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The difference between "Causal" and "Impredicative" loops, etc.



One of the areas of confusion I'm seeing in many different settings, including the ISSS conference I attended in July, is caused by a difference my father specified in his use of the phrases "Causal loops" and "Impredicative loops". The ideas are connected because they both describe chains of entailment, which is why it gets confusing, but "Causal loops" exist in natural complex systems whereas "Impredicative loops" exist in formalisms (i.e., models).
 
There is also a difference between loops of this sort and simple recursions. Recursive loops are what happen in a room with a furnace and a thermostat, when it's cold outside.
 
There are many such boondoggles in his written work because he was fluent in so many modes of expressing the ideas he was seeing inside his head. The word "Dynamical" is another one. A "dynamical system" refers to Newtonian mechanics, whereas "dynamic" might not. So a "dynamical system" is not a complex system. Yet, the word "dynamic" certainly seems to apply to complexity. There's a world of difference, though. It's like the difference between perversity and perversion; they sound alike but they definitely don't imply each other! Yet I've seen people use the word "perverse" when what they meant was "perverted". Big difference there.
 
Judith