Reduction and Elimination in Philosophy and the Sciences

Properties and Reduction between Metaphysics and Physics
Matteo Morganti, London, England, UK
1. Tropes
Trope theory is the ontological view that reality is constituted
by so-called abstract particulars (property-instances
not derived from multiply instantiable universals) grouped
together in concrete particulars (objects).
Such a view must first of all explain similarity, which,
so to speak, ‘comes for free’ if one subscribes to realism
about universals. Normally, trope ontologists argue that a
trope a resembles another trope b exclusively in virtue of a
and b, that is, of their primitively given ‘causal role’ in the
world. This may appear more contentious than the realist’s
claim that similarity is determined by the numerical identity
of all instances of the same universal. In fact, however, it is
analogous to what the realist must accept insofar as nonexact
resemblances are concerned. For, surely nonexactly-resembling
entities can still be similar to various
degrees, and this must be explained in terms other than
numerical identity even in ontologies with universals.
Hence the trope ontologist’s typical claim of primitiveness
appears plausible in this case.
Something must also be said with respect to the
way in which tropes constitute complex particulars. Initially
(Williams 1953), compresence was taken to be sufficient.
However, if compresence is regarded as an external
relation additional to the compresent tropes, it seems that
a form of regress cannot be avoided: what connects the
compresence trope and the compresent tropes? More
generally, compresence does not appear sufficient for
grounding the internal unity of things: what about
overlapping objects?
This leads the trope theorist to account for the inner
cohesion of concrete particulars in terms of internal
relations of existential dependence among their constituent
tropes. The first suggestion in this sense was made in
(Simons 1994), who takes his clue from Husserl’s
foundation relations. As pointed out by (Denkel 1997), if
one wants to provide room for substantial change (that is,
for the type of change involving the partial or total loss of
an object’s essence) these relations must be regarded as
holding not between specific tropes, but rather between
tropes as tokens of more general trope-types (so that
replacement of any trope – including essential ones
belonging to what Simons calls the ‘nucleus’, or ‘kernel’, of
the object - with another that acts as determinate for the
same determinable is possible).
Lastly, if tropes truly are the basic ‘building blocks’
of reality, it seems that they had better be understood from
the perspective of a sparse conception of properties,
according to which not all predicates correspond to actual
properties. For obviously not all meaningful predicates can
plausibly be taken to refer to fundamental, non-furtheranalysable
tropes. Following the ‘scientific’ approach to
sparseness (Armstrong 1978), this implies that it is
necessary to look at physical theory in order to identify the
fundamental tropes.
2. Applying Trope Ontology
(Campbell 1990) suggests taking physical fields as the
elementary tropes. However, the canonical definition of a
field as an extended entity with varying intensities at various
points of space seems to suggest an internal complexity
and the existence of (dis)similarities between fieldvalues,
which immediately leads one to think that something
more basic exists.
It seems more advisable to follow (Simons 1994) in
looking for fundamental tropes at the level of particles. In
fact, Simons’ view, based on particles as ‘kernels’ of
foundationally related tropes plus ‘peripheral’ tropes, just
needs some further articulation and specification.
The hypothesis that is taken nowadays to be the
best available description of the elementary constituents of
reality and their interactions is the so-called Standard
Model. According to it, the fundamental particles are 12
fermions constituting matter and 12 bosons mediating
forces. Fermions can be either quarks (six types, or
‘flavours’) or leptons (six more flavours). Bosons comprise
photons, W + , W - and Z 0 gauge bosons, and eight gluons.
Fermions have antiparticles, that is, particles identical to
them but with opposite electric (and, possibly, colour)
charge. Each boson-type constitutes instead its own
antiparticle, except for the W + and W - bosons, which are
each other’s antiparticle. Each one of these particles has
at least one of three possible properties: mass, colour and
electric charge, and in most cases they have both mass
and electric charge. (Photons may seem to constitute an
exception to this latter claim. However, each photon
possesses energy, which entails that it can in fact be
attributed relativistic mass. True, the latter is distinct from
the masses of the other types of particles, as those are
invariant masses. Nevertheless, the difference is one of
‘form’ rather than ‘substance’: as is well-known, according
to relativity theory energy and mass are two ‘aspects’ of
the same thing. Hence, tropes from the same ‘family’ can
be attributed to photons and to the other particles as their
‘masses’).
In addition to these ‘fully state-independent’
properties, which remain completely the same throughout
the whole of a particle’s existence (unless, of course,
substantial change occurs), all particles have spin.
However, only the absolute magnitude of spin is fixed for
each particle (1/2 for fermions, 1 for bosons), while the
sign can change. In fact, particles can be in a
‘superposition’ of the two spin values. How is this to be
accounted for from the trope-theoretic perspective?
In general, in quantum mechanics a specific
property can be possessed with probability p such that
0≤p≤1. Following (Suarez 2007), I suggest a dispositional
interpretation of this: whenever a quantum system does
not have a specific property with probability 1, it possesses
a dispositional property (or ‘propensity’) corresponding to a
weighted sum of possible actual properties. In more
technical terms, if Q is a discrete observable for the
system Ψ with spectral decomposition given by Q =
n n n aP ∑ ,
where Pn = vn v , and the system is in a state
n
Ψ=∑ cn v (a linear superposition of eigenstates of Q for
n
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