Draft of a paper to be published
UNIVERSALIZING TROPES: A SIMPLE WAY
Summary:
Donald Williams suggested that under the assumption
of a trope ontology, universals can be understood as sets of tropes. My aim in
this article is to show that there is an easier and more convincing way to
construct universals using tropes. It consists of appropriating Berkeley’s
solution to the problem of universals by the trope theorist. Instead of
similarities between ideas associated with conceptual words and the ideas given
by perception, as Berkeley’s solution demanded, what must be required is simply
the ability to identify precise similarities between tropes
used as models and tropes given by experience. This alone will explain the conceptual
word's general applicability, dropping a more controversial demand for
extensional universals.
Keywords:
Trope theory,
ontology, universals, metaphysics
I begin with a summary of Donald Williams’
solution to the problem of universals using tropes, then present some main
objections to his solution. Afterward, by contrast, I present the solution to
the problem of universals as defended by the empiricist philosophers Berkeley
and Hume. I suggest replacing the word ‘idea’ with ‘trope’ in these solutions.
This move opens the way to a renewed solution to the problem of universals
using tropes. Furthermore, I suggest that this solution can be refined beyond
the narrow limits of the imagistic view of empiricist philosophers in ways that
aren’t also open to the difficulties we have found in Williams’ strategy.
1
As Donald Williams wrote in his
characterization of the universal of color component (named ‘Harlac’) of a
lollipop (called by him Heraplen):
…the set or sum or
tropes precisely similar to a trope, say Harlac again, may be supposed to be,
or at least to correspond formally to, the abstract universal or ‘essence’
which it may be said to exemplify a definite shade of redness. (The tropes
approximately similar to the given one provide a less definite universal. (1953a:
9)
For him, universals are sets or sums of
tropes that are precisely similar to a given trope. Consider, for
instance, the universal red. For a Platonist, it should be the idea or form of
red or, as Plato also would have said, “that very thing that red is,” “the
redness,” or, as I will use here, “the-red-in-itself.” (See Kenny 2004: 50).
For a class nominalist, it could be, to put it in its most accessible way, the
class of red objects (Armstrong 1989: 8-14). However, following Williams’ view,
it could be paraphrased as nothing but the set of all tropes that are precisely
similar to each other as tropes of red. So, one could interpret “Red is a
color” as “the set of precisely similar tropes of red is contained in the set
of precisely similar tropes of color.”
2
A standard objection
against William’s view is that if we need to identify a set of tropes by their
precise similarity, we get a problem concerning the ontological status of
precise similarity (Campbell 1990: 32-42). The problem can be stated as
follows: Assuming that precise similarities are also tropes, we are led to ask
what the ontological status of a precise similarity is. Accepting William’s
stance that all ontologically relevant elements in our world must be tropes, it
seems that a precise similarity must be a trope. However, if so, precise
similarities of the tropes belonging to the set of precisely similar tropes
must be precisely similar. But in this case, we have generated a second-order
set of precise similarity tropes. Since these second-order tropes must also be
precisely similar, we need to admit a third-order set of tropes of precise
similarity, and so on indefinitely. The conclusion is that a kind of “pyramidal”
regression of similarities is inevitable.
The
question is whether such a regression is virtuous or vicious. A regression is
virtuous if it can be stopped as one wishes. Otherwise, it is not. (Cf. Maurin
2007). Consider, for instance, Plato’s doctrine of ideas. The explanation of
the doctrine contains ideas of ideas. But he later criticized his theory, which
means that he had, in his criticism, inevitably appealed to ideas of ideas of
ideas... This points to a regression, but it is clear that none of these steps demands
the consideration of ideas at a higher level. Thus, it is a virtuous regress.
One could argue that the same goes for the concept of precisely similar tropes
in William’s definition of universals. If there is regression, it is virtuous.
Hence, we don’t need to get bored with it.
However,
William’s solution has more worrisome drawbacks. What is the ontological status
of the universal as a set of tropes? Is the set a trope? How can we grasp the
universal as a set of tropes? For medical reasons, we cannot grasp any huge set
of tropes as the universal. Suppose that the set is infinite. In this case, it
would be logically impossible for us to grasp the universal.
Moreover,
a set can grow or shrink in size. But can a universal grow or shrink? An
alternative would be to treat a tropical universal as an open set. But isn’t an
open set a construction existing only in our minds, while things are more
completely determined in the outside nature? And what would be its minimal
size?
3
At this point, an
advocate of William’s view could suggest that we must distinguish two
questions. The first is ontological: are there universals meant as sets or
classes built from tropes? The second is epistemological: how can we grasp
universals meant as classes built from tropes? The really exciting question,
she would argue, is the first one since it is the only genuinely metaphysical
one. As the problems above seem to arise from epistemological issues, we do not
need to worry too much about them.
Nonetheless,
a closer look into this vein of reasoning would show that this would be a big
mistake. It is not true that the metaphysical problem comes first, but rather
the other way around. In my view, disregarding this point lurks the main
trouble of Williams’s approach. Next, I will explain why.
We can justify the priority of the epistemological question by going back in
time to the origins of the problem of universals. They remounted to Plato and
Aristotle. The problem arises from the issue of how we can apply the same
predicate to many different things. Plato well-known answer is: “We are in the
habit of positing a simple idea or form in the case of the various
multiplicities to which we give the same name” (1961: 596a-b). That is, he
appealed to an idea or form as a universal that
would be “copied” by many different things or from which those many things
would “participate” in order to explain how we are able to apply the same
general term to many different things. Aristotle, from his side, coined the
term ‘universal’ (catholou), aiming
to say “that which is by its nature predicated of a number of things” (1984a: 17a 38). According to a widespread
interpretation, the universal would be, for him, the non-transcendent unifying form
of those many diferent things. Considering this, it is clear that the critical
problem initially posed was not metaphysical but epistemological and that the
appeal to universals is subsequent. So, the fundamental question was always the
following:
How can we apply the same general term to
many different things?
How is predication cognitively possible?
How can we achieve this most fundamental kind
of synthesis?
Nothing would be lost
if we could answer these questions without appealing to universals. Indeed,
with his doctrine of ideas, Plato offered a metaphysical solution to a
linguistically formulated epistemological problem that came first. In other
words, Plato’s metaphysical solution that leads to the problem of universals
arose from an epistemological question concerning our cognitive capacities. The
same can be said of Aristotle’s solution since, according to a plausible
interpretation, he appealed to his forms to warrant that we can say the
same of many (1984b 1034a 5-8). Hence, we will have nothing
to lose if we can answer the epistemological question without further
metaphysical embroilment.
4
Assuming the priority
of the epistemological problem, the question of universals regarding tropes can
be stated as follows: how can we apply the same conceptual word to many
different things, assuming that the conceptual word designates a trope? The
answer to this question does not need to include the hypothesis that we are
acquainted with a set or class of tropes. I suggest we get a much better answer
when we remember how bishop Berkeley solved the problem of universals without
appealing to metaphysical entities— a solution considered by Hume “one of the
greatest and the most valuable discoveries in the republic of letters,” as he
tried to improve on it (1978: I, I, VII). According to Berkeley, all of the
universe, except the spirits (like we and God) is made of ideas.
Ideas, he considered, can be general but not abstract, intending to say that
they cannot be Platonic entities. Now, how can ideas be general without having
to be abstract? Well, because we associate a general term with a particular
idea or group of similar ideas, using it as a pattern to identify external
things given to us insofar as these things are sufficiently similar to the
pattern. As Berkeley writes:
But
it seems that a word becomes general by being made the sign, not of an abstract
general idea but of several particular ideas, any one of which it indifferently
suggests to the mind. (1975a: Intr. Sec. 11)
This means that to
identify a given object as a triangle, we only need to retrieve some particular
ideas (meant as images) of triangles like the isosceles, the scalenus, the
obtuse, etc., which we associate in our minds with the word ‘triangle,’ and by
perceptually experiencing the object, we look for the similarities. Consider,
for example, the concept of ‘chair’: we can have stocked in our minds the
images of a table chair, an armchair, an easy chair, a rocking chair, a
wheelchair, a beach chair, an electric chair, and a throne, associating
them with the word ‘chair.’ By being presented with a new chair, we only need
to retrieve a similar image and see that it matches sufficiently. The same
would work with a concept like ‘dog.’ At first, a person would associate the
word ‘dog’ with a bunch of appearances of dogs, say, a Labrador, a German
Shepard dog, a poodle, a bulldog, and a Pekingese. With these images in mind,
it will not be difficult to identify a new dog, such as a golden retriever, as
a dog insofar as one finds similar to the image of a Labrador.
We will
later consider the problems with this view. Important for now is to understand
that Berkeley’s solution to the problem of universals is an epistemological
solution in which all that is needed is a mental operation, which can be
called a universalizing operation, which does not require any further
metaphysical commitment with universals.
5
The gist of my
approach to the problem of universals consists of replacing the term ‘idea’
with the term ‘trope’ in a fundamentally Berkeleyan strategy. To recast a similar
procedure using tropes instead of ideas, what we need is that the epistemic
agent had previous contact or information about a particular trope and its name
and, afterward, is able to identify any given trope that is precisely similar
to the trope or tropes to which he was initially acquainted with. Having this
in mind, the solution to the problem of predication of the same of many is the
following: we can apply the same conceptual word to many different referents insofar
as we make ourselves able to distinguish any given tropical referent precisely
similar to a trope model or to those trope-models we
remember to have experienced in association with the name. We really don’t need
universals. All we need is to have the ability to perform a universalizing
operation.
Consider, for instance,
a very specific trope like the color of burnt Siena. Let’s say that Karen took
a painting course and gained familiarity with this shade of color and
its name. After that, she visited Italy, where she identified many buildings
painted the same color. Indeed, this will suffice for us to agree that she
has the general concept of the Siena earth color. But what can we mean by
this? Certainly not that she access the immense set of precisely similar tropes
of Sienese earth, even if such a set exists. That was the path taken by
Williams. All we need to mean is that she possesses the memory of the burnt
Siena earth model associated with the general term ‘burnt Sienna’, a memory
resulting from her multiple contacts with this color and with its name when she
took his painting course and that she is now able to identify precisely similar
tropes when they are presented to her.
Memory
has here a complementary role. We can imagine a language game that clarifies
the essentials to show this. A group of people lacking color memories is placed
within an exhibition of paintings to find which paintings a specific tonality
of color belongs to. To make this possible, each person receives a tablet
with a patch with a shade of color, its name, and a sheet of paper to mark the
number of the painting where the same shade of color is found. For instance,
suppose that the color is burnt Siena and that the person has marked paintings
1, 5, and 8 under 12. Now, this is an exercise of finding the one under the
many in which the memory of the model isn’t necessary. Furthermore, the
operation will generate a set, which is the set of tropes of burnt Siena,
namely {T1, T5, T8}. Following Williams, this set of burnt Siena tropes could
be seen as a universal, though limited to a particular domain. In contrast to
him, our adaptation of Berkeley’s suggestion says that all we need to consider
is the ability to universalize, namely, to identify the tropes. Moreover,
suppose we insist on speaking of universals. In that case, we can define the universal
here as the trope model of burnt Sienna in the tablet or any other patch
of color that, in the domain, is precisely similar to the model prescribed on
the tablet. It is true that my suggestion also generates the set {T1, T5, T8}. However,
this set is not part of our explanation of how the same predicate applies to
many different referents. We do not need to explain why we can say the same of
many.
As noted,
the epistemic approach is the only necessary one insofar as it can explain how
we can apply the same general term to many diverse things without further aid.
We answer it by a cognitive operation in which we can identify any trope
precisely similar to the trope chosen as a model. We can, however, look for the
extensional set {p1, p5, p8}, which can be generated by comparing the model and
the patches. Its establishment was the finality of the game, and it can be
abstracted from the operations the person applies the same general term to many
different things. But the formation of this set is irrelevant to our original
problem, which was limited to the predication of the same from many since the
set {p1, p5, p8} takes no part of our explanation of how the same predicate
applies to many different objects. It is not a universal since it has no
role in explaining predication. To summarize, instead of a universal, all we
must have is the operation of universalization through which we discover
patches similar to the model.
Going
beyond our language game, we can now consider how a model trope can be used in
the ability to operate universalization regarding the color of burnt Siena:
The ability
to perform the universalization operation regarding the trope of burned Siena (Df.)
= the ability to identify any given model trope of burnt Siena as precisely
similar to a (randomly chosen) model trope of burnt Siena.
Understood this way, the
operation can always, in principle, generate a set of tropes, which is often
impossible to determine in an actual situation. No one knows the innumerable
patches of burned Siena that could be found worldwide. And no one cares since the
real problem is already solved before such metaphysical commitment occurs.
The
explanation of how we can apply the same conceptual word to many different
things lies in our universalizing ability, defined as follows:
The ability to perform
the universalizing operation for a trope T (Df.) = the ability to identify
any given trope Tm as precisely
similar to a (randomly chosen) model trope Tm.
This view has the
immense advantage of simplicity. It does not generate infinite regression since
we do not need to verify whether the precise similarities between models and
examples are precisely similar.
Needless
to say, we usually appeal to memory, unlike the language game presented above.
We hold in our memory the model trope, which we once learned to attach with the
conceptual word, in the most basic cases by perceiving one or more tropes in the
interpersonal circumstances of teaching the names of things. But memory has no
mystery. It is like a copy of something by something that we learned to trust
because it usually works well enough to be trusted. Moreover, we do not need to
appeal to any fixed model, and we can change our memorized model arbitrarily as
long as it remains precisely the same as some model trope initially associated
with the conceptual word by convention.
6
By all its merits, the
empiricist solution to the problem of universals is generally viewed as flawed
because of the imagistic conception of the ideas of empiricist philosophers
like Berkeley and Hume. After all, many conceptual words are not linked with
any image, and many are only vaguely associated with images. In his discussion
of schematism, Kant has replaced the imagistic empiricist view with a more
sophisticated one, in which concepts are abilities governed by rules, though
conceding that these abilities usually require producing images as criteria. As he wrote:
The concept
of a dog signifies a rule according to which my imagination can trace,
delineate, or draw a general outline, figure, or shape of a four-footed animal
without being restricted to any single and particular shape supplied by
experience. (1970: A 141).
Far from refuting our
explanation of generalization as a capacity to identify precisely similar
tropes, replacing the empiricist explanation employing imagistic ideas with
tropes shows here a further advantage. Tropes do not need to be imagistic. A
trope can be defined as a spatiotemporally localizable property of any
complexity and degree of vagueness. Consequently, we can identify concepts as
the ability to follow rules with tropes. After all, we can see the ability to
follow a rule as a disposition, namely, the disposition of, under
adequate circumstances, to follow the conceptual rule, enabling us to identify
a new trope precisely the same as some pattern. Such a disposition can be
a trope since it is also inevitably spatially and temporally localizable in the
mind-brain of the ruler’s user, even if not in the most precise way. The
conclusion is that the general applicability of a conceptual word must demand
an ability to follow a rule in the sense of a disposition to follow it, which
is nothing but a trope. We can call it a conceptual trope.
Interestingly,
a conceptual trope can be associated with imagistic criteria. So, a triangle is
defined as a three-sided polygon consisting of three edges and three vertices.
This definition expresses the rule for the construction of triangles. We can
acquire the ability to follow this rule as a disposition to derive individual
images of triangles like an equilateral triangle, an isosceles triangle, a
scalenus triangle, a right triangle… Having this ability, when we have the
sensory experience of a geometric figure like a triangle, we can match the
triangle we are experiencing with the image of a triangle generated by our
ability to follow the rule prescribed by its definition. All these phenomena
are spatiotemporally localizable tropical phenomena. Now, we can conceive our
ability to follow a tropical rule as the dispositional ability to perform a
universalizing operation insofar as we can apply this rule to any given
triangle. In this way, we can conceive of applying one conceptual word to
many individuals without appealing to Platonic ideas or sets of tropes as
universals.
7
I can provide further
examples to clarify things. Consider the concept of dance, exemplified by Hume
as a “mode.” A dance can be defined as a set of rhythmic body movements typically accompanied
by music. We associate this definition with a set of different moving images,
such as classical ballet, valse, tango, samba, and rock-and-roll. The definition is a dispositional trope, and
the other moving images are tropes that can match the experience in a way that
remembers Kant’s schemata. By these means, we produce tropical arrangements
that are precisely similar in their essences. Our ability to identify tropical dance
arrangements as precisely similar to the tropical arrangements we have derived
from our definition is, again, the application of our capacity for
universalization.
There are also cases
of count-names, concepts with objects and not properties in their extensions
that go beyond Williams’ definition of universals as sets of precisely similar
tropes. Consider the concept of a dog, a count noun, and of a natural species. A
dog is defined as a domesticated wolf descendant, artificially selected in
many different breeds. To this definition, some identifying characteristics of
a dog as a domestic quadruped that barks, that is akin to humans, etc., must be
added. Moreover, a collection of different images associated with these animals
in their evolutionary origin is of great importance for identifying dogs since the
image of a chihuahua differs significantly from that of a saint Bernardo.
However, the definition of a dog can be explained by combinations of
localizable properties extended in time (the process of domestication…), and
the further criteria for the identification of dogs can also be seen as space-temporally
localizable properties (barking figures of different breads…). This means that to
identify a dog, we need to have the universalizing operation for the tropical
object dog, which is the capacity to identify any given set of images given as
a dog as, in essence, precisely similar to images derived from the tropical
object model of a dog.
Consider now the concept of a chair, an artifact, and a count
name. A chair is an artifact that can be defined as a non-vehicular seat with a
backrest designed for use by only one person at a time (it usually has four
legs, sometimes has armrests, is sometimes upholstered, etc.) (Costa 2018: 214).
Now, this definition expresses a rule for the identification of a chair. With
the help of it, we can identify many different chairs: table chairs, armchairs,
easy chairs, rocking chairs, wheelchairs, beach chairs, electric chairs,
thrones… We identify them as chairs because the images we form of these chairs
can match images we might produce employing the definition. These images are
criteria that can be or cannot be satisfied. In the case of a seat, for
example, it isn’t a chair because it lacks the backrest. The image of a sit
cannot match any criterial image derived from the definition of a chair, leaving
the criteria unsatisfied. The same is true of seats in cars and airplanes.
They cannot be called chairs because they are vehicular, and their images
within vehicles oppose any criterial image derived from the definition. A sofa
isn’t a chair because it is made to be seated by two or more persons. It cannot
satisfy the criterial image of being seated by only one person at a time. Last
but not least, we cannot imagine a chair that the winds have carved into the
seaside rocks to be a chair in a proper sense since the wind is no
craftsman. All these images and our (dispositional) ability to employ the
rule are tropes.
I
wonder if this explanation of concepts through tropes as space-temporally
localizable entities can be extended to all conceptual words. However, I cannot
find any prior hindrance to this view. If we insist on using the term
‘universal,’ we can identify it with our capacity for universalization,
understood as the dispositional trope of an ability to perform the
universalizing operation regarding a conceptual rule.
8
Why have Williams and
many others after he found the appeal to universals as sets or classes of
tropes necessary? The answer is a misleading emphasis originated from an
unnecessary metaphysical commitment to universals, forgetting that this
commitment has only arisen as a sequel of the relevant epistemic problem.
Traditionally, Platonists viewed the universal as the reference of nominalized
predicates, while nominalists viewed them as extensions. Following this lead,
Williams had the original idea of identifying the universal with a class of
tropes that are precisely similar. However, in the end, his choice has betrayed
one of those insistent “images” that often trouble philosophers because they
forget to consider what they should be looking for in the first place.
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