Semantic Closure

See Closing the Loop: How Semantic Closure Enables Open-Ended Evolution? by Amahury J. López-Díaz and Carlos Gershenson.  

I found this sentence quite striking: "This manuscript explores the evolutionary emergence of semantic closure—the self-referential mechanism through which symbols actively construct and interpret their own functional contexts, ..." The paper has apparently been accepted for publication in the Royal Society's journal Interface.

One wonders what these little symbols could be getting up to while mathematical biologists aren't paying attention, ... I suppose we should ask Steven Wolfram.

See Martin Elsman - Deriving a Kronecker-Free Functional Quantum Simulator.

That talk Samson Abramsky gave in 2012 was really thought-provoking:

 

In particular A computable expression of closure to efficient causation by Matteo Mossio, Giuseppe Longo and John Stewart. The question about self-representation in total functional programming is an interesting one. See Andrej Bauer's self-interpreter for System-T in On Self-interpreters for System-F and Other Typed λ-calculi, which I just noticed was funded by the USAF who are finally taking Karger and Schell seriously by the sounds of it. Way to go!

Subscribe to INI Seminar Room 2. 

I think it would all be much clearer if we recognised that is us who decide what we mean when we use symbols. So we can represent a self-interpreter consistently, provided we recognise that the act of representation introduces an extended context in which we have established a new symbol. See Kris Brown's talk on semantics from pragmatics in Intensional and Extensional Semantics in Programming Languages and Type Theory and my miniature tower of Babel: 

See Jenann Ismael - Cracks in the Edifice of Determinism and On Mathematics and Abstract Language. 

Paul Dancstep on the library of Babel

16:18 On ordinals in Category theory. 

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