Undecidability and opacity of metacognition in animals and humans

Metacognition, defined either epistemologically as knowledge about knowledge or operationally as behavior about behavior (Koriat, 2007), presumably enables intelligent agents to self-referentially and, in social contexts (Bahrami et al., 2010, 2012), group-referentially monitor and control emotions, moods, perceptions, memories, reasoning, decisions, and actions. At an epistemological level of description, the nested referent nature of metacognition succumbs to problems originating from recursively enumerable propositional logic; that, as Kurt Gödel (1931) first proved for Bertrand Russell and Alfred North Whitehead’s axiomatic Principia Mathematica, the meaning of statements created about conditions of a system or set of systems by the respective same system or set of systems can be formally undecidable. Momentarily ignoring peripheral confounds introduced by stochastic and imperfect biological systems, animal and human metacognitive operations and all their possibilities must thus exist in a universe of graded logicomathematical consistency (i.e., All theorems are true syntax-correct propositions of the system.) and completeness (i.e., All true syntax-correct propositions of the system are theorems.) (Kreisel, 1967). Because strong consistency excludes strong completeness, the knotted statements of metacognition may show themselves to be falsehoods, truths, or truths essentially unverifiable in theory as well as in subjective and objective practice (Figure 1) (Raattkainen, 2005). Psychologists well understand the fallibility of formal logic systems and of axiomatic animal and human psychological processes, including, among other phenomena, feature detection, inferential judgments, error diagnosis and correction, concept formation, memory storage and retrieval, and introspection (cf. Nisbett and Ross, 1980; Kahneman et al., 1982; Watanabe and Huber, 2006). We often stipulate—with qualifications—the flawed definition(s) and agent execution of cognition and metacognition (e.g., Shimamura and Metcalfe, 1994; Koriat and Goldsmith, 1996, 1998; Smith, 2009; Terrace and Son, 2009; Frith, 2012; Fleming et al., 2012; Yeung and Summerfield, 2012). For pragmatic reasons, many of us enthusiastic about studying metacognition also avoid the strange, looping causality of selfreference exposed with Gödelian numbering to concentrate on solving basic and/or clinical empirical difficulties that arise when trying to identify this stubbornly opaque hypothetical construct of healthy and pathological minds (e.g., Bach and David, 2006; Koren et al., 2006; Vance, 2006; Carruthers, 2009; Gumley, 2011; Brevers et al., 2013). The operational opacity of metacognition becomes arguably most apparent when considering: (1) poor subjective accessibility to the cognition and metacognition of animals and humans of limited or no language proficiency (cf. Hampton, 2009; Fleming and Dolan, 2012; Kepecs and Mainen, 2012; Smith et al., 2012), (2) the synergism and antagonism of unreliable explicit and implicit psychological components that mask real metacognitive abilities and capacities from agent and external observer (cf. Hampton, 2009; Fleming et al., 2012), and (3) the occasional independence between metacognition and cognitive skills which may exacerbate the preceding two problems (cf. Koriat and Goldsmith, 1998; Schneider, 1999). A case illustrating these three classes of problems is found for Paulus et al. (2013), who report evidence of implicit metacognition in normal preschool children performing a paired-associates learning and memory task. The authors confront the dilemma of metacognition opacity with a paradigm common to belief, memory, Theory of Mind, and now metacognition research (cf. Nisbett and Ross, 1980; Penn and Povinelli, 2007; Carruthers, 2009; Hampton, 2009; Izard, 2009; Frith, 2012; Skarratt et al., 2012); they prescribe objectively observable, variable primary and secondary behaviors that can be scored for accuracy and/or efficiency and for crosscorrelations involving use of secondary behaviors to monitor and control primary behaviors. A typical test scenario has subjects follow associative learning with forced-choice declarative recognition of perceptual/conceptual pairings between two separate images. Subjects subsequently give confidence judgments of memory accuracy through explicit self-reports, such as scalar feelings, and implicit reactions, such as changes in traceable voluntary gaze or involuntary saccades, pupil dilation, pressor effects, and electrical properties of skin. Ratings of accuracy confidence reflect an agent’s more-or-less accessible knowledge representation and decisional or post-decisional monitoring and control. By combining experimental protocols that test for self-reports and behavioral reactions, scientists, including Paulus et al. (2013), hope to objectify a subject’s mental states irrespective of his/her language skills as well as dissociate and double dissociate confounding explicit and implicit information processing. For example, Paulus et al. (2013) demonstrate implicit confidence judgments (i.e., gaze direction and duration and pupil area) can be superior in memory accuracy to prompted explicit judgments (i.e., self-report). Increased eye responses coincide with increased (pre)attention demand or load, suggesting humans might be more capable of successfully monitoring judgments at a preattentive or non-conscious level during