Let’s say you are thinking of something–about some species which might eventually become qualified to be called a theory–a theoretical structure about that thing you are thinking:
* <—=—> *
(I wish WordPress can read my mind and format accordingly, but until then what we have above is a pair of dots with an arrow going from the dot on the left to the dot on the right and another arrow going from the dot on the right to the dot on the left.)
With an eye on sharing–on communicating–my thoughts with my fellow gypsies, I think of describing–think of bringing my thoughts into being–of endowing my finite thought a material existence using a systematic procedure–a reproducible method.
I start with naming. Given my messianic complex I label one of my two dots, say, the one on the left, ‘true.’
Reflecting on my thought I notice that if I start with truth and go (along the arrow going from the dot on the left to the dot on the right) to the dot on the right, and then going from the dot on the right along the arrow going from the dot on the right to the dot on the left, then I return to the ‘true’ I started out with; all of which pleases me so much so that I write it down (even if it means invoking a negation a couple of times):
not (not (true)) = true
Of course I could have penned a [slightly] different script i.e. a different opening line naming the dot on the right as ‘false’ and then rewrite the whole story as
not (not (false)) = false
What we have here is a slow-moving plot of a finite [dynamical] system with two descriptions:
Generator G: true
Labels L: true, not (true)
Relation R: not (not (true)) = true
Generator G: false
Labels L: false, not (false)
Relation R: not (not (false)) = false
What about the ‘defining interpretation’ that you advertised in the title? Please don’t tell me you have to go away now–to go study. I’m sorry to disappoint you again, but I need to study (seriously; for my own [selfish] good):
An important method of defining an interpretation of one presented structure into another is in terms of mapping generators and verifying relations.
Much of the above is to protect myself from falling prey [yet again] to scandalous brain theories that the Society for Neuroscience shamelessly palms off on the unsuspecting public all the while refusing to acknowledge an important thesis of science, which is absolutely necessary for the advancement of science–a sincere means of making sense of the ‘blooming buzzing confusion,’ simply because it is scared of learning.
Sad, a sad state-of-science. Please don’t get me wrong: technology is going great even if it means engineering deans have to spend a lot of time scratching their heads–whom to call in which company (google, facebook, twitter… so many—so confusing)–to figure out what to “teach” their students.
Tailpiece: One–only one–sensible brain theory, according to someone claiming to have coined computational neuroscience, in the study of brain, is the one he heard from his preteen daughter at their dinner table: Brain, while sitting on top of you, steals all the food you eat. It sort of makes sense not only in terms of energy, but also in light of my feeling–wasted :-(
Before I go, let me [leave you, in the spirit of the joyous season, on a happy note] thank Professor F. William Lawvere for the best Christmas gift (Algebraic Foundations of Physics and Engineering) I ever got :-) Thank you Professor Lawvere!