The Question of 'Transitory Worlds' in Plato's Metaphysics: Part 1

Motivation

In the Meno, Plato argues for concept innatism, based on the observation that concept empiricism at face value does not seem to explain how we seemingly acquire knowledge of universals even while being exposed only to particulars through our senses. For example, we can only observe swarms of acts exemplifying virtue, but to know that they instantiate virtue, we must already possess the deeper idea of what virtue is as a concept. Plato goes on to demonstrate how one of Meno’s slaves acquires knowledge of mathematical universals such as squares, even though the latter had never been trained in the subject.

Suppose we think of principles as overarching constraints on how we think of concepts in some given field. Furthermore, let us say a hypothesis is a detailed proposition about a concerned field’s working, which incorporates its principles in a particular structure and seeks to either explain the principles in the context of the structure, or simply explore principle-consistent consequences of the proposition in the said context ¹.

For example, a principle of Newtonian mechanics is that of Galilean relativity, which is the statement that an observer moving with uniform velocity in some reference frame should not be able to measure their motion using any experiment in their frame alone (i.e., velocity is always relative to some other frame). A hypothesis consistent with the principle of Galilean relativity, in the particular framework of electrodynamics, is that since the electric field is a measurable quantity, a moving charge must have the same electric field as measured by an observer, whether the charge-observer supersystem is moving in its entirety or not, in some given reference frame.

In this light, we can think of Plato as formulating concept innatism as a principle of epistemology, in his exposition. The nature of this formulation is dialectical, and he focuses more on the very logic of concepts such as virtue and its knowledge. Interestingly, the hypothesis Plato comes up with to flesh out and go over and beyond the epistemological principle of concept innatism, is the metaphysical notion of anamnesis. This is the conclusion of the argument:

1. Knowledge is innate (this is motivated by the problem of knowledge of universals by acquaintance).
2. A participant of the Socratic method is capable of forming inner knowledge of things (as seen with Meno’s slave), HENCE,
3. Forming inner knowledge i.e. knowledge within one’s mind is recollection (as the knowledge must have been innate).
4. One either acquires knowledge or has always possessed it (by definition).
5. One does either of the above either in this life, or potentially, earlier.
6. If one has always possessed knowledge, they would have no need for recollecting it.
7. Socratic participants such as Meno’s slave cannot have acquired relevant knowledge in this life, THEREFORE,
8. Such participants must have acquired said knowledge (such as that of universals) before this life and merely recollected it in this life.

The corresponding dialogue from the Meno is from “(Socrates): What do you think, Meno? In giving his answers, has he expressed any opinion that was not his own?” to “(Meno): Here again, I think you are right, Socrates.”

Interpretation of Plato’s Anamnesis

If we look at the above interpretation of Plato’s argument for anamnesis, we see that he draws metaphysical conclusions from semantical wordplay. It is no wonder that the philosopher Jaegwon Kim, in his article What is “Naturalized Epistemology”?, refers to the ‘true’ part of the traditional tripartite analysis of knowledge (justified-true-belief) as its semantical-metaphysical element. This also captures the dichotomous nature of truth as found in universals i.e. concepts and their meaning, as well as particulars we encounter around us. Therefore, one would expect that important aspects of Plato’s metaphysics of anamnesis are reflected in the semantical side of his abstract argument. With this in mind, let us see how the argument structurally functions.

We see that Plato’s argument rests on the dialectics of ideas such as the acquiring, possession and recollection of knowledge; as well as general observations such as how Meno’s slave responds to questions in terms of previously unassessed true beliefs. So far, his argument seems valid if we try to think from his point of view. However, we must consider implicit principles (similar to principles in the sense discussed in the previous section) internal to his premises. In particular, premises (4) and (5) imply, at least at the stage of the argument in (5), that there are 4 things a person (or rather, a Platonic soul) could do:

1. possess knowledge in this life.
2. acquire knowledge in this life.
3. possess knowledge from before this life.
4. acquire knowledge before this life.

Plato rules out the first two possibilities by arguing that Meno’s slave cannot have possessed or acquired knowledge of geometry in this life. The third possibility suggests possession of knowledge from an indefinitely distant point in the past, and before this life, which he rules out in premise (6). Therefore, we are only left with the last possibility.

This is where a logician would say, “Hold up Plato! You’ve just used an extended form of the principle of excluded middle!”. In its simple form, the principle constrains how we think of possibilities and actualization: if we have potentially A or B and A cannot be actualized, then B must be actualized (as long as one of them must be). This is to avoid contradiction, as per the principle of contradiction, which together with the principle of identity (to the effect that every object is identical with itself) forms the three principles of thought. A fun fact is that principles for rational discourse itself can be traced back to Plato, and were extended into the framework of Aristotelian logic.

The Question of Transitory Worlds

In my opinion, we should be careful before applying the principle of excluded middle to premises (4) and onward in Plato’s argument for anamnesis, because it seems to assume that the distinction between this life and his envisioned beforelife where we acquired knowledge of universals is not vague.

In other words, what happens if we consider ‘transitory worlds’ between the beforelife with access to universals and this life? Or what if this life is a transitory world? There are many ways to interpret such a notion, and hence ask the question:

• Suppose the beforelife has access to universals, including The idea of particulars itself. If such a beforelife is a world of universals, how can it convey the idea of particulars to its full depth until it is actually experienced — via particulars — in this life?

• If the above process is unclear, would it be helpful to consider transitory worlds ‘between’ The beforelife with access to pure universals, and this one, will increasing amounts of perception of particulars?

• By the above reasoning, what if this life is a transitory world and the ‘next’ world is even more perception-based and further away from pure ideas?

Another question that pops up is — is the first question as related to Russell’s paradox as it seems? There seems to be a hierarchy where universals precede particulars, and perhaps combining the two results in logical paradoxes. On a side note, it is interesting that Russell’s name came up, for, as he writes in this regard in his book A History of Western Philosophy (in the chapter ‘Plato’s Theory of Immortality’),

Moreover, unless our existence before birth was not one of sense-perception, it would have been as incapable of generating the idea as this life is; and if our previous existence is supposed to have been partly super-sensible, why not make the same supposition concerning our present existence?

In general, it feels like it would be interesting exploring the logical principles implicit in Plato’s hypotheses, and exploring how alternative logics would modify his metaphysics. For example, not being able to apply the principle of excluded middle to vague, transition-filled beforelife and present life might be a form of fuzzy logic. Similarly, there is some temporality implicit in his notion of beforelife, which must transcend the particular notion of time we experience in this life — is this a hint of temporal logic?

These are the kind of questions which I hope to shed some light on (hopefully), in the next post in this series! Thanks for reading and stay tuned for more philosophy and new math/physics posts :)

1. This is inspired by the phenomenal chapter ‘First, Principles’ in Lee Smolin’s very original book (as usual), Einstein’s Unfinished Revolution: The Search for What Lies Beyond the Quantum. ↩