Abstract
Scientific evidence and scientific values under risk and uncertainty are strictly connected from the point of view of Peirce’s pragmaticism. In addition, economy and statistics play a key role in both choosing and testing hypotheses. Hence we may show also the connection between the methodology of the economy of research and statistical frequentism, both originating from pragmaticism. The connection is drawn by the regulative principles of synechism, tychism and uberty. These principles are values that have both epistemic and non-epistemic dimension. They concern both the decisions to test a hypothesis as well as inductive risk. The validity of this result stems from the values cost–benefit analysis imposes on scientific inquiry. Values associated with the economy of research are important not only in the pre-test phases of generating hypotheses but also when hypotheses are effectively tested. Peirce took these economic considerations to leave room for an interpretation of probability which is not only a frequentist and propensity-theoretic but also a conceptualist one referring to degrees of belief. We show that this leeway nonetheless agrees with the theory of the economy of scientific methods.
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Abbreviations for the Works of C. S. Peirce
CP, followed by volume and paragraph number: Peirce (1931–1958). MS, followed by manuscript number and, when available, page number: unpublished manuscripts in the Houghton Library, Harvard University. MS enumeration according to Robin (1967). L, followed by letter number and, when available, page number: unpublished manuscripts in the Houghton Library, Harvard University. L enumeration according to Robin (1967).
Notes
On fundamental uncertainty and decision making see Chiffi and Pietarinen (2017). Subjectivist degrees of probability may also be assigned to remote uncertain events. However, probability requires the partitions of the set of all alternatives Ω to be known, which may be problematic in case of remote events. Alternatively, certain heuristics may be used to ground our judgments on fundamentally uncertain events. We think that abductive modes of reasoning play a key role in this framework.
This may be one of the main reasons for the confusion between abduction and inference to the best explanation.
However, it is worth noticing that the contemporary terminology of epistemic and non-epistemic values is not present in Peirce’s philosophy. Still, a more general distinction between epistemic and non-epistemic aspects of scientific inquiry permeates Peirce’s pragmaticist epistemology.
It is well-known that probabilistic reasoning is affected by biases. Some hypotheses may be pursued because the predicted results show a greater resemblance to some desired outcome (representative heuristics), or because they can be easily imagined (availability heuristics). Economic considerations—if properly applied—may combat biases that affect selections of hypotheses to be tested. We thank a referee for this remark.
We thank a referee for suggesting us this remarkable point.
Applying probability to fundamental uncertainty—which may be somehow problematic—it could be nonetheless possible to rely on the idea that people tend to create patterns and adopt heuristics to deal with uncertainty, which might show a probabilistic behaviour.
Not unlike the precautionary principle, to give an example. We leave the study of the similarities between precautions to act and synechism, such as their role in expediting the inquiry and future events, as a topic awaiting for a separate investigation.
And this continuum is huge, it is not exhausted by any multitude whatsoever. Hence continuity is not definable with standard notions of the real line or point sets.
“Find a scientific man who proposes to get along without any metaphysics… and you have found one whose doctrines are thoroughly vitiated by the crude and uncriticized metaphysics with which they are packed” (CP 1.129).
This joint embracement of the principles of tychism, synechism and uberty, taken as scientific values, is what Laudan (1981) might have needed to consider in order to patch up the argument for scientific progress and to nudge him away from the path to pessimistic meta-induction.
Cf. MS 300 (1908), and especially MS 855 (1911): “By Induction, I mean a reasoning which provisionally conclude something to be true of every member of a collection, or, more frequently, of whatever there may be of a definite general kind, for no other reason than that firstly the same thing has been found to be true of a part of that collection, or of a finite collection of things of that kind, and secondly, that the manner in which this partial collection had come to be known to have the character which is concluded to belong to the whole, compels, or at least authorizes, us to regard it, provisionally, approximately, and probably, as an image of that whole”.
The validity of induction depends on the validity of deduction, as well as on “our confidence that a run of one kind of experience will not be changed or cease without some indication before it ceases” (Peirce to Woods, 1913), among others. This is another, yet related topic which is dealt with elsewhere.
One could claim that inference expresses the justified action to derive a conclusion starting from premises However, this is not enough to create a behaviour, since the notion of behaviour requires also the possibility to respond or adapt to the environment in order to achieve a goal.
Mayo (2005) has uncovered certain key connections between Peirce’s inductive methodology and the frequentist views of Newman and Pearson. As indicated in Hacking (1980), Peirce’s ideas on induction had also a great influence on Edwin B. Wilson. We add the historical tidbit that this is the same Wilson who once in the early 1920s started working on a draft biography of Peirce (deposited at Harvard University Archives) and who anticipated many aspects of the confidence interval methodology in statistics. See, for instance, Wilson (1926).
To express Fisher’s ideas in a better way, we use the term “disregarded” rather than rejected. The terms “acceptance” and “rejection” are better suited to reflect Newman and Pearson’s views.
Fisher clarifies the distinction between decisions and statistical inference as follows: “An important difference is that decisions are final, while the state of opinion derived from a test of significance is provisional, and capable, not only of confirmation, but of revision […]. A test of significance […] is intended to aid the process of learning by observational experience. In what it has to teach, each case is unique, though we may judge that our information needs supplementing by further observations of the same, or of a different kind” (Fisher 1956, 100–101).
Relative risk is the ratio of the incidence rates of an event occurring in one group to the incidence rates among the other group.
To be precise, and as pointed out in (Mayo 1993), inductive behaviour was the view supported only by Neyman.
We may leave open the possibility that in some cases scientific hypotheses may be accepted in a purely epistemic framework, which may happen, for instance, with hypotheses in astrophysics. For a balanced and system-based approach to the roles of values in science, see Agazzi (1987). For a detailed discussion on risk, uncertainty and values in science, see Hansson (2013).
If multiple conditions are being compared to each other, the possibility of Type-I error increases and therefore the value required for significance is usually reduced.
For instance, in a diagnostic framework, we should decide the consequences of failing to acknowledge an expression of a genetic mutation when the expression is in fact present, or to diagnose a disease when the mutation in fact is not present.
In Jeffrey’s example, however, one knows at least that the vaccine can inoculate some organism (otherwise it would not be a vaccine), even if the specific organism to be inoculated is unknown.
Jeffrey holds the view that there is no acceptance or rejection of scientific hypotheses in pure science, but only the assessment of their probability.
It is worth noting that disagreement on the role of values in science can also be due to the lack of distinctions between different senses of science, values, and their interplay.
A promising methodology to compute optimal inferential thresholds (also in virtue of economic considerations) and that may provide (at least) some guidelines is Signal Detection Theory (SDT) (Green and Swets 1966; McNicol 1972). Interestingly, the unacknowledged origins of SDT—despite having been developed quite independently—also date back to Peirce’s early experimental work on perception with Jastrow (Peirce and Jastrow 1885), especially their rebuttal of the Weber–Fechner’s discrete threshold principle in psychophysics and its reliance on unviable Laplacian principles of probability. The early goal of the SDT was to statistically understand the mechanisms by which human perceptual system is able to decide and report upon reception of signals amidst insignificant noise.
Notice, for instance, how Peirce singles out concepts such as “the state of knowledge”, “chance of an event”, “degrees and intensity of belief” and the subjectivist “feeling of believing” to these degrees to “vary with the chance”. Peirce affirms that: “probability and chance undoubtedly belong primarily to consequences, and are relative to premisses; but we may, nevertheless, speak of the chance of an event absolutely, meaning by that the chance of the combination of all arguments in reference to it which exist for us in the given state of our knowledge. Taken in this sense it is incontestable that the chance of an event has an intimate connection with the degree of our belief in it. Belief is certainly something more than a mere feeling; yet there is a feeling of believing, and this feeling does and ought to vary with the chance of the thing believed, as deduced from all the arguments. Any quantity which varies with the chance might, therefore, it would seem, serve as a thermometer for the proper intensity of belief” (Peirce 2014, 135).
For instance, one of the paradoxes that arises is Bertrand’s paradox. One cannot encircle an area on a continuous chart at will and claim the result to be informative without specifying what the precise method and the purpose of doing so would be for the calculation of the relevant probabilities, especially when as in Peirce’s example such distributions are continuous and important information about priors is missing. For instance encircling the entire graph would be to specify a method and the result would not be arbitrary. See also Carnap (1955) and van Fraassen (1989) on problems with the principle of indifference.
According to Levi (2006), subjective judgements of probability should ultimately be based on objective and statistical probability and expressed by comparative preferences rather than precise numerical values.
This parallels the changes in how expectation of a signal or cost of a missed signal influence the decision rule in SDT (Green and Swets 1966).
On this point, see also Tiercelin (2018).
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Acknowledgements
We thank for their comments: Mattia Andreoletti, Alessandro Balducci, Cristina Barés Gómez, Francesco Bellucci, Mario Castellana, Simona Chiodo, Francesco Curci, Matthieu Fontaine, Pierdaniele Giaretta, Lorenzo Magnani, Scira Menoni, Stefano Moroni, Gabriele Pasqui, Agostino Petrillo, Alessandro Rocca, Viola Schiaffonati, Paolo Volotè, and John Woods.
Funding
Estonian Research Council, “Abduction in the age of Fundamental Uncertainty”, Research Grant, (PUT 1305). Portuguese Foundation for Science and Technology as part of the project “Values in Argumentative Discourse” (PTDC/MHC-FIL/0521/2014), “Formal Philosophy”, Russian Academic Excellence Grant “5-100” and “Dipartimento di Eccellenza” (project) - “Fragilità territoriali”.
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Chiffi, D., Pietarinen, AV. Risk and Values in Science: A Peircean View. Axiomathes 29, 329–346 (2019). https://doi.org/10.1007/s10516-019-09419-0
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DOI: https://doi.org/10.1007/s10516-019-09419-0