Are There Abstract Objects? Essay Examples

In Philosophy, especially Metaphysics, the existence (or non-existence) of Abstract Objects has been an important point of debate. The problem is of epic proportions since one tends to use the term ‘Abstract’ in virtually every field ranging from Mathematics to the Social Sciences. Most persons would concur that things such as numerals, proposals, aspects of objects, probabilities, sets or even plays such as “Hamlet” could be abstract objects. On the other hand, the same group of persons would likely slot things such as musical instruments or sofas and related objects as tangible (real or concrete). Therefore, this essay will start by defining abstract objects and then proceed to chiefly examine two contradictory views and will attempt to find out the most practical and efficient of the two views, thus successfully answering the central question of this essay.
This essay will start by defining Abstract Objects. Of the 3 chief methods that David Lewis uses to define the concept of Abstract, this essay would consider the Method of Abstraction over the Method of Conflation. (Lewis 83) This method matches the distinction between the abstract and the tangible to others, for instance, between persons and groups of persons or specific and universal et.al. The Method of Abstraction classifies abstract entities as abstractions from the tangible or the real entities. Abstract entities are those where if one provides an imperfect description of the original tangible entity one would be able to understand complete description of the resulting abstract notion. (Lewis 85) This concept clearly shows that humans identify abstract objects through a thought process that enables them to focus on a singular characteristic of tangible entities. For instance, if one looks at the number “1” one sees can abstract the property of a straight line. “Straightness” on a standalone basis is an inaccurate portrayal of the numeral “1” but it becomes a full portrayal of the idea of straightness. However, in order for one to further consider and analyze abstract entities one must take an additional step of assuming that abstract thoughts are, in fact, the rational depiction of objects that exist independently of our mind. Such entities are called abstract objects.
This essay proceeds to examine the view of Chris Swoyer. In his work on the subject, Swoyer describes the critical features of the standard examples of abstract objects from a philosophical perspective. He describes them as “atemporal, non-spatial and acausal.” (Swoyer 4). Basically, Swoyer implies that abstract objects are ontologically independent from humans since these objects are also independent of human language and thought. This means that they are in common usage somewhere, independent of words and notions. Such objects exist, neither in time nor in space; and do not exist even in a ‘space-time’ frame. (4) Also, these objects can neither change nor affect change since they are causally static and ineffective. Similarly, unlike tangible objects, one can neither see these abstract entities, nor feel or taste them; yet they exist in this world in a latent form.
However, there are some experts who do feel that abstract objects exist, including Swoyer who argues in this paper about the role of abstract entities solving philosophical problems. One can slot these people as realists, while those who do not believe in the existence of abstract objects could be slotted as nominalists. The main argument put forth by the realists is the descriptive efficacy of abstract objects. By acknowledging their existence, supposedly, one could elucidate both of the following points, a) One can give a semantic certainty to statements that fall in their purview, and b) the central role that these abstract things (or concepts) play in either rationalizing or simplifying our well-known theories within the natural sciences. If one considers numerals, as an example, realists believe that numbers (sets, properties, equations et.al), although abstract form the basis of the natural sciences since these sciences would be meaningless and most fundamental concepts would cease to exist without these abstract concepts. Therefore, the indispensability argument summarily assumes that – Abstract entities are indispensable to theories of the natural science and the field of Mathematics is committed to the existence of abstract entities. Thus, it follows that Abstract entities exist, without a doubt.
Swoyer agrees to a large extent with parts of the reasoning, but points out critical problems in the realist view as depicted by the nominalist. The first objection would be that the abstract concepts are as applicable to Philosophy as they are to other natural sciences. He points out the possible problems with both the realist as well as the nominalist approach. As per believers in the deflationary (nominal) approach, such abstract concepts could be applied to the natural sciences, but for a variety of reasons they fail in their scope when one tries to use them to elucidate philosophical thoughts. However, Swoyer does mention that a good semantic theory based on properties can also be used to explain philosophical concepts and thoughts. (29) Further, the second objection that nominalists claim is that Philosophy cannot be slotted into the category of natural sciences. However, Swoyer disagrees since Philosophy too has notions of agreement, disagreement and argument. (30) Therefore, as per Swoyer, Philosophy does function like science and, as a result, the abstract objects and properties would be applicable to Philosophy as well. The best instance of this would be the field of logic within Philosophy that uses numbers and properties to elucidate and explain problems.
Swoyer proceeds to highlight the benefits of abstract entities by explaining that these entities have great explanatory power. Similarly, Epistemology is the only barrier within Philosophy since Epistemological problems are severe. The absence of Epistemology would actually ensure that the abstract concepts would be successful. Thus, in essence, Swoyer seems to be a realist who supports the existence of abstract objects.
At this point, it would be useful to examine the nominalist viewpoint on the subject. A person with this viewpoint would, in essence, question the existence of abstract objects and possible even deny the same or, if they do exist, reduce these objects to have a minimal impact on fundamental topics. At this point if one examines the work of Quine, something appears highly inconsistent about the conjecture that refuting the reality of an abstract object, by some means, presupposes that object in the same sense that asserts that entity’s reality does. Quine accurately assesses logical possibilities (though not in those exact words) as meaningful, but does not make the error of “stealing” the concept of existence by making it a predicate. (Quine 31) Thus, Quine took the middle path by accepting certain abstract objects such as sets or classes, yet rejected universals. In this way, they were neither totally nominalists nor were they complete realists. One could possibly argue that most of our sciences are at this stage – a mixed approach where neither nominalism nor complete realism dominates.
However, the essay will proceed to examine the nominalist viewpoint. In his paper, Cian Dorr explores the nominalist viewpoint in which his thesis itself starts out by denying the very existence of numbers, properties, relations or sets as abstract concepts. He classifies these broad statements as conceptually nominal (nominalism) in nature. (Dorr 4) With this concept in mind, Dorr introduces the idea of paraphrasing as “a sentence that, when taken in the fundamental sense, says how things would have to be for the original sentence to be true in the superficial sense.” (9) Since nominalism is a concept that is metaphysically necessary if true, the realist thesis automatically gets rejected. The most important reason for the nominalist viewpoint to succeed in this case is the fact that the burden of proof (proving that relations, sets, numbers, properties as abstract concept exist) lies on the realist. In this case, Dorr also agrees with Swoyer (realist viewpoint) that, on a fundamental basis, abstract objects exist only if there is a good explanation of something that could not be explained any other way. (12) However, Dorr argues to the contrary, to Swoyer’s assertion – that the descriptive benefits that abstract objects purportedly bring may only be imaginary and, therefore, void.
In order to do this Dorr examines if abstract objects have a crucial role to play in scientific theories. Basically, he examines the indispensability argument that this essay examined previously. Although, as explained by Swoyer, the case looks strong prima facie, Dorr manages to prove that the indispensability argument and the role of abstract objects in scientific theories is not as a critical as one would like to think. In order to support this stand, one can also examine the work of Zoltan Szabo on Nominalism. In this scholarly work, Szabo not only rubbishes the need for abstract objects in science, but also proves the same. For instance, he builds up a complete account of Newton’s laws of gravity, completely based only on space-time coordinates and related points as well as regions. (Szabo 36) One could critically say that such a system would also require the usage of abstract objects such as numbers; nevertheless, the system operates well on concrete entities, which, in itself, is an achievement for the proponents of nominalism. From an epistemological perspective, if scientific theories can tell us about the unobservable, one important thing it has shown is that matter is not all identical, but comes in many diverse kinds. If one compares two different types of matter that are alike in respect of shape, size and motion – one still discovers that they cannot be precise replicas of each other. In short, as far as the applicability of abstract objects to scientific theories are concerned, Dorr maintains that it is possible and shifts the burden of proof to the realists who consider abstract objects to have an important role in the natural sciences.
If one draws a parallel to our discussion on realism, it would be apt to examine if abstract objects have any role in philosophy. Rudolf Carnap was one of the earliest philosophers who wrote on this topic in the late 1940s, supported the nominalist approach as a more logical approach when applied to philosophical concepts. (11) However, Carnap also cautioned nominalists about the potential problems of the nominal approach since efficiency was a prime concern and the use of only concrete concepts without the use of abstract could be inefficient. If one recalls Swoyer’s assertion on the topic, a nominalist has three choices: 1. To accept the analyses and conclude that the statements under consideration are fundamentally false. 2. To suggest possible substitute analyses, or 3. The last option would be to assert that the pertinent ideas are archaic and lack analyzable content. (Dorr 22)
However, the point of efficiency does come up in the nominal analyses of topics, especially in subjects such as Physics that are not easily prone to reductionism. Dorr illustrates the schemata with the example of the Helium atom. (24) However, if one reviews this scheme, it strikes the reader as being superficial and without enough material to prove anything concrete, although the author has mostly used concrete concepts to build this scheme. The reason for this problem is the lack of basic physical predicates that could be easily applied by the user in such schemes. Due to the lack of these predicates, the scheme comes off as a superficial and an inconclusive attempt. The author discusses the physical strategy and the structural strategy in an attempt to make things easier for the user of the scheme.
The physical strategy involves looking to science to provide us a set of basic physical predicates that would help to simplify second order predicates of the general and structural type. (26) The main issue with this strategy is its inability to contain those perceptions that there could possibly be alien properties that have no bearing with any of the real or actual properties. Thus, the direct effect of implementing this strategy would be the assumption that the world is entirely homogenous from a physical perspective, which is inherently wrong. Thus, the physical strategy would fail if a nominalist were to apply it to explain theories – both scientific as well as philosophical.
On the other hand, the structural strategy places the nominalist in a somewhat better stead as compared to the physical one, although it has its own share of problems. This approach primarily considers that the definition of a real object must be in conjunction with that of its duplicate. (28) This concept is also called Resemblance Nominalism. However, this concept has its own share of shortcomings. Firstly, the arbitrary nature of the choice of paradigms is a worrisome issue. Secondly, the idea of intrinsicness may not necessarily be universal in nature. Thirdly, any practical analysis of this nature will require that at least some of those objects exist, that is, if there are indeed any electrons. Of these, the third problem leads the nominalist to give up on specific structural analysis and, instead, rely solely on general structural analyses. Thus, the approach has a problem with modal intuition. The author feels that it is partly Hume’s intuition that leads to this problem that for the nominalist thought to succeed, it becomes essential to give up the Hume intuition altogether. (34)
As a result of the analysis, in line with the notion of ‘brute necessities,’ Dorr initially recommends rejecting the nominalist approach since it is incompatible with the most relevant theories of physical sciences. However, upon further analysis he arrives at his conclusion that “we have not managed to find a stable argument against nominalism based on the use of abstract objects in explaining necessities.” (38) He, therefore, says that there are no brute necessities and, instead, postulates that the argument favors nominalism in a complete sense. Lastly, he recommends that with respect to Natural Sciences, it is better that one considers Natural Class Nominalism to Resemblance Nominalism within the concept of structural strategy. Thus, he says that Nominalism provides two different research paths for metaphysical theorizing, while Realism provides none. (Dorr 40)
The essay now arrives at the central question – Do abstract objects exist? Having reviewed the work of both Swoyer and Dorr, one understands that Swoyer is one on an easier ground. The presence of abstract objects reduces the problems associated with nominalism, although nominalism may have more options for metaphysical theorizing. While nominalism could be applied with some effort in the field of natural sciences, the fields of applied sciences as well as newer fields such as computing and genetics would require abstract entities to function efficiently. In many such cases, the usage of concrete and tangible concepts would only seek to increase the problem and would impede the process of arriving at a precise solution. There would also be no way of testing one’s findings since most scientists have been trained to test their concrete findings using numbers, the coordinate system or any such abstract object. If one sees these problems, it would probably be wiser to utilize the path taken by Quine. Most scientific theories take Quine’s route – they neither complete reject nor fully accept the existence of abstract objects.
However, for the purpose of this essay, one can conclude that abstract objects not only exist, but (at least at present) are used in daily life. Modern fields of work such as computing have made abstract objects almost indispensable (the indispensability argument is at play in most fields which utilize sets, properties and numbers). Similarly, the emergence of such systems has made it difficult for nominalists to make a comeback. One can say with some level of confidence that the nominalist approach would be a good approach to theorize, but like any grounded theory it is difficult to implement. Thus, the realist approach and the existence of abstract objects must be accepted and if that is not possible, one can at least agree with Quine and take the middle route.

Works Cited

Dorr, C. There Are No Abstract Objects. Eds. T. Sider, & D. W. John Hawthorne, Contemporary debates in Metaphysics. (2008) Singapore: Blackwell Publishing Ltd. Print.
Lewis, David. On the Plurality of Worlds. Eds. Liu, M., & Liu, X. S. Chomsky and Knowledge of Language. (1986). Oxford, England: Blackwell. Print.
Quine, Willard. “On What There Is.” The Review of Metaphysics. 2.5 (1948): 21 – 38.Web. 23 Apr 2015.
Rudolf, Carnap. Empiricism, Semantics, and Ontology. Revue Internationale de Philosophie Journal. 4 (1956): 20 – 40. Web. 23 Apr 2015.
Swoyer, Chris. Abstract Entities. Eds T. Sider, J. Hawthorne, & D. W. Zimmermann, Contemporary debates in Metaphysics. (2008). Singapore: Blackwell Publishing Ltd. Print.
Szabo, Zoltan. Nominalism. Eds. M. J. Loux, & D. W. Zimmerman. The Oxford Handbook of Metaphysics. Oxford: Oxford University Press. (2003). 11 – 45. Print.