Abstract
Analogical reasoning addresses the question how evidence from various phenomena can be combined and made relevant for theory development and prediction. In the first part of my contribution, I review some influential accounts of analogical reasoning, both historical and contemporary, focusing in particular on Keynes, Carnap, Hesse, and more recently Bartha. In the second part, I sketch a general framework. To this purpose, a distinction between a predictive and a conceptual type of analogical reasoning is introduced. I then take up a common intuition according to which (predictive) analogical inferences hold if the differences between source and target concern only irrelevant circumstances. I attempt to make this idea more precise by addressing possible objections and in particular by specifying a notion of causal irrelevance based on difference making in homogeneous contexts.
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Notes
Note that the absence of universal rules for analogical inferences does not necessarily imply that such inferences cannot be reliable. An interesting proposal in this regard is John Norton’s material theory of induction (cp. Norton 2011 and references therein). A critique of Norton’s theory of induction is beyond the scope of this paper.
Note that Bayesian approaches to confirmation often assume a similar role for analogy as being confined to prior considerations (e.g. Salmon 1990): “I suspect that the use of arguments by analogy in science is almost always aimed at establishing prior probabilities. […] The moral I would draw concerning prior probabilities is that they can be understood as our best estimates of the frequencies with which certain kinds of hypotheses succeed. These estimates are rough and inexact” (ibid., 186–187).
I.e. systematically speaking, historically of course Keynes was prior to Carnap.
Carnap qualifies that the strict inequality only holds if the original confirmation function is not zero or one.
While the approach proposed in this essay builds on Keynes’s ideas in many ways, one of the advantages with respect to Keynes is that to some extent it is quantitative. In particular, a sufficient and necessary criterion is given for analogical inferences in deterministic contexts. Thus, analogical inferences fulfilling this criterion are valid with probability 1. In Sect. 5, an extension of the proposed framework is briefly sketched, under which circumstances one can meaningfully assign a probability to a prediction based on analogical reasoning.
The proposal is embedded within a broader distinction between phenomenological science on the one hand and abstract or theoretical science on the other hand. Perhaps the most important difference between phenomenological and theoretical science concerns the aim: the former is mainly interested in reliable prediction and successful manipulation, the latter in the development of a conceptual and explanatory framework. Thus, predictive analogies fit well with phenomenological science, conceptual analogies fit well with theoretical science. There are a number of further characteristics that both distinctions share, for example whether the laws that are used are causal or not. Some of the claims in this section can only be understood from the perspective of this broader distinction between phenomenological and abstract science, for which unfortunately I cannot argue here due to lack of space. Notable scholars, who have made and argued for the distinction, include Duhem (1954) and Cartwright (1983).
This is a typical formulation (e.g. Sober 2001, 331). Reichenbach was somewhat more cautious: “the principle of the common cause […] can be stated in the form: If an improbable coincidence has occurred, there must exist a common cause. […] Chance coincidences, of course, are not impossible […]. The existence of a common cause is therefore […] only probable. This probability is greatly increased if coincidences occur repeatedly” (Reichenbach 1956, 157–158).
Due to lack of space, we cannot address here certain interesting, but controversial cases, such as correlations due to indeterministic relationships, which arise for example in connection with the Bell Inequalities, or correlations due to conservation laws.
One might object that the validity of an analogical inference should not be confused with whether a prediction turns out true or not. Notably, it has been argued that valid inferences are those that adhere to commonly accepted methodological conventions, largely independently of empirical success. However, in the case of (predictive) analogical inferences, a necessary and sufficient criterion for empirical success can be stated. Under these circumstances, it seems adequate to identify valid (predictive) analogical inferences with those that obey the criterion.
In this category falls a well-known example concerning the inference that there is life on Mars based on the existence of life on Earth, even though there apparently are relevant differences between both planets. How to deal with such examples will be outlined in Sect. 4.3.
While I will eventually seek a deterministic notion of causal irrelevance, it is nevertheless helpful to first also look at related suggestions, including statistical notions.
I.e. factors that are causally relevant to Y but to which X is not causally relevant—excluding in particular factors that lie on a causal chain from X to Y.
I have emphasized repeatedly Cartwright’s point that causation allows for implementing effective strategies. Note that this does not necessarily imply an interventionist take on causation. Instead, I favor an understanding in terms of difference making. The latter is more general and requires less ontological commitments compared with the interventionist approach.
For a more extensive argument in favor of the proposed framework, compare Pietsch (2016).
As in Eells’s approach, there are mixed cases, in which a circumstance is neither relevant nor irrelevant with respect to a given context.
Note that the definition has some seemingly counterintuitive implications. If, for example, a light is controlled by two switches A and A*, where the light is on if at least one of the switches is on, and if it is presupposed as part of the background conditions that A* is on, then A will be classified as causally irrelevant according to the definition (CI). While this sounds counterintuitive, the definitions above are intended as refinements or improvements of our everyday notions in order to make causal language more precise and avoid contradictions. Eventually, these seemingly counterintuitive implications will allow to resolve the first group of problems for (PA) as discussed in Sect. 4.1.
Building on the example of footnote 16, A is causally relevant to C, if it is part of the background conditions that A* is always off, while A is causally irrelevant to C, if it is part of the background conditions that A* is always on. Again, this seeming contradiction only underlines the need to always relativize causal dependencies to a background.
Homogeneity broadly corresponds to context-unanimity in Eells’s account.
The notion of ‘causal relevance in virtue of’ cannot be discussed here in further detail due to lack of space. An exact explication is: “A condition X is causally relevant to C in virtue of A being causally relevant to C with respect to a background B, iff in all contexts within B, in which X is causally relevant to C, A is causally relevant to C as well (but not necessarily vice versa).”
Requiring irrelevance for all possible combinations of variables or for each variable individually would be much too strong such that (PA′) as stated below would not be a necessary criterion. For example, analogical inferences, in which two causally relevant factors exactly cancel each other, would be wrongly identified as invalid.
Basically, one needs to replace in (PA), (CI), (CR), and (H) “causally irrelevant” with “causally and definitionally irrelevant” as well as “causally relevant” with “causally or definitionally relevant”. Note that for predictive analogies, all changes in the definitions of relevant terms must be known in advance in order to clearly distinguish predictive from conceptual analogies according to the criterion discussed in Sect. 3 that only for conceptual analogies one is prepared to engage in conceptual work.
I am grateful to one of the referees for this example, which I have quite shamelessly copied almost verbatim from the referee report.
I am grateful to one of the referees for bringing up this issue.
I am grateful to one of the referees for suggesting this helpful distinction.
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I am grateful to two anonymous referees for extremely helpful comments and suggestions.
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Pietsch, W. A Causal Approach to Analogy. J Gen Philos Sci 50, 489–520 (2019). https://doi.org/10.1007/s10838-019-09463-9
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DOI: https://doi.org/10.1007/s10838-019-09463-9