The goal of science is to understand the physical nature of the universe we inhabit. Science therefore requires the senses, because reason alone is insufficient and potentially deceptive. For the senses bind us to the real physical universe, whereas reason is unconstrained: Through reason, one may postulate on the physical as well as the nonphysical, the real as well as the non-real, with no way to independently discern between them.
The senses, though, present their own problem: Although through the senses we may obtain knowledge about the real physical universe, the information the senses provides describes only individuals, not universals. It would be futile to attempt to understand the universe by studying each individual independently, since such an extensive investigation would take an infinite amount of time. Science, then, is not primarily concerned with understanding individuals, which can only paint a limited picture of reality. For a comprehensive picture, science needs to understand universals. After all, how much more meaningful it is to comment on the properties of every single piece of metal there ever was, and that there ever will be, rather than to only know absolutely a single shard.
And so, the issue at hand is clear: Knowledge of universals is necessary to produce a meaningful description of the universe, yet our bind to the senses restricts us to observing individuals since universals cannot be observed with the senses. How, then, is science to proceed?
The viability of science is grounded on two foundational principles. First, universal laws, which predict and define every natural phenomenon, exist. These laws are consistent through space and time; for instance, gravity will cause a ball to roll down a hill tomorrow in Europe the same way it would 1000 years from now on Europa. Second, while every individual has characteristics (let us call them features) which make it distinct from every other individual, there also exist commonalities between individuals (let us call them forms). These commonalities are what allow us to observe individuals with the senses and still extend our observations to describe universals. In other words, they are what allow us to produce a meaningful description of the real physical universe.
In this essay, I will demonstrate that universals are abstract simplifications in the sense that they do not exist in the real physical world, but they are also categorically real in the sense that they have objective features. I will also demonstrate the second foundational principle of science: because universals are real, the scientific approach provides a viable means of coming to understand the real physical universe. Note that for the purposes of this essay, I will take the principle of universal laws as a given. I will also take as a given that individuals have features, and that the information the senses provide is reliable and allows us to observe features as they objectively are.
Every physical individual, every object, say, is distinct from every other object in the universe. My coffee cup is white, with a plastic lid and a “Starbucks” label. Your coffee cup is brown, with a paper lid, and a “Second Cup” label. Let us imagine a number of individual coffee cups on a continuum, illustrated in Figure 3.1. We see that some coffee cups have many of the same features, so we may imagine them as being closer together on the continuum. Other coffee cups have fewer features in common. Still, every individual is distinct from every other individual upon examination of its complete collection of features.
Figure 3.1: Three individual coffee cups shown on a continuum, with a subset of their features given. Note that individuals with more features in common are closer together on the continuum.
Every individual has innumerable features, and some individuals have features in common. Forms are defined by the features common to a group of individuals. For example, let us imagine another collection of individuals, shown in Figure 3.2. There are six individuals on the continuum given. Each individual is distinct, because no individual has the exact same complete set of features as any other individual. However, there are clearly some individuals which have more features in common than others. The three individuals on the left of the continuum all say “meow”, have long tails, and weigh less than the three individuals on the right of the continuum, which all say “woof” and have short tails. These common features define a form for each of the two subgroups: The individuals on the left have a form we call “cat”, and the individuals on the right have a form we call “dog”.
Figure 3.2: Six individuals shown on a continuum, with a subset of their features given. Note that individuals with more features in common are closer together on the continuum. In this example, two forms on the continuum are beginning to emerge.
Now, suppose that there is another individual, not shown on the continuum given in Figure 3.2, which has the following features: a long tail, a mass of 2.1kg, says “meow”, etc. This individual clearly has the form “cat”, because it has features that match the features of the form “cat”. This definition of forms raises an important question: Are forms real, or are they merely convenient simplifications, or representations of something real? In order to answer this question, we must first define “real”. I define something as “real” if it has features which are objective. Forms are real because they have the same features (features of the form) no matter who is evaluating them, or even whether they are being evaluated at all. This will be shown in more detail in section 3.3 of this essay.
The features that are common to every individual of a form may be characterized as features of the form. Individuals, though, still have other features which aren’t included in the form, which may be called features of the individual. What distinguishes features of the individual from features of the form? The individual on the far left of Figure 3.1 and the individual on the far left of Figure 3.2 both have the feature “brown”. Since they have a common feature, are these individuals of the same form?
This question is where the continuum of individuals becomes significant. In the examples given in this essay, only a small selection of features are shown for each individual, but in reality, every individual has innumerable features. The individual on the far left of Figure 3.2 is not only brown, 3.6kg, with a long tail, and says “meow”; it also has a particular DNA sequence, arrangement of organs inside its body, and temperament. As more and more features are taken into consideration, the distribution of individuals along the continuum becomes more and more defined. Individuals settle into their place like a graph being fitted to a data set as more data points are included. Finally, given all of the features, the arrangement of individuals along the continuum will be a clumped distribution: individuals with the most features in common will form a subgroup, with some separation from other related subgroups of individuals, and with furthest separation from subgroups that have fewest features in common. Due to its very nature having many features in common, each subgroup on the continuum defines a form. The features that are common to each individual in the subgroup are features of the form, and the features that are not common to each individual in the subgroup are features of the individual.
Let us refer again to our previous example. If the whole continuum of individuals were displayed before us, we would see that the individual on the far left of Figure 3.1 has a form which we call “coffee cup”. We would see that the feature “brown” is not common to every coffee cup, so “brown” is a feature of the individual, rather than a feature of the form. Similarly, the individual on the far left of Figure 3.2 has the form “cat”, for which “brown” is also a feature of the individual. These individuals do not have common features of the form, so they do not have the same form.
Can forms be described more definitively than this? Is there a “benchmark” number of features necessary to define a form? One consequence of this definition of forms is that an individual can have several forms simultaneously. On the continuum given in Figure 3.2, “cats” are individuals which say “meow”. On a different continuum, which includes cats, dogs, and coffee cups, cats and dogs might both be defined to have the form “animal”. The subgroups “cat” and “dog” will be much closer together than “cat” and “coffee cup”, since cats and dogs have more features in common. There is another, larger subgroup containing both cats and dogs, such that features of the form “animal” are features that are common to both cats and dogs. It is easy to see how one might get lost in the semantics of forms, but by keeping in mind the fractal-like hierarchal nature of the continuum of individuals, the confusion is resolved. (See Figure 3.3 for a pictorial representation of this concept.) There is, then, no “benchmark” that can be used to define forms. An object can have the narrow form “Starbucks coffee cup”, up to “cup”, up to “object”, and each of these forms is equally real.
Figure 3.3: A pictorial representation of the continuum of individuals: Forms as subgroups and the fractal-like hierarchy of forms.
A more interesting question arises when we examine the boundaries of forms, since, as I have demonstrated, forms are merely subgroups on a continuum of individuals. Consider, for instance, Figure 3.4, in which five individuals are given. We see that the two individuals on the far left both have prongs at the end of a handle (among numerous other common features, not shown), so they have the same form: “fork”. The two individuals on the far right have a shallow bowl at the end of a handle, so they have the form “spoon”. But what is the form of the central individual, which has both prongs and a shallow bowl at the end of a handle? Some might suggest that the central individual has the form of both “fork” and “spoon”. Others might say that the central individual has its own form: “spork”.
Figure 3.4: Five individuals shown on a continuum, with a subset of their features given.
In fact, both are reasonable answers. Describing outliers as being of multiple forms at once or of their own form is primarily a question of semantics: By “zooming out” of the fractal-like continuum, outliers may be engulfed in a form (for instance, outliers between “cat” and “dog” would be engulfed in the form “animal”); equivalently, “zooming in” on the continuum would consequent in the production of outliers. Ultimately, by zooming in far enough, the whole continuum is reduced to individual points. In this way, the blurry edges of the form are a consequence of the fact that forms are subgroups on a continuum. However, the blurry edges of the form in no way detract from the reality of the form as a whole. Even though there may be outliers on the continuum of individuals, not clearly belonging to one particular subgroup over another, the subgroups themselves are still there. No one would deny that the individuals on the far left are both forks, and the individuals on the far right are both spoons, even though the form of the outlier – the central individual – is unclear.
Suppose, now, that we are presented with an individual that is not a physical individual, such as a two-dimensional circle or the number five. How are such individuals distributed on the continuum, do they have forms, and are they or their forms real?
When we considered physical individuals – namely objects – we defined forms as the commonalities between individuals, since every individual object is necessarily distinct. However, abstract individuals need not be distinct, since they do not exist in the physical world. For example, two circles with the same radius are entirely identical. So, every circle of the same radius is located at the exact same point on the continuum of individuals. With this picture in mind, we may apply our former definition of using subgroups to define forms. The difference is that now, instead of having a subgroup of individuals distributed over a range, we have a subgroup of individuals all located at the exact same point on the continuum.
Defining subgroups as forms has some of the same consequences for abstract individuals as it did for objects. As with a physical individual, an abstract individual can have several forms simultaneously. For instance, “circles” are also “shapes”, if we “zoom out” on our continuum far enough to include “squares” and “triangles”. This is because circles have more features in common with squares than they do with the number five. Notice that by “zooming out” we are including a range of forms and individuals, similar to the ranges we saw for objects. The critical difference, however, between objects and abstract individuals is that the edges of the abstract individual’s form are are not blurry. By “zooming in” on a subgroup of objects we produce outliers. However, “zooming in” on a subgroup of abstract individuals will not produce outliers, since every abstract individual is located at the same point. In a sense, then, abstract individuals are forms, in that they have no features of the individual: every individual on the point (in the “subgroup”) shares all of the same features, so those features are features of the form.
The next question to consider is whether abstract individuals (and equivalently, their forms) are real. Recall my definition of real: something is real if it has objective features. Given this definition, abstract individuals and forms are real. A circle has the feature of a radius, and this is an objective feature. The difference between objects and abstract individuals is that objects have physical features, and abstract individuals do not. This means that abstract individuals cannot be observed with the senses, which can only detect physical features.
In summary, forms are subgroups of individuals on the total continuum of individuals. Some individuals have many forms, in a hierarchal nature, and some outlying individuals have unclear forms. Despite this, it would be too simplistic to say that forms are merely semantical simplifications, for there are subsets of individuals on the continuum which objectively have features in common, and no construction or logical abstraction is necessary for these subsets of individuals to exist.
Universals are individuals which only possess features of the form; that is, they have no features of the individual. Universals are real because they have features of the form, which I have already demonstrated to be objective. In the case of abstract individuals, universals are not constructed, because individuals which possess only the features of the abstract form already exist: they are the abstract individuals themselves. But in the case of physical individuals, universals are constructions – they do not exist – in the sense that no such individual exists: every individual in the physical world has both features of the form and features of the individual. So there is an abstract jump between the physical (individuals) and the nonphysical (universals). This is why universals cannot be observed with the senses, and equivalently why science requires individuals, which is the problem I put forward in the preface to this essay, and which I will refer to in the next section.
In section three of this essay, I demonstrated that forms are real, and therefore universals are real (more than convenient simplifications) because they have objective features (features of the form). Despite their realness, universals do not exist in the physical world. A jump is therefore required make statements about universals based on observations of physical individuals. How does science make this jump?
Recall that universals are abstract individuals that have only features of the form. So in order for science to describe universals, science by definition must only explain features of the form. This is a critical point because recall that every individual of a form possesses all of the features of a form (in addition to their features of the individual). So, any individual of a form may be studied to characterize a universal of that form, as long as the features that are being studied are features of the form. For example, consider a collection of pieces of copper. Some pieces are small, some are large; some have smooth edges, others ragged; but all have a particular atomic configuration, conductivity, and brownish-orange colour. The size and smoothness of the pieces are features of the individual, and the atomic configuration, conductivity, and colour are features of the form. Science can therefore make statements about, say, the conductivity of the universal “copper” (for instance, copper’s conductivity varies in such-and-such a way with temperature); but science cannot make statements about the raggedness of copper edges (for instance, science cannot say that “copper” has smooth edges).
The remaining question is this: how does science distinguish between features of the form and features of the individual? I.e. how do scientists know which features they can study? One of the beautiful aspects of science is that it is self-correcting, due to its bind to observations of physical individuals. This means that a scientist can propose a model to describe a universal based on one set of observations, and that model can be tested (and contested) based on another set of observations. For example, consider again our pieces of copper. If I come across a piece of copper that has the same atomic configuration, colour, etc. as the other pieces but its conductivity is inconsistent with the other pieces, this is a problem. If this were the case, it would mean that conductivity is not a feature of the form, so the conductivity of the universal “copper” could not be described.
Based on current scientific knowledge, conductivity is a feature of the form “copper” (at least, at the macroscale), so the above might be a confusing example. Consider now a collection of pieces of copper that all measure 2cmx2cm, and this is all the copper that a scientist has ever observed. Based on this collection, the scientist might conclude that size is a feature of the form “copper”, and that the universal “copper” measures 2cmx2cm. However, they would only need to observe a single piece of copper that does not measure 2cmx2cm to conclude that size is not a feature of the form, and correct their models.
Universals are real because they describe real subgroups of individuals that objectively have many features in common. In a sense, universals can be thought of as perfect individuals, in that all of their features are features of the form. Even though they don’t exist in the physical world, science is able to describe universals because individuals that have all the features of universals do exist, and can be observed with the senses. This, combined with the principle of universal laws, is what makes science possible, enabling an understanding of the universe that is at once both precise and profound.
© 2021-2024 Megan Cowie