Opposites, Properties, and Plato

“And if it becomes smaller, it must have been greater and then have become smaller?”

“That is true,” said he.

“And the weaker is generated from the stronger, and the slower from the quicker?”

“Certainly.”

“And the worse from the better and the more just from the more unjust?”

“Of course.”

“Then,” said he, “we have this fact sufficiently established, that all things are generated in this way, opposites from opposites?”

— Plato, Phaedo (71a)

Phaedo, a dialogue of Plato, is set during the last hours prior to Socrates famous execution by drinking hemlock. Characteristically, Socrates spends his final moments discussing philosophy with his friends. The topic of discussion is primarily the immortality of the soul, make more palpable by the interlocutors' knowledge of Socrates impending death.

In this dialogue Socrates puts forth many arguments for the existence and immortality of the soul, specifically his view that all souls will be reincarnated. One of these arguments is what might be called "the argument from opposites". As I understand it, this argument essentially says that all things come out of their opposites. For example, for something to become light, it must first have been dark. For something to become hot, it must first have been cold, etc.

Plato suggests that opposites, such as

• Weaker and stronger
• Slower and quicker
• Worse and better

must be generated from each other. This idea definitely has some intuitive appeal. After all, nothing can just spontaneously come into existence, so everything must come from its opposite in some sense.

Plato's point of course is to bring these intuitions to the case of "life" and "death". If they are opposites, then in the same way that we know that death comes from life, life must also come from death, and life and death must be in a constant cycle, one coming into being out of the other.

This argument is interesting, but does it work? To understand this argument a bit deeper, I think that it would be helpful to consider what we even mean when we say the word "opposite".

At first, it might seem like "opposite" means that two things are different in all respects. But obviously this is not the case in everyday language. Consider the opposite of white which is black. You are trained from a young age to say that black is the opposite of white. But notice that black and white are not altogether that different from one another. After all, they are both colors, and the set of all colors is relatively small! There are lots of things that are less like white than black; for instance, the number 3 doesn't even share the property of being a color.

Obviously relating the color white to the number 3 doesn't appear to be at all useful or interesting. The point I am making is that opposites always have some quality that persists, and in everyday language that quality is often implicit. For black and white, the persisting property is that they are both colors. For "night" and "day" the persisting property is that both are times of the day. Another way of looking at this is that two things being opposites implies that they are at two ends of some spectrum (which again is often implicit). For colors, that spectrum is the color frequency spectrum and we imagine white and black at either end.

Sometimes words have just one dimension to them (like "beginning" and "end"), but oftentimes, when a word has more than one property, you have a choice of which property should persist when choosing its "opposite". One interesting thing about opposite words like this is how quick your brain is to response with the "correct" answer, automatically inferring the quality that should persist.

Here is a table to demonstrate how there is some arbitrariness to how how opposites are defined.

Each of the Alternative opposites considers an alternative dimension or spectrum along which a word and its polar opposite could exist.

For a word where there is no related spectrum that comes to mind, there will not be an opposite. For example, if I asked you for the opposite of "rubber duck", you would think I am messing with you.

Now that we've established some criterion for what an opposite is in the usual sense (opposites are related by a persisting quality and a corresponding spectrum), let's look at Plato's opposites of "life" and "death", which I will call the state of "existence", and the state of "nonexistence" from here on out.

Right off the bat it seems difficult to define a spectrum relating existence and nonexistence. Unlike most properties which exist along a continuum (e.g., color can range across the spectrum, size can vary in magnitude, a day can be sunnier or cloudier etc.), existence appears to only consists of two possible distinct states: "either something exists or it doesn't". Further existence is not a property that you can give or take away while keeping other properties the same. If I destroy a red squishy ball with a hammer, then the redness and squishiness of the ball must perish along with its existence property (importantly I'm not talking about the ball's potential existence as an idea, but as an actual thing instantiated in the real world).

It doesn't appear that existence and nonexistence are really opposites in the same sense that "black and white" or "love and hate" are. In particular, it would be strange to say that an object had the property of nonexistence and then gained existence.

At this point it becomes necessary to make a distinction between two different models of change: generation and alteration. Plato's student Aristotle made this distinction in his work On Generation and Corruption. Say that I painted my house a bright orange color. This would be considered an alteration because a property (color) of a preexisting object (my house) has changed. If I instead built a new house from the ground up, then that would be considered generation because a brand new object has come into existence. It would be weird to say that my house had the property of nonexistence, but then I built it and it gained the property of existence.

At this point many philosophers such as Immanuel Kant suggest that existence shouldn't even be considered a property, since it doesn't behave like other things we call properties, and because it doesn’t add any descriptive information about an entity. Rather, existence is a fundamental condition that must be met for something to be instantiated and even have properties.

Given that existence and nonexistence are not even properties, it becomes clear that "life" and "death", if they are to be considered opposites, are not opposites in the same sense as Plato's examples. Therefore, concluding that life must come from death by induction on the class of facts such as "the strong must be generated from the weak", or, "for something to have been better it must first have been worse", would be a false analogy.

Takeaways

Two things being opposites is not always a very well defined notion in everyday language, and that there is usually some implicit quality that is maintained between the two poles of the spectrum being considered.

Existence and nonexistence are special cases. If we do consider them opposites, then they don't appear to be opposites in the usual sense ^[1] since they don't live at either end of a spectrum (either something exists or it doesn't).

In any case, Plato's Argument from Opposites appears not to work.