What Consciousness Explains in Causal Reasoning: Sketch of Metatheory, Theory, and Experiment Donelson E. Dulany, Psychology, University of Illinois Richard A. Carlson, Psychology, Pennsylvania State University Understanding consciousness calls not only for an explanation of consciousness but also for what consciousness explains—a view in agreement with Carlson (1997, 2002), and several elaborations of a mentalistic metatheory (Dulany, 1991, 1997, 2004, 2009, 2011, in press). What should be the place of consciousness in theories of phenomena that have been the focus of research in psychology—from perception and categorization, through learning and memory, to decision and reasoning? This work focused on an analysis of causal learning that entails causal reasoning.
Mentalistic Metatheory What in the fuller developments of this metatheory (Dulany, 1991 to in press) is most relevant for the analysis of causal learning and reasoning?
Objective. The aim is theories of lawful causal relations among conscious states within mental activity, their antecedents and consequent actions. This in no way entails ontological non-materialism or “free will” in the sense of indeterminism—despite enduring confusions of theoretical assertions with metaphysical assertions. The metatheory is consistent with working assumptions, however, that the states have a causal orderliness and are coordinate with brain states in some way.
Symbols. Fundamentally, too, conscious states are the carriers of symbolic representations of external events in first order awareness--a present in perceiving, a past in remembering , and a future in expecting, hoping, or fearing. And both past and future events may be represented in less contrained imaginings—what Brentano (1960, 1874) termed “intentional inexistents”. The
power of symbolic representation even permits representation of conscious states and mental episodes in higher order awareness. Symbols are functionally specified by their roles in a network of propositions and associative linkages, and in some cases, in actions that confirm a representation. The symbolic idea of “cup”? You can successfully reach for it on your desk. In this study, subjects were provided a causal problem—a murder mystery and trial by trial clues to imagine--clues to believe were or were not associated with each suspect, clues that would activate various implicational beliefs. These were all beliefs that would appear in first order awareness, imaginings of a criminal reality. The subjects then reported higher order awareness of their conscious belief states.
Components of conscious states. A conscious state consists of (a) a mode such as belief, perception, fear, etc. varying in value, and carrying (b) contents that can vary in value, as when a response varies in likelihood it will be “correct”, or some frequency or value is predicated of a subject. They can also be held with varying sense of possession, often termed (c) agency. Thus a conscious state is at the intersection of a set of variables.
Mental episodes. Understanding the role of conscious states in mental activity calls for an analysis of mental episodes--something more analytic than viewing consciousness as a “system” or “space.”
What characterizes a deliberative mental episode? a. Propositional contents are carried by conscious propositional modes, for example, belief that _____. b. Propositional content is yielded by two or more propositional contents by nonconscious deliberative operations of inference, decision.
What characterizes an evocative (associative) mental episode? a. Sub-propositional contents are carried by sub-propositional modes, a perception (feeling, sense) of _______ . b. Sub-propositional content is yielded by one or more sub-propositional contents by non-conscious operations of associative activation.
What do deliberative and evocative mental episodes have in common? a. For a general form, we have Cs Statein+1 ← NonCs Op (Cs Statejn ,…, Cs Statek,n ) , a conscious state yielded by nonconscious operation from other conscious states. b. And when represented in a quantitative model, as conscious state values vary, Cs Statesin+1 = f(Cs Statejn ,…, Cs Stateskmn), with the function f representing the set of nonconscious operations. What represents any mental episode is then an n-tuple within a particular function and set of conscious states.
The self? Not another entity, but an abstraction over a class of mental activity, deliberative and evocative, with “I” as subject or “me” as object.
The non-conscious. With greater elaboration in Dulany (1991 to 2011), the non-conscious is recognized as non-symbolic—the neural networks in inactive memory, the sensory and motor transduction systems, and the mental operations transforming conscious contents within these mental episodes.
Deliberative-Evocative relations. There are conditions in which learning may be primarily evocative (implicit) or deliberative (explicit), with some interlacing, as described more fully in Dulany (in press). This study used the theory and model of propositional learning, as described in Dulany (1979) and reported Carlson &I Dulany (1988), to represent a kind of learning that is primarily deliberative, with evocative activation of clue significance.
Theory and Model of Propositional Learning: Causal Reasoning in Causal Learning Consider various kinds of causal learning in which there is some prior knowledge of the significance particular pieces of evidence would have for implicating one of several causes for an observed effect. This would be true of learning which of possible causes in science, which of possible disorders in a medical diagnoses, and which of various suspects is guilty in a murder mystery. With prior knowledge, the causal hypothesis is a “causal theory” that some possible cause, Ci, is the true cause, Cx, , β(Hi) = β(Ci = Cx),
(1)
where that means that the true cause has a place in causal schemas, each a cluster of beliefs about the relation of certain evidence, affirmation or denial of clues in this case, to the true cause, the murderer— implicational beliefs that may be activated into awareness for use. The learner’s own causal theories, the set of hypotheses tested, are theories that a possible cause will fit the true cause’s place in those causal schemas. For simplification of the equations, “Belief” values are scaled as β = 2P-1. Since subjects were presented the mystery of a murder (effect) to solve with a succession of clues selectively associated with suspects (possible causes) , for simplicity the theory will be described in those terms here.
Belief in Association, β(Aij). On each trial with a cluej selectively associated with particular suspectsi, the subject should acquire degree of belief that the evidence is true, a positive value, or is false, a negative value, of a particular suspect.
Forward Clue Implication, β(Fj). For a set of clues there is a “forward clue schema”, and presentation of a clue should activate its own implication into awareness. It is the degree of belief that this clue would be true of the
murderer (cause) only, a positive value, or of the innocent (non-cause) only, a negative value.
Subjective Evidence, β(Eij). Subjective evidence is the degree of belief that clue suggests guilt, a positive value, or suggests innocence, a negative value, specifically for a particular suspect. From the belief in a suspect’s association with a clue, together with belief in the clue’s implication of guilt or innocence, the subject should infer that strength of Subjective Evidence. With this scaling, the belief value of Subjective Evidence, β(Eij), should be the product of those two beliefs: β(Eij) = β(Aij) β(Fj).
(2)
Backward Clue Implication, β(Bj). For a set of clues, there is also a “backward clue schema”, and presentation of a clue should also activate its own implication into awareness. In this case, it is the degree of belief that the murderer (cause) would be would be someone of whom the clues is true, a positive value, or someone of whom the clue is false, a negative value. We can think of this as a moderator on the values of subjective evidence.
Convincingness of the Evidence, β(Vij). Simply put, we can think of the Backward Clue Implication, β(Bj), as a moderator of the Subjective Evidence, β(Eij, ). Thus, β(Vij) = β(Eij) /β(Bj)/.
(3)
We can then think of revision of belief as some proportion of the distance to Certain Guilty, β(Hin+1) = +1, when the Subjective Evidence is positive, or to Certain Innocent, β(Hin+1) = -1, when the Subjective Evidence is negative. That is a proportion given by absolute value of Convincingness of the Evidence, /β(Vij)/. β(Hin+1) = β(Hin) + / β(Eij) β(Bij/ [1- β(Hin)], if β(Eij) > 0 β(Hin+1) = β(Hin ),
if β(Eij) = 0
β(Hin+1) = β(Hin), - / β(Eij) β(Bij)/ [1+ β(Hin)], if β(Eij) < 0.
(4)
From theory to model, degrees of belief were mapped directly to variables, and mental operations were mapped directly to the function within linear difference equations for revision of belief. We may describe the relations among these conscious states in equations, but the conscious states are also constructs to be represented in a theoretical network specifying the meanings of the constructs. We can also see that this network is hierarchically organized (Carlson & Dulany, 1988, p. 467):
Theory of Propositional Learning as a Theoretical Network
Experimental Procedures of Experiment 1 Task. Experiment 1 addressed these theoretical and metatheoretical questions most directly and can be briefly described here, with reference to Experiments 2 and 3 that address further questions that might be raised. Twelve subjects were each asked to imagine a murder mystery—for example, Mr. Phelps found dead in his study—followed by a second murder
mystery, each with 12 trials in which clues were presented. The ratio of clues tending to “incriminate” or “ exonerate” was 9/3 for the “murderer” and 7/5, 5/7, or 3/9 for each of the other three suspects. The scope of clues—over 1, 2, or 3 suspects—varied with counterbalancing over clues and suspects. For example, as presented on the computer screen, “This clue is true of this (all of these) and only this (these) suspect(s)”: “This suspect had recently had quarrels with Mr. Phelps.”
Or,
“This suspect has taken the side of Mr. Phelps in quarrels.”
Assessment of conscious states: With further presentation on the computer screen, there were questions clue-suspect pairings and an eleven point scale, for the answer. Forward implication, β(F): What is the relative likelihood that this clue would be true of the murderer or an innocent suspect? Innocent Only
Equally Likely
Murderer Only
Backward implication, β(B): What is the relative that the murderer would be someone of whom this clue is true or someone of whom this clue is false? False Only
Equally Likely
True Only
Subjective evidence, β(E): How strongly do you believe the evidence presented by this clue suggests guilt or suggests innocence for (Sam)? Suggests Innocence
Completely Uncertain
Suggests Guilt
Convincingness of the evidence, β(V): How convincing that (Sam) is guilty or innocent do you find the evidence presented by this clue? Convincing Innocent
Completely Uncertain
Convincing Guilty
Belief in Causal hypothesis, β(H): How certain are you that (Sam) is guilty or innocent? Certain Innocent
Completely Uncertain
Certain Guilty
Results of Experiment 1 Revision of Belief in a Causal Hypothesis, β(H) . For this important prediction of the theory, Equation 4, all test results were strong. First of all, it is clear from this figure that predicted belief values closely follow reported conscious belief values over both sets of 12 trials, computed for means over subjects, suspects, clue scopes, and clue ratios (Carlson & Dulany, 1988, p. 467). Observed Values as a Function of Predicted Values Over Trials
Furthermore, for the 1096 observations—over subjects, trials, and conditions—correlation of predicted and observed values of β(H) was .90 with a slope of .94 and an intercept of -.002. As expected, predictability was strong for individual subjects, although somewhat variable, from r = .80, slope of .83, and intercept of .024 to r = .97, Slope of 1.05, and intercept of .003—the latter revealing theoretical fit obtainable under what must be the best of individual conditions.
It is important, too, that when β(E) = 0, the 0 predicted revision occurred in 88% of the cases, and the revisions were so small that the mean absolute
value of revision for all trials at β(E) = 0 was only .04 on a .20 scale unit. Convincingness of the Evidence, β(V), did provide the proportion of revision of β(H) toward “Certain Guilty”, +1, or “Certain innocent,” -1. Revision of β(H) was predicted in multiple regression by β(V) and D (the absolute value of that distance to certainty), with the effect of their product revealed in their interaction, F(1,1092) = 148.43, p < .01. Error of prediction? Signed error of prediction over all was .004, and error of prediction was -.02, .01, .00, .03 for subjects incriminated on 9, 7, 5, and 3 of 12 trials respectively.
Subjective Evidence, β(E). Subjective evidence should vary with the product of Belief in Association, β(A), as well as the Forward Implication, β(F). In crime solution or medical practice—and in science—the association of a piece of evidence with a potential cause can be uncertain, and an assessment of that subjective β(A) would be needed along with this assessment of the Forward Implication, β(F). In this case, however, that asserted association of clue value, Incriminating or Exonerating, with presence or absence of the suspect was clear enough. Therefore this β(A), the reported β(F) value, and their product were examined in a regression analysis, with β(E) the predicted variable. In accord with Equation 2, Subjective Evidence, β(E), was predicted by the product of β(A) and β(F), as revealed in their strong interaction, F(1,569) = 1379.61.
Convincingness of the Evidence, β(V). By Equation 3, Subjective Evidence, β(E), should be moderated by /β(B)/ , the clue’s Backward Implication, in prediction of Convincingness of the Evidence, β(V). This, too, was revealed in multiple regression with an interaction, F(1,1092) = 5.29, p = .02.
Discussion Are there competing formulations that would explain these data?
Associative models. As Gopnik & Schultz (2007) write, “Indeed in the adult cognitive science literature, researchers have largely focused on the role of contingency and covariation in causal learning as opposed to principles about mechanisms” (p. 10). From Shanks & Dickenson (1987) through Cheng (1997) and beyond, the problem has been represented within a 2 X 2 table, for cause vs. non-cause and effect vs. non-effect. Causal learning has been given by increases in attributed ∆P = P(e|c) – P(e|~c), with competing causes having different weights, as in Cheng & Novick (1993), or by q = ∆P/1-P(e|~c) so that “causal powers” could be different for the same ∆P when P(e|~c) differs—or by incorporating the Rescorla-Wagner (1972) rule for proportional increases, or with a decay parameter for decreases. In all of these models, however, there is the process assumption that the association of cause and effect, as given by the particular model, directly strengthens the cause-effect relation for the subject. 1. Could the conscious states and phenomenal reports be post-process emergents of an associative process linking incriminating vs. exonerating clues to clues to the murderer vs. non-murderer? A first answer is that differences in the over-trials functions for reported β(H) are closely in accord with theoretically predicted values of β(H) , but those β(H) report values are not closely in accord with the 9/3, 7/5, 5/7, 3/9 proportions of incriminating vs. exonerating clue-suspect associations. Furthermore, there are no available and plausible assumptions on which an association process would exude these conscious states and reports. 2. Could these various assessments themselves—of forward implications, subjective evidence, backward implications, convincingness of the evidence-have created these specific causal reports, despite an underlying association? An Experiment 3 with the same procedures assessed only Belief in the Causal Hypothesis, β(H). Across the experiments, the over-trials functions were
closely similar (Carlson & Dulany, 1988, Figure 8, p. 486), and the correlation across experiments over trials of mean β(H) .96. 3. Or could the simple process of assessment itself have led subjects to put their reports together in the theoretically specified way—despite underlying association? The obvious answer in this case would be this: Only if the subjects knew these equations. Even if we should recognize the possibility of associative strengthening of conscious but sub-propositional contents in other paradigms, it would be important to specify those evocative mental episodes theoretically. And it is especially important to analyze the deliberative processing of propositional awareness in the varieties of causal learning that call for causal reasoning.
Logic of competitive support. In each case the answer to the question provides low credibility for an auxiliary assumption an associatieve theory would need to explain these data On a logic of competitive support for theories of hypothetical unobservables, a logic elaborated more fully in Dulany (in press), these are the central principles: 1. The Hypothesis advanced and tested is a complex of Theory, Mappings, and Auxiliaries such as various experimental controls: H = (T,M,A). As Quine (1951) put it famously, “They go to the court of experience as a corporate body”. In this case, a key Mapping is the hypothetical relation of a conscious state to a phenomenal report, with validity maximized by observing common standards of attention, memory relating first order awareness to higher order reported awareness, and verbalizability. Reports are handled in the investigator’s physicalistic, “second person,” data language. 2. Although TPL was found to be descriptively accurate for subjects, and could be more broadly, a form of the Bayes’ rule can provide a normative model for the relative credibility of two competing theories—as in the present case. For a competing theory to predict the data, it must add Auxiliaries, and in the examples given, we see that the price of predictability with low credibility
auxiliaries, even “pushing a likelihood ratio to 1”, is lack of credibility in the Hypothesis in the Bayesian prior and thus also given the available data. 3. In general, too, credible Auxiliaries for competing Hypotheses are less available to the degree the data are rich and predicted by a comparatively rich theoretical network—as they are here.
Other non-associative approaches to causal learning. With limitations of space here, these will only be summarily characterized.
Bayesian. Bayes models can be variously formed and have been variously applied. One ambitious possibility is the use of Bayes nets (e.g. Glymour, 2001; Pearl, 2000) to represent more complex causal structures, with probabilistic interrelations that are only inferred from selective patterns of evidence. Theory of Propositional Learning has not been applied to this paradigm. In Experiment 2 of Carlson & Dulany, (1988), however, a form of Bayes’ rule was examined in the murder mystery paradigm. On a probability scale, P(H) and P(~H) became the a priories, and P(Fpos) and P(Fneg), values of the Forward Implication, provided components of the likelihood ratio, P(E|H) and P(E|~H). The value of clue denial then became 1- clue affirmation. Then with a standard form of Bayes rule, Pn(H|E) predicted, the overall correlation of predicted and observed values was .66, with a slope of only .52 and an intercept of .26, and a mean absolute prediction error of .17. Prediction may have been superior with TPL because it included the Backward Implication and a parameter for proportion revision of belief.
Mechanisms and theories. Another challenge to associative models has been evidence in certain paradigms that subjects can hypothesize mechanisms to explain causal effects—“causal theories”, we may say, for mechanisms so used (Ahn, Kalish, Medin, & Gelman, 1995). They may also infer unobserved causes, as in the model presented by Lumann & Ahn (2007). Griffiths & Tenenbaum (2009) also write that “causal induction is the product of
domain-general statistical inference guided by domain specific prior knowledge, in the form of abstract causal theory” (p. 661). In this murder mystery paradigm with causes imagined, we must also say that the possible causes, the suspects—like the effect and the evidence are “unobserved” in the sense of being only imagined. Furthermore, the Forward Schemas and Backward Schemas “wrap” each cause-effect combination and constitute one kind of mechanism—a theoretical mechanism. In fact, central to this theory of propositional learning, as expressed in Equation 1, is a set of theoretical hypotheses, each the theory that a possible cause, Ci, has the place of the true cause, Cx, in those sets of Forward and Backward implications.
Final comment. We can recognize the value of these detailed and elaborated expressions of central principles, principles that recall the earlier theory of propositional causal learning. As is generally the case, too, we should recognize that the phenomenon of causal learning has a number of variants and it is for further research to determine the generality across paradigms of particular models. Theory of propositional causal learning stands apart, however, explicitly in these ways: (a) It specifies causal roles for particular conscious states within the learning process—something that could be made explicit in any of these domains. (b) It is analytic in specifying forms of mental episodes interlinking propositional contents of conscious states by nonconscious operations. And (c) those contents symbolically represent, both within and outside experimental paradigms. What consciousness explains contributes to the explanation of consciousness—its adaptive significance.
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References
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Presented Association for Scientific Study of Consciousness, Brighton, England, 2012
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