Metaphysics, Philosophy

Plato’s Answer to the One and The Many: What Have We Learned?

by Dave Seng

Before moving on to Aristotle, I thought it would be helpful to review what we learned from Plato’s metaphysics.

This is the final installment in our series of Plato’s metaphysics.

Part one can be found here.

Part two can be found here.

Part three can be found here.

Why is Plato important in the development of Western metaphysics? One answer is his discovery of form or essence. The idea of essence will be developed in future posts. For now, however, the idea of essence is simply that which makes something the kind of thing it is. Essence is the “whatness” of a thing. It is usually distinguished from substance. In modern philosophical terms, substance is the foundation which underlies sensible qualities or intellectual activities. It is that which underlies or upholds the particular things of our experience.

Plato was correct to point out that things have form or essences. A cat, for example, has a certain nature and character that makes it different from a dog. If the cat, however, runs into the road, is hit by a truck, and sadly dies, it undergoes substantial change but the essence of cat does not expire. Conceptually, properties of “catness” such as chasing mice and meowing for attention perdure and are instantiated in other cats.

In a real sense, Plato’s philosophy of Forms is trying to solve the problem he inherited from the pre-Socratics. Plato realized that reality can not be simply reduced to chaos and flux as Heraclitus and Protagoras suggested. On the other hand, all reality can not be one and immutable as Parmenides argued. We must have an objective basis for reality and value judgments. Plato’s “Form philosophy” was his attempt to ground reality in an objective truth which constitutes the real essence or being of a thing.

Essences, or essential forms, are properties of all things. An essential form is simply a feature or characteristic which belongs to the nature of a thing. We can conceive of “tableness” even when I dismantle my particular table and use it for fire wood. We all have a good idea of what it means to be human or when we consider the nature of humanity.

The idea of form or essence, discovered by Plato, is one of the greatest contributions to Western metaphysics. Metaphysics is about describing the world in the most general way and trying to explain the genuine nature of the world which is the foundation of this physical world. Essence is a real property of existence or Being. Other properties of Being such as the law of noncontradiction, the axioms and principles of mathematics, and the law of causality (which is really an extension of the law of noncontradiction) are also transcendent metaphysical truths. As we will see later, Aristotle considered the categories of act and potency to be foundational metaphysical truths. The study of metaphysics really does provide knowledge about our world. In fact, these metaphysical truths makes every other field of human inquiry possible.

But does Plato really solve the problem of the one and the many? For Plato the question of the one and the many is translated into Being (the one) and Becoming (the many). Being is the transcendent world of form and Becoming is the physical world we live in every day. Today, most philosophers speak in terms of Being and Becoming but the question of the one and the many is what underlies those categories.

Plato does not stop with a simple division between Being and Becoming. As we have seen, Being is divided into mathematical forms, and then the higher forms (sometimes he calls it the Form of the Good). Becoming is also divided into images and then the higher level of sensible objects.

The problem arises, however, of how the forms of Being actually participate or interact with the realm of Becoming. Unfortunately, Plato never resolves this situation. Dividing the two realms into further realms only complicates the issue. This, unfortunately, has been a significant problem in the Platonic tradition. Plotinus tried to solve the problem with his Forms of the All-Soul, Intellectual Principle, and other forms all the way down to physical things, but the Neo-Platonism of Plotinus still confuses the matter. Adding more Forms does not help the situation. The problem occurs whenever things get divided up unnecessarily. Within the Platonic tradition, the question always remains—what is the relationship supposed to be between the Form and particular, Being and Becoming, the one and the many? Plato never answers this.

A further problem is that Plato never really addresses the problem of change. The question that needs to be answered, is when a physical thing changes, does the transcendent Form of the thing also change? Or does the Form cause the change? But then we are back to our original question of how the Forms interact or participate in physical reality.

It is also worth noting the inherent Gnosticism within the Platonic tradition. Gnosticism is the ancient philosophical and theological view which disparaged and denigrated physical reality. In Plato’s overall philosophy, the physical reality of this world mattered very little because the true reality existed in a transcendent heavenly realm of Forms. This view was even stronger with the neo-Platonist, Plotinus.

(To be fair, the middle and late Plato indicates stronger Gnostic tendencies than the early Plato. In the Charmides, for example, Plato has Socrates speak of the union between essence and matter and the error of separating these things. In regards to Plotinus, although he wrote the last part of his second Ennead as a refutation Gnosticism, his Gnosticism is clearly stronger than that of Plato’s.)

So, the story continues. If essence is a valid metaphysical principle (and it is), what is its relationship to physical reality? And how do we account for change and causation? Fortunately, there are good answers to these questions and they come from Aristotle. His metaphysical scheme is complex but the part we will examine is what has come to be known as immanent realism.

Metaphysics, Philosophy

Plato’s Metaphysical Answer to The One And The Many, Part Three.

by Dave Seng

Part one of this series can be found here.

Part two of this series can be found here.

Plato, however, does not simply divide reality into the transcendent world of Being and the physical world of Becoming. He further divides his two worlds in what has become known as the “divided line” in book six of the Republic.1 The divided line analogy not only seeks to provide a rational description of reality but also has epistemological implications. First, Plato gives this description:

Now take a line which has been cut into two unequal parts, and divide each of them again in the same proportion, and suppose the two main divisions to answer, one to the visible and the other to the intelligible, and then compare the subdivisions in respect of their clearness and want of clearness, and you will find that the first section in the sphere of the visible consists of images. And by images I mean, in the first place, shadows, and the second place, reflection in water and in solid, smooth and polished bodies and the like. (386 – 387)

In this part of book six of the Republic, Plato divides all reality into four sections, not two. Plato gives us a description of a line which itself attempts to divide metaphysics from epistemology. The line is then divided into four sections. This line still represents Plato’s hierarchy of reality but interestingly, he begins his presentation at the bottom of his hierarchy with the realm of images. Images such as shadows and reflections have the least degree of reality. The next section in the world of Becoming is the sensible objects of this world, which partake of a slightly stronger degree of reality. The next section divides Being from Becoming and is the section of mathematical Forms. Above the sections of mathematical Forms are the higher Forms. Plato, in this passage, does not define the “higher Forms,” but from a general reading of Plato, one would guess that he has the Forms of Goodness, Truth, or Justice in mind. All reality and knowledge is a hierarchy for Plato, and Plato has Socrates provide an epistemological understanding of his divided line:

You have quite conceived my meaning, I said; and now, corresponding to these four divisions, let there be four faculties in the soul – reason answering the highest, understanding to the second, faith (or conviction) to the third, and perception of shadows to the last – and let there be a scale of them, and let us suppose that the several faculties have clearness in the same degree that their subjects have truth. (387)

In this analogy and throughout various passages of Plato, Becoming epistemically corresponds to Opinion and Being to Knowledge. The realm of Opinion is divided into Imagination as the lowest and Perception as the higher category. In the transcendent world, Knowledge is divided into Reason as the lowest realm and Understanding as the ultimate. While Plato does not always explain how clearly divided these categories are to be, he does indicate that the realm of Being somehow emanates into the world of Becoming and somehow participates in it. In the Phaedo, Plato speaks of the Form as participating in the sensible world and the source of causation. In the Euthephro, however, Plato speaks as if sensible objects are copies or imitations of the Forms. In this way, Plato resolves the problem of the One and the Many. The Forms in the transcendent world (the One) emanate and participate in the world of Becoming (the Many).

The question remains, why was the problem of the one and the many so important to Plato? First, Plato understands that things that are Becoming cannot be their own causes; to become is to pass from non-Being to Being and non-Being cannot be a cause2. If non-Being cannot be a cause, Plato needs to find a source of change and cause in this world. Plato attempts to resolve this with his theory of Forms. The Forms participate in the world of Becoming and are the source of change and causation. As Socrates explains in the Euthephro, there must be some kind of standard to decide ethical decisions. Similarly, there must be some kind of standard for logical discourse if our thinking and discourse are to be meaningful. Plato posits the Forms as a kind of unchanging standard for meaningful discourse and ethical and moral actions. A world of only flux, change, and Becoming is a world of chaos. Furthermore, Plato also understands that the question of metaphysics is a basic one. How one views the world will determine how one views a variety of other things. If one believes the universe is simply governed by matter and mechanical causes, one could make a pretty good guess about what he or she believes about many other things. If, however, one believes in a transcendent standard of reality that is universal and unchanging, one could guess his or her understanding of things would be very different. In this way, metaphysics is a basic question and probably the reason why Socrates was so interested in examining the nature of reality and connecting it to ethics. For Plato, the transcendent realm of the Forms and their interaction with the world was his way of attempting to resolve these difficult philosophical matters.

As so often is the case in intellectual history, not everyone is convinced that Plato resolved the problem of the one and the many. Although most believe that his discovery of Form is very significant in one way or another. In our next post, I hope to explore how Aristotle, Plato’s greatest student, approached the problem of the one and the many and Aristotle’s contribution to metaphysics.

1 The divided line passage is too long to quote in its entirety, but I will summarize it here and point out the primary sections of his argument.

2 Plato explores this theme in the Timeaus and Parmenides among other places.

Works cited

Plato. The Dialogues of Plato. Trans. Benjamin Jowett. Great Books of the Western World. Vol. 6. Chicago: Encycyclopedia Britannica, Inc., 1996.

Metaphysics, Philosophy, Philosophy of Science

Newton’s Constant and The Plague

by Dave Seng

The more I investigate metaphysics the more I become interested in the philosophy of science. As I write this, my university is closed although instruction has moved online.

Nonetheless, I came across this interesting post from MIT mathematician Cal Newport. By way of introduction, it is important to think about how we can apply ourselves to innovative thinking during these difficult times resulting from our own experience with the COVID-19 outbreak.

As it turns out, Isaac Newton did just that. In 1666, due to the Black Plague, Newton found himself self-quarantined in one of his family estates because Cambridge closed down for about eighteen months. (I sure hope our present situation does not last that long!)

Anyway, here’s how James Trefil, author of Reading the Mind of God: In Search of the Principle of Universality describes the situation and how Newton discovered the principle of universal gravity and what has become known as Newton’s constant:

It is hard to say when this notion of separateness of the earth and the heavens began to break down. In his later years, Newton claimed that the incident of the apple took place in 1666, when Cambridge University was closed because of the plague and he was spending eighteen months in isolation on the family estates. His findings were published in final form in 1687, in his monumental three-volume Principia Mathematica. Somewhere between these two dates, then, the separation of earth and sky, which had ruled men’s minds for a millenium and a half, finally disappeared. (Trefil, 9)

The end result of Newton’s formulation (along with developing an advanced form of calculus) is that the older Greek cosmologies were overturned. Newton discovered the principle of universal gravity which laid the foundation for the principle of uniformity now considered a foundational and indispensable postulate of science. We now understand that objects in space do not conform to different scientific laws than the earth, as the Greek cosmologists believed.

And all of this came because Cambridge was closed due to the plague. I wonder if any of our students today, bored at home, will come up with a similar innovation? I certainly hope so.

For some excellent quarantine reading, I highly recommend James Trefil’s book entitled Reading the Mind of God: In Search of the Principle of Universality.

And here is Cal Newport’s post. Enjoy!

Metaphysics, Philosophy

Plato’s Metaphysical Answer to the One and the Many, Part Two

by Dave Seng

Part one of this series can be found here.

Plato attempts to resolve this question of the One and the Many with his theory of Forms. In order to understand how Plato discovers the transcendent world of the Forms, however, it is necessary to understand his categories of Being and Becoming. These categories are closely connected to the problem of the One and the Many. Basically, Plato’s conception of Being corresponds to the One and his category of Becoming corresponds to the Many. For Plato, Being must be one and unchanging. Being cannot involve multiplicity and change because that would include non-Being. That which is, cannot be that which is not. Due to the law of non-contradiction, Being cannot include non-Being. Plato’s category of Becoming (the Many) includes change and involves a mixture of multiplicity, change, and non-Being. If all reality involves the world of change, flux, and transformation – rationality, science, and thoughtful discourse would be impossible. Plato realized there had to be something that supported the basic nature of existence and provided a ground for understanding reality, logic, mathematics, and scientific inquiry. Plato conceived of this essential nature of reality as the transcendent and eternal realm of pure Being (the One). In his dialogue the Timeaeus, Plato describes his conception of Being and Becoming this way:

First then, in my judgment, we must make a distinction and ask, What is that which always is and has no becoming; and what is that which is always becoming and never is? That which is apprehended by intelligence and reason is always in the same state; but that which is conceived by opinion with the help of sensation and without reason, is always in a process of becoming and perishing and never really is. (447)

It is important to understand Plato’s dual worlds of Being and Becoming in order to fully grasp his metaphysical theory of Forms and to see how he resolved the question of the One and the Many. Plato’s theory of Forms states that every perishable and changing thing in the world of Becoming (the Many) is caused by a transcendent world (the One), which is populated by immutable, eternal Forms. Plato’s conception of transcendent reality is a world that lies beyond both space and time. In other words, according to Plato, every example of chair, human, instance of justice, or act of love has a perfect, unchangeable, transcendent Form that corresponds to it in the world of pure Being. In the Phaedo dialogue, Plato presents this passage which explains how sensible things participate in their transcendent Form:

I cannot help thinking, if there be anything beautiful other than absolute beauty should there be such, that it can be beautiful only in so far as it partakes of absolute beauty – and I should say the same of everything. Do you agree in this notion of the cause?

Yes, he said, I agree.

He proceeded: I know nothing and can understand nothing of any other of those wise causes which are alleged; and if a person says to me that the bloom of colour, or form or any such thing is a source of beauty, I leave all that, which is only confusing to me and simply and singly, and perhaps foolishly, hold and am assured in my own mind that nothing makes a thing beautiful but the presence and participation of beauty in whatever way or manner obtained. (242)

Tables not only participate or correspond to their perfect transcendent Form, but so do moral realities. In this way, Plato resolves the problem of the One and the Many. The Form existing in pure Being participates in the physical world of Becoming. Sometimes the Forms are referred to as Ideas because they can only be grasped through the intellect and human reason.

For Plato, the theory of the Forms and their interaction in the world of Becoming is not only true of the physical world, but also in the area of ethics in the attempt to discover what makes actions right or wrong. In the Euthyphro, Plato attempts to explore and describe how piety participates in the transcendent Form or Idea1 of piety:

Soc. Remember that I did not ask you to give me two or three examples of piety, but to explain the general idea which makes all pious things to be pious. Do you not recollect that there was one idea which made the impious impious and the pious pious?

Euth. I remember.

Soc. Tell me what is the nature of this idea, and then I shall have a standard to which I may look, and by which I may measure actions, whether yours or those of any one else, and then I shall be able to say that such and such an action is pious, such another impious. (193)

For Plato, not only do the things of becoming, things of this physical world, participate in an eternal Form, so do moral actions. In this way, Plato would tell us that the Bill of Rights (the first ten amendments of the United States Constitution) actually participates in the eternal and immutable Form of justice, although imperfectly. In the Republic, for example, Plato explains his project of attempting to define the big metaphysical idea of justice as a first step in discovering how it applies to particular individual instances of justice:

First let us complete the old investigation, which we began, as you remember, under the impression that, if we could previously examine justice on the larger scale, there would be less difficulty in discerning her in the individual. That larger example appeared to be the State, and accordingly we constructed as good a one as we could, knowing well that in the good State justice would be found. Let the discovery which we made be now applied to the individual. (350)

Metaphysically, Plato is interested in finding the perfect model of justice and then trying to figure out how that model or idea of justice works out at the particular level. In part three, we will discover how Plato further divides reality. Then we will evaluate whether or not Plato was successful in his attempt to resolve the problem of the one and the many.

Works cited

Plato. The Dialogues of Plato. Trans. Benjamin Jowett. Great Books of the Western World. Vol. 6. Chicago: Encycyclopedia Britannica, Inc., 1996.

1 The Greek word ‘eidos’ can mean both Form and Idea.