UNIVERSALIZING TROPES (DRAFT)

 This ROUGH DRAFT elaborates on a suggestion presented in the book How Do Proper Names Really Work? (De Gruyter 2023), p. 44.

 

 

 

UNIVERSALIZING TROPES: A SIMPLE WAY

 

I intend to propose what seems to me the right way of building universals by means of tropes. I will examine Donald Williams’s standard method (2018: 29) and then consider some of its shortcomings. In the sequence, I present what seems to be the most credible alternative solution.

 

I

 

According to Williams, universals are nothing but sets, classes, or even groups of tropes precisely similar. Consider the universal of red. For a Platonist, it should be the idea of red or “the-red-in-itself.” For a class nominalist, it could be the class of red objects. For Williams, however, it is nothing but the set of all the tropes that are precisely similar to each other as tropes of red. A sentence such as “Red is a color” could be analyzed by him as: “The set of precisely similar tropes of red is contained in the set of precisely similar tropes of color.”

   The standard objection against William’s is that if we need to identify a set of tropes as a set of precisely similar tropes, then we have a problem concerning the ontological status of precise similarity. Assuming, as Williams does, that precise similarities are tropes, we are allowed to ask what the ontological status of a precise similarity is. Assuming William’s view that our world must be completely constituted by its tropes, a precise similarity is a trope. Precise similarities of the tropes belonging to the set must be precisely similar to the other. But if so, we have generated a second-order set of precise similarity tropes. This would not be too much if two second-order tropes of similarity would not need to be precisely similar. This leads to the admission of a third-order set of similarity tropes, and so on indefinitely. Regression is inevitable.

   The question is if this regression is virtuous or vicious. To evaluate whether the regression is vicious here, we can be satisfied with the view that a virtuous regression is a regression that can be stopped as one wishes, while a vicious regression is not (Maurin 2007). Consider, for instance, Plato’s doctrine of ideas. The explanation of the doctrine contains ideas of ideas. One could even appeal to ideas of the ideas of ideas by considering his theory further. But no step requires any consideration of ideas in a still higher level... The same goes for the concept of precisely similar tropes in William’s definition of universals. There is a regression, but it is virtuous, and we do not need to get bored with it.

   However, William’s solution has more worrisome drawbacks. What is the ontological status of the set of tropes? How can we grasp a universal as a set of tropes? Suppose that the set is infinite. In this case, it seems we could not grasp the universal. And for medical reasons, we couldn’t grasp any universal as a great set of tropes. 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?   

   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 classes or sets built from tropes? The second is epistemological: how can we grasp universals meant as classes built from tropes? At first view, the really interesting question is the first one, the only truly metaphysical. Since the problems above seem to arise from epistemological questions, we do not need to worry too much about them. A closer look, however, shows that this is a misleading way to see the problem because it is not true that the metaphysical problem comes first, but rather the other way around.

   Doubts arise when we ask ourselves about the origins of the problem of universals. They remounted to Plato and Aristotle. The problem arises from the question: “How can we apply the same predicate to many different things? Plato’s answer was that “we are in the habit of posit a simple idea or form in the case of the various multiplicities to which we give the same name” (1961: 596 a-b). That is, we appeal to an idea or form that would be “copied” by many different things, or from which those many different things would “participate.” A nominalist answer could be that we apply a general term to a class of objects so that the universal would be that reference class (Wolterstorff 1970: 173 ss.). We see here that the important problem posed by Plato was not metaphysical but epistemological, namely, how can we apply the same general term to many different things? How is predication possible? How can we achieve this most fundamental kind of synthesis? The metaphysical solution arose from an epistemological question concerning our cognitive capacities. Hence, we will have nothing to lose if we can answer the epistemological question without further metaphysical embroilment.

   Assuming the priority of the cognitive problem, the question regarding the universalization of tropes is: 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 class, set, or group of tropes. I suggest we get a much better answer when we remember how bishop Berkeley solved the problem of universals – the solution considered by Hume “one of the greatest and the most valuable discoveries in the republic of letters” (1978: I, I, VII), as he tried to implement on it. According to Berkeley, all the universe, except the spirits (like we and God), is totally constituted, not by tropes, but by ideas. Ideas, he considered, can be general but not abstract, that is, not platonic entities. Now, how can ideas be general without having to be abstract? Well, because we associate a general term with one or more similar particular ideas, using them as a pattern to identify external things given to us insofar as these things (that for him are literally ideas existing in the mind of God (1975b: 224)) 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: Introd. 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., associated in our minds with the word ‘triangle’ and by experiencing the object look for the similarities. For Berkeley and Hume, the problem of universals is solved by employing a simple operation of the mind without requiring any further metaphysical commitment. It is true that this empiricist solution is generally viewed as defective because of the imagistic concept of the idea held by those empiricist philosophers… However, this problem does not need to worry us at all since the bulk of my proposal will be to adopt Berkeley’s schema, replacing the concept of idea with the concept of trope. My countenance is that since tropes are not necessarily imagistic and have the most varied structure, they will be able to perform the expected role much better than purely sensory images.

   To recast a procedure similar to that of Berkeley-Hume using tropes instead of ideas, what we, as a rule, need is that the epistemic agent had previous contact or information with a particular trope and its name and, afterward, can identify a given trope that is precisely similar to the trope or tropes he or she was originally acquainted with. Having this in mind, the solution to the problem of predication is the following: we can apply the same concept word for many referents of names insofar as we make ourselves able to distinguish any given trope as precisely similar to a trope model or those trope models we remember to have experienced.

   To highlight the essentials, we can imagine a simple language game. A group of persons lacking color memories is placed within an exposition of paintings to find in which paintings a certain tonality of color can be found. 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 paintings. Now, this is an exercise of finding the one over many in which the memory of the model isn’t necessary. Now, the operation will generate a set. For instance, the set is formed by paintings 1, 5, and 8. This is the set of paintings that have the trope of burnt Siena. The question is: if there is something that could be called a universal here, what is it? Two answers are at hand. The first is that the universal is the set generated in the room's domain, namely, the set formed by the objects 1, 5, and 8. This would be William’s type of answer. The second answer is that the universal is the trope model of burnt Sienna in the tablet or any other patch of color that, in the established domain, is precisely similar to the model prescribed in the tablet. This is the answer that follows Berkeley’s model.

   As we noted, the second type of answer is prior because we begin with the question of how we can apply the same general term to many different things. We answer it by a cognitive operation through which we could identify any trope precisely similar to the trope chosen as a model. We can, however, search for something we could call the ‘ontological universal,’ namely, the set {1, 5, 8}. This set 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 in which the person applies the same general term to many different things.

   Considering the priority of the cognitive element, I suggest that in the above case, the universal must be identified with the operation itself, namely, the universalization operation through which one discovers patches similar to the model.

   Going beyond the language game, we can now consider how a model-trope can produce the universal of burnt Siena.

 

The universal for the trope of burnt Siena (Df.) = a (randomly chosen) model trope of color called ‘burnt Siena’ or any other trope that can be identified as precisely similar to the model trope.

 

Understood this way, a universal can always, in principle, generate a set of tropes, which is often impossible to determine in a real situation. No one knows the innumerable patches of burnt Siena that could be found worldwide. And no one cares since a metaphysical commitment becomes idle after the real problem is satisfactorily solved.

   We can now generalize our definition of universal to any trope:

 

The universal for a trope T (Df.) = a (randomly chosen) model trope of color called Tm or any other trope that can be identified as precisely similar to that model trope.

 

This view has an immense advantage of simplicity. Though it generates infinite regress, it is a virtuous one. We do not need to verify whether the precise similarities between models and examples are precisely similar. Moreover, the simplicity of my example (burnt Siena) should not deceive. Tropes can be of any complexity. They can also be rules, satisfying Kant’s condition that to learn a concept is to acquire an ability governed by rules (Allison 2004: 79-80, 208-9), which is said to have historically overthrown the simplistic imagism of the empiricist philosophers

   Needless to say, unlike the language game presented above, we usually appeal to memory. We hold in our memory the model trope, which we once learned to attach with the conceptual word, in the most primitive cases by perceiving one or more tropes in interpersonal circumstances of teaching the names of things. 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 first concept word was conventionally associated with a model.

   Why have Williams and many others after him followed the same lead of replacing the universal with a set or a class of tropes? The answer seems to be the misleading emphasis on the metaphysical commitment, forgetting that it has only arisen as a sequel of some answer to the relevant epistemic problem. The universal was traditionally seen by Platonists as the reference of nominalized predicates, together with the nominalist tradition of using logic extensions as the reference of predicates. Thus, instead of a class of objects sharing a property, Williams had the original idea of using a class of tropes that are precisely similar. Interesting as it was, this choice in the end betrays what Wittgenstein called those persisting “images” that insistently trouble philosophers because they forget to consider what they were looking for in the first place.

 

 

Literature:

Allison, H. E. (2004): Kant’s Transcendental Idealism: An Interpretation and Defense. New Haven: Yale University Press.

Berkeley, George (1973a): The Principles of Human Knowledge. In Philosophical Works Including the Works on Vision ed. by M. R, Ayers (London: Everyman).

Berkeley, George (1973b): Three Dialogues Between Hylas and Philonous. In Philosophical Works Including the Works on Vision ed. by M. R, Ayers (London: Everyman).

Hume, David (1978): A Treatise of Human Nature. Edited by L. A. Selby-Bigge, Oxford: Clarendon Press.  

Maurin, Anna-Sofia (2007): “Infinite Regress: Virtue or Vice?”, in: Hommage à Wlodek. Philosophical Papers Dedicated to Wlodek Rabinowicz. Ed. T. Rønnow-Rasmussen, B. Petersson, J. Josefsson & D. Egonsson.

Plato (1961): The Republic. In The Collected Dialogues of Plato. Edited by Edith Hamilton and Huntington Cairns. Princeton: Princeton University Press.

Williams, D. C. (2018): The Elements and Patterns of Being: Essays in Metaphysics, edited by R. J. Fisher (Oxford: Oxford University Press).

Wolterstorff, Nicholas (1970): On Universals: An Essay in Ontology. Chicago: Chicago University Press).