## 1. Historical Background



The father of the contemporary debate on tropes was D. C. Williams
(1953*a*; 1953*b*; 1963; 1986 [1959];
 2018).[2]
 Williams defends a one-category theory of tropes (for the first time
so labeled), a bundle theory of concrete particulars, and a
resemblance class theory of universals. All of which are now elements
of the so-called 'standard' view of tropes. Who to count
among Williams' trope-theoretical predecessors is unavoidably
contentious. It depends on one's views on the nature of the
trope itself, as well as on which theses, besides the thesis that
tropes exist, one is prepared to accept as part of a trope--or
*trope-like*--theory.



According to some philosophers, trope theory has roots going back at
least to Aristotle (perhaps to Plato (*cf.* Buckels 2018), or
even the pre-Socratics (*cf.* Mertz 1996: 83-118)). In
the *Categories*, Aristotle points out that Substance and
Quality both come in what we may call a universal and a particular
variety (*man* and *this man* in the case of substance,
and *pallor* and *this pale*--to ti leukon--in
the case of quality). Not everyone believe that this means that
Aristotle accepts the existence of tropes, however. On one
interpretation (Owen 1965) *this pale* names an absolutely
determinate, yet perfectly shareable, shade of pallor. But on a more
traditional interpretation (*cf.* Ackrill 1963 and, more
recently, Kampa & Wilkins 2018), it picks out a trope, i.e., a
particular 'bit' of pallor peculiar to the substance that
happens to exemplify it (for a discussion, *cf.* Cohen
2013).



In view of the strong Aristotelian influence on medieval thinkers, it
is perhaps not surprising that tropes or trope-like entities are found
also here. Often mentioned in this connection is Ockham (*cf.*
also Aquinas, Duns Scotus, and Suarez). Ockham held that there are in
total four sorts of individual things: substances, qualities,
substantial forms, and matter. Claude Panaccio (2015) argues that all
four sorts of individual things are best understood as tropes or, in
the case of substances, as bundles of tropes (more precisely as
*nuclear* bundles of tropes similar to those defended by e.g.,
Simons 1994 and Keinanen 2015).



This list of early proponents of trope-like entities could have been
made much longer. D. W. Mertz (1996) mentions, besides those already
listed, Boethius, Avicenna, and Averroes. And Kevin Mulligan
et al. (1984) point out that similar views can be found defended by
early modern philosophers, including Leibniz, Locke, Spinoza,
Descartes, Berkeley and Hume.



Still, it is in the writings of 19th century
phenomenological philosophers that the earliest and most systematic
pre-Williams 'trope'-theories are found (Mulligan et al.
1984: 293). The clearest example of an early trope theorist of this
variety is undoubtedly Edmund Husserl. In the third part of his
*Logical Investigations* (2001 [1900/1913]), Husserl sets out
his theory of *moments*, which is his name for the
world's abstract (and essentially dependent) individual parts
(Correia 2004; Beyer 2016). Husserl was most likely heavily influenced
by Bernard Bolzano, who held that everything real is either a
substance or an adherence, i.e., an attribute that cannot be shared
(Bolzano
 1950 [1851]).[3]
 Husserl thought of his moments as (one of) the fundamental
constituents of *phenomenal* reality. This was also how fellow
phenomenologists G. F. Stout (1921;
 1952),[4]
 Roman Ingarden (1964 [1947-1948]) and Ivar Segelberg
 (1999 [1945;1947;1953])[5]
 viewed their fundamental and trope-like posits. Williams' views
are not so easily classified. Although he maintained that all our
knowledge rests on perceptual experience, he agreed that it should not
be limited to the perceptually given and that it could be extended
beyond that by legitimate inference (Campbell et al. 2015). That more
or less all post-Williams proponents of tropes treat their posits as
the fundamental constituents of *mind-independent*--not
phenomenal--reality, is however clear (*cf.* e.g., Heil
2003).



After Williams, the second most influential trope theorist is arguably
Keith Campbell (1997 [1981]; 1990). Campbell adopted the basics of
Williams' (standard) theory and then further developed and
defended it. Later proponents of more or less standard versions of the
trope view include Peter Simons, John Bacon, Anna-Sofia Maurin,
Douglas Ehring, Jonathan Schaffer, Kris McDaniel, Markku
Keinanen, Jani Hakkarainen, Marta Ujvari, Daniel Giberman,
Robert K. Garcia, and Anthony Fisher (all of whose most central works
on the topic are listed in the Bibliography).



A very influential paper also arguing for a version of the theory
(inspired more by Husserl than by Williams) is
"Truth-Makers" (Mulligan et al. 1984; *cf.* also
Denkel 1996). This paper defends the view that tropes are essentially
dependent entities, the objects of perception, and the world's
basic truthmakers. Proponents of trope theories which posit tropes as
one of *several* fundamental categories include C. B. Martin
(1980), John Heil (2003), George Molnar (2003), and Jonathan Lowe
(2006). Molnar and Heil both defend ontologies that include (but are
not limited to) tropes understood as powers, and Lowe counts tropes as
one of *four* fundamental categories. Even more unorthodox are
the views of Mertz (1996, 2016), whose trope-like entities are
categorized as a kind of
 relation.[6]


## 2. The Nature of Tropes



According to several trope theorists--perhaps most notably,
according to Williams--what exists when a trope does is an
*abstract* particular. The word 'abstract' is
ambiguous. On the one hand, Williams tells us, it means
"*transcending individual existence*, as a universal,
essence, or Platonic idea is supposed to transcend it"
(1953*a*: 15). On this meaning, to be abstract is to be
non-spatiotemporal. Tropes--which are standardly taken to exist
*in* spacetime--are clearly *not* (or, not
necessarily) abstract in this sense (which explains why some
philosophers--e.g., Kung 1967; Giberman 2014, 2022;
*cf.* also Simons 1994: 557--insist on referring to the
trope as 'concrete'). But then there is this
other--according to Williams "aboriginal"--sense
of the term. A sense in which, to be 'abstract' is to be
"*partial, incomplete, or fragmentary*, the trait of what
is less than its including whole" (Williams 1953*a*: 15).
It is in *this* sense that the trope is supposed to be
abstract.



Is saying of the trope that it is abstract in this sense enlightening?
Some have worried that it isn't (*cf.* e.g., Maurin 2002:
21; *cf.* also Daly 1997). That this worry is unwarranted has
recently been pretty convincingly argued by Fisher (2020). When
Williams argues that the trope is abstract in the sense of
"partial, incomplete, or fragmentary", Fisher notes, what
he means is that it "fails to exhaust the content of the region
it occupies or is merely part of the content of that region"
(Fisher 2020: 45; *cf.* also Williams 1986 [1959]: 3). One
consequence of this, is that the trope can only be attended to via a
process of *abstraction*. (In Campbell's words (1990: 2),
it can only be "brought before the mind ... by a process of
selection, of systematic setting aside, of these other qualities of
which we are aware".) But this, Fisher points out, does
*not* mean that the trope is abstract *because* it is a
product of abstraction (if it did, then since attending to basically
anything (short of everything) involves abstracting away from the
surrounding environment, saying of the trope that it is
'abstract' *would* be saying nothing very
informative at all). What it means, rather, is that the trope is
something that requires abstraction to be brought before the mind
*because* it is abstract (which, in turn, it is
*because* it is such that it does not exhaust the content of
the region it occupies or is merely part of the content of that
region). This takes care of this worry (for more reasons to view the
abstractness of the trope as integral to its nature, see the
discussion in section 3.1 below).


### 2.1 Property or Object?



In philosophy, new posits are regularly introduced by being compared
with, or likened to, an already familiar item. Tropes are no exception
to this rule. In fact, tropes have been introduced by being compared
with and likened to not one but *two* distinct but equally
familiar kinds of things: properties and objects (Loux 2015). Up until
very recently, that tropes can be introduced in both of these ways was
considered a feature of the theory, not a source of concern. Tropes,
was the idea, can be compared with and likened to both properties and
objects, because tropes *are* a bit of both. Recently, however,
both friends and foes of tropes have started to question whether
tropes *can be* a bit of both. At any rate, this will depend on
what *being a property* and *being an object* amounts
to, an issue on which there is no clear consensus.



Looking more closely at existing versions of the trope view, whether
one thinks of one's posit primarily as a kind of property or as
a kind of object certainly influences what one takes to be true (or
not) of it. To see this, compare the tropes defended by Williams with
those defended by Mulligan et al. Williams seems to belong to the camp
of those who view the trope (primarily) as a kind of object. Tropes
are that out of which everything else there is, is constructed. As a
consequence, names for tropes should not be understood as abbreviated
definite descriptions of the kind 'the Ph-ness of
*x*'. Instead, to name a trope should be likened with
baptizing a child or with introducing a man "present in the
flesh", i.e., ostensively (Williams 1953*a*: 5). Mulligan
et al. (1984), on the other hand, seem to regard the trope more as a
kind of property, and as a consequence of this, argue to the contrary
that the correct (in fact the only) way to refer to tropes is
precisely by way of expressions such as 'the Ph-ness of
*x*'. This, they claim (again *pace* Williams), is
because tropes are essentially *of* some object, because they
are *ways* the object is (*cf.* also Heil 2003: 126f).
In general, a theory which models its posit primarily on the property
hence thinks of it as a dependent sort of entity, as *of*
something else. And a theory which thinks of its tropes more as
objects--as 'the alphabet of being'--thinks of
them as independent, either in the sense that they need not make up
the things they actually make up, or--more radically--in the
sense that they need not make up anything at all (that they could be
so-called 'free-floaters').



How one views the nature of properties and objects, respectively, also
plays a role for some of the criticisms the trope view has had to
face. So, for instance, does Jerrold Levinson think that tropes cannot
be a kind of property because having a property--being
red--amounts to being in a certain condition, where conditions
are not particular (Levinson 1980; 2006). The alternative is that
tropes are what he calls 'qualities', by which he means
something resembling bits of abstract stuff. However, since a theory
accepting the existence of bits of abstract stuff would be both
"ontologically extravagant and conceptually outlandish"
(Levinson 2006: 564), abstract stuff most likely doesn't exist.
Which means that, according to Levinson, tropes are *neither* a
kind of property *nor* a kind of object. A circumstance that
makes him conclude that tropes do not exist.



Arkadiusz Chrudzimski, next, has argued that, although tropes
*can* be viewed either as a kind of property or as a kind of
object, they cannot be viewed as a bit of both (Chrudzimski 2002).
Which means that the theory loses its coveted
'middle-position', and with it any advantage it might have
had over rival views. For, he argues, to conceptualize the trope as a
property--a *way things are*--means imputing in it a
*propositional structure* (Levinson 1980: 107 holds a similar
view). Not so if the trope is understood as a kind of object. But
then, although tropes understood as properties are suitable as
semantically efficient truthmakers, the same is not true of tropes
understood as a kind of object. Conversely, although tropes understood
as a kind of object are suitable candidates for being that from which
both concrete particulars and abstract universals are constructed,
tropes understood as properties are not. Whichever way we conceive of
tropes, therefore, the theory's overall appeal is severely
diminished.



Both Levinson's and Chrudzimski's pessimistic conclusions
can be resisted. One option is simply to refuse to accept that one
cannot seriously propose that there are "abstract stuffs".
Levinson offers us little more than an incredulous stare in defense of
this claim, and incredulous stares are well-known for lacking the
force to convince those not similarly incredulous. Another option is
to reject the claim that tropes understood as properties must be
propositionally structured. Or, more specifically, to reject the claim
that complex truths need complex--(again)
*propositionally* structured--truthmakers. Some truthmaker
theorists--not surprisingly, Mulligan *et al*. (1984) are
among them--reject this claim. In so doing, they avoid having to
draw the sorts of conclusions to which Levinson and (perhaps
especially) Chrudzimski gesture.



A more radical option, finally, is to simply reject the idea that
tropes can be informatively categorized either as a kind of property
or as a kind of object. Some of the features we want to attribute to
tropes seem to cut across those categories anyhow. So, for instance,
if you think 'being shareable' is essential to
'being a property', then, obviously, tropes are not
properties. Yet tropes, even if not shareable, can still be
*ways* objects are, and they can still essentially depend on
the objects that have them. Likewise, if 'monopolizing
one's position in space-time' is understood as a central
trait for objects, tropes are not objects. Yet tropes can still be the
independent building-blocks out of which everything else there is, is
constructed.



According to Garcia (2015*a*, 2016), this is why we ought to
frame our discussion of the nature(s) of tropes in terms of another
distinction. Rather than distinguishing between tropes understood as a
kind of property, and tropes understood as a kind of object--and
risk getting caught up in infected debates about the nature of objects
and properties generally--Garcia suggests we distinguish between
tropes understood as 'modifiers' and tropes understood as
'modules'. The main difference between tropes understood
in these two ways--a difference that is the source of a great
many further differences--is that tropes understood as modifiers
do not have the character they confer (on objects), whereas tropes
understood as modules do. With recourse to this way of distinguishing
between different versions of the trope-view, Garcia argues, we can
now evaluate each version separately, independently of how we view
objects and properties,
 respectively.[7]


### 2.2 Complex or Simple?



According to most trope-theorists, tropes are ontologically simple.
Here this should be taken to mean that tropes have no constituents, in
the sense that they are not 'made up' or
'built' from entities *belonging to some other
category*. Simple tropes, thus understood, can still have
parts--even necessarily so--as long as those parts are also
tropes (*cf.* e.g., Giberman 2022; Robb 2005:
 469).[8],[9]



That tropes are ontologically simple arguably provides the trope
theorist with a tie-breaker vis-a-vis states of affairs (if
states of affairs are understood as substrates instantiating
universals). *Prima facie* a theory positing states of affairs
has the same explanatory power as a theory positing tropes. But a
theory of states of affairs posits--apart from the state of
affairs itself--at least two (fundamental) sorts of things
(universals and substrates), whereas a theory of tropes (at least a
theory of tropes according to which tropes are simple and objects are
bundles of tropes) posits only one (tropes). From the point of view of
ontological parsimony, therefore, the trope view ought to be
 preferred.[10]



*Can* the trope be simple? According to a number of the
theory's critics, it cannot. Here is Herbert Hochberg's
argument to that effect (2004: 39; *cf.* also his 2001:
178-179; for versions of the argument *cf.* also
Brownstein 1973: 47; Moreland 2001; Armstrong 2004; Ehring
 2011):[11]



> 
> 
> Let a basic proposition be one that is either atomic or the negation
> of an atomic proposition. Then consider tropes *t* and
> *t*\* where '*t* is different from
> *t*\*' and '*t* is exactly similar to
> *t*\*' are both true. Assume you take either
> 'diversity' or 'identity' as primitive. Then
> both propositions are basic propositions. But they are logically
> independent. Hence, they cannot have the same truth makers. Yet,
> for...trope theory /.../ they do and must have the same
> truth makers. Thus the theory fails.
> 
> 
> 



A number of different things can be said in response to this argument.
It assumes, first, that if tropes are simple, trope theory must
violate what appears to be a truly fundamental principle (call it HP,
short for 'Hochberg's principle'): that
*logically independent basic propositions must have distinct
truthmakers*. Having to reject HP is hence a cost of having simple
tropes. Perhaps this cost is acceptable. That it is, seems to be a
view held by Mulligan et al. (a similar view is, according to
Armstrong 2005: 310 also held by Robb). For, they claim (1984:
296):



> 
> 
> ...[w]e conceive it as in principle possible that one and the
> same truth-maker may make true sentences with different meanings: this
> happens anyway if we take non-atomic sentences into account, and no
> arguments occur to us which suggest that this cannot happen for atomic
> sentences as well.
> 
> 
> 



One reason for rejecting HP has been put forward by Fraser MacBride
(2004). HP, he notes, is formulated in terms of
'*logically* independent basic propositions'.
However, HP is only plausible if it takes more than logical (what
MacBride calls 'formal') (in)dependence into account:
*material* independent also
 matters![12]
 Only if two propositions are logically *and* materially
independent does it follow that they must have distinct truthmakers.
But formal and material independence can--and in this case most
likely will--come apart. For (ibid: 190):



> 
> 
> ...[i]nsofar as truth-makers are conceived as inhabitants of the
> world, as creatures that exist independently of language, it is far
> from evident that logically independent statements in the formal sense
> are compelled to correspond to distinct truth-makers.
> 
> 
> 



Another argument against the simplicity of tropes comes from Ehring
and was inspired by an argument first delivered by Moreland (2001:
64). J. P. Moreland's argument concludes that trope theory is
unintelligible. Ehring thinks this is much too strong. This is
therefore the formulation of the objection he prefers (2011: 180):



> 
> 
> The nature and particularity of a trope are intrinsically grounded in
> that trope. If tropes are simple, their nature and their particularity
> are hence identical. The natures of a red trope and an orange trope
> are inexactly similar. Hence their respective particularities should
> be inexactly similar as well. However, these particularities are
> *exactly* similar. Hence, their particularities are not
> identical to their natures, and tropes are not simple.
> 
> 
> 



Here the trope theorist could probably reply that the objection rests
on a kind of category mistake: that 'particularities' are
quite simply not things amenable to standing in similarity relations.
Alternatively, she might just concede that tropes are complex, yet
argue that they are so in the innocent sense of having other tropes as
parts (one particularity-trope and a distinct nature-trope). Against
this, Ehring (2011: 183f) has argued that if the trope has its
particularity reside in one of the tropes that make it up, we can
always ask about *that* trope what grounds *its*
particularity and nature respectively. Which would seem to lead us
into an infinite--and most probably vicious--regress.



Ehring's own solution to the problem is to adopt a version of
the trope view (what he calls Natural Class Trope Nominalism) on which
tropes do not resemble each other in virtue of their nature, but
rather in virtue of belonging to this or that natural class. On this
view, what makes two tropes qualitatively the same (their belonging to
the same natural class of tropes) is different from what makes them
distinct (the tropes themselves, primitively being what they are).
Which means that, that tropes can be distinct yet exactly resemble
each other is no longer a reason to think that tropes are complex.



A different kind of solution has recently been proposed by Giberman
(2022*,* *cf.* also his 2014). According to him, because
at least some of the tropes there are, are spatiotemporally located
(they are what he calls
 'concrete')[13],
 they must have size, shape, and duration. That tropes have these
different features means that they are capable of multiple
resemblances. Which, claims Giberman, means that they are
qualitatively complex. Yet that they are does not threaten the trope
view in any way. For, according to Giberman, tropes are (qualitatively
complex) *ostriches*. What this means is that tropes are such
that they "primitively account for their own multiple
resemblance capacities". Which means that "no (further)
ontological machinery is required to explain that an ostrich trope has
multiple properties" (even though we are admitting that it
does!) (Giberman 2022: 18). In this sense, the trope is like the
Quinean concrete particular (Giberman ibid.; *cf.* also Quine
1948, Devitt 1980):



> 
> 
> When the Quinean is asked what it is about a given electron that
> metaphysically explains its ability to resemble both massive things
> and charged things, he will likely answer 'nothing!--it
> just is that way'... Similarly, when asked what it is about the
> *n* charge trope that metaphysically explains its ability to
> resemble both charged things and things of a certain size, the ostrich
> trope theorist answers: 'the trope itself--no more
> structure to it than that'.
> 
> 
> 



But then, on Giberman's view--and *pace*
Ehring--we are *not* allowed to ask of the properties of
the trope what grounds *their* particularity and nature
(that's primitive!). And if asking this is not allowed, is the
idea, no infinite regress can be generated (*cf.* also fn 20,
this entry).



What about the advantage the trope view was supposed to have over the
state-of-affairs view? Primitive or not, if the complexity is there,
doesn't this mean that those views are now on a par
parsimony-wise? Giberman doesn't think so, and gives two reasons
why not: (1) although the ostrich trope is qualitatively complex, it
is *not*--unlike the state of affairs--categorially
complex (no trope has a constituent from outside the category
*trope*) (2022: 16); (2) (more contentiously) even states of
affairs, in being spatiotemporal, need to have size and shape etc. But
then, apart from having to accept the existence of categorially
distinct substrates, the state of affairs theorist must also accept
that universals--like tropes--are primitively qualitatively
complex (ibid: 18).


### 2.3 Trope Individuation



What makes two tropes, existing in the same world at the same time,
 distinct?[14]



A natural suggestion is that we take the way we normally identify and
refer to tropes very literally and individuate tropes with reference
to the objects that 'have' them:



**Object Individuation** (OI):
For any tropes *a* and *b* such that *a* exactly
resembles *b*, *a* [?] *b* iff *a*
belongs to an object that is distinct from the object to which
*b* belongs.


No trope theorist endorses this natural suggestion, however. The
reason why not is that, at least if objects are bundles of tropes, the
individuation of objects will depend on the individuation of the
tropes that make them up, which means that, on OI, individuation
becomes circular (Lowe 1998: 206f.; Schaffer 2001: 249; Ehring 2011:
77). Indeed, matters improve only marginally if objects are understood
as substrates in which tropes are instantiated. For, although on this
view, OI does not force one to accept a circular account of
individuation, this is because it is now the substrate which carries
the individuating burden. This leaves the individuation of the
substrate still unaccounted for, and so we appear to have gotten
nowhere (Mertz 2001). Any trope theorist who accepts the possible
existence of 'free-floating' tropes--i.e., tropes
that exist unattached to any object--*must* in any case
reject this account of trope individuation (at least as long as she
accepts the possibility of there being *more than one*
free-floating trope at any given time).



The main-contenders are instead *spatiotemporal individuation*
(SI) and *primitivist individuation* (PI). According to SI,
first, that two tropes belonging to the same world are distinct can be
metaphysically explained with reference to a difference in their
respective spatiotemporal position (Campbell 1990: 53f.; Lowe 1998:
207; Schaffer 2001: 249; Giberman 2022: 18):



**Spatiotemporal Individuation** (SI):
For any tropes *a* and *b* such that *a*
exactly resemble *b*, *a* [?] *b* iff *a*
is at non-zero distance from *b*.


This is an account of trope individuation that seems to respect the
way tropes are normally picked out, yet which does
not--circularly--individuate tropes with reference to the
objects they make up and which does not rule out the existence of
'free-floaters'. In spite of this, the majority of the
trope theorists (Schaffer 2001 being one important exception) have
opted instead for primitivism (*cf.* e.g., Ehring 2011: 76;
Campbell 1990: 69; Keinanen & Hakkarainen 2014). Primitivism
is best understood as the denial of the idea that there is any true
and informative way of filling out the biconditional 'For any
exactly resembling tropes *a* and *b*, *a* [?]
*b* iff ...'. That *a* and *b* are
distinct--if they are--is hence primitive. It has no further
(ontological) analysis or (metaphysical) explanation.



According to what is probably the most influential argument in favor
of PI over SI (an argument that changed Campbell's mind:
*cf.* his 1990: 55f.; *cf.* also Moreland 1985: 65), SI
should be abandoned because it rules out the (non-empty) possibility
that (parts of) reality could be
 *non*-spatiotemporal.[15]
 Against this, proponents of SI have argued that the thesis that
reality must be spatiotemporal can be independently justified
(primarily because naturalism can be independently justified,
*cf.* Schaffer 2001: 251). And even if it cannot, SI could
easily be modified to accommodate *the analogue* of the
locational order of space (Campbell 1997 [1981]: 136; Schaffer
 ibid.).[16]



A common argument *in favor* of SI is that it allows its
proponents to rule out what most agree *are* empty
possibilities: swapping and piling.



*Swapping*: According to the so-called 'swapping
argument' (first formulated in Armstrong 1989: 131-132;
*cf.* also Schaffer 2001: 250f; Ehring 2011:
 78f.),[17], [18]
 if properties are tropes, and individuation is primitive, two
distinct yet exactly similar tropes might swap places (this redness
*here* might have been *there*, and vice versa). The
result, post-swap, is a situation that is ontologically distinct from
that pre-swap. However, empirically/causally the pre- and post-swap
situations are the same (*cf.* LaBossiere 1993: 262 and Denkel
1996: 173f. for reasons to doubt that they *are* the same).
That is, given the natural laws as we know them, that this red-trope
*here* swaps places with that red-trope *there* makes no
difference to the future evolution of things. Which means that, not
only would the world look, feel and smell exactly the same to us pre-
and post-swap, it would be in principle impossible to construct a
device able to distinguish the two situations from one another. For
any device able to detect the (primitive) difference between the two
situations would also have to be a device able to communicate this
difference (by making a sound, by turning a handle, etc...) yet
this is precisely what the fact that swapping makes no difference to
the future evolution of things prevents (*cf.* Dasgupta 2009).
This makes admitting the possibility of swapping seem unnecessary. If
we also accept the (arguably reasonable) Eleatic principle according
to which only changes that matter empirically/causally should count as
genuine, we can draw the even stronger conclusion that swapping is not
genuinely possible, and, hence, that any account of individuation from
which it follows that it is, should be
 abandoned.[19]



To accept SI does not immediately block swapping (Schaffer 2001: 250).
For, SI (just like OI and PI) is a principle about trope individuation
that holds *intra*-worldly. In this case: within any given
world, no two exactly similar tropes are at zero distance from each
other. Swapping, on the other hand, concerns what is possibly true (or
not) of exactly similar tropes considered *inter*-worldly. But
this means that, although SI does not declare swapping possible, it
doesn't rule it out either. According to the proponent of SI,
this is actually a good thing. For there is one possibility that it
would be unfortunate if one's principle of individuation
*did* block, namely the possibility--called
*sliding*--that this red-trope *here* could have
been *there* had the wind blown differently (Schaffer 2001:
251). To get the desired result (i.e., to block swapping while
allowing for sliding), Schaffer suggests we combine trope theory with
SI *and* a Lewisian counterpart theory of transworld identity
(Lewis 1986). The result is an account according to which exactly
resembling tropes are *intra*-worldly identical if they inhabit
the same position in space-time. And according to which they are
*inter*-worldly counterparts, if they are distinct, yet stand
in sufficiently similar distance- and other types of relations to
their respective (intra-worldly) neighbors. With this addition in
place, Schaffer claims, a trope theory which individuates its posits
with reference to their spatiotemporal position *will* make
room for the possibility of sliding, because (2001: 253):



> 
> 
> On the counterfactual supposition of a shift in wind, what results is
> a redness exactly like the actual one, which is in perfectly
> isomorphic resemblance relations to its worldmates as the actual one
> is to its worldmates, with just a slight difference in distance with
> respect to, e.g., the roundness of the moon.
> 
> 
> 



...yet it *won't* allow for the possibility of
swapping, because:



> 
> 
> ...the nearest relative of the redness of the rose which is
> *here* at our world would be the redness still *here*
> 'post-swap'. The redness which would be here has exactly
> the same inter- and intraworld resemblance relations as the redness
> which actually is here, and the same distance relations, and hence is
> a better counterpart than the redness which would be
> *there*.
> 
> 
> 



This is not necessarily a reason to prefer SI over PI, however. For,
PI, just like SI, is an inter-worldly principle of individuation,
which means that it, just like SI, could be combined with a Lewisian
counterpart theory, thereby preventing swapping yet making room for
sliding. It is, in other words, the counterpart theory, and not SI (or
PI), which does all the work. In any case, it is not clear that
intra-worldly swapping *is* an empty possibility. According to
Ehring, there are circumstances in which a series of slidings
constitute one case of swapping, something that he thinks would make
swapping more a reason *for* than against PI (Ehring 2011:
81-85).



*Piling*: Even if swapping does not give us a reason to prefer
SI over PI, perhaps its close cousin 'piling' does.
Consider a particular red rose. Given trope theory, this rose is red
because it is partly constituted by a redness-trope. But what is to
prevent *more than one*--even indefinitely
many--exactly similar red-tropes from partly constituting this
rose? Given PI: nothing. It is however far from clear how one could
empirically detect that the rose has more than one redness trope, just
like it is not clear how one could empirically detect how many redness
tropes it has, provided it has more than one. This is primarily
because it is far from clear how having more than one redness trope
could make a causal difference in the world. But if piling makes no
empirical/causal difference, then given a (plausible) Eleatic
principle, the possibility of piling is empty, which means that PI
ought to be rejected (Armstrong 1978: 86; *cf.* also Simons
1994: 558; Schaffer 2001: 254, *fn*. 11).



In defense of PI, its proponents now point to a special case of
piling, called 'pyramiding' (an example being a 5 kg
object consisting of five 1 kg tropes). Pyramiding *does* seem
genuinely possible. Yet, if piling is ruled out, so is pyramiding
(Ehring 2011: 87ff.; *cf.* also Armstrong 1997: 64f.; Daly
1997: 155). According to Schaffer, this is fine. For, although
admittedly not quite as objectionable as other types of piling (which
he calls 'stacking'), pyramiding faces a serious problem
with predication: if admitted, it will be true of the 5 kg object that
"[i]t has the property of weighing 1 kg" (Schaffer 2001:
254). Against this, Ehring has pointed out that to say of the 5 kg
object that "[i]t has the property of weighing 1 kg" is at
most pragmatically odd, and that, even if this oddness is regarded as
unacceptable, to avoid it would not require the considerable
complication of one's theory of predication imagined by Schaffer
(Ehring 2011: 88-91).



According to Schaffer, the best argument for the possibility of
piling--hence the best argument against SI--is rather
provided by the existence of so-called bosons (photons being one
example). Bosons are entities which do not obey Pauli's
Exclusion Principle, and hence such that two or more bosons
*can* occupy the same quantum state. A 'one-high'
boson-pile is hence empirically distinguishable from a
'two-high' one, which means that the possibility of piling
in general is not ruled out even if we accept an Eleatic principle.
Schaffer (2001: 255) suggests we solve this problem for SI by
considering the wave--not the particle/boson--as the way the
object 'really' is. But this solution comes with
complications of its own for the proponent of SI. For, "[t]he
wave function lives in configuration space rather than physical space,
and the ontology of the wave function, its relation to physical space,
and its relation to the relativistic conception of spacetime which SI
so naturally fits remain deeply mysterious" (Schaffer 2001:
 256).[20]


## 3. Tropes as Building Blocks



As we have seen, tropes can be conceptualized, not just as
particularized *ways* things are, but also--and on some
versions of trope theory, primarily--as that out of which
everything else there is, is constructed. Minimally, this means that
tropes must fulfill at least two constructive tasks: that of making up
(the equivalent of) the realist's universal, and that of making
up (the equivalent of) the nominalist's concrete particular.


### 3.1 Tropes and Universals



How can distinct things have things--their properties--in
common? This is the problem of 'the One over Many'
(*cf.* e.g., Rodriguez-Pereyra 2000; Maurin 2022: sect. 2).
Universals provide a straightforward solution to this problem:
distinct things can have things in common, because there is a type of
entity--the universal--capable of existing in (and hence
characterizing) more than one object at once. The trope
theorist--at least if she does not accept the existence of
universals *in addition to*
 tropes[21]--does
 not have recourse to entities that can be likewise identical in
distinct instances. She must therefore come up with an alternative
solution. Here I'll consider three.



*The Resemblance Class Theory:* The most commonly accepted
trope-solution to the problem of the One over Many takes two objects
*a* and *b* to 'share' a
property--*F-ness*-- if at least one of of the tropes
that make up *a* belongs to the same (exact) resemblance class
as at least one of the (numerically distinct) tropes that make up
*b* (*cf.* Williams 1953*a*: 10; Campbell 1990:
31f.; *cf.* also Lewis 1986: 64f.). Exact resemblance is an
*equivalence relation* (although *cf.* Mormann 1995 for
an alternative view), which means that it is a *symmetrical*,
*reflexive*, and *transitive* relation. Because it is an
equivalence relation, exact resemblance partitions the set of tropes
into mutually excluding and non-overlapping classes. Exact resemblance
classes of tropes, thus understood, function more or less as the
traditional universal does. Which is why proponents of this view think
the problem can be solved with reference to them.



A point of contention among those who hold this view is if accepting
it mean having to accept the existence of resemblance relations. Those
who think it doesn't, point out that resemblance is an
*internal* relation which supervenes on whatever it relates:
that the (degree of) resemblance between distinct tropes is entailed
simply given their
 existence.[22]
 Assuming that our ontology is 'sparse' (a thought many
believe can be independently justified, *cf.* e.g., Schaffer
2004 and Armstrong 1978), only what is minimally required to make true
all truths exists. Which means that, if resemblance is an internal
relation, what exists when distinct tropes resemble each
other--and so what plays the role of the realist's
universal--is nothing but the resembling tropes themselves
(Williams 1963: 608; Campbell 1990: 37f.; *cf.* also Armstrong
1989: 56).



Does it follow from the fact that exact resemblance must obtain given
the existence of its relata, that it is no ontological addition to
them? Some philosophers (Daly 1997: 152 is among them) do not think
so. But if it doesn't follow, some have argued, the trope
theorist must combat a trope theoretical version of what has become
known as 'Russell's regress'. Russell's
regress (perhaps better: Russell's regress *argument*) is
an argument to the effect that, if some particulars (Russell was
thinking of concrete particulars, not of tropes) (exactly) resemble
each other, then either the relation of resemblance exists *and is
a universal*, or we end up in (vicious) infinite regress (Russell
1997 [1912]: 48; *cf.* also Kung 1967). Chris Daly (1997:
149) provides us with a trope-theoretical version of this
 argument:[23]



> 
> 
> Consider three concrete particulars which are the same shade of
> red...each of these concrete particulars has a red
> trope--call these tropes *F*, *G*, and
> *H*--and these concrete particulars exactly resemble each
> other in colour because *F*, *G*, and *H* exactly
> resemble each other in colour. But it seems that this account is
> incomplete. It seems that the account should further claim that
> resemblance tropes hold between *F*, *G*, and
> *H*. That is, it seems that there are resemblance tropes
> holding between the members of the pairs *F* and *G*,
> *G* and *H*, and *F* and *H*... Let
> us call the resemblance tropes in question *R*1,
> *R*2, and *R*3...each of
> these resemblance tropes in turn exactly resemble each other.
> Therefore, certain resemblance tropes hold between these
> tropes...we are launched on a regress.
> 
> 
> 



This regress is a problem only if it is *vicious*. The most
convincing reason for thinking that it is not is provided if we
consider the 'pattern of dependence' it
 instantiates.[24]
 For, as we have seen, even those who do not think that the
internality of exact resemblance makes it a mere
'pseudo-addition' to its subvenient base, agree that
resemblance, whatever it is, is such that its existence is necessarily
incurred simply given the existence of its relata. But then, no matter
how many resemblances we regressively generate, ultimately they all
depend for their existence on the existence of the resembling tropes,
which resemble each other because of their individual nature, which is
primitive. This means that the existence of the regress in no way
contradicts--it does not function as a *reductio*
against--the resemblance of the original tropes. On the contrary;
it is *because* the tropes resemble each other, that the
regress exists. Therefore, the regress is benign (*cf.* e.g.,
Campbell 1990: 37; Maurin 2013).



This response only works if the nature of individual
tropes--*their being what they are*--is primitive and
not further analyzable (i.e., it only works if we assume a standard
view of the nature of tropes). To see this, compare the standard view
with a view with which it is often confused: resemblance nominalism.
On a version of the trope view according to which universals are
resemblance classes of tropes, tropes have the same nature if they
resemble each other. Yet, importantly, they resemble each other (or
not) *in virtue of the (primitive) nature they each
'have'* (or 'are'). Resemblance
nominalism, on the other hand, is the view that two objects have the
natures they do in virtue of the resemblance relations which obtain
between them. This means that, whether they resemble or not, is not
decided given the existence and nature of the objects themselves.
Rather, the pattern of dependence is the other way around. And
this--arguably--makes the regress vicious. Perhaps for that
reason, resemblance nominalism has no explicit proponent among the
trope theorists.



*The Natural Class Theory*: Those not convinced that
'Daly's regress' is benign might prefer a view
(first defended by Ehring 2011: 175f) according to which the trope is
not what it is either primitively or because of whatever resemblance
relations it stands in to other tropes, but because of the natural
class to which it belongs. Accepting this view provides us with a new
solution to the problem of the One over Many, one that does not depend
on the existence (or not) of exact resemblance relations. On this
view, more precisely, two objects *a* and *b*
'share' a property--*F-ness*-- if at
least one of the tropes that make up *a* belongs to the same
natural class as at least one of the tropes that make up *b.*
The problem with this alternative is that it appears
to--implausibly--turn explanation on its head. If accepted,
tropes do not belong to this or that class because of their nature.
Rather, tropes have the natures they do because they belong to this or
that class.



*The Trope-Kind Theory*: Although he in his (1953*a*)
briefly 'dallied' (his word) with the view that, to be a
universal is to be a resemblance class of tropes, Williams soon
thereafter changed his mind (*cf*. esp. his 1986 [1959] and
 1963).[25]
 According to the view he adopted instead of the resemblance view,
universals are neither "made" nor "discovered"
but are something we acknowledge "by a relaxation of the
identity conditions of thought and language" (1986 [1959]: 8;
*cf.* also Campbell 1990: 44). If the F-ness of *a* and
the F-ness of *b* is counted in a way that is subject to the
rule that anything indiscernible is identical, their sameness is
explained with reference to the universal they share. And if the
F-ness of *a* and the F-ness of *b* is counted in a way
that *isn't* subject to that rule, their sameness is
explained with reference to their individual, distinct, yet exactly
resembling tropes. Importantly, Williams thinks of this as a kind of
realism--an *immanent* realism--about
universals (Fisher 2017: 346; *cf.* also Fisher 2018 and
Heil 2012: 102f.). It takes universals to be "present in, and in
fact components of, their instances" (Williams 1986 [1959]: 10).
Yet, as noted by Fisher (2017: 346) tropes are still the primitive
elements of being. Universals are real in virtue of being
*mind-independent*. Yet, universals aren't fundamental
(Fisher: ibid.):



> 
> 
> Their reality is determined by mind-independent facts about tropes.
> Tropes manifest universals in the sense that universals are nothing
> over and above property instances as tropes are by their nature of
> kinds.
> 
> 
> 



The trope-kind theory offers an interesting and so far surprisingly
little discussed solution to the problem of the One over Many. So far,
it is a view with few if any explicit contemporary proponents (though
*cf*. Paul 2002, 2017 and van Inwagen 2017:
 348f.[26]).
 It is not unlikely that this state of affairs is now about to
change.


### 3.2 Tropes and Concrete Particulars



The second constructive task facing the trope theorist is that of
building something that behaves like a concrete particular, using only
tropes. Exactly how a concrete particular behaves is of course a
matter that can be debated. This is not a debate to which the trope
theorist has had very much--or at least not anything very
original--to contribute. Instead, the trope theoretical
discussion has been focused on an issue that needs solving
*before* questions concerning what a concrete particular can or
cannot do more precisely become relevant: the issue of *if* and
*how* tropes make up concrete particulars in the first
place.



Whether this issue is best approached by considering if and how tropes
can make up or ground the existence of what me might call
'ordinary' or 'everyday' objects, or if it is
better to concentrate instead on the world's simplest, most
fundamental, objects--like those you find discussed in e.g.,
fundamental physics--is another issue on which trope theorists
disagree. Campbell thinks we should concentrate on the latter sort of
object. In particular, he thinks we should concentrate on objects that
have no other objects as parts, as that way we avoid confusing
'substantial' complexity (and unity) with the--here
relevant--qualitative one. David Robb (2005) and Kris McDaniel
(2001) disagree. This may in part be due to the fact that they both
(*cf.* also Paul 2002, 2017) think that objects are
mereologically composed *both* on the level of their
substantial parts and on the level of their
 qualitative--trope--parts.[27]



According to a majority of the trope theorists, objects are bundles of
tropes. The alternative is to understand objects as complexes
consisting of a substrate in which tropes are instantiated (a view
defended by e.g., Martin 1980; Heil 2003; and Lowe 2006). Indeed,
according to D. M. Armstrong (1989, 2004)--a staunch but
comparatively speaking rather friendly trope-critic--this
minority view *ought to* be accepted by the trope theorist.
Armstrong is most likely wrong, however: several reasons exist for why
one ought to prefer the bundle view (Maurin 2016). One such reason has
to do with parsimony. If you adopt a substrate-attribute view, you
accept the existence of substrates on top of the existence of tropes.
Accepting this additional category of entity makes at least some sense
if properties are universals. For if objects are bundles of universals
and universals are entities which are numerically identical across
instances, then if object *a* is qualitatively identical to
object *b*, *a* is also numerically identical to
*b*. Which means that, if objects are bundles of universals,
the Identity of Indiscernibles is not just true, but necessarily true,
a consequence few universal realists have been prepared to accept
(indeed, a consequence that may turn out to be unacceptable *as a
matter of empirical fact*--*cf.* e.g., French 1988).
If objects are substrates exemplifying universals, on the other hand,
although *a* and *b* are qualitatively identical, they
are nevertheless distinct. They are distinct, that is, *in virtue
of* being partly constituted by (primitively) distinct
substrates.



This sort of argument in favor of the substrate-attribute view cannot
be recreated for a view on which properties are tropes, however. For,
if objects are bundles of tropes, because tropes are particulars
*not* universals, even if *a* and *b* are
qualitatively identical, they are not numerically identical. And they
are not numerically identical *because* they are constituted by
numerically distinct tropes. No need for substrates!



According to the bundle view, objects consist of, are made up by, or
are grounded in, a sufficient number of mutually *compresent*
and/or in some other way mutually dependent tropes (*cf.* e.g.,
McDaniel 2001, 2006 and Giberman 2014 for slightly different takes on
bundling). What is compresence? When the same question was asked about
(exact) resemblance, the trope theorist had the option of treating the
relation as a 'pseudo-addition'. This was because
resemblance is an internal relation and so holds necessarily simply
given the existence of its relata. According to most trope-theorists,
however, compresence is an *external* relation, and hence a
real addition to the tropes it
 relates.[28]
 But then adding compresence gives rise to an infinite regress (often
called 'Bradley's regress' after Bradley 1930 [1893];
*cf.* also Armstrong 1978; Vallicella 2002 and 2005; Schnieder
2004; Cameron 2008, 2022; Maurin 2012).



Unlike what was true in the case of resemblance, this regress is most
likely a vicious regress. This is because the 'pattern of
dependence' it instantiates is the opposite of that instantiated
by the resemblance regress. In the resemblance case, for tropes
*t*1, *t*2, and
*t*3 to exactly resemble each other, it is enough
that they exist. Not so in the compresence case. Tropes
*t*1, *t*2, and
*t*3 could exist and not be compresent, which means
that in order to ensure that they *are* compresent, a
compresence-trope, *c*1, must be added to the
bundle. But *c*1 could exist without being
compresent with those very tropes. Therefore, in order for
*t*1, *t*2, *t*3
*and* *c*1 to be compresent, there must be
something--call it *c*2--that makes them
so. But since *c*2 could exist and not be compresent
with *t*1, *t*2,
*t*3 and *c*1, it too needs
something that ensures its compresence with those entities. Enter
*c*3. And so on. The existence of this regress
arguably contradicts--and hence functions as a *reductio*
against--the compresence of the original (first-order) tropes
and, thereby, the (possible) existence of the concrete particular.



Since concrete particulars (possibly) exist, something must be wrong
with this argument. One option is to claim that compresence is
internal after all, in which case the regress (if there even is one)
is benign (Molnar 2003; Heil 2003 and 2012; *cf.* also
Armstrong 2006). This may seem attractive especially to those who
think of their tropes as *non-transferable* and as *ways
things are*. Even given this way of thinking of the nature of the
trope, however, to take compresence as internal means having to give
up what are arguably some deeply held modal beliefs. For even if you
have reason to think that properties must be 'borne' by
some object, to be able to solve the regress-problem one would have to
accept the much stronger thesis that every trope must be borne by a
*specific* object. If the *only* reason we have for
thinking that compresence is internal in this sense is that this
solves the problem with Bradley's regress, therefore, we should
opt to go down this route as a last resort only (*cf.* Cameron
2006; Maurin 2010).



As a way of saving at least some of our modal intuitions while still
avoiding Bradley's regress, Simons (1994; *cf.* also
Keinanen 2011 and Keinanen and Hakkarainen 2014 for a
slightly different version of this
 view[29])
 suggests we view the concrete particular as constituted partly by a
'nucleus' (made up from mutually and specifically
dependent tropes) and partly--at least in the normal
case--by a 'halo' (made up from tropes that depend
specifically on the tropes in the nucleus). The result is a structured
bundle such that, although the tropes in the nucleus at most depend
for their existence on the existence of tropes *of the same
kind* as those now in its halo, they do not depend specifically on
those tropes. In this way, at least some room is made for contingency,
yet Bradley's regress is avoided. For, as the tropes in the halo
depend specifically for their existence on the tropes that make up the
nucleus, their existence is enough to guarantee the existence of the
whole to which they belong. This is better but perhaps not good
enough. For, although the same object could now have had a slightly
different halo, the possibility that the tropes that actually make up
the halo could exist and not be joined to *this* particular
nucleus is ruled out with no apparent justification (other than that
this helps its proponent solve the problem with the Bradley regress)
(*cf.* also Garcia 2014 for more kinds of criticism of this
view).



According to several between themselves very different sorts of trope
theorists, finally, we should stop bothering with the (nature and
dependence of the) related tropes and investigate instead the
(special) nature of compresence itself. This seems intuitive enough.
After all, is it not the business of a relation to relate? According
to one suggestion along these lines (defended in Simons 2010; Maurin
2002, 2010 and 2011; and Wieland and Betti 2008; *cf.* also
Mertz 1996, Robb 2005 and Giberman 2014 for similar views),
non-relational tropes have an existence that is independent of the
existence of some specific--either non-relational or
relational--trope, but relational tropes (including compresence)
depend specifically for their existence on the very tropes they
relate. This means that if *c*1 exists, it
*must* relate the tropes it in fact relates, even though those
tropes might very well exist and not be compresent (at least not with
each other). There is, then, no regress, and except for
*c*1, the tropes involved in constituting the
concrete particular could exist without being compresent with each
other. And this, in turn, means that our modal intuitions are left
more or less
 intact.[30]



According to Mertz, moreover, to be able to do the unifying work for
which it is introduced, compresence cannot be a universal. If it were,
then if one of the concrete particulars whose constituents it joins
ceases to exist, so will every other concrete particular unified by
the same (universal) relation of compresence. But, as Mertz points
out, "this is absurdly counterfactual!" (Mertz 1996: 190).
Nor can it be a state of affairs. For, states of affairs are in
themselves complexes, and so could not be used to solve the Bradley
 problem.[31]
 It seems, then, that compresence, if understood in a way that
blocks the regress, is a trope. Assuming that Bradley's regress
threatens *any* account according to which many things make up
one unified thing (i.e., assuming that it does not only threaten the
trope-bundle theorist), that there is this threat may therefore turn
out to be a reason *in favor of* positing tropes (Maurin
2011).



The suggestion is not without its critics. To these belong MacBride
who argues that, "...to call a trope relational is to pack
into its essence the relating function it is supposed to perform
without explaining what Bradley's regress calls into question,
viz. the capacity of relations to relate" (2011: 173). Rather
than solve the problem, in other words, MacBride thinks the suggestion
"transfers our original puzzlement to that thing [i.e., the
compresence-relation]". For, he asks "how can positing the
existence of a relational trope explain anything about its capacity to
relate when it has been stipulated to be the very essence of R that it
relates *a* and *b*. It is as though the capacity of
relational tropes to relate is explained by mentioning the fact that
they have a 'virtus relativa'"(ibid.).



Assuming we agree that there is *something* that needs
explaining (i.e., assuming we agree that how several tropes
can--contingently--make up one object needs explaining), we
can either reject a proposed solution because we prefer what we think
is a better solution, or we can reject it because it is *in
itself* bad or unacceptable (irrespective of whether there are any
alternative solutions on offer). MacBride appears to suggest we do the
latter. More precisely, what MacBride proposes is that the solution
fails because it leaves unexplained the special 'power' to
relate it attributes to the compresence trope. If this is why the
suggestion fails, however, then either this is because *no*
explanation that posits something ('primitively') apt to
perform whatever function we need explained, is acceptable, or it is
because *in this particular case*, an explanation of this kind
will not do. If the former, the objection risks leading to an
overgeneration of explanatory failures. Everyone will at some point
need to posit some things as fundamental. And in order for those
fundamental posits to be able to contribute somehow to the theory in
question, it seems we must be allowed to say something about them. We
must, to use the terminology introduced by Schaffer, outfit our
fundamental posits with axioms. But then, as Schaffer also points out
(2016: 587): "it is a bad question--albeit one that has
tempted excellent philosophers from Bradley through van Fraassen and
Lewis--to ask how a posit can do what its axioms say, for that
work is simply the business of the posit. End of story".



If, on the other hand, the problem is isolated to the case at hand, we
are owed an explanation of what makes this case so special. MacBride
complains that if the 'explanatory task' is that of
accounting for the capacity of compresence to relate, being told that
compresence has that capacity 'by nature', will not do.
Perhaps he is right about this. But, then, the explanatory task is
arguably not that one, but rather the task of accounting for the
possible existence of concrete objects (contingently) made up from
tropes. If *this* is the explanatory task, it is far from clear
why positing a special kind of (relational) trope that is 'by
nature' apt to perform its relating function, will not do as an
explanation.


## 4. Trope Applications



According to the trope proponent, if you accept the existence of
tropes, you have the means available to solve or to dissolve a number
of serious problems, not just in metaphysics but in philosophy
generally. In what follows, the most common trope-applications
proposed in the literature are very briefly introduced.


### 4.1 Tropes in Causation and Persistence



According to a majority of the trope theorists, an important reason
for thinking tropes exist is the role they play in causation. It is
after all not the whole stove that burns you, it is its temperature
that does the damage. And it is not any temperature, nor temperature
in general, which leaves a red mark. That mark is left by *the
particular temperature had by this particular stove now*. It makes
sense, therefore, to say that the mark is left by the stove's
temperature-*trope*, which means that tropes are very good
candidates for being the world's basic causal relata (Williams
1953*a*; Campbell 1990; Denkel 1996; Molnar 2003; Heil 2003; ;
Garcia-Encinas 2009; Ehring 2011).



That tropes *can* play a role in causation can hardly be
doubted. But can this role also provide the trope-proponent with a
reason to think that tropes exist? According to the theory's
critics, it cannot. The role tropes (can) play in causation does not
provide the trope proponent with any special reason to prefer an
ontology of tropes over alternative ontologies. More specifically, it
does not give her any special reason to prefer an ontology of tropes
over one of states of affairs or events. Just like tropes, state of
affairs and events are particular. Just like tropes, they are
localized. And, just like tropes, they are non-repeatable (although at
least the state of affairs contains a repeatable item--the
universal--as one of its constituents). Every reason for thinking
that tropes are the world's basic causal relata is therefore
also a reason to think that this role is played by states of affairs
and/or
 events.[32]



Ehring disagrees. To see why, he asks us to consider the following
simple scenario: a property-instance at *t*1 is
causally responsible for an instance *of the same property* at
*t*2. This is a case of causation which is also a
case of *property persistence*. But what does property
persistence involve? According to Ehring, property persistence is not
just a matter of something not changing its properties. For, even in
cases where nothing discernibly changes, the property instantiated at
*t*1 could nevertheless have been replaced by
another property of the same type during the period between
*t*1 and *t*2. To be able to
ontologically explain the scenario, therefore, we first need an
account of property persistence able to distinguish 'true'
property persistence from cases of 'non-salient property
change' or what may also be called property *type*
persistence. But, Ehring claims, this is something a theory according
to which property instances are states of affairs cannot do (this he
demonstrates with the help of a number of thought experiments, which
space does not allow me to reproduce here, but *cf.* Ehring
1997: 91ff). Therefore, causation gives us reason to think that tropes
exist.



Ehring is not the only one who regards the relationship between
(theories of) persistence and tropes as an intimate one. According to
McDaniel (2001)--who defends a theory (TOPO) according to which
ordinary physical objects are mereological fusions of monadic and
polyadic tropes--adopting (his version of) the trope view can be
used to argue for one particular theory of persistence:
 3-dimensionalism.[33]
 And according to Benovsky (2013), because (non-presentist)
endurantism is *incompatible* with the view that properties are
(immanent) universals, the endurantist *must* embrace trope
 theory.[34]



According to Garcia (2016), finally, what role tropes can play in
causation will depend on how we conceive of the nature of tropes. If
tropes are what he calls 'modifiers', they do not have the
character they confer, a fact that would seem to make them less
suitable as causal relata. Not so if tropes are of the module kind
(and so have the character they confer). But if tropes have the
character they confer, Garcia points out, we may always ask, e.g.: Is
it the couch or is it the couch's couch-shaped mass-trope that
causes the indentation in the carpet? Garcia thinks we have reason to
think they both do. The couch causes the indentation by courtesy, but
the mass trope would have sufficed to cause it even if it had existed
alone, unbundled with the couch's other tropes. But this
suggests that if tropes are of the module kind, we end up with a world
that is (objectionably) systematically causally overdetermined. The
role tropes play in causation may therefore be more problematic than
what it might initially seem (though *cf.* Giberman 2022 for an
objection to Garcia's argument).


### 4.2 Tropes and Issues in the Philosophy of Mind



Suppose Lisa burns herself on the hot stove. One of the causal
transactions that then follow can be described thus: Lisa removed her
hand from the stove *because* she felt pain. This is a
description which seems to pick out 'being in pain' as one
*causally relevant* property of the cause. That 'being in
pain' *is* a causally relevant property accords well with
our intuitions. However, to say it is leads to trouble. The reason for
this is that mental properties, like that of 'being in
pain', can be realized by physically very different systems.
Therefore, mental properties cannot be *identified* with
physical ones. On the other hand, we seem to live in a physically
closed and causally non-overdetermined universe. But this means that,
contrary to what we have supposed so far, Lisa did not remove her hand
because she felt pain. In general, it means that mental properties are
not causally relevant, however much they seem to be (*cf.* Kim
1989 for a famous expression of this problem).



If properties are tropes, some trope theorists have proposed, this
conclusion can be resisted (*cf.* Robb 1997; Martin and Heil
1999; Heil and Robb 2003; for a hybrid version *cf.* Nanay
2009; *cf.* also Gozzano and Orilia 2008). To see this, we need
first to disambiguate our notion of a property. This notion, it is
argued, is really *two* notions, namely:


* Property1 = that which imparts on an individual thing
its particular nature (property as *token*), and
* Property2 = that which makes distinct things the same
(property as *type*).



Once 'property' has been disambiguated, we can see how
mental properties can be causally relevant after all. For now, if
mental properties1 are tropes, they can be identified with
physical properties1. Mental properties2 can
still be distinguished from physical properties2, for
properties considered as *types* are--in line with the
standard view of tropes--identified with *similarity classes
of tropes*. When Lisa removes her hand from the stove because she
feels pain, therefore, she removes her hand *in virtue of*
something that is partly characterized by a trope which is such that
it belongs to a class of mentally similar tropes. This trope is
identical with a physical trope--it is *both* mental and
physical--because it *also* belongs to a (distinct)
similarity class of physically similar tropes. Therefore, mental
properties can be causally relevant in spite of the fact that the
mental is multiply realizable by the physical, and in spite of the
fact that we live in a physically closed and non-overdetermined
universe.



This suggestion has been criticized. According to Paul Noordhof (1998:
223) it fails because it does not respect the "bulge in the
carpet constraint". For now the question which was ambiguously
asked about properties, can be unambiguously asked about tropes: is it
in virtue of being mental or in virtue of being physical that the
trope is causally relevant for the effect (for a response,
*cf.* Robb 2001 and Ehring 2003)? And Sophie Gibb (2004) has
complained that the trope's simple and primitive nature makes it
unsuitable for membership in two such radically different classes as
that of the mentally and of the physically similar tropes,
respectively (for more reasons against the suggestion *cf.*
Macdonald and Macdonald 2006 and Zhang 2021).


### 4.3 Tropes and Perception



Another important reason for thinking that tropes exist, it has been
proposed, is the role tropes play in perception. That what we perceive
are the qualities of the things rather than the things themselves,
first, seems plausible (for various claims to this effect,
*cf.* Williams 1953*a*: 16; Campbell 1997 [1981]: 130;
Schaffer 2001: 247; *cf.* also Nanay 2012 and Almang
2013). And that the qualities we perceive are tropes rather than
universals or instantiations of universals (states of affairs) is,
according to Lowe, a matter that can be determined with reference to
our experience (*cf.* e.g., Skrzypulec 2021 for an argument to
the contrary). Lowe argues (1998: 205; *cf.* also, Lowe 2008;
Mulligan 1999):



> 
> 
> [W]hen I see the leaf *change* in colour--perhaps as it
> turned brown by a flame--I seem to see something *cease to
> exist* in the location of the leaf, namely, its greenness. But it
> could not be the *universal* greenness which ceases to exist,
> at least so long as other green things continue to exist. My opponent
> must say that really what I see is not something ceasing to exist, but
> merely the leaf's ceasing to instantiate greenness, or greenness
> ceasing to be 'wholly present' just here. I can only say
> that that suggestion strikes me as being quite false to the
> phenomenology of perception. The objects of perception seem, one and
> all, to be particulars--and, indeed, a causal theory of
> perception (which I myself favour) would appear to require this, since
> particulars alone seem capable of entering into causal relations.
> 
> 
> 



A similar view is put forth by Mulligan et al. They argue (1984:
306):



> 
> 
> [W]hoever wishes to reject moments [i.e., tropes] must of course give
> an account of those cases where we seem to see and hear them, cases we
> report using definite descriptions such as 'the smile that just
> appeared on Rupert's face'. This means that he must claim
> that in such circumstances we see not just *independent things per
> se*, but also *things as falling under certain concepts* or
> *as exemplifying certain universals*. On some
> accounts...it is even claimed that we see the universal in the
> thing. But the friend of moments finds this counterintuitive. When we
> see Rupert's smile, we see something just as spatio-temporal as
> Rupert himself, and not something as absurd as a spatio-temporal
> entity that somehow contains a concept or a universal.
> 
> 
> 



These are admittedly not very strong reasons for thinking that it is
tropes and not state of affairs that are the objects of perception.
For the view that our perception of a trope is not only distinct, but
also phenomenologically distinguishable, from our perception of a
state of affairs seems grounded in little more than its
proponent's introspective intuitions. States of affairs, just
like tropes, are particulars (*cf.* Armstrong 1997: 126 on the
"victory of particularity"). And to say, as Mulligan et
al. do, that the very idea of something spatiotemporal containing a
universal is absurd, clearly begs the question against the view they
are opposing.


### 4.4 Tropes and Semantics



That language furnishes the trope theorist with solid reasons for
thinking that there are tropes has been indicated by several trope
theorists and it has also been forcefully argued, especially by
Friederike Moltmann (2003, 2007, 2009, 2013*a* and
2013*b*; *cf.* also Mertz 1996: 3-6). Taking
(Mulligan et al. 1984) as her point of departure, Moltmann argues that
natural language contains several phenomena whose semantic treatment
is best spelled out in terms of an ontology that includes tropes.



*Nominalizations*, first, may seem to point in the opposite
direction. For, in the classical discussion, the nominalization of
predicates such as *is wise* into nouns fit to refer, has been
taken to count in favor of universal realism. A sub-class of
nominalizations--such as *John's wisdom*--can,
however, be taken to speak in favor of the existence of tropes. This
is a kind of nominalization which, as Moltmann puts it,
"introduce 'new' objects, but only partially
characterize them" (2007: 363). That these nominalizations refer
to tropes rather than to states of affairs, she argues, can be seen
once we consider the vast range of adjectival modifiers they allow
for, modifiers only tropes and not states of affairs can be the
recipients of (2009: 62-63; *cf.* also her 2003).



*Bare demonstratives*, next, especially as they occur in
so-called identificational sentences, provide another reason for
thinking that tropes exist (Moltmann 2013*a*). In combination
with the preposition *like*--as in *Turquoise looks
like that*--they straightforwardly refer to tropes. But even
in cases where they do not refer to tropes, tropes nevertheless
contribute to the semantics of sentences in which they figure. In
particular, tropes contribute to the meaning of sentences like
*This is Mary* or *That is a beautiful woman*. These are
no ordinary identity statements. What makes them stand out, Moltmann
points out, is the exceptional neutrality of the demonstratives in
subject position. These sentences are best understood in such a way
that the bare demonstratives that figure in them do not refer to
individuals (like Mary), but rather to perceptual features (which
Moltmann thinks of as tropes) in the situation at hand.
Identificational sentences, then, involve the identification of a
bearer of a trope *via* the denotation (if not reference) of a
(perceptual) trope.



*Comparatives*--like *John is happier than
Mary*--finally, are according to the received view such that
they refer to abstract objects that form a total ordering (so-called
degrees). According to Moltmann, a better way to understand these
sorts of sentences is with reference to tropes. *John is happier
than Mary* should hence be understood as *John's
happiness exceeds Mary's happiness*. Moltmann thinks this
way of understanding comparatives is preferable to the standard view,
because tropes are easier to live with than "abstract, rarely
explicit entities such as degrees or sets of degrees" (Moltmann
2009: 64).



Whether nominalizations, bare demonstratives and/or comparatives
succeed in providing the trope theorist with strong reasons to think
tropes exist will, among other things, depend on whether or not they
really do manage to distinguish between tropes and states of affairs.
Moltmann thinks they do but, again, this depends on how one
understands the nature of the items in question. It will also depend
on if and how one thinks goings on at the linguistic level can tell us
anything much about what there is at the ontological level. According
to quite a few trope theorists (*cf.* esp. Heil 2003), we
should avoid arguing from the way we conceptualize reality to
conclusions about the nature of reality itself. Depending on
one's take on the relationship between language and world,
therefore, semantics might turn out to have precious little to say
about the existence (or not) of tropes.


### 4.5 Tropes in Science



Discussions of what use can be made of tropes in science can be found
scattered in the literature. Examples include Rom Harre's
(2009) discussion of the role tropes play (and don't play) in
chemistry, and Bence Nanay's (2010) attempt to use tropes to
improve on Ernst Mayr's population thinking in biology. Most
discussions have however been focused on the relationship between
tropes and physics (Kuhlmann et al. 2002). Most influential in this
respect is Campbell's field-theory of tropes (defended in his
1990: Ch. 6; *cf.* also Von Wachter 2000) and Simons'
'nuclear' theory of tropes and the scientific use he
tentatively makes of it (Simons 1994; *cf.* also Morganti 2009
and Wayne 2008).



According to Campbell, the world is constituted by a rather limited
number of field tropes which, according to our (current) best science,
ought to be identified with the fields of gravitation,
electromagnetism, and the weak and strong nuclear forces (plus a
spacetime field). Standardly, these forces are understood as exerted
by bodies that are not themselves fields. Not so on Campbell's
view. Instead, matter is thought of as spread out and as present in
various strengths across a region without any sharp boundaries to its
location. What parts of the mass field we choose to focus on will be
to a certain degree arbitrary. A zone in which several fields all
sharply increase their intensity will likely be taken as one single
entity or particle. But given the overall framework, individuals of
this kind are to be viewed as "well-founded appearances"
(Campbell 1990: 151).



Campbell's views have been criticized by e.g., Christina
Schneider (2006). According to Schneider, the field ontology proposed
by Campbell (and by Von Wachter) fails, because the notion of a field
with which they seem to be working, is not mathematically
 rigorous.[35]
 And Matteo Morganti who, just like Campbell, wants to identify tropes
with entities described by quantum physics, finds several problems
with the identifications actually made by Campbell. He proposes
instead that we follow Simons and identify the basic constituents of
reality with the fundamental particles, understood as bundles of
tropes (Morganti 2009). If we take the basic properties described by
the Standard Model as fundamental tropes, is the idea, then the
constitution of particles out of more elementary constituents can be
readily reconstructed (possibly by using the sheaf-theoretical
framework proposed by Mormann 1995, or the algebraic framework
suggested by Fuhrmann 1991).


### 4.6 Tropes and Issues in Moral Philosophy



Relatively little has so far been written on the topic of tropes in
relation to issues in moral philosophy and value theory. Two things
have however been argued. First, that tropes (and not, as is more
commonly supposed, objects or persons or states of affairs) are the
bearers of final value. Second, that moral non-naturalists (who hold
that moral facts are fundamentally autonomous from natural facts) must
regard properties as tropes to be able to account for the
supervenience of the moral on the natural.



That tropes are the bearers of (final) value is a view held by several
trope theorists. To say that what we value are the *particular
properties* of things and persons is *prima facie*
intuitive (Williams 1953*a*: 16). And since concrete
particulars--but not tropes--are sometimes the subjects of
simultaneous yet conflicting evaluations, tropes seem
*especially* suited for the job as (final) value-bearers
(Campbell 1997 [1981]: 130-131). That tropes are the
*only* bearers of final value has however been questioned.
According to Rabinowicz and Ronnow-Rasmussen (2003), this is
because different pro-attitudes are fitting with respect to different
kinds of valuable objects. However, according to Olson (2003), even if
this is so, it does not show that tropes are not the only bearers of
final value. For that conclusion only follows if we assume that, to
what we direct our evaluative attitude is indicative of where value is
localized. But final value should be understood strictly as the value
something has *for its own sake*, which means that if e.g., a
person is valuable because of her courage, then she is not valuable
for her own sake but is valuable, rather, for the sake of one of her
properties (i.e., her tropes). But this means that, although the
evaluative attitude may well be directed at a person or a thing, the
person or thing is nevertheless valued because of, or for the sake of,
the tropes which characterize it.



Non-naturalists, next, are often charged with not being able to
explain what appears to be a necessary dependence of moral facts on
natural facts. Normally this dependence is explained in terms of
supervenience, but in order for such an account to be compatible with
the basic tenets of moral non-naturalism, it has been argued, this
supervenience must, in turn, be explainable in purely non-naturalistic
terms (for an overview of this debate, *cf.* Ridge 2018).
According to Shafer-Landau (2003) (as interpreted by Ridge 2007) this
problem is solved if moral and physical properties in the sense of
kinds, are distinguished from moral and physical properties in the
sense of tokens, or tropes. For then we can say, in analogy with what
has been suggested in the debate on the causal relevance of mental
properties, that although (necessarily) every moral trope is
constituted by some concatenation of natural tropes, it does not
follow that every moral type is identical to a natural type. This
suggestion is criticized in Ridge (2007).