A formal setting of how a scientific theory selects reality can be the following: Let N “things” share some M-dimensional space of their states so that N < M. Then M-N dimensions and thus a corresponding (M-N)-dimensional subspace of the initial M-dimensional space, in which all those “things” can be situated, are necessarily common. That subspace can be interpreted as the selection of reality relevant to the things in question and possibly studied by some scientific discipline and described by relevant and competitive theories.
The “things” can be interpreted as the elements of a set. The space of states is describable as a well-ordered set of “dimensions” (interpretable as qualities or quantities of the things). Any dimension has to have at least two discernibly distinguishable state being a quality and furthermore some one-to-one mapping into a number set being quantity rather than quality. The mathematical concept of vector space is an example of that kind of space.
In other words, the selection of reality relevant to some scientific theory or theories is seen as sharing a few common and inherent qualities or quantities of the things studied. Thus the selected reality corresponds to the extension of the theory, i.e. all common properties and relations shared by all studied things and preferably only by them.
Furthermore, reality can be thought as dividing the space of states into two parts or subspaces: constant and variable.
One can think of reality selected by some scientific theory also as a partial, but working concept of reality addressed just to that theory. If that is granted, its intension is the constant and invariant part of the space of states described by the theory, and its extension is the other, the variable part. Then the general sense of the concept of reality valid for any partial reality of any scientific theory is just that dividing the space of states into two disjunctive and exhausting subspaces corresponding to those constant and variable parts.
In other words, selecting relevant reality means the choice of a relevant boundary between the variable and constant, and thus between extension and intension to be defined rather implicitly by the context of the theory as a whole.
In fact, the practicality of selecting reality is only relative, in relation to another, parent or competitive, and thus commeasurable theory. That implies a comparison will select a few or even only one dimension(s), which change their (its) modus: from the constant part (intension of the partial reality) to the variable one (extension) or vice versa.
The core of that approach is to be substituted the general and in fact metaphysical problem about reality at all by the practically useful and in fact methodological issue about the change of the concept of partial reality between two (or more) very close and thereupon commeasurable theories. Consequently, selective realism is interpreted in thus in a fundamentally relative rather than absolute way: What are selected are only a few dimensions of the space of states changed its modus: either from intentional to extensional or vice versa.
That kind of selective realism is used as a methodology to be compared the implicit concept of partial reality in three successive theories in statistic thermodynamics: those of Boltzmann, Gibbs, and Einstein. All of them, being some additional specifications of thermodynamics, are naturally situated in the reference frame of Carnot’s theory.
The implicit concept of the corresponding partial reality has been changed is changed as follows:
0. (Carnot) Classical thermodynamics describes laws in terms of quantities of that reality, which is as macroscopic as empirically and experimentally observable.
1. (Boltzmann) The mechanical motions of the huge number of microscopic elements of a statistical ensemble result into the thermodynamic quantities of any macroscopic physical object averagely. The empirically and experimentally observable quantities are deduced as derivative from a hidden theoretical reality of microscopic elements such as atoms and molecules.
2. (Gibbs) The mechanical motions of the huge number of microscopic elements are substituted by different possible states of a macroscopic physical object equivalently and mathematically. The empirically and experimentally observable thermodynamic quantities are deduced as derivative from a hidden theoretical reality of different possible macroscopic states of the physical object as a whole.
3. (Einstein) The mechanically and experimentally observable thermodynamic quantities are some function of the Gibbs ensemble of all possible states (and thus some relation to it). They can be furthermore also referred to the Boltzmann ensemble of microscopic elements. Reality includes both the observable object and the hidden theoretical model as whether a Gibbs or a Boltzmann ensemble as well as the function or relation between the object and that model.
The following conclusion can be deduced: Reality in those reference frames can be identified in the following oppositions: macroscopic – microscopic; elements – states; relational – non-relational; observable – theoretical:
0. (Carnot): Macroscopic, both observable and theoretical.1. (Boltzmann): Microscopic, elements, non-relational, theoretical.
2. (Gibbs): Macroscopic, states, non-relational, theoretical.
3. (Einstein): Both macroscopic and microscopic, both elements and states, relational, both observable and theoretical.
One can summarize the case study comparing the three theories in thus: The concept of “reality” is changed or generalized, or even exemplified (i.e. “de-generalized”) from a theory to another. The change can be described as the explicit introduction of some new opposition as a still one and new dimension of relevant reality, and the generalization as a synthesis to some already involved opposition so that the theory is invariant to the relevant dimension of reality. The exemplification can also be observed being a condition for introducing a few new dimensions of reality. Thus, that exemplification simplifies reality in a dimension (“a step back”) complicating it in a few others (“two steps forward”).
No comments:
Post a Comment