The Opposing Arguments of Rene Descartes and John Locke: the Transition to a more Mathematical View of Objects in Reality

Imagine sitting in a classroom typing notes when a brick is thrown at a student. Everyone gasps and jumps out of the way of the incoming object, flabbergasted that a professor would throw something so dangerous at a student. After the fact, one student realizes that it is not a traditional brick made of clay or concrete; rather, it is an object that appears to be a brick but is made of Styrofoam. This Styrofoam brick did not have the potential to hurt the students, but they still jumped out of the way.

In order to understand why this occurred, it becomes necessary to examine the ways that objects in reality can be understood. As time has progressed, so has the approach for understanding objects in reality. Using the Aristotelian and Galilean perspectives as a foundation, René Descartes and John Locke were able to develop their own positions for understanding objects in reality, like the Styrofoam brick. In order to understand the definition of an object in reality, Aristotle would use its defining causes.

Aristotle’s four main causes are ways to describe an object using its characteristics. These causes include the material, the efficient, the formal, and the teleological. An object’s material cause is what it is made out of. Its efficient cause is what or who brings the object into existence. The formal cause is the organizing principle or, for natural objects, the internal substance that guides an object. Finally, the teleological cause is the object’s goal or purpose. These causes and his additional categories of substance, quantity, quality, relatives, somewhere, sometime, being in a position, having, acting, and being acted upon could be used to understand objects in reality (Studtmann). However, if all of the important categories of an object were abstracted away, the only thing left was the quantity, which he believed was irrelevant.

This shows that Aristotle was not all that interested in the mathematical aspects of an object. Aristotle’s lack of interest in the mathematics is sharply contrasted by the viewpoint that Galileo Galilei (1564 – 1642) shares in “The Assayer.” He states: Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark labyrinth. (237-238) Whereas Aristotle viewed quantity and mathematics as the least important aspect of an object, Galileo believed that it was impossible to define the world without using mathematics. He believed that many of the mathematical aspects of an object were the objects primary qualities. Examples of these primary qualities include: shape, position, motion, contact, and numbers.

These primary qualities exist in the external world and are a part of the object that one is trying to define. The aspects that reside in the conscious of an individual are considered the secondary qualities of an object. Examples of these are: tastes, colors, and odors. Since these secondary qualities are different according to different individuals, Galileo believed that there is no such thing as the quality itself but only experiences of the objects. For example, an object did not have an odor because each person had the potential to experience this odor differently. Therefore, the object had odor experiences, but not the quality of a specific odor. This made Galileo’s definition of an object in reality different according to the senses of different individuals. René Descartes (1596—1650) was taught the scholasticism of Aristotle, but he was skeptical about its underpinnings. He believed that the only parts of reality that could be true were those things that could be accepted beyond the shadow of a doubt. Therefore, he starts his theory by eliminating anything that is doubtful.

The only thing he knew for sure was that he existed. He was able to conclude this by bringing res cogitans, or thinking things, into existence through the fact that he was doubting, and therefore thinking. He realized that anything that thinks must also exist; since he is a thinking thing, he must exist. Also, since he could not prove that he was not asleep and dreaming, he concluded that reality might only exist in his mind. This put res extensa, or the external world, into suspension. He also puts math and God into suspension. God is placed into suspension by recognizing the possibility of an evil genius. However, he is able to bring God back by looking into his thoughts and ideas. He examines his emotions, judgments, and ideas. Emotions and judgements are indicative of the person who holds them, while ideas seem to come from an external cause. Then, he ponders where the idea of God came from.

Since God cannot be sensed or thought of, Descartes concluded that the cause of God is innate. God must also exist because nothing can be created from nothing, so God must exist in order for the world to have been created. In order to prove that God is not an evil genius, he examines the reason for deception, which he concludes to be a lack of something. Since God is perfect and therefore lacks nothing, he cannot be a deceiver. This also brings math out of suspension. If God is not deceiving, then math must be reality, or God would not have placed it in reality. Bringing God out of suspension also brings res extensa out of suspension. Descartes refers to this as the corporeal substance that everything else must be made out of (Smith). This causes his definition of an object to be different from Aristotle’s in that it is more mathematical and has a single universal substance out of which objects in reality are made. This is in direct opposition to Aristotle’s formal cause, which can be different for different objects. John Locke (1632 – 1704) built on the ideas of Galileo concerning the primary and secondary qualities of an object. Like Galileo, Locke’s primary qualities were both mind-independent and mathematical.

However, he added more subcategories, as he believed that Galileo did not include all the categories that were necessary to define an object. Locke’s primary qualities are truly indicative of the object, and include: extension, position, figure, motion, solidity, and number. This is different from Descartes, as he would have thought of the corporeal substance for the primary quality. For Locke, a secondary quality is defined as the ability of an object to stimulate the senses and produce an idea or sensation in one’s mind. These qualities are indicative of the individual. These qualities include: color, taste, smell, and sound. Unlike Galileo, Locke did not think that the secondary qualities were merely experiences. He believed that, although different individuals may experience secondary qualities in different ways, the quality itself still existed. Since Descartes doubted the senses, he may not have agreed with Locke in this regard.

However, Descartes probably would have related more to Galileo’s idea of sense experiences. Aristotle, Galileo, Descartes, and Locke would have all explained the Styrofoam brick in different ways. In terms of the brick not being made of what one normally expects a brick to be made of, Aristotle would have highlighted the importance of determining the teleological cause or purpose of the brick. He would have determined that it was meant to be a toy, and therefore, would have defined it as such. Galileo would have defined the primary and secondary qualities once he realized it was made out of Styrofoam. He would have taken a geometric approach to his definitions. Descartes would have said that God cannot deceive and, therefore, it was him who had deceived himself. Locke would have defined the brick using his primary and secondary qualities focusing on his sense perceptions of the brick.

Each thinker’s ideas about the more mathematical qualities of the brick also would have been different. In terms of the position of the brick, Aristotle would have defined it in terms of prepositions like in front of, behind, and below. Galileo, Descartes, and Locke would have taken a more mathematical approach to define the position of the brick. For Galileo, the position would be about the geometrical shapes between the brick and other objects. Descartes would have used his Cartesian coordinate system to assign a position to the brick and an equation to describe the brick’s motion as it was being thrown at the student. Locke would have used a combination of Galileo’s and Descartes’ tactics and would have also found the motion of the object important; however, he may or may not have described it as his predecessors did. The transformation from an Aristotelian view of the brick to a mathematical view of the brick signifies the transition into a scientific and empirical approach to defining reality and its objects. 

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