Abstract
In a recent publication, Nicholas Smith discussed some elements of the Republic’s divided line (Rep. 509d6-511e4) to demonstrate that they create an unresolved problem. I tackle Smith’s argumentation to show that elements of the divided line that are mentioned by him do not create problems in interpreting this passage. On the contrary, these features convey one of the most important doctrines behind this passage. This is the idea that the world of sensible things holds a dependence upon the world of Forms in the same way that shadows and reflections depend on the things that are shadowed and reflected. Following this line of reasoning, I propose an interpretation of the divided line in which both knowledge and opinion are set over the same kind of objects F. One has an opinion about F whenever apprehending F by means of its effects, and one has knowledge about F whenever apprehending F itself.
Highlights
In a recent publication in Plato Journal, Nicholas Smith (2018) proposes a problem of interpreting the Republic’s divided line
In the two figures below, that means (I1 + I2) / (V1 + V2) = V2/V1.2. This mathematical feature of the line is supposed to create a philosophical problem of considerable importance: “As far as I know, there has been no notice in the literature about the problem that this seems to create, namely, that V1 + V2 must be clearer than either V1 or V2 by themselves. This seems to me to create nonsense: How can V1 + V2 be clearer or truer than either V1 or V2? Why would adding the relative lack of clarity in V1 to whatever we find in V2 make V1 + V2 clearer than V2 just by itself? Plato tells us that V1 consists in shadows and reflections in water and other reflective surfaces
Vlastos advises contemporary platonists to stop talking about degrees of existence and instead give attention to different ways by which Forms and sensible particulars are related to their predicates
Summary
Vlastos advises contemporary platonists to stop talking about degrees of existence and instead give attention to different ways by which Forms and sensible particulars are related to their predicates The importance of this lesson for platonism can hardly be understated. The word εἰκόνες could be used to characterize statues, pictures, or any other kind of representations, Plato makes it clear that he is populating this segment of the line with shadows and reflections (σκιάς; φαντάσματα). We must ask why he is so careful in describing the nature of these images and what features shadows and reflections have in common when considered relative to the original of which they are images What these kinds of images have in common is that they are all direct effects of their models in a way that a painting or a statue is not. Attributing the same degree of existence to every entity in the line it could be considered puzzling the fact that two consecutive segments taken together represent a clearer and truer apprehension of reality than just the upper segment
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