The concept of a universal learning system as a basis for creating a general mathematical theory of learning
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Minds and Machines 14 (4):453-484 (2004)
The number of studies related to natural and artificial mechanisms of learning rapidly increases. However, there is no general theory of learning that could provide a unifying basis for exploring different directions in this growing field. For a long time the development of such a theory has been hindered by nativists' belief that the development of a biological organism during ontogeny should be viewed as parameterization of an innate, encoded in the genome structure by an innate algorithm, and nothing essentially new is created during this process. Noam Chomsky has claimed, therefore, that the creation of a non-trivial general mathematical theory of learning is not feasible, since any algorithm cannot produce a more complex algorithm. This study refutes the above argumentation by developing a counter-example based on the mathematical theory of algorithms and computable functions. It introduces a novel concept of a Universal Learning System (ULS) capable of learning to control in an optimal way any given constructive system from a certain class. The necessary conditions for the existence of a ULS and its main functional properties are investigated. The impossibility of building an algorithmic ULS for a sufficiently complex class of controlled objects is shown, and a proof of the existence of a non-algorithmic ULS based on the axioms of classical mathematics is presented. It is argued that a non-algorithmic ULS is a legitimate object of not only mathematics, but also the world of nature. These results indicate that an algorithmic description of the organization and adaptive development of biological systems in general is not sufficient. At the same time, it is possible to create a rigorous non-algorithmic general theory of learning as a theory of ULS. The utilization of this framework for integrating learning-related studies is discussed.
|Keywords||computability creativity physical constructiveness recursive function theory theory of learning|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Reza Zamani (2010). An Object-Oriented View on Problem Representation as a Search-Efficiency Facet: Minds Vs. Machines. [REVIEW] Minds and Machines 20 (1):103-117.
Similar books and articles
Eric Margolis & Stephen Laurence (2011). Learning Matters: The Role of Learning in Concept Acquisition. Mind and Language 26 (5):507-539.
Kuo-Chin Chang, Tzung-Pei Hong & Shian-Shyong Tseng (1996). Machine Learning by Imitating Human Learning. Minds and Machines 6 (2):203-228.
Marion Blute (2001). A Single-Process Learning Theory. Behavioral and Brain Sciences 24 (3):529-531.
Kenneth R. Livingston (1998). The Case for General Mechanisms in Concept Formation. Behavioral and Brain Sciences 21 (4):581-582.
Alison Gopnik & Laura Schulz (eds.) (2007). Causal Learning: Psychology, Philosophy, and Computation. Oxford University Press.
Sean A. Fulop (2010). Grammar Induction by Unification of Type-Logical Lexicons. Journal of Logic, Language and Information 19 (3):353-381.
Stewart Ranson, Jane Martin, Jon Nixon & Penny McKeown (1996). Towards a Theory of Learning. British Journal of Educational Studies 44 (1):9 - 26.
Added to index2009-01-28
Total downloads4 ( #247,771 of 1,096,899 )
Recent downloads (6 months)2 ( #164,383 of 1,096,899 )
How can I increase my downloads?