Reduction and Elimination in Philosophy and the Sciences

On the Characterization of Objects by the Language of Science
Paul Weingartner, Salzburg, Austria
1. The Objects Described by the Laws of a
Scientific Discipline
In the natural sciences we usually make use of a twofold
picture for the description of the observed phenomena: the
objects of experience and the laws of nature, where the
behaviour of objects is governed by the laws of nature. To
give some examples: Newton’s laws of motion describe
the spatio-temporal behaviour of mass points. Kepler ’s
laws determine the trajectories of planets in the solar system.
The fundamental law of Quantum Mechanics, the
Schrödinger equation, governs objects like atoms, electrons,
neutrons … etc. Mendel’s laws rule the transmission
of genes into the next generation.
These objects (mass points, planets, electrons,
genes … etc.) the behaviour of which is described by the
laws of nature cannot be individualised. For instance mass
points are not individualised objects, but stand for any
object possessing mass; also the trajectories of Kepler ’s
laws are not individualised, they stand for any trajectory
belonging to a certain category which obeys certain
conditions like being periodical and having a certain type
of stability 1 ; further the objects like neutrons or electrons
cannot be individualised by the Schrödinger equation,
since this equation describes the behaviour of kinds of
elementary particles for example of electrons and of
neutrons. Similarly Mendel’s laws do not distinguish
between individual genes transmitted but are concerned
with classes or categories of genes.
From this consideration it seems to follow that the
objects of science which are governed by the laws are
always incomplete in the sense of Meinong. Even if this is
correct, we have to point out however, that the
incompleteness is only relative here.
These objects are incomplete w.r.t. to the
individualised object, but they are not incomplete w.r.t.
what laws of nature describe. Thus for example it holds for
the laws of Quantum Mechanics (for Schrödinger’s
equation) that they are permutational symmetric
(invariant). That means that “different individual” particles
of the “same kind” are treated identical by the law. Thus
the laws and the respective physical reality described by
these laws remain the same if we interchange any two
particles of the same kind, for example two electrons. The
same holds for protons, neutrons, neutinos and photons.
Concerning physical systems or states permutational
invariance holds only for bosons not for fermions because
the latter obey Pauli’s exclusion principle.
What has to be underlined here is, that invariance
properties of laws of nature are just the essential
characteristics of what a law is. So let us move further to
the most important invariance of laws of nature: It is that
the laws of nature are space time invariant. That means
that the laws do not change with time, i. e. they abstract
from any particular point of time (translational invariance or
translational symmetry) and they do not change from one
space point to another, i. e. they abstract from any
1 For a detailed discussion of the conditions for dynamical (and also: statistical)
laws see Mittelstaedt-Weingartner (LNt, 2005) ch. 7.
particular space point. 2 From this it follows that laws of
nature do not describe individualised objects. However a
dynamical law describes the time development from an
individual state of the system at t1 to an individual state of
the system at t2. But this individual state at t2 is only
derivable from the law (as a special solution of the
differential equation) if the state at t1 is known and
instantiated; i.e. the later state is a definite function of the
earlier. In the case of statistical laws even this is not
possible. Individual microstates cannot be used as an
instantiation: Statistical laws describe and predict only the
states of the whole system, the macrostates, which can be
realised by a huge number of different microstates; i.e. no
particular individual microstate is required, anyone of the
huge number will do. This means also that although the
microstates cause the macrostate, no particular microstate
is a necessary condition for the macrostate.
The result of this section is that the objects
described by laws of nature 3 are not objects which satisfy
uniqueness in the sense of Russell. Relative to individual
objects satisfying uniqueness they are incomplete. But
they are not incomplete w.r.t. laws, since laws have to
have invariance (or symmetry) properties as their essential
characteristics. The question whether real particular
objects of modern physics are complete in the sense of
Meinong or are individualised in the sense of satisfying
uniqueness, will be treated below.
2. Russell’s Ontological Presuppositions
Concerning the Objects of Reference in the
Sciences
2.1
Names directly designate an individual (object) which is its
meaning. 4 That is the relation of denoting, designating or
referring is a two-place relation and reference is identified
with meaning. Russell drops the middle part of the Medieval
Theory (also adopted by Meinong):
2.2
name concept reference
description conceptual construction object
meaning, content
In Russell's understanding, the relation of denotation (designation)
or reference is the same if the objects of reference
are mathematical (conceptual) entities or physical
objects; i.e. this relation is independent of whether the
relata are conceptual objects (which are neither spatial,
nor temporal) or physical objects /(in space and time).
2 If instead of space point we speak of invariance w.r.t. moving reference
systems the things get more complicated. For details see Mittelstaedt-
Weingartner (2005, LNt) ch. 6.
3 For a detailed discussion see Mittelstaedt-Weingartner (2005, LNt) ch. 10.
4 Cf. the quotation from Russell (1919, IMP), p. 174, note 3.
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