Re: Cathy O’Neil • The Art of Definition
In classical logical traditions the concepts of definition and determination are closely related and their bond acquires all the more force if you view the overarching concept of constraint from an information-theoretic point of view, as C.S. Peirce did beginning in the 1860s. That makes an understanding of these intertwined concepts critical to the application of Peirce’s theories of information and inquiry.
Here’s a running thread with links to a collection of notes I’ve been gathering.
cc: Inquiry List • Peirce List (1) (2) (3)
Inquiry Into Inquiry 
A discussion of definitions might benefit from considering some of the most basic forms of positive and negative association we know about. We can see a very basic level of association in the attraction and repulsion of electrical charges, for example. Can we see the origins of things like logic and language in particle physics?
Information and information processing systems preceded what we think of as nervous systems and brains, much less language. Think of DNA interacting with other parts of a cell, for example. Do “definitions” exist at that level? Different working parts of a cell often identify each other by shape–a “lock and key” metaphor is sometimes used. There is a negative form, a receptacle, on one part into which a positive structure on another part fits. Either one defines (i.e. specifies) the other.
When we get to neurons, the process of forming associations gains a much more flexible, programmable, or virtual aspect. Also, the complexity of associations created by neurons and groups of neurons go far beyond the binary “lock and key” associations of particle physics and chemistry. At this level associations can be much more “fuzzy” and probabilistic. Is this the level at which abstraction first occurs?
The known universe seems to exhibit a tree-shaped (branching) development process with a time arrow; diversity and complexity generally increasing over time:
particle physics < chemistry < biology < neurons < brains < cognition < communication < high-order language
There also seems to be some kind of progression from:
– basic behavior patterns of particles and forces
– physical templates
– abstract definitions and "recipes"
In this context things like logic, association, definition, cognition, abstraction, language, mathematics, models, inquiry, etc. all have natural histories. I wonder if there is enough attention to the physical world and this natural history in modern philosophy, math, and theoretical sciences. It often seems to me that theoreticians want to separate themselves from this as far as possible.
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