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A bit of a long shot, but since there is a Hegel page on ncatlab, I thought it would be interesting to see if there are any thoughts on the very interesting way Ruth Garett Millikan uses the word Category in her 1984 Book Language, Thought and Other Biological Categories. Btw, this can be thought of as a biological extension of Game Theoretical work by David Lewis on Language, such in his Languages and Language. There are categories of games, and even as coalgebras, so why not categories that would allow one to think of the biological, understood as that which reproduces.
Her departure point is that what seperates the physcial from the biological is the concept of reproduction. She starts with an example of a photocopier. Paper comes in, a copy comes out. There is clearly something that is the same from the input and the output, but that is not that the atoms are the same. This she argues can only be understood by taking the function of the photocopier into account. Its purpose is to make patterns of ink on a new paper that match those on the input, and other things can vary: eg. paper quality, color, etc… need to be the same.
With devices this function is (for us) easy to ascertain. For living things though as there is no manual for each species we need to work out what is the case by observing and theorizing. Here statistics by itself won’t do: she uses as example that most sperm never fertilise an egg. One has to look at the role the organ plays in the evolutionary survival of the organism, even the prehistory of that organism.
She then goes on to show how language fits then into that category, as words are reproduced from speaker to listener, and their function she argues is referential correctness. But not always: only at key points. So a single person could take a massive computer hard drive and fill it with “2+43=3” and that would not render arithmetic as we understand it nonsense, by overwhelming all existing literature on the subject with falsities. This is already very enlightening in so far as it I think correctly highlights the importance of etymology in the meaning of a word.
The twitter discussion could be informative.
Since Mac Lane chose ’category’ from philosophy partly for ’the pleasure of purloining words from the philosophers’ (as explained here), I’m not sure I’d hold out much hope of a tight connection.
But if you’re looking for a biology-category theory connection, there are moves afoot, especially in the ’applied category theory’ movement.
John Baez Biology as Information Dynamics.
Erwan Beurier, Interfacing biology, category theory & mathematical statistics.
Ken Scambler, Applied Category Theory - The Emerging Science of Compositionality
What do programming, quantum physics, chemistry, neuroscience, systems biology, natural language parsing, causality, network theory, game theory, dynamical systems and database theory have in common?
yes, I am actually more interested in whether Category Theory can make precise in new ways her philosophy, perhaps reveal angles that were not apparent in what she says, than whether her use of the term fits the notion of Categories as used here.
The first link by Baez starts well with “If biology is the study of self-replicating entities,…” which is close to Millikan’s starting point, if one extends the notion of self to make the human part of the car or indeed other tools including language.
Thanks for the pointers :-)
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