Synaptic

I nominated his paper for the Anthology because it does something that it is very hard to do in brief space for readers lacking prior acquaintance with the topic. That is, for a thoughtful reader it makes a compelling case that the famous dictum is wrong about “the measure of all things.” It is not humanity (“man,” in traditional translations) that is the measure of all things, as Protagoras has it; rather, it is the intelligible yet incorporeal realities which Plato calls “Forms” that are the measure. Sophomoric textbooks appear patronizing in their expositions of Plato’s theory by suggesting that the Forms are literally mental images, and Aristotle himself seems to trivialize it in his criticisms at Metaphysics I.9.

-Chad Ray

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Throughout the Republic and other Platonic dialogues, Plato gives arguments for the reality of the Forms through the mouth of Socrates. Plato’s Argument from Opposites paints a picture of what is meant by the Forms, and makes a compelling case for their existence. I will also address a second argument for the Forms that I will call the Craftsman Argument. My intention is to present and defend these two arguments for the reality of the Forms.

In the Argument from Opposites, from the Republic (523-5), Plato asks us to consider three fingers. One finger is the biggest, one the smallest, and one in the middle. When viewing the medium-sized finger, it appears big compared to the small finger, and small compared to the large finger. Our senses view the same object as being both big and small. In fact, anytime we identify something that is big, we immediately draw comparisons to smaller things. Something is big only relative to smaller things, and a big thing only becomes big out of a previously smaller state. But when a finger is identified as both big and small, there is a contradiction. Big and small are opposites, so the finger could not be identical to Bigness itself and to Smallness itself. In the finger, the senses perceive the one size as both big and small, as though Big and Small were mixed together; but the mind understands Bigness and Smallness themselves as opposites, which are clearly separate from the finger. In fact, Bigness and Smallness must be distinct from the entirety of the physical world, since all physical objects participate in Bigness and Smallness to varying extents, and the size can be compared to either or both. Though they participate in Bigness and Smallness to varying extents, those physical objects should not be confused with Bigness itself and Smallness itself. The fingers refer us to Bigness and Smallness but are not identical with them. We understand what it means to say that one object is bigger than another object, because we understand the Big. This suggests that we are capable of understanding an intelligible reality that cannot be perceived by the senses. This reality that is not sensed but is understood is the reality of the Forms.

This is a powerful and compelling argument. Rational beings understand many things that they never encounter in the physical world. No one disputes that the Pythagorean Theorem is true for right triangles, yet no one has ever observed a right triangle or the Pythagorean Theorem. If you doubt this, consider that lines in geometry have no width and points have no dimensions at all; they are “seen” by the mind, not by the senses. We can mentally grasp concepts that seem to explain truths about right triangles, even though we have never encountered a right triangle. Even after the death of humanity and the universe itself, the Pythagorean Theorem will express an eternal, unchanging truth about reality. Given this fact, it is difficult to deny that the Pythagorean Theorem has some kind of reality, apparently independent of us. This intelligible reality is grasped by rational beings, but the Pythagorean Theorem endures even when no rational beings are around to understand it.

Plato’s second argument, the Craftsman Argument, is taken from the Republic at 596b, when Socrates says:

“Aren’t we also accustomed to say that it is in looking to the idea of each implement that one craftsman makes the couches and another the chairs we use, and similarly for other things? For presumably none of the craftsmen fabricates the idea itself. How could he? ”

The ideas of chairs and couches are not all that powerful, so consider an artist that wants to draw a circle. The artist gives his best attempt at drawing a circle, but it inevitably fails to be a perfect circle. The drawing will share some similarities to a circle, and participates in the Form of Circularity to some extent. Yet the drawing is not the same thing as Circularity itself. When we examine the drawing, we observe the imperfections that prevent the drawing from being a circle. We can do this even though no one has ever seen a perfect circle, or Circularity itself. Our minds have the mental capacity to grasp the Form of Circularity, and that Form is the standard to which we compare the drawing. The fact that the artist can come close to drawing a circle shows that he also has access to the intelligible reality of the Form of Circularity. Some Forms are more difficult to grasp than Circularity, yet we seem to have some knowledge of them. When we hear of someone abducting a child, we feel compelled to say that the abductor has performed an unjust act, even if we do not have a complete understanding of the Form of justice. It seems that there are objective truths about the Forms of Circularity and Justice that do not depend on human knowledge or existence.

The Craftsman argument is compelling as well, as it is difficult to describe reality without acknowledging the existence of eternal, unchanging, imperceptible realities. How could an artist attempt to draw a perfect circle without knowledge of the Form of Circularity? Circularity is no mere human construct; it is a reality in which material objects participate to varying degrees. Note too that Circularity itself is not round or a circle, any more than Bigness is gargantuan. The Form is what the artist understands and renders sensible or material by imitation, but is not a sensible or material thing itself. The artist’s understanding of Circularity allows him to draw an approximation of a circle that refers observers to the Form of Circularity. What the craftsman understands is that in virtue of which sensible circles are more or less round. This might be an intelligible formula, like “the complete set of points on a given plane, at a given distance from some given point on that plane.” The formula is perfectly intelligible; its physical approximations, mutable and imperfect.

Plato succeeds in arguing for the reality of the Forms. The Argument from Opposites considers a finger that we perceive as both big and small, and concludes that Bigness and Smallness must be distinct from the finger, because Bigness and Smallness are opposites, and therefore could not be the same thing. The Craftsman argument shows that a craftsman cannot create the object of his craft without knowledge of the Form of that craft. Our ability to judge the object of his craft suggests that we understand a reality that is distinct from the physical world.