Formalizing Whole/Parts Model

Cognitive whole is spatio-temporal whole. It can be determined further only if it has possibilities for determination – which we call differentiation.

• Differentiation is determination of specific aspect of the cognitive context
• Result of the differentiation is new cognitive context, on which new differentiations can be applied.
• Starting cognitive context is the perceptual spatiotemporal whole.

Differentiation is implicitly abstracting, as by determining the context in one aspect, other possible aspects are neglected.

We will call differentiation tree (DT) a series of differentiations applied one by one to certain cognitive context, in such way that every next differentiation is done on the result of the previous differentiation, and with the possibility to branch.

With applying differentiation by *same* aspect on *different* cognitive contexts we can get to context for which we can apply *same* further differentiations.

With applying more differentiations by *different* aspect on *same* cognitive context we can get to sub-contexts for which we *can’t apply same* further differentiations.

Note: you should note word *can* and *can’t* there, and that their meaning is not cleared up here. For now I will just point that explanation of what this means would be given later.

Here we could remind that mathematical differentiation has both this properties, for example it can be abstraction which brings to same results having different starting contexts, e.g.:

d(x­²+3y²+4z)/dx=2x and d(x²+5y³)/dx=2x.

Or it can be done by different arguments, which means with same context we can receive different results.

d(x²+y²)/dx=2x  , but

d(x²+y²)/dy=2y.

Both those examples are given just as analogy. It shouldn’t be understood in any other way.