to produce useful scientific outcomes such as correct predictions, successful applications and fertile ideas.
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Sterpetti, F. (2018). The Noetic Account of Scientific Progress and the Factivity of Understanding. In: Danks, D., Ippoliti, E. (eds) Building Theories. Studies in Applied Philosophy, Epistemology and Rational Ethics, vol 41. Springer, Cham. https://doi.org/10.1007/978-3-319-72787-5_11
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