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The overall program "arborescent numbers" is to similarly perform the constructions from the natural numbers (N) to the positive fractional numbers (Q+) to positive real numbers (R+) beginning with (specific) binary trees instead of natural numbers. N can be regarded as the associative binary trees. The binary trees B and the left-commutative binary trees P allow the hassle-free definition of arbitrary high arithmetic operations (hyper ... hyperpowers). To construct the division trees the algebraic structure "coppice" is introduced which is a group with an addition over which the multiplication is right-distributive. Q+ is the initial associative coppice. The present work accomplishes one step in the program "arborescent numbers". That is the construction of the arborescent equivalent(s) of the positive fractional numbers. These equivalents are the "division binary trees" and the "fractional trees". A representation with decidable word problem for each of them is given. The set of functions f:R1->R1 generated from identity by taking powers is isomorphic to P and can be embedded into a coppice by taking inverses.
In this work the concept of 'context' is considered in five main points. First, context is seen as always necessary for an adequate explication of the concepts of meaning and understanding. Context always plays a role and is not merely brought into consideration when handling a special class of statements or terms, or when there is doubt and clarification is necessary. Second, context cannot be completely reduced to some system of representation. The reason for this is the presence of humans, which is always an important component of a context. Humans experience situations in ways that are not always reducible to symbolic representation. Third, contexts are in principle open. In normal cases they cannot be determined or described in advance. A context is not to be equated with a set of information. Fourth, we understand the parameters of a context pragmatically, which is why we are not led into doubt or even to meaning skepticism by the open nature of a context. This pragmatic knowledge belongs to the category of an ability. Fifth, contexts are, in principle, accessible. This denies the idea that some contexts are incommensurable. There are a number of pragmatic ways of accessing unfamiliar contexts. Some of these are here examined in light of the so-called 'culture wars' in the U.S.A.