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Outputs (4)

Brouwer’s Weak Counterexamples and the Creative Subject: A Critical Survey (2020)
Journal Article
Fletcher. (2020). Brouwer’s Weak Counterexamples and the Creative Subject: A Critical Survey. Journal of Philosophical Logic, 49, 1111-1157. https://doi.org/10.1007/s10992-020-09551-y

I survey Brouwer’s weak counterexamples to classical theorems, with a view to discovering (i) what useful mathematical work is done by weak counterexamples; (ii) whether they are rigorous mathematical proofs or just plausibility arguments; (iii) the... Read More about Brouwer’s Weak Counterexamples and the Creative Subject: A Critical Survey.

Approaches to analysis with infinitesimals following Robinson, Nelson, and others (2017)
Journal Article
Fletcher, P., Hrbacek, K., Kanovei, V., Katz, M. G., Lobry, C., & Sanders, S. (2017). Approaches to analysis with infinitesimals following Robinson, Nelson, and others. Real Analysis Exchange, 1 -59. https://doi.org/10.14321/realanalexch.42.2.0193

This is a survey of several approaches to the framework for working with infinitesimals and infinite numbers, originally developed by Abraham Robinson in the 1960s, and their constructive engagement with the Cantor-Dedekind postulate and the Intended... Read More about Approaches to analysis with infinitesimals following Robinson, Nelson, and others.

Connectionist learning of regular graph grammars (2001)
Journal Article
Fletcher. (2001). Connectionist learning of regular graph grammars. Connection science, 127 - 188. https://doi.org/10.1080/09540090110072327

This paper presents a new connectionist approach to grammatical inference. Using only positive examples, the algorithm learns regular graph grammars, representing two-dimensional iterative structures drawn on a discrete Cartesian grid. This work is i... Read More about Connectionist learning of regular graph grammars.