Abstract: Human beliefs have remarkable robustness in the face of disconfirmation. This robustness is often explained as the product of heuristics or motivated reasoning. However, robustness can also arise from purely rational principles when the reasoner has recourse to ad hoc auxiliary hypotheses. Auxiliary hypotheses primarily function as the linking assumptions connecting different beliefs to one another and to observational data, but they can also function as a “protective belt” that explains away disconfirmation by absorbing some of the blame. The present article traces the role of auxiliary hypotheses from philosophy of science to Bayesian models of cognition and a host of behavioral phenomena, demonstrating their wide-ranging implications.
Keywords: Bayesian modeling Computational learning theories Philosophy of science
Introduction
Since the discovery of Uranus in 1781, astronomers were troubled by certain irregularities in its orbit, which appeared to contradict the prevailing Newtonian theory of gravitation. Then, in 1845, Le Verrier and Adams independently completed calculations showing that these irregularities could be entirely explained by the gravity of a previously unobserved planetary body. This hypothesis was confirmed a year later through telescopic observation, and thus an 8th planet (Neptune) was added to the solar system. Le Verrier and Adams succeeded on two fronts: they discovered a new planet, and they rescued the Newtonian theory from disconfirmation.
Neptune is a classic example of what philosophers of science call an ad hoc auxiliary hypothesis (Popper, 1959; Hempel, 1966). All scientific theories make use of auxiliary assumptions that allow them to interpret experimental data. For example, an astronomer makes use of optical assumptions to interpret telescope data, but one would not say that these assumptions are a core part of an astronomical theory; they can be replaced by other assumptions as the need arises (e.g., when using a different measurement device), without threatening the integrity of the theory. An auxiliary assumption becomes an ad hoc hypothesis when it entails unconfirmed claims that are specifically designed to accommodate disconfirmatory evidence.
Ad hoc auxiliary hypotheses have long worried philosophers of science, because they suggest a slippery slope toward unfalsifiability (Harding, 1976). If any theory can be rescued in the face of disconfirmation by changing auxiliary assumptions, how can we tell good theories from bad theories? While Le Verrier and Adams were celebrated for their discovery, many other scientists were less fortunate. For example, in the late 19th century, Michelson and Morley reported experiments apparently contradicting the prevailing theory that electromagnetic radiation is propagated through a space-pervading medium (ether). FitzGerald and Lorentz attempted to rescue this theory by hypothesizing electrical effects of ether that were of exactly the right magnitude to produce the Michelson and Morley results. Ultimately, the ether theory was abandoned, and Popper (1959) derided the FitzGerald–Lorentz explanation as “unsatisfactory” because it “merely served to restore agreement between theory and experiment.”
Ironically, Le Verrier himself was misled by an ad hoc auxiliary hypothesis. The same methodology that had served him so well in the discovery of Neptune failed catastrophically in his “discovery” of Vulcan, a hypothetical planet postulated to explain excess precession in Mercury’s orbit. Le Verrier died convinced that Vulcan existed, and many astronomers subsequently reported sightings of the planet, but the hypothesis was eventually discredited by Einstein’s theory of general relativity, which accounted precisely for the excess precession without recourse to an additional planet.
The basic problem posed by these examples is how to assign credit or blame to central hypotheses vs. auxiliary hypotheses. An influential view, known as the Duhem–Quine thesis (reviewed in the next section), asserts that this credit assignment problem is insoluble—central and auxiliary hypotheses must face observational data “as a corporate body” (Quine, 1951). This thesis implies that theories will be resistant to disconfirmation as long as they have recourse to ad hoc auxiliary hypotheses.
Psychologists recognize such resistance as a ubiquitous cognitive phenomenon, commonly viewed as one among many flaws in human reasoning (Gilovich, 1991). However, as the Neptune example attests, such hypotheses can also be instruments for discovery. The purpose of this paper is to discuss how a Bayesian framework for induction deals with ad hoc auxiliary hypotheses (Dorling, 1979; Earman, 1992; Howson and Urbach, 2006; Strevens, 2001), and then to leverage this framework to understand a range of phenomena in human cognition. According to the Bayesian framework, resistance to disconfirmation can arise from rational belief-updating mechanisms, provided that an individual’s “intuitive theory” satisfies certain properties: a strong prior belief in the central hypothesis, coupled with an inductive bias to posit auxiliary hypotheses that place high probability on observed anomalies. The question then becomes whether human intuitive theories satisfy these properties, and several lines of evidence suggest the answer is yes.1 In this light, humans are surprisingly rational. Human beliefs are guided by strong inductive biases about the world. These biases enable the development of robust intuitive theories, but can sometimes lead to preposterous beliefs.
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The true self
Beliefs about the self provide a particularly powerful example of resistance to disconfirmation. People make a distinction between a “superficial” self and a “true” self, and these selves are associated with distinct patterns of behavior (Strohminger, Knobe, & Newman, 2017). In particular, people hold a strong prior belief that the true self is good (the central hypothesis h in our terminology). This proposition is supported by several lines of evidence. First, positive, desirable personality traits are viewed as more essential to the true self than negative, undesirable traits (Haslam, Bastian, & Bissett, 2004). Second, people feel that they know someone most deeply when given positive information about them Christy et al., (2017). Third, negative changes in traits are perceived as more disruptive to the true self than positive changes (Molouki and Bartels, 2017; De Freitas et al., 2017).
The key question for our purposes is what happens when one observes bad behavior: do people revise their belief in the goodness of the actor’s true self? The answer is largely no. Bad behavior is attributed to the superficial self, whereas good behavior is attributed to the true self (Newman, Bloom, & Knobe, 2014). This tendency is true even of individuals who generally have a negative attitude toward others, such as misanthropes and pessimists (De Freitas et al., 2016). And even if people are told explicitly that an actor’s true self is bad, they are still reluctant to see the actor as truly bad (Newman, De Freitas, & Knobe, 2015). Conversely, observing positive changes in behavior (e.g., becoming an involved father after being a deadbeat) are perceived as indicating “self-discovery” (Bench et al., 2015; De Freitas et al., 2017).
These findings support the view that belief in the true good self shapes the perception of evidence about other individuals: evidence that disconfirms this belief tends to be discounted. The Bayesian framework suggests that this may occur because people infer alternative auxiliary hypotheses, such as situational factors that sever the link between the true self and observed behavior (e.g., he behaved badly because is mother just died). However, this possibility remains to be studied directly.
Conceptual change in childhood
Children undergo dramatic restructuring of their knowledge during development, inspiring analogies with conceptual change in science (Carey, 2009; Gopnik, 2012). According to this “child-as-scientist” analogy, children engage in many of the same epistemic practices as scientists: probabilistically weighing evidence for different theories, balancing simplicity and fit, inferring causal relationships, carrying out experiments. If this analogy holds, then we should expect to see signs of resistance to disconfirmation early in development. In particular, Gopnik and Wellman (1992) have argued that children form ad hoc auxiliary hypotheses to reason about anomalous data until they can discover more coherent alternative theories.
For example, upon being told that the earth is round, some children preserve their preinstructional belief that the earth is flat by inferring that the earth is disk-shaped (Vosniadou & Brewer, 1992). After being shown two blocks of different weights hitting the ground at the same time when dropped from the same height, some middle-school students inferred that they hit the ground at different times but the difference was too small to observe, or that the blocks were in fact (contrary to the teacher’s claims) the same weight (Champagne et al., 1985). Children who hold a geometric-center theory of balancing believe that blocks must be balanced in the middle; when faced with the failure of this theory applied to uneven blocks, children declare that the uneven blocks are impossible to balance (Karmiloff-Smith & Inhelder, 1975).
Experimental work by Schulz, Goodman, Tenenbaum, and Jenkins (2008) has illuminated the role played by auxiliary hypotheses in children’s causal learning. In these experiments, children viewed contact interactions between various blocks, resulting in particular outcomes (e.g., a train noise or a siren noise). Children then made inferences about novel blocks based on ambiguous evidence. The data suggest that children infer abstract laws that describe causal relations between classes of blocks (see also Schulz and Sommerville, 2006; Saxe et al., 2005). Schulz and colleagues argue for a connection between the rapid learning abilities of children (supported by abstract causal theories) and resistance to disconfirmation: the explanatory scope of abstract causal laws confer a strong inductive bias that enables learning from small amounts of data, and this same inductive bias confers robustness in the face of anomalous data by assigning responsibility to auxiliary hypotheses (e.g., hidden causes). A single anomaly will typically be insufficient to disconfirm an abstract causal theory that explains a wide range of data.
The use of auxiliary hypotheses has important implications for education. In their discussion of the educational literature, Chinn and Brewer (1993) point out that anomalous data are often used in the classroom to spur conceptual change, yet “the use of anomalous data is no panacea. Science students frequently react to anomalous data by discounting the data in some way, thus preserving their preinstructional theories” (p. 2). They provide examples of children employing a variety of discounting strategies, such as ignoring anomalous data, excluding it from the domain of the theory, holding it in abeyance (promising to deal with it later), and reinterpreting it. Careful attention to these strategies leads to pedagogical approaches that more effectively produce theory change. For example, Chinn and Brewer recommend helping children construct necessary background knowledge before introduction of the anomalous data, combined with the presentation of an intelligible and plausible alternative theory. In addition, bolstering the credibility of the anomalous data, avoiding ambiguities, and using multiple lines of evidence can be effective at producing theory change.
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