#1: Is there such a thing as universals?
Universals can be defined as those properties that can be instantiated by different objects in different places. Something can be categorized as a Universal only if it fully instantiates into multiple different objects that have the ability to be present at different places at the same point in time and hence are repetitive and recurrent. They are non-physical properties that can be attributed to objects that have a physical presence and occupy space. In this paper, I will argue that there is such a thing as Universals, even though the existence of the same varies and is dependent on various factors such as the nature of the property/idea itself.
In Plato's Theory of Forms, Plato makes the argument that the Non-physical forms are a representative of the most accurate reality. Plato looks at these "Forms" as the ideal representation of an idea, a concept or an object. Universals, on the other hand, cannot be looked at as the ideal representation from a general point of view. They are just general attributes or properties that provide specificity to a certain object. For example, the redness of an apple and a cherry or the roundness of an orange and an apple.
In my opinion, Universals can be appropriately represented by their categorization as Platonic Objects. Existing as a Platonic element means to somewhat exist independently, this existence can be timeless, for example like a relation or just a number that exists irrespective of time. Such an element is usually considered to be non-physical and according to a Conceptionalist point of view existing only in a thinking mind. For instance, consider Pythagoras theorem, that fact that it was initially put forward by Pythagoras in the 500 BC does not change the fact that the relation has existed for all eternity and was only discovered and acknowledged by Pythagoras in the later stages. But the same thing cannot be said about the game of Chess. Chess originated in India sometime in the 7th Century and stating the same about chess would lead to an uncertainty regarding the whole concept of abstract objects adding to it a certain uniqueness and creating a dependency on the mind. After all, chess was an invention, a concept or idea that formerly did not exist. Hence, we can conclude that Chess is not an object or idea that exists independent of mind. In these two cases, we can attribute the property of existing independent of mind as an ambiguous property of certain objects which can correctly be stated to be Universals.
Conceptualism is another interesting way to look at the whole concept of Universals. It was embraced by some of the known philosophers like Rene Descartes, John Locke etc. It brings emphasis to the idea that explains the universality of particulars as conceptualized frameworks situated within the thinking mind [1]. While the Platonic view of abstract objects points to the outright existence of abstract objects, Conceptualism agrees with the idea that these objects do exist but only in a thinking mind.
Considering the whole numeric system, numbers have been used to keep count, make predictions since the emergence of human beings into this world. Numbers here just play an important role in describing a certain object, without numbers we would be losing an essential part of the description of this object. A nominalist may argue that one might come across two similar items but one will never come across "two" itself stating that it is just a part of a certain sentence. The ideal argument in terms of conceptualism would be that the fact that "two" exists as a descriptive term should be enough to demonstrate that they do exist in the mind. The argument simply would not conclude here because according to a Platonist, the similarity of the idea and the description of the object itself is not unique to the mind of each thinking being, it is the same and hence universal to all. The Platonist can also add to the same argument that these properties are an essential part of science which helps corroborate the existence of numbers or the numeric system through its usage in real time calculations and predictions.
In order to account for these arguments, we must come to an understanding of what it really means to exist. Russel based his definition of existence as to something that could be experienced based on one's sensory experiences. Willard Van Orman Quine initially started as a Nominalist, using physics as a method for determining what exists or doesn't exist. He believed that physics was the most accurate way of determining this. Eventually, he realized that couldn't account for physics without the Set theory and so came to a point where he granted existence to mathematics and the numeric system and in the process becoming a Platonist.
If one focuses on the views of all three – the Nominalists, the Conceptualists and the Platonists, there is no instance where we will be able to arrive at a clear-cut answer. All three of these ideas have some truth to it for one will never bump into the number "two" anywhere and so one can rather conclude that "two" is not a physical entity but rather something that we think about. The Platonists argue about the unique source of the description regarding an object. They state that since we have all arrived at the same final conclusion regarding that object we can firmly assert that this description does not exist in the mind but rather independent of it. But eventually we can state that Universals definitely exist as a non-physical rather descriptive part of any object because without these properties it would be impossible to imagine the object as the same.