UNIVERSALIZING TROPES: A SIMPLE WAY

 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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