Towards a Trope Nominalist Theory of Natural Kinds Nominalism: A ...

Towards a Trope Nominalist
Theory of Natural Kinds
Nominalism: A Reassessment, University of Geneva 18/9 2012
Dr Markku Keinänen
University of Turku

Introduction
• My aim is present the beginnings of a trope nominalist
theory of natural kinds.
• Its principal rivals are Neo-Aristotelian (Lowe 1998;
Ellis 2001) and Reductive Realist (Hawley & Bird 2011)
theories.
• The theory is trope nominalist (all entities are
particulars). The only fundamental categories are
property and relation tropes.
• It denies the existence of natural kinds as separate
entities. Natural kinds are not identified with anything
in the mind-independent reality.
• It identifies natural kinds with natural kind terms with
certain application conditions.

Tropes
Tropes are fundamental concrete (spatiotemporal)
particulars. They have the following category features.
1.Particular: tropes exist in a single location.
2.Determinate identity conditions: it is determinate
whether or not trope t is identical with some entity e.
3.Countable: it is determinate how many tropes there are
in some location.
4.Categorially simple: all parts of tropes are further
tropes.

Tropes
5. Identity independent existents: a trope has
determinate identity conditions independently of the
identity any other entity (substance, spacetime point).
Tropes are particular properties: entities with the
above five category features and a thin particular
nature:
• Thin nature: a trope has a thin particular nature to
determine a single feature of the object possessing the
trope (e.g., -e charge of an electron).

Tropes
●
●
●
Moreover, all trope theories assume that trope t can
exist spatiotemporally co-located with the other
tropes.
The different trope theories (trope bundle theories of
substance) construct objects (or, substances) as
aggregates of tropes that fulfil certain conditions but
differ in the conditions that property tropes must fulfil.
According to independence theorists (Williams 1953;
Campbell 1990), objects are mereological sums of
mutually spatiotemporally co-located (compresent)
tropes.

The SNT
• The SNT (Strong Nuclear Theory) constructs simple
substances as aggregates of tropes connected by rigid
dependence.
o Nuclear tropes of substance i are either single
trope t, or two or several tropes t 1
, ..., t n
rigidly
dependent on each other.
o If there are more than one nuclear tropes, they are
"qualitatively diverse": they fall under distinct
determinables.
o Trope t is a part of substance i iff t is rigidly
dependent only on the nuclear tropes of i.

Determinate and Determinable
kinds of tropes
• According to the SNT, all tropes are properties of some
basic physical quantity (mass, electric charge, etc.)
•
Quantity tropes falling under some determinable D are
all mutually connected by:
a. By some relation of (positive or negative)
proportion (such as 2 : 1 - proportion)
b. By the relation of order (equal or greater than).
•
The tropes falling under a single determinable (e.g.,
all mass tropes) are all connected by some relation of
proportion, while the tropes falling under distinct
determinables (mass and charge tropes) are not.
•
Tropes fall under a single determinable because they
are all connected by some relation of proportion.

Determinate and Determinable
kinds of tropes
• The relations of proportion (and order) are formal
relations:
o they can (in principle) connect any kind of entity.
o the existence of an entity presupposes that its
place in the network of formal relations is fixed.
o they are ungrounded internal relations: given that
-e trope trope t 1
and -e/3 trope t 2
exist, they are in
the relation of 3 : 1 proportion to each other.
o
they allow of an operational characterization (cf.
Smith & Mulligan 1983).

Determinate and Determinable
kinds of tropes
• According to many standard presentations, the trope theory
claims that "property universals" are classes of exactly
similar tropes. This has two possible interpretations:
a. universals are sets of tropes (abstract individuals)
b. universals are pluralities of tropes
• I reject both of these accounts:
a. for the reasons of economy, it is reasonable to avoid the
postulation of sets.
b. we cannot identify a universal, which is one (or, a
unity), with a plurality. Pace WIlliams' (1986) painless
realism, we cannot coherently consider a plurality of
tropes as one, i.e., a universal.

Determinate and Determinable
kinds of tropes
• Moreover, determinate and determinable kinds are
natural kinds of tropes. Tropes are instances of
determinate and determinable kinds: e.g., 1 kg trope t
is an instance of the determinable kind mass (the kind
of mass tropes).
• Prima facie, determinate and determinable kinds are
distinct from their instances and they could have
different numbers of instances.

Determinate and determinable
kinds of tropes
• I suggest to identify determinate and determinable
kinds with kind terms having certain determinate
application conditions:
o for instance, the kind of 1 kg tropes is an
abstractum from the kind terms exactly applying to
a group of tropes in the relation of 1 : 1 proportion
to each other.
o the determinable kind of mass tropes is an
abstractum from the kind terms exactly applying to
a group of tropes mutually connected by some
relation of proportion and the relation of order.

Determinate and Determinable
kinds of tropes
• The talk about a "kind term" can refer:
a. to a type of interpreted tokens
b. to any token of that type: any kind term token with
certain determinate application conditions
•
Here, I identify determinable and determinate kinds
with abstracta the from kind terms in the sense of b.
•
For instance, the kind of mass tropes is an abstractum
from a group of kind terms exactly applying to a group
of tropes mutually connected by the some formal
relation of proportion and the relation of order.
•
A determinable/determinate kind is an abstractum
from a plurality, not itself a unity (it is not a universal
or a proxy universal).

Determinable kinds and
truthmaking
• The determinable kind term is a mass trope exactly
applies to the tropes in some relation of proportion
and in the relation of order to any particular mass
trope.
• Mass trope t is the truthmaker of claim A:
A. t is a mass trope.
• Trope t has a thin particular nature (e.g., it is a 1 kg
trope). Because of its nature, t is in some formal
relation of proportion and the relation of order to any
other mass trope. Claim A is is true because t exists.

Determinate kinds and truthmaking
• The determinate kind term is a 1 kg trope exactly
applies to the tropes in the relation 1 : 1 proportion
and in the relation of equal in order to any 1 kg trope.
• 1 kg trope t is the sole truthmaker of claim B:
B. t is a 1 kg trope.
●
Trope t has a thin particular nature of a 1 kg trope.
Because of its nature, t is in the formal relation of 1 :
1 proportion and in the relation of equality to any
other 1 kg trope. Claim B is true because t exists.

Natural kinds of substances
• Since trope theory identifies substances with trope
bundles, natural kinds of substances (substantial
natural kinds) are more difficult case for a trope
theorist.
•
Objects divide into natural kinds and the division is
ubiquitous:
o natural kinds of fundamental micro-particles
(leptons, quarks, bosons)
o
o
natural kinds of complex objects studied by physics
and chemistry (atoms, chemical compounds)
natural kinds of still more complex objects (living
organisms, complex natural objects)

Natural kinds of substances
• The members of a natural kind are usually similar in
various distinct respects and behave in similar ways in
the same kind of circumstances.

Natural kinds of substances
The following functions are assigned to natural kinds:
1.[Semantic theory]: Natural kinds are referents of
natural kind terms (cf., e.g., Lowe 2009).
2.[Metaphysics of science]: Natural kinds instantiate the
basic dispositional properties and the fundamental laws
of nature are true of each member of some kind K (Ellis
2001; Lowe 2009).
3.[Neo-Aristotelian essentialism]: Every substance
necessarily belongs to some (sufficiently general)
natural kind, which determines its identity conditions
and rules out bare particulars (Loux 1978; Lowe 1998,
2009).

Perfectly and less than perfectly
natural kinds
• It is instructive to distinguish between perfectly and
less than perfectly natural kinds (i.e., the naturalness
of kinds admits of degrees).
•
Perfectly natural kinds must satisfy a set of constraints
(cf. Ellis 2001: 21-23):
o [E1]: they have determinate boundaries: it is
determinate whether object i is member of kind K.
o
o
[E2]: members of a natural kind K share a set of
intrinsic features, and the members of distinct
kinds have distinct intrinsic features.
[E3]: natural kind K has a kind essence: a set of
intrinsic features necessary to every member of K.

Perfectly and less than perfectly
natural kinds
• Natural kinds of fundamental micro-particles and of some
complex objects studied physics and chemistry (e.g.,
electron, d-quark, helium atom, water molecule) are prima
facie examples of perfectly natural kinds.
• The kinds of organisms (i.e., biological species e.g., polar
bear), and also kinds of some chemical compounds are not
perfectly natural.
• Prima facie, the perfectly natural kinds fit roles 2 and 3
assigned to kinds. By contrast, role 1 seems to require a
more liberal conception of kinds. A part of the motivation of
the more liberal conceptions is to clarify the role of
scientific kinds in scientific explanation and as referents of
kind terms (cf. Boyd 1999, 2010).

A trope nominalist theory of
substantial kinds
• I suggest "a bottom up approach" based on the SNT.
First, we account for natural kinds of simple
substances. The second step is to generalize the theory
to the other perfectly natural kinds (i.e., kinds of
complex substances). Finally, we take up less than
perfectly natural kinds.
• In each step, we identify natural kinds with kind terms
with certain application conditions.
• However, the application conditions of kind terms
differ in different steps.
• Only in the first step (the kinds of simple substances),
we make a direct reference to tropes.

Natural kinds of simple substances
• According to the SNT, simple substances are trope
bundles with nuclear tropes:
o every simple substance has one nuclear trope or
two or more nuclear tropes rigidly dependent on
each other.
o
o
nuclear trope t belongs to determinate kind D
because t is in the relation of 1 : 1 proportion to
every D-trope.
if there are several nuclear tropes, they are in the
relations proportion to the tropes falling under
distinct determinables, i.e., fall under distinct
determinables themselves.

Natural kinds of simple substances
• Let us call natural natural K necessary to substance i
the primary kind of i.
• I suggest to identify natural kinds of simple substances
with abstracta from the kind terms applying to
substances.
• Substance i belongs to primary kind K (e.g., electron)
iff there is a group of kind terms with certain
determinate application conditions and any kind tem K
belonging to that group applies to i.
• The application conditions of the kind term of a
primary kind K can be specified as follows:

Natural kinds of simple substances
[P1]: Kind term K applies to any simple substance i that
satisfies the following two conditions:
a. substance i has nuclear tropes t 1
,...,t n
.
b. tropes t 1
,...,t n
belong to determinate kinds
D 1
,...,D n
.
[P2]: Tropes t 1
,...,t n
satisfy condition b because they are
the tropes they are. Their existence is also sufficient for
the existence substance i. Consequently, tropes t 1
,...,t n
make jointly true the claim that i belongs to kind K.

Natural kinds of simple substances
• Condition [P1] lays down the application conditions of
a natural kind term of primary kind K.
o clause [a] claims that certain tropes are naturally
unified by being mutually rigidly dependent. They
determine the necessary features of a member of K
(the kind essence of K).
o
•
in this case, kind essence of K is also necessary to i
(K is a primary kind).
It is easy to check that the nuclear tropes of
substance i are truthmakers of the claim that i belongs
to kind K ([P2]).

Natural kinds of simple substances
• By modifying clause [P1a], we can formulate application
conditions of the kind terms of other perfectly natural kinds
than just primary kinds.
• For instance, some natural kind K might be contingent to its
members. Still, it has a kind essence (it satisfies [E3]). In
such case, the tropes that make substance i member of K
are its nuclear tropes and some mutually rigidly dependent
tropes contingent to i.
• By modifying clause [P1b], we obtain natural kinds which
are not perfectly natural but still have determinate
boundaries (fulfil [E1]): for instance, one might suggest that
due to nuclear tropes that belong to certain determinate
and determinable kinds, substance i is of kind K' (e.g., is a
lepton).

Generalisation to complex
substances
• The present approach can be generalized to the
perfectly natural kinds of complex substances. [C1]
illustrates how that might happen:
[C1]: Kind term K applies to any complex substance i that
satisfies the following three conditions:
a. substance i has substances i 1
,...,i n
as its proper parts.
b. substances i 1
,...,i n
belong to natural kinds K 1
,...,K n
.
c. i 1
,...,i n
are naturally unified due to their relative
spatial locations and causal powers.

Generalisation to complex
substances
• The basic idea of [C1] is: we start with simple (or. simpler)
substances belonging to certain natural kinds that compose
complex substance i.
• Conversely, substance i belongs to kind K because it has
certain kinds substances as its essential/kind essential
proper parts.
• Tentative examples: neutrons, protons, different kinds of
atoms.
• The natural unification condition [C1c] is crucial and would
deserve more discussion. An adequate formulation of the
condition would give a partial anwers to van Inwagen's
(1990) special composition question.

Conclusion
• The present theory denies the existence of natural kinds as
constituents of the mind-independent reality. They are
identified with kind terms having certain determinate
application conditions.
• However, the truthmakers of the attributions of perfectly
natural kinds are independent of us.
• It builds on the SNT and on the assumption that there are
simple substances that divide into natural kinds with a set
of intrinsic properties essential to each kind K.
• Unlike reductive realist theory of Hawley & Bird (2011), it
does not introduce complex properties or causal proceses
binding properties. All entities bound by processes are
already trope bundles (substances).

References
Boyd, R. (1999): “Homeostasis, Species and Higher Taxa”, In Robert Wilson (ed.): Species: New
Interdisciplinary Essays, (London: The MIT Press).
Boyd, R. (2010): “ Realism, Natural Kinds, and Philosophical Methods”, in Beebee, H. &
Sabbarton-Leary, Metaphysics and Semantics of Natural Kinds (London: Routledge), 212-234.
Campbell, K. K. (1990): Abstract Particulars. (Oxford: Basil Blackwell)..
Ellis, B. (2001): Scientific Essentialism, (Cambridge: Cambridge University Press).
Hawley, K. & Bird, A. (2011): “What are Natural Kinds”, Philosophical Perspectives 25, 205-221.
Keinänen, M. (2011): “Tropes – the Basic Constituents of Powerful Particulars?”, Dialectica 65: 3,
419-450.
Lowe, E. J. (1998): The Possibility of Metaphysics - Substance, Identity and Time, (Oxford:
Clarendon Press).
Lowe, E. J. (2009): More Kinds of Being, (Oxford: Wiley-Blackwell).
van Inwagen, P. (1990): Material Beings, (Ithaca: Cornell University Press.
Williams, D. C. (1953a): “On the Elements of Being I”, Review of Metaphysics 7, 3-18.
Williams, D. C. (1986): “Universals and Existents”, Australasian Journal of Philosophy 64, 1, 1-18