Nicholas Denyer: Sun and Line: The Role of the Good

Nicholas Denyer’s article, Sun and Line: The Role of the Good, looks at Plato’s theory of forms through teleological considerations. He starts off his argument by examining the good, as it relates to the form of artifacts: “the Good has the privileged position of being what accounts for the existence and intelligibility of Forms” (Denyer 284). Ideal artifacts can be understood through teleological examinations. When looking at the features of an artifact, it is important to find the most important features, ideal features. These are the perfect feature that lead to the Goodness of the artifact: “the Good accounts in this way for every aspect of the ideal [artifact]” (Denyer 285). The good is what causes the ideal artifacts existence and “intelligibility”. (Denyer 284-285)

            To determine what aspects of an artifact are pertinent to the Good, we must use thought: “When, in the light of the Good, we come to understand a form, we must, claims the analogy with the sun, use our minds, not our senses’ (Denyer 285). What mans perceives the Good to be is not what it truly is, because the senses cannot determine the form of Good; this is why man often falls short of understanding the theory of forms. Denyer argues that man’s teleological understanding often falls short due to the failure to understand the time frame, the inability of ideal objects to be reduced to perceptible objects, and the number of objects distinct from perception that share the same name. Denyer days, “the truths about ideal artifacts that we can discern by the light of the Good are everlasting and unshakably true” (Denyer 287). These truths are timeless and are unchangeable. The second reason why our teleological understanding fails is because of the names given to ideal objects. Once a name is given to the form of an ideal artifact, it can be inferred that there is another artifact that can be compared to the ideal one. This would lower the first artifact down, from the ideal, to the level of perception. The third defect in our teleological understanding results from the multitude of objects that share the definition of the ideal object. Dneyer give the example of a flat surface, and how the term flat surface could be attributed to many different objects. He then states how mathematics tries to establish ideals through a seemingly non teleological way. (Denyer 286-289)

            Geometry becomes imperfect when it is brought into the realm of intelligibility. Denyer argus that, “Geometrical objects too must be seen in the light of the Good” (Denyer 289). He then discusses Plato’s description of the, “the internal structure of the intelligible realm that is governed by the Good, and its connection with the visible realm that is governed by the sun” (Denyer 289). Descriptions often only have to do with the visible realm, as man concerns himself mostly with the visible when trying to understand the world. Denyer uses the example of an object and its shadow or reflection, and how most think of the reflection as an exact exact counterparts of the image, as a correlation with trust and fancy. He defines fancy as, “the state of mind in which one is looking at some shadow or reflection, without appreciating that it is only a shadow or reflection” (Denyer 290). Fancy is less clear than trust and is put at the bottom of the divided line. When trying to understand the theory of forms one must use trust instead of fancy: “Trust by contrast, is the state of mind of one who appreciates that shadows and reflections are only shadows and reflections” (Denyer 290). The visible realm is less perfect than the intelligible so on must use trust to gain a true understanding of forms.

            Fancy and trust fall under opinion on the divided line, and opinion, just as fancy is less than trust, is less clear than knowledge. Opinion is based highly on perception of the visible realm and often leads to misjudgments. Knowledge based on misjudgments of an object is not actually knowledge on that object, but rather, “knowledge about something else, whose degree of truth matches the degree of clarity of the knowledge” (Denyer 292). On the divided line knowledge, just as opinion, is broken down into the segments thought and intellect. Intellect holds the highest level on the divided line but thought is where, “we will be able to locate mathematics and its objects” (Denyer 292).  

            After defining all the segments of the divided line, Denyer analyzes how the divided line should be drawn out. Plato does not give an exact description of how the image of the divide line should look, so those trying to interpret it are presented with “arbitrary” choices. Denyer argues that the reason behind this is, “because of our universal ease with interpreting visible things that Plato uses our dealings with such images to expound to us the intelligible realm” (Denyer 294). Trying to create a mathematical representation of the divided line ultimately ends in the realization that thought is equal to trust. Denyer presents three reasons that Plato might have made thought equal to trust. The first being, that it serves Plato in the long run: “It is central to Plato’s thought about images that an image always falls short of the original of which it is an image”. (Deyner 296). The counter view to that would be that thought is not superior to trust, and that thought does not lead to a better understanding. The third reason given for thought being equal to trust is that it “allows both these incompatible interpretations”. (Denyer 296). If the image is simple, there would be no need to overanalyze it and there would be know higher understanding reached. (Denyer 292-296).

            Engaging in mathematical thought about images deepens the understanding of the object of thought and brings the physical object into an “intelligible reality” (Denyer 296). Using the less clear physical objects as a representation of reality makes thought superior to trust, while making thought inferior to intellect. As intellect has no use for images but is much harder for the average person to understand. The use of images and hypotheses is able to increase thought but it fails to bring ones understanding to the level of intellect. Hypotheses, proofs, and theorems all rely on mathematical assumptions not grounded in in intellect. They are the same as fancy because mathematical forms differ from the actual form of the object. They share some of the same characteristics of forms, such as being eternal, but they exist: “as something intermediate between opinion and intellect” (Deyner 303). Mathematical thought has some truth but it is not as clear as the forms that exist in the intellect. Mathematical forms clutter the “so-and-so itself” associated with regular forms. (Deyner 296-3040

            The last part of the essay addresses the reason why intellect is better than thought. Denyer quote Plato saying, “intellect reasons dialectically, and proficiency in dialect requires a maturity, and prior education, that even under best of circumstances few will have” (536d-540b). Intellect is the highest form of knowledge but it is near impossible to reach compared to thought. Mathematical forms rely on unhypothetical starting points, which Denyer attribute to the Good: “having a teleological explanation of something means seeing what is good about it; and it will be for this reason that the Good is the unhypothetical starting point for all that is teleologically explicable” (Denyer 307). Denyer reasons that intellect might not actually be better when it comes to teleological understanding because mathematical forms are still found in the light of the Good. Mathematical forms can exist because of a natural order or beauty in the world.

           

(1) How should the divided line diagram be drawn?

(2) Is intellect really that much better when it comes to our teleological understandings?

(3) How closely should we analyze  diagrams when  they represent a thought?

(4) Why do you think Plato left the divided line diagram up to interpretation?

(5) Are mathematical forms equal to forms of thought?