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Comment from Paul Prueitt
Recommind Inc developed an alternative to algebraic Latent Semantic Indexing (Landauer and Dumais), which is based not on linear algebra, but rather on the development of stochastic envelops similar in nature to Hidden Markov Models or the Markov Field algorithms.
The foundational work on differential and formative ontology can be used with either algebraic or stochastic latent semantic technology.
Work on algebraic latent semantic technology is underlined at:
Another issue is raised by Paul Werbos’s comment. This has to do with the completeness of Bayesian kinds of “reasoning”, and more generally to mathematical models of human reasoning.
Werbos presents the notion that anything natural can be modeled by mathematics. Others will respectfully disagree, and appeal to a literature that suggests that the strengths of mathematics fail to capture the open nature of some aspects of natural systems, particularly those that exhibit emergence.
The case against the limitation of mathematics are made throughout the history of modern mathematics, most notable the case is made by Brower that at the very base of mathematics lies a primitive intuition, allied, no doubt, to our temporal sense of before and after, that allows us to conceive a single object, then one more, then one more, and so on endlessly. Mathematics is constructed from this and other intuitions.
But the construction of mathematics leads also to the use of the concept of consistency, from which useful new constructions are made. These constructions have been shown to be essential in the development of a great deal of the mathematical applications.
The problem comes not from the successes of formal mathematics, but from the problems that have not as yet yielded themselves to these constructions.