Can a common, uneducated slave do complex geometry without ever learning it? This is one of the questions in Plato’s Meno. Plato was hoping that the answer to this question was yes, for that would give hope to slaves everywhere.
This and other unusual aspects of the dialogue make it one of Plato’s most interesting and thought-provoking dialogues.
Meno centers around the nature of virtue (aretê in Greek). In this regard, it is similar to other Platonic dialogues. One of Plato’s favorite subjects was discussing the nature of virtue and justice. The Greeks believed that, without these elements, a society becomes a failed state. That is why discussions around such matters were central to many of Plato’s dialogues.
The Question of Virtue
The dialogue centers around the main question of whether or not virtue can be taught. Meno, a young man from Thessaly, asks Socrates the central question of the dialogue:
Can you tell me, Socrates, is virtue acquired by teaching?-70a
Or not by teaching but by training? Or neither by training or learning but comes to men naturally or in some other way?
As mentioned in Post 75, this dialogue is divided into three parts. Part one concerns the nature of virtue itself. I covered this section in Post 75. As usual, Socrates uncovers his opponent’s, in this case Meno’s, ignorance. At the end of Section 1, the dialogue establishes that neither Socrates nor Meno knows the nature of virtue. And of course, this leads to the question: if we don’t know the nature of virtue, how can we pursue it, and how will we know it if we find it? In other words, if you don’t know what a duck looks like, how will you know that it is a duck even if you stumble upon it? This is the subject of the middle section, which is really the heart of the dialogue.
Part 2: Pursuing Virtue and Epistemology
The operative question concerning virtue that introduces Section Two is this one by Meno:
How will you look for it, Socrates, when you do not know at all what it is? How will you aim to search for something you do not know at all? If you should meet with it, how will you know that there is a thing that you did not know?-80b
Meno is about two things. It is about virtue, for sure, but it is also about epistemology. And here is where it gets interesting. Epistemology personally intrigues me. Therefore, I find this section of the dialogue most interesting.
Socrates brings up what he calls the “debater’s argument.” This argument states that a person cannot search for what he already knows, since he already knows it, nor for what he does not know, since he does not know what to look for. In other words, he does not know what he does not know. Socrates goes on to say how this is a false dichotomy because there is an in-between state between pure knowing and pure ignorance. But to understand this state, we must turn to the divine, to those who spoke of a “glorious truth,” as Socrates states. Socrates waxes eloquently on this divine truth.
Some of them were priests and priestesses, who had studied how they might be able to give a reason of their profession: there have been poets also, who spoke of these things by inspiration, like Pindar, and many others who were inspired. And they say—mark, now, and see whether their words are true—they say that the soul of man is immortal, and at one time has an end, which is termed dying, and at another time is born again, but is never destroyed. And the moral is, that a man ought to live always in perfect holiness.-81 a-b
Why should a man live in perfect holiness? To answer that question, Socrates quotes from Pindar the poet. If our modern philosophers occasionally used poetry instead of just technical language, maybe their ideas would be a little more palatable. Here is the excerpt from Pindar:
For in the ninth year Persephone sends the souls of those from whom she has received the penalty of ancient crime back again from beneath into the light of the sun above, and these are they who become noble kings and mighty men and great in wisdom and are called saintly heroes in after ages.-81 b-c
Socrates is making a case for reincarnation, which he and most other Greeks believed in at the time. 1 The case being that the human soul is immortal. It may seem to “die,” but continuous cycles recycle it, bringing it back again and again. This is where Socrates introduces the key element in this entire dialogue, the idea of recollection. The idea is that if a soul keeps moving through the world and the afterlife, it keeps gaining knowledge and experiences that it might be able to remember. And this included the knowledge of virtue.
The soul, then, as being immortal, and having been born again many times, and having seen all things that exist, whether in this world or in the world below, has knowledge of them all; and it is no wonder that she should be able to call to remembrance all that she ever knew about virtue, and about everything; for as all nature is akin, and the soul has learned all things; there is no difficulty in her eliciting or as men say learning, out of a single recollection all the rest, if a man is strenuous and does not faint; for all enquiry and all learning is but recollection.-81 c-d
This is Socrates’ epistemological theory, which provides a route of escape from the necessity of total ignorance or total knowledge. The last phrase, “all inquiry and all learning is but recollection,” is the key. Because of this, according to Socrates, we need not give up the pursuit of the knowledge of virtue but rather enquire into this subject with renewed vigor. Socrates goes on to say that there is not true learning in life, but only recollection! Meno is incredulous, but Socrates is now ready to conduct a lab experiment to illustrate the truth of what he said.
Socrates then asks for audience participation. Meno calls one of his servants to prove that even he has innate knowledge garnered from previous lives and doesn’t need to be taught anything but only needs to recall what he already knows, as directed by him. Through a rigorous process of cross-examination, Socrates leads the slave to do complex geometry in order to prove his assertion of “recollected knowledge.” Meno asserts that his servant has no prior knowledge of geometry. Socrates wants to be clear that he is not teaching the slave but merely revealing his knowledge through neutral questioning. He tells Meno:
Pay attention then whether you think the slave is recollecting or learning from me.-82 b
Doubling the Square
The geometric exercise in question is a process that is called “doubling the square.” If one takes a square, how can he double it using simple tools such as a straight edge? The summary of this process is in the diagram below:
Here is a static version of the same concept:
If we put the small square inside the larger, we get:
Even though this process had been known to the ancient Greeks for some time, it was the dialogue of Plato’s Meno that popularized it, and its popularity has remained strong down through the ages. As an aside, the beauty of this did not go unnoticed by artists and architects. For example, below is the Cosmati Pavement of Westminster Abbey that was designed in the 13th century:
Notice how this design of a square within a square, as pictured in Diagram 3 above, is prominent in the central part of the Cosmati pavement design. Interestingly enough, if we take the central square in Diagram 3 above and rotate it 90 degrees, then we get the following design:
We see the relationship between these two squares in the Cosmati Pavement above, where the larger square that forms the outer border is twice the size of the smaller square that is inset from that. The space in between those two squares in the Cosmati Pavement above acts as a sort of picture frame or even a “mat” to highlight the central designs. There is something beautiful about this relationship between two squares, one half the size of the other. There are reasons for why this is beautiful, and I have much more to say on the matter, but if I did, I would be too far afield from my original topic.
Finally, the design of diagram 4, prior to the modern era, are often used in architecture to convey beauty. For example, notice the enclosed walkway to the right of the church. Not only is it functional, but it is beautiful as well, because the outer perimeter of the walkway is twice the size of the inner perimeter. Architects used to intentionally do things like this, but they don’t anymore.
I took this diversion to illustrate that doubling the square is more than just a schoolboy’s geometry exercise but rather has implications for art and architecture down through the centuries.
A Common Slave Does Geometry
It would be too cumbersome to put the entire dialogue in this post where Socrates questions Meno’s slave to the point that he discovers the procedure for doubling the square. Therefore I have put a link below in the footnotes if you want to read it for yourself.2 But I will include a sample so that you can get an idea of it:
Soc. And if one side of the figure be of two feet, and the other side be of two feet, how much will the whole be? Let me explain: if in one direction the space was of two feet, and in other direction of one foot, the whole would be of two feet taken once?
Soc. But since this side is also of two feet, there are twice two feet?
Soc. Then the square is of twice two feet?
Soc. And how many are twice two feet? count and tell me.
Soc. And might there not be another square twice as large as this, and having like this the lines equal?
Boy. Yes.-82 c-d
For the sake of simplicity, I will summarize the entire process that Socrates takes the slave through in order to double the square by using the homemade drawing below.
The original square in question is ACBG. We divide a square into four equal parts to use it as a measurement basis. Then we aim to double the size of this square. To do this, we extend the square to make a larger one, four times the original size, but we only want to double it. We achieve this by connecting the midpoints of the larger square, creating a smaller square. By doing that, we double the square. We prove that by counting the full and half squares within the recently created square. The sum of the squares is eight, which is twice the size of the original blue square and divides into four squares.
If you don’t quite understand this, don’t worry. The important thing is Socrates’ conclusions below, not the math.
The Conclusion of Socrates’s Experiment
Socrates’ conclusion of this whole matter is that innate knowledge exists. For he asks Meno a question concerning his slave, which Meno answers in the affirmative:
So the man who does not know has within himself true opinions about the things that he does not know?-85c
He then states his conclusion on the matter in the form of a question (of course), which is really one of the key declarations of the entire dialogue:
Then if the truth about reality is always in our soul, the soul would be immortal so that you should always confidently try to seek out and recollect what you do not know at present – that is, what you do not recollect?-86a
In this dialogue, Plato makes it possible to even consider such a thing as innate knowledge. Many people today don’t believe Plato’s ideas about reincarnation and innate knowledge. However, I think that the fact that he brought them up was a big reason why so many philosophers and theologians, from Descartes to Jung, were influenced by them in the centuries since.
Do Humans have an Innate Sense of the Divine?
Since this blog has to do with faith and reason, I think it is important to consider how innate knowledge pertains to knowledge of God. Do humans know naturally that God exists? Some of the early Church Fathers adopted ideas similar to Plato’s that our knowledge of God is not something we learn, but rather something God has implanted in us.Thomas Aquinas later disagreed with this, denying that humans have innate knowledge, whether of God or other things, but that it must be illuminated from the outside. Aquinas, more akin to Aristotle, put more emphasis on the senses. Aristotle, Plato’s pupil, also denied innate knowledge.
On the other hand, Aquinas affirmed that humans, made in the image of God (imago Dei), have the capacity to know not only that God exists but also to know about him and to know him. Humans have a divine sense; it is universal.
To know that God exists in a general and confused way is implanted in us by nature, inasmuch as God is man’s beatitude. For man naturally desires happiness, and what is desired by him must be naturally known to him.–Summa, Part First, Q. 2, A. 1
God gave us this common knowledge, yet it qualifies as “natural” because it is accessible to everyone.All humans have a “sense” of God, although it is very imperfect. I call it God consciousness. Aquinas calls this “natural light”. Even though humans have this innate capacity to know God, Aquinas states that we must receive our knowledge of God from outside sources, whether sensory input or illumination by faith through the Holy Spirit. To support his point about nature, Aquinas quotes the following verse:
For since the creation of the world God’s invisible qualities—his eternal power and divine nature—have been clearly seen, being understood from what has been made, so that people are without excuse.-Epistle to the Romans 1:20
We have a natural capacity to know that God exists, but the information to that effect comes from the outside through our senses. It is similar to having the capacity to speak. As humans, we are born with this amazing ability, but unless we are exposed to speech from an early age, we will never learn a language. I think this is an apt parallel. Capacity does not mean automatic knowledge; we must be exposed to the right information through our senses. The same thing applies to the innate capacity that humans have to reason or to appreciate art and beauty. In regards to languages, Socrates would probably say that we already know a specific language from a past life. The process of learning a language calls to mind what we already know.
According to Aquinas, our natural capacity to know God is not enough to know specifics about Him. In other words, things like the beauty of nature or the complexity of the human eye can tell us that God exists, but they can’t tell us that God is a Trinity.For this, we need what Aquinas calls a “new illumination,” or the light of faith. This is through the agency of the Holy Spirit. He summarized both of these types of knowledge very well in the following quote:
Moreover, in the attempt to arrive at some knowledge of God, the human mind is greatly assisted when its natural light is fortified by a new illumination: namely, the light of faith and that of the gifts of wisdom and of understanding, by which the mind is elevated about itself in contemplation, inasmuch as it knows God to be above anything which it naturally apprehends.3
According to Aquinas, the knowledge of God that we naturally acquire through our senses is general and even muddled, and it is subject to natural override.To reinforce this point, he quotes from Psalm 14:1.
The fool says in his heart, ‘There is no God’.
I think this talk about Aquinas sums up the main idea of my blog, which is that faith and reason are both important for figuring out what is true.We need to use our natural abilities, such as our ability to think and our senses, along with the Holy Spirit’s illumination of things that can only be known through faith.Both reason and revelation are legitimate sources of knowledge, but secular, materialistic universities of course reject revelation.Nevertheless, that denial does not nullify the validity of that source of knowledge. Having said that, what we know about God must come through an outside agency, whether naturally through our senses or supernaturally through the Holy Spirit.
Descartes and Innate Ideas
After Aquinas, there were no earth-shattering ideas in the realm of innate ideas until René Descartes in the 17th century. In his Meditations, Descartes talks about three modes of ideas: innate ideas, adventitious ideas, and factitious ideas. 4 He states the following:
Among my ideas, some appear to be innate, some to be adventitious, and others to have been invented by me. My understanding of what a thing is, what truth is, and what thought is, seems to derive simply from my own nature. But my hearing a noise, as I do now, or seeing the sun, or feeling the fire, comes from things which are located outside me, or so I have hitherto judged. Lastly, sirens, hippogriffs and the like are my own invention.-AT VII 37–8; CSM II 26
Innate Ideas that come naturally from one’s own thinking are called “innate ideas,” while ideas that come from outside of oneself, such as sensory experiences, are called “accidental ideas.”For example, does one feel hot or cold? Factitious ideas are invented concepts that originate in other ideas. For example, we get the invented idea of a unicorn from the combination of the idea of a horse and the idea of a horn. For our purposes here, I would like to discuss his concept of innate ideas.
Descartes divides his idea of innate ideas even further into the ideas of an infinite God, a finite mind, and an infinite body.In his Third Meditation, Descartes proceeds to examine the origin of his innate ideas. He says that the concepts derived from his innate ideas have their origins outside the mind. He also discusses the idea that an effect can never be greater than its cause. This derives from the self-evident principle that something cannot come from nothing. 5 Thus, one’s innate ideas must have their origin, or “cause,” in something greater than themselves. He says the following:
And although one idea may perhaps originate from another, there cannot be an infinite regress here; eventually one must reach a primary idea, the cause of which will be like an archetype which contains formally (and in fact) all the reality (or perfection) which is present only objectively (or representatively) in the idea.-AT VII 42; CSM II 29
This at first sounds like a contradiction. How can some of our innate ideas be innate if they originate somewhere outside the mind and are independent of the mind? This is where he introduces the concept of the primary idea.
A primary idea is one that exists outside of the mind and is independent of it. The objective, innate ideas that we have have their origins in the corresponding formal realities, or archetypes. These archetypes are the formal causes (i.e., in the sense of forms) of the perfect reality of the ideas that are present in a representative sense in the innate idea. Innate thoughts are innate in the sense that they don’t physically originate outside of our minds; rather, they are merely images of the realities that the archetypes represent.This is total Plato through and through; the world we inhabit is at most an image of the reality of the forms that they represent.
What Descartes is obviously doing is combining Aristotle’s idea of the unmoved mover with the idea of Platonic Forms. By doing so, he arrives at the origin and perfection of some innate ideas. 6 Interestingly, he took this concept of the unmoved mover that Aristotle applied to the cosmos in general and made a specific application to abstract thought in a very ingenious way. In addition, Plato had a significant influence on him, both in terms of his appeal to forms and in terms of his stark mind-body dualism.
Descartes unique contribution to the ideas of Aristotle and Plato in particular was to apply them more explicitly to the world of thought and ideas in a way that opened the door for later thinkers like Hume, John Locke, and even Carl Jung to develop further. Jung’s ideas, especially his theory of archetypes, really are the modern psychological development of both Plato’s theory of forms and Descartes’ theory of innate ideas.
The Innate Ideas of God, the Mind, and the Body
One of the biggest misunderstandings about Descartes was that he believed only in his own thoughts as proof of his existence (cogito ergo sum) and that we could never know anything else, such as the existence of God, for certain. This is not true at all. Descartes merely said that, besides our own thinking, which we know exists, we must take a skeptical posture towards everything else. Other things can be proven, but only after working through the doubts about those objects. With that being said, Descartes extreme orientation toward skepticism has had deleterious effects, to say the least, on Western thought.
The best way to sum up Descartes’ concept of his primary idea is as follows:
Primary idea A represents object B only if the objective reality of idea A has its origin in the formal reality of object B.7
So how did Descartes apply this to God, the Mind, and the Body? For Descartes, once we work through the doubts, it really can be shown that, not only the body and the mind, but indeed God Himself exists beyond the shadow of a doubt.8
Descartes said that we can be sure that God exists because we couldn’t think of God or an infinite being if they didn’t exist.Our senses do not convey any such idea to us. Therefore, this idea must be innate to us; for how can a finite, imperfect being create such a concept on his own? We can only know of such a concept because God created it within us. But because of this, we can be certain, without a doubt, that God exists. Descartes’ ideas are truly paradoxical.
To tie this to the main idea, the innate idea of God is a representation of God because the idea of God’s objective reality comes from God’s formal reality.The same is true with the mind. The objective reality of Descartes’ mind has its origin in the formal reality of his mind. So too, the objective reality of the body has its origin in the formal reality of a bodily substance.
When we think of Descartes’ use of the word “formal”, we should think of Plato’s theory of forms. The form is the reality. What we experience is the representation of that reality. What we experience with our minds and bodies is simply an image of the true reality of mind and body. Our innate ideas of God, mind, and body are like the reflection of ourselves that we see in a mirror. The substance is not the image but the reflection, and without the substance, there is no image.
Thinkers that came later, like John Locke, completely rejected the concept of innate ideas. Locke proposed just the opposite: that humans are born with a blank slate, a tabula rasa. The only ideas that develop in our minds are ones that form through information that we receive through our senses. Thus we have the modern conflict, until Kant, of the tension between the rationalists and the empiricists. This concept of innate ideas in modern times is fascinating and deserves further exploration. Kant had his own unique way of dealing with innate ideas, but that is a topic for another time.
Part 3: Can Virtue Be Taught
We finally get to the last part of the dialogue. Socrates had just gone through an elaborate exercise with Meno’s slave in order to prove that we can know what virtue is simply because we already know what it is through our suppressed memories. He now opens the door for him and Meno to explore the knowledge of true virtue. And what does Meno do? He tells Socrates that he does not want to pursue this, but rather would like to discuss the original question of whether or not virtue can be taught. after all that! What is going on here?
There are two things at play, one literary and the other pedantic. Plato was a master at literary devices. After starting off with the question of whether virtue could be taught, Plato establishes that virtue can indeed be known and then brings the dialogue back to the original question, thus bringing closure to the entire conversation.
My theory has always been that Plato frustrates us by not providing answers to important questions about the nature of virtue because he wants us to figure it out. We are aware of its significance. Plato demonstrates that it is possible to know, so it is now our responsibility to discover these truths. In this respect, Plato was unique and refreshing. People are not hesitant to give you their opinion, as we live in an era where everyone is an expert on everything. Plato, on the other hand, withholds judgement and returns the burden of responsibility to us. As responsible citizens, we should all care about these issues. We should be humble truth-seekers rather than arrogant know-it-alls.
Ultimately, the Greeks were concerned with the polis, or city-state. Socrates and Plato were both concerned that without true virtue, the polis could not survive. Ultimately, it was corruption that brought down the entire city-state system. Stability was not realized until the Romans brought order, but that is another story altogether. So, if it’s up to us to figure out what virtue is, the second question is whether we can transmit it to others, especially subsequent generations. If the answer is no, then it is all for naught anyway. This is the topic of the third part of the dialogue. No matter how theoretical Socrates, Plato, and Aristotle were, they always brought things down to practical concerns.
Virtue as Knowledge:
The question really is this: is virtue knowledge? If it is, then it can be taught. In the closing dialogue between Socrates and Meno, Socrates leads Meno to two contradictory conclusions on this matter:
- Virtue is knowledge and therefore can be taught.
- Nobody teaches virtue, therefore it cannot be taught and must not then be knowledge.
Anytus, a well-known politician in the state, and Meno’s host then join the conversation and say that younger men can be taught virtue by older men. If this is the case, Socrates replies, then why are the children of politicians not virtuous? Ouch! Without naming him directly, Socrates lumps Anytus into that category of politicians who have failed to teach virtue to their children. Anytus already disrespected Socrates because he deemed him to be a sophist, but that sealed the deal and made Socrates an enemy of Anytus. Anytus leaves in anger. That will teach Socrates not to speak truth to a politician! Anytus shows up in another dialogue in Socrates’ trial, accusing him of corrupting the youth. How ironic.
Socrates concludes that people do good things not because they know what’s right but because other thinks it’s right. We have virtuous people in society, even politicians, it is not because of knowledge but “some kind of divine gift”. To the original question of this dialogue—whether virtue can be taught—one must first define virtue!
It follows from this reasoning, Meno, that virtue appears to be present in those of us who may possess it as a gift from the gods. We shall have clear knowledge of this when, before we investigate how it comes to be present in men, we first try to find out what virtue in itself is.-Socrates, Meno 100b
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Footnotes and Endnotes:
- For more on this, please see Post 56 entitled “The Hope of Resurrection and the Hopelessness of Reincarnation”.
- Meno, 82b-85b
- On Boethius’ De Trinitate by St. Thomas Aquinas, Question 1, Article 2
- Smith, Kurt, “Descartes’ Theory of Ideas”, The Stanford Encyclopedia of Philosophy (Fall 2021 Edition), Edward N. Zalta (ed.)
- Despite his great paradigm shift, He asserts that something cannot come from nothing, so there can’t be an infinite regress. The very skepticism that he introduced into modern thinking eventually undermined even this principle.
- Smith, Kurt, “Descartes’ Theory of Ideas”
- I can’t say for sure, but I think Descartes was trying to do was to say that once an idea pass the extreme doubt test, then we can even be more certain of it then under previous classical Greek and Christian ways of thinking. If this was the case, it unfortunately backfired and has brought us to the point in which unbelief is the norm, not only vis a vis God, but with almost everything else.
- Smith, Kurt, “Descartes’ Theory of Ideas”
Aquinas, St. Thomas, On Boethius’ De Trinitate
Descartes, Rene, Meditations, Hackett Publishing Company; 3rd edition (October 1, 1993)
Plato, Five Dialogues, translated by G.M.A. Grube, second edition, Hackett Publishing, 2002