Contrasting Contradictory Beliefs
In “Theory-based Bayesian models of inductive learning and reasoning,” authors Joshua Tenenbaum, Thomas Griffiths and Charles Kemp argue that both traditional accounts of induction and strong constraints from structured domain knowledge are important in explaining the nature, use and acquisition of human knowledge. The authors offer a theory-based Bayesian framework as model for inductive reasoning and learning (Tenenbaum, Griffiths and Kemp, p. 309). Thus, the article presents a theory-based Bayesian model as a combination of the traditional induction and structured domain knowledge constraints.
On the other hand, formal learning theory suggests that an agent or an individual should make certain observations regarding one’s environment in order to formulate correct conclusions that are informative. The theory also espouses the ways in which how such observations are to be made so as to arrive at the precise conclusions. The theory is basically accepted as a normative framework used for inductive inference as well as scientific reasoning.
The assumptions for the first article include the idea that human cognition relies on our ability to arrive at generalized knowledge founded on sparse but specific examples. It assumes that there are two approaches in arriving at an inductive generalization: one which considers statistical mechanisms of inference and another which focuses on intuitive theories. The statistical mechanisms of inference are said to be “relatively domain-general” and “knowledge-independent” which are “based on similarity, association, correlation or other statistical metrics” (Tenenbaum, Griffiths and Kemp, p. 309). The intuitive theories, on the other hand, seek “to capture more of the richness of human inference” through an appeal to “sophisticated domain-specific knowledge representations” (Tenenbaum, Griffiths and Kemp, p. 309).
On the other hand, the assumptions for the formal learning theory include the idea that learned information stems from observations from the environment. It is also assumed that learning theory espouses the empirical study of learning of both humans and animals. This is founded on the psychological behaviorist paradigm. More importantly, the formal learning theory gives focus on informal arguments and examples instead of definitions and theorems, thus making the theory one which specifically abandons theories which are supplanted by investigative strategies which lead to presumably incorrect beliefs.
Strengths and Weaknesses of the Bayesian model
It should be noted that the Bayesian models of induction interpret probability computations as learning and reasoning. These probability computations are juxtaposed with the hypothesis space of possible concepts, causal laws as well as word meanings. The strength of the Bayesian model rests on its method of putting together two approaches which have been considered to not go well with one another. That is, the Bayesian model places domain-specific prior knowledge side by side with domain-general statistical principles, a combination which makes the best of both approaches.
However, the weakness of the Bayesian models of inductive learning and reasoning rests on the fact that it combines two seemingly separate approaches. By doing so, the individual weaknesses corresponding to each of the separate approaches are also taken into account. For instance, the approach which makes use of domain-specific prior knowledge such as prior knowledge of economics in assessing the learning and reasoning levels of individuals is faced with the difficulty of knowing exactly how much or how little individuals know so that addressing the areas of improvement for human cognition will be achieved. More importantly, it is difficult to ascertain how much prior knowledge about a specific domain an individual has considering the idea that novice learners can hardly indicate the extent of their learning. In effect, instructors, for instance, are prompted to conduct initial tests first in order to measure the domain-specific prior knowledge of their students. If this is the case, then the method to understand and measure the domain-specific prior knowledge of novice learners would have to be executed first before any claims to that prior knowledge can be made.
More significantly, if there is hardly a concrete way of knowing the domain-specific prior knowledge of novice learners especially in a primary school setting, then there is little reason to believe that there is an exact method that predetermines the prior knowledge of novice learners on specific domains before instructors can execute tests to measure such prior knowledge. As a consequence, efforts to identify or know the domain-specific prior knowledge of individuals will only produce results when a test which measures such knowledge has already been made. Further, more difficulty rests on gauging such a test. How exactly are instructors going to gauge the tests? Will they have to presume that novice learners know this and that so that a test which will measure the extent of their prior knowledge on this and that areas can be made?
As far as the Bayesian model is concerned, it also uses domain-general statistical principles. There have been many criticisms against domain-general forms of reasoning such as Donald Symons who argued that domain-general reasoning is unable to formulate interesting and original findings (1989). As with any domain-general type of scientific reasoning, it can be said that domain-general reasoning as a whole includes heuristics, strategies as well as procedures that can be applied to anything without any regard to the content of the thing being investigated or looked into. Because of this standing perception of the procedure of domain-general types of reasoning, it has become the trend for criticisms to attack the very applicability of domain-general reasoning to extremely specific cases, from simple to complex ones, as it is unable to provide for any lucid explanation, let alone an explanation which gives due importance to the roles of the specific elements involved in specific circumstances.
Hence, given the fact that the Bayesian model being espoused by Tenenbaum, Griffitsh and Kemp incorporates the traditional form of reasoning which is domain-general and the domain-specific approach in reasoning into a single theory, it can be said that it also drags with it the weaknesses entailed by the respective reasoning techniques. There is strong reason to believe in this precisely because even when the traditional form of reasoning is juxtaposed with domain-specific approaches, it does not altogether resolve the weaknesses corresponding to each side. Rather, what it does is to simply address the weakness of one side by using the other technique to resolve that weakness. For instance, given the criticism that domain-general reasoning is inadequate insofar as it fails to address the specific elements in a specific circumstance by merely providing general types of strategies, the Bayesian model attacks that weakness through the simultaneous incorporation of the domain-specific strategy with the traditional form of reasoning. The idea is to basically mount a domain-general strategy and curb the flaws through the simultaneous application of domain-specific strategies.
In essence, the weakness of the Bayesian model rests on the assumption that combining the two approaches will negate the corresponding weaknesses of each types of reasoning when what it does is to further bring into light the contradictions that traditional reasoning and domain-specific reasoning cast on one over the other. In real world cases, one can hardly be able to arrive at a reasoning comprising of both domain-specific and domain-general approaches. It is so because simple to complex real world problems require an approach which is applicable to the situation. That being said, it should be the case that every circumstance requires a unique form of reasoning that is not only apt but also concretely addresses the issues at hand. With a combined approach such as the Bayesian model, a complex scheme of analysis is required which does not bode well with simple real worlds scenarios although it may give us a different way of looking into things.
Being different, however, does not always come about with satisfactory results. For instance, La Cerra and Bingham argue that “humans have inherited a vast array of cognitive adaptations that facilitated social negotiations” such as the basic and simple circumstance where one is compelled “to be motivated to cultivate specialized skills” (p. 11290) and, as such, humans have generally patterned their reasoning according to what they have learned to best fit the mold, so to speak. So long as one approach continues to work for people, they tend to continue to subscribe to that form of reasoning strategy. In effect, if the Bayesian model is indeed a new form of reasoning as espoused by the authors of the article, it would not necessarily have an immediate place in the society primarily because there are insubstantial records to show that choosing the Bayesian model over a sole domain-specific type or domain-general type of reasoning would be the better option.
More importantly, the prior specific knowledge of people is likely to impose strong theoretical biases when they reason about real-world contexts (Penner and Klahr, p. 2709). That is to say that people tend to make use of the specific knowledge that they already have when dealing with real-world situations, which is opposite of the idea that people make use of their prior general knowledge. But authors Hannon and Trehub suggest that even infants acquire perceptual knowledge with domain-general tuning processes. It tells us the idea that it is not always the case that domain-specific knowledge holds the most significant weight in most cases, if not all. This takes us back to the traditional theory of learning: formal learning theory.
Revisiting Formal Learning Theory
Since formal learning theory generally espouses the method for arriving at the truth non-demonstratively and is considered to belong to Inductive Logic, it is enough to say that formal learning theory requires a careful observation of the environment that ought to provide us with the basic knowledge to make rationalizations. Although the Bayesian model of learning parallels formal learning theory in terms of the acceptance of the idea of examples as necessary to arrive at knowledge, the difference rests on the idea that the Bayesian model gives more importance to specific examples although it also touches on general ones on certain degrees whereas formal learning theory deals with the general ones.
Formal learning theory presents human cognition in such a way that humans have prior knowledge which they use in forming more and more complex reasoning techniques. One example to this is the concept of inductive logic which presents the idea that, given a finite number of elements or objects, one can create a generalization about those elements and the more general concepts involved. Hence, formal learning theory would basically suggest an approach which compels humans to observe their environment at the most basic level and produce generalizations out of what they have observed. But these observations should not only come about without certain guidelines in order to ensure that the data and generalization obtained will be accurate and informative. These guidelines come in various forms, one of which is an informal argument. Informal arguments are arguments which simply make certain assertions or point something out as it contains little or no supporting evidence.
Moreover, formal learning theory makes use of examples as it does not make use of definitions and theorems. This is because definitions and theorems utilize formalized arguments in order to arrive at them, thus making the reasoning behind them founded on structured synthesized claims based on specific evidences. While Bayesian model of inductive reasoning evaluates inductive arguments by acquiring information about a specific property specifically the categories which make the property either true or false, formal learning theory does not delve deep into those areas. Rather, formal learning theory is predisposed to laying down the schemes for making observations instead of scrutinizing what has been observed or the premises which lead to the inducted conclusion or generalization.
Since the Bayesian model combines traditional inductive logic with structured domain knowledge constraints, it therefore goes beyond mere observation of the environment as it uses statistical mechanisms of inference aside from intuitive theories or systems of concepts that are interrelated which produce explanations and predictions in particular domains of our experience. It is in my belief that formal learning theory is more right than the theory-based Bayesian model of inductive learning and reasoning although it does not mean that the latter is wrong. The reason behind is simple: inductive reasoning should be guided accordingly by the questions on how to observe the environment rather than looking into the premises and elements of reasoning and valuating their truthfulness and falseness. That is so because the acquisition of the variables of inductive reasoning from the environment comes first before the appraisal of these variables or evidences in statistical or technical terms.
The primacy of acquiring observations in the environment indeed goes first before the appraisal of these observations espoused by the theory-based Bayesian model. That does not, however, presume the Bayesian model as futile or is empty of any purpose in ascertaining the inductive reasoning. More importantly, it can supplement the techniques behind formal learning theory in arriving at a more comprehensive valuation of the conclusions. Nonetheless, the Bayesian model should not interfere simultaneously with formal learning theory because, if it does, it will burden the task of guiding the process of observing the environment. More importantly, one can hardly conceive of informal arguments when the process of deliberating with these arguments is suffused with the rigidness of the Bayesian model. The thing that makes formal learning theory more interesting and therefore more conducive to the inquisitive mind is its consideration for informal arguments and examples instead of strict definitions and theorems. The mind which is naturally inclined to make observations as a product of its inquisitive nature should be given the utmost liberty to make these observations without having first to think of whether or not these observations can stand at par with domain knowledge or intuitive theories. Formal learning theory may not be able to thoroughly arrive at a comprehensive inductive explanation of specific things but so is the Bayesian model not fully able to concentrate on either domain-general or domain-specific prior knowledge. However, formal learning theory satisfies the immediate need of how to properly observe one’s environment.
Hannon, Erin E., and Sandra E. Trehub. “Tuning in to Musical Rhythms: Infants Learn More Readily Than Adults.” Proceedings of the National Academy of Sciences of the United States of America 102.35 (2005): 12639.
La Cerra, Peggy and Roger Bingham. “The Adaptive Nature of the Human Neurocognitive Architecture: An Alternative Model.” Proceedings of the National Academy of Sciences of the United States of America 95.19 (1998): 11290.
Penner, David E., and David Klahr. “The Interaction of Domain-Specific Knowledge and Domain-General Discovery Strategies: A Study with Sinking Objects.” Child Development 67.6 (1996): 2709.
Symons, Donald. “A Critique of Darwinian Anthropology.” Ethnology and Sociobiology 10 (1989): 131-144.
Tenenbaum, Joshua B., Thomas L. Griffiths, and Charles Kemp. “Theory-Based Bayesian Models of Inductive Learning and Reasoning.” Trends in Cognitive Sciences 10.7 (2006): 309.