Fleeting thoughts:Understanding, Explanation and Forecast by a Formal and Mathematical Approach

Prehistory and background:

The exact experimental sciences applying furthermore mathematical models, and first of all: physics, require for the suggested hypothesis to forecast experimentally testable effects.

On the contrary, almost all other sciences, and first of all: humanities, do not require forecast, but only some kind explanation of the most of the known relevant facts admitting even various exceptions.  

Accordingly, one can distinguish “forecasting understanding” among the former kind from the “explaining understanding” of the latter kind.

Then, one can grant understanding as the unification of explanation and forecast and thus found a set-theory approach to model explanation and forecast as two modifications of understanding.

Thesis:

1 The explanation and forecast as two ways of understanding can be modeled in terms of set theory disjunctively if and only if the concept of infinity is involved at least implicitly.

2 Then, both explanation and forecast correspond to the property definitive for the set of all relevant facts meant by the hypothesis.

2.1 The former suggests that property not to be finite, which means practically unlimited links between the text of the hypothesis and its context.

2.2 The latter suggests that property is finite and its text should be disjunctively distinguishable from its context.

3 Understanding in both cases means referring to the relevant context, however in the latter case it is negligible for the context can be recreated thoroughly by uniform continuation of the text.

3.1 That uniform continuation of the text is the essence of forecast once mathematical model is utilizable as in the latter case.

3.2 Any uniform continuation is impossible in principle and thus any forecast in the former case. It needs some choices and therefore interpretation and interpreter.

A series of arguments for the thesis based on:

-          The relation between Peano arithmetic and set theory

-          The axiom of choice and well-ordering principle

-          The Gödel completeness (1930) and incompleteness (1931) theorems