Reduction and Elimination in Philosophy and the Sciences

the system), then it is possible uniquely to identify a mixed
state W(Q) as the ‘standard representative’ of Q over the
Hilbert space of Ψ. This can be taken as a representation
of the dispositional property possessed by Ψ that
corresponds to the observable Q. (W(Q) is, in particular,
equal to ∑ Tr ( PΨP n) W , with Pn
n Wn = ).
Tr( P )
236
n
An important antireductionist conclusion follows: not
all properties are actual and provided with well-defined
values, or reducible to ‘categorical bases’: some aspects of
reality are in fact irreducibly dispositional.
The other, state-dependent, properties of quantum
particles (e.g., position, momentum, kinetic energy etc.), I
claim, are mere descriptions of the particles’ dynamic
‘behaviour’ and/or of their relationships with the rest of
reality. As such, they needn’t be reified, and consequently
do not require one to enlarge the set of the basic tropes.
For example, space(-time) location is not a trope: it simply
expresses the relation between a trope (or trope-bundle)
and other tropes (or bundles) - or between tropes and
space-time points. In short, the sparse view of properties is
intended here as the view that the basic ‘building blocks’ of
reality are only those properties that literally constitute
things.
Given the above, the way in which the truly basic
tropes give rise to the whole of material reality is readily
reconstructed. For instance, it is possible that a trope of
mass 0.511 MeV coexists (in a relation of existential dependence
of the sort described earlier) with a +1 charge
trope and a ±½ spin trope. The individual resulting from
the reciprocal existential dependence between these
tropes is a positron. The same applies mutatis mutandis
for the other elementary particles, and for the progressively
more complex levels of reality. For instance, 79 electrons,
79 protons and 118 neutrons give rise to an atom of stable
gold. And many such atoms determine molecules and
bigger pieces of gold. The ‘new’ properties of the emerging
complexes, such as ‘melts at a temperature of 1064.18 C’
or ‘is a good conductor of heat’ for gold, are not tropes, but
rather ‘derivative’ properties determined by the way in
which the basic tropes get structured together. This means
that they are certainly real, but also analysable in terms of
simpler entities. With this, the sparse conception of properties
and the ‘scientific’ approach to their identification find
confirmation and application.
The foregoing vindicates the claim that tropes are
independent and simple basic constituents of reality (incidentally,
it also allows one to get rid of the so-called
‘boundary problem’ consisting of the fact that tropes are
presented as fundamental ontological units but seem in
fact arbitrarily divisible: the truly fundamental properties
are not divisible, and what is is in fact just a composite
trope-structure).
3. Other Properties
As is well-known, quantum mechanics allows for the possibility
of many-particle systems in which the (supposed)
component entities do not have well-defined values for a
given property separately, and are instead mutually correlated
with respect to the measurement outcomes concerning
that property (even though determinate separate values
will appear upon measurement).
The ‘non-factorisability’ of the ‘entangled’ states describing
such systems into simpler states of the components,
it is commonly agreed, points to some form of ho-
Properties and Reduction between Metaphysics and Physics — Matteo Morganti
n
lism. Namely, to the fact that certain properties of certain
physical systems cannot be analysed in terms of properties
of the system’s component parts, either because the
system doesn’t have parts (ontological holism), or because
it exemplifies properties that are not reducible to the properties
of its components (property holism). This entails that
the relevant properties of entangled systems should be
regarded as emergent tropes in the present context - either
monadic and belonging to the whole system, or irreducibly
relational.
Here is, then, one more antireductionist theme: the
evidence just pointed at blocks all attempts at reducing all
properties of physical objects to the ‘truly basic’ tropes. In
the specific perspective of property holism, moreover, this
comes together with the impossibility to reduce all relations
to monadic properties. This in turn opens the way to a
more general rejection of physicalism: for it is possible that
non-reducible tropes emerge at levels of higher complexity
than physics. (All this, however, needn’t worry the trope
ontologist, who is not required to commit him/herself to any
of these forms of reductionism).
4. Metaphysics and Science
One last point concerns the significance of metaphysics in
its relationship with science. In particular, the idea of ‘experimental
metaphysics’ is of obvious relevance here.
The notion of experimental metaphysics was first
introduced by (Shimony 1981), who defined it in the
context of a discussion of quantum mechanics, and in
particular of the Einstein-Podolski-Rosen (EPR) ‘paradox’
and of the violations of Bell’s inequalities by quantum
systems. According to Shimony, a general pattern of
reasoning can be individuated of the form E&H → P,
where E is an accepted theory used to describe the
relevant experimental setup (in the EPR/Bell case,
quantum mechanics as it is employed to perform actual
tests of Bell’s inequalities); H a general (allegedly)
metaphysical hypothesis (in the EPR/Bell case, locality as
prescribed by relativity), and P a certain empirical
prediction (in the EPR/Bell case, that the Bell inequalities
hold). If P is disconfirmed and E is kept fixed, says
Shimony, by modus tollens we should get to a rejection or
modification of H, so bringing experiment to bear upon a
metaphysical thesis. And this is exactly what happens in
the case under discussion, for quantum mechanics forces
us to give up locality, or at least to reformulate it in terms
that allow for a ‘peaceful coexistence’ between quantum
mechanics and relativity.
The question to ask is, though, whether
experimental metaphysics is metaphysics at all. What is at
stake in discussions of EPR is the status of what ultimately
appears to be only a very general statement extracted
from our best-established theories, and that lies entirely
within the domain of science. Einstein’s presupposition to
the effect that the world must be local seems indeed to be
exclusively a consequence of his endorsement of a
specific theory (relativity); or, at any rate, of a general
worldview that was the by-product of (common sense and)
successful theories prior to, and including, relativity. Of
course, one might call presuppositions such as locality (or,
to give another relevant example, the Principle of the
Identity of the Indiscernibles) ‘metaphysical’, on the basis
that they are (among) the most general statements about
reality we can make. But this would be a merely
terminological choice, and would not detract from the fact
that those ‘principles’ appear to be nothing but empirical
generalizations.