Metaphysics, Philosophy

Aristotle’s Metaphyisics: Form

by Dave Seng

In the previous post, I explained a few of Aristotle’s objections to Plato’s teaching that essences, or Forms, are separated from matter and particular things. In this essay, I will explain what Aristotle’s idea of form and matter is, and why it is significant to Western metaphysics. Indeed, Aristotle’s conception of the world around us has important consequences for how we view reality today, especially in the areas of math, science, ethics, and ultimately what it means to be human.

As I have noted, Aristotle sought an answer to the question raised by Plato, “How do the Forms participate in the individual things we experience every day?” Plato did not have an answer to this question, and much of Aristotle’s project was to discover a solution. We have already seen that Aristotle did not throw out Plato’s theory of Forms entirely.

Essentially, Aristotle’s theory of Forms is that they must be in the things themselves. According to Aristotle, Forms, or essences, exist within the sensible particular things of this world. Matter and Form, or essences, are inseparable for Aristotle. Particular concrete things have mathematical properties such as weight, volume, and extension because the mathematical properties (Forms or essences) are in those things, not separated from them. In physical and biological life, Forms must be a natural and immanent part of material beings in order to account for the drive, impetus, and direction towards the good that all living things display. The technical term that has come to represent the Aristotelian position is called “hylomorphic composition” or “hylomorphism.” Hylomorphic composition literally means, “matter-form composition,” and represents the view that all natural things require for their existence both passive “stuff” and active, determining essence.

Forms can be causes of things only if they are in those things. Mathematical notions of symmetry, ratio, and order are considered the cause of beauty in the world. The Form must be in the thing itself and is the basis for causation. For these reasons, Aristotle’s view has come to be known as “immanent realism.” Realism is simply the idea that forms, or essences, actually exist in reality. Aristotle’s immanent realism can be easily understood. The form of a circle does not exist in a transcendent Platonic realm, but immanently within the circularity of the tire on my car, or the circularity of my coffee cup. (They may not be absolutely mathematically perfect Platonic circles, but the quest for absolute perfection has been the downfall of many philosophers and their theories.)

Since Forms exist within particular things, there is now an account for causation. Forms are causes because they are in those things. My coffee cup is circular only because the essence of circularity is in the cup. Essences are immanent and inherent to particular things. Against Plato, Aristotle emphasized that there is no “circularity” floating around in a transcendent realm outside the world of particular things. For a particular thing to exist, and to be considered real, the essence, that which makes something the kind of thing it is and without which it cannot be, must be combined with matter to give the essence a concrete and particular existence or expression. From a realist perspective, reality itself is the determinant of order, not disembodied Forms (for the Platonist), the categories of the mind (for the Idealist), or conventions of language (for the Nominalist). Forms are basic properties of being, or reality itself. The law of noncontradiction is not a principle hanging in suspended animation somewhere in a transcendent realm, but a concrete fundamental property of being. The laws of logic and principles of mathematics are essential properties of being.

The point of immanent realism or Aristotelian realism is that reality has its own intractable way of being. While not being pure naturalists or materialists, (because of the real existence of essences) Aristotelians believe that one can discern important mathematical, ethical, scientific, and philosophical truths from this world’s concrete objects of this world. What this also means is that all things in the natural world have an immaterial aspect to them. While there is no Form without matter and no matter without Form, it is also important to keep in mind that matter is not Form and Form is not matter.

Sometimes an objection is made to the Aristotelian view of reality. It could be queried that if someone were to destroy all the circular objects in the world, would then the essence of circularity be destroyed? There are a few Aristotelian responses to this challenge. One might counter that since essences and mathematical properties or foundational to being itself, a destruction of all circular objects would be the complete elimination of all being. In such a case, the question would be moot since there would be nothing left to discuss. There is another Aristotelian response to this challenge, however. One might appeal to the potentiality of essences. For Aristotle, all physically existing things have potential, so the matter in a thing or object has potential by virtue that it may be changed into something different. If something has the potential for circularity, the essence of circularity exists. In other words, the potential for circular objects is sufficient to ground mathematical circles. Yet another Aristotelian response can be made. Suppose we do not privilege the present in our understanding of time. Essences would exist in the things themselves, but they exist in all time equally—past, present, and future. Here, all things that ever had or ever will be at any time are included. If a circular coffee cup exists somewhere (in the past, present, or future), even if just once, circularity exists and is real.

With Plato, Aristotle understood that essences are a necessary part of reality and that it is really impossible to understand the nature of reality without them. When we recognize kinds, types, and species, we are dealing with manifestations of essences. Further, when we discern symmetry, ratio, and mathematical truths we are dealing with essences. As we have seen, the central problem with Form or essences, for the Platonist, is that the Form can never be in the ever-changing and unstable material thing. With the Aristotelian understanding, we recognize that essences are basic foundational properties of being and particular objects, without which we could not recognize what kind of thing something is. In the next post, I will briefly examine a few Platonists who struggle with their own position in confronting the fact that reality is the determinant of order.

For a great introduction to Aristotle, see Aristotle For Everybody: Difficult Thought Made Easy by Mortimer J. Adler.

For an interesting and easy understanding of an Aristotelian understanding of mathematical properties see James Franklin, Aristotle Was Right About Mathematics After All.

Intellectual History, Metaphysics, Philosophy

Empty Words and Poetical Metaphors: Aristotle’s Critique of Platonic Forms

by Dave Seng

For more context about Plato’s metaphysics these posts should be helpful. For Aristotle, these might provide a helpful background.

It is important to realize that Aristotle did not entirely reject Plato’s view of reality. He did, however, believe it needed improvement. In this essay, we turn to Aristotle’s view of ultimate reality and contrast it with Plato’s because that is where the biggest difference lies between the two thinkers. It is certainly the most significant difference when it comes to the development of metaphysics in Western intellectual history.

We saw in our series on Plato, that his conception of Forms1 (or universals) were his answer to the classical problem of the one and the many. He believed that by positing universal forms he could explain the unity of the diversity we see all around us. Aristotle agreed with Plato on this point. Only by the objective essences of things, can we account for the order around us, both in nature and in morality. Further, essences account for the very possibility of knowledge about things. The difference, however, between Plato and Aristotle, rests in how the Forms or essences are related to particular things.

Early in the Metaphysics, Aristotle provides his own summary of Plato’s conceptual scheme:

…[Plato], having in his youth first become familiar with Cratylus2 and with the Heraclitean doctrines (that all sensible things are ever in a state of flux and there is no knowledge about them), these views he held even in later years. Socrates, however was busying himself about ethical matters and neglecting the world of nature as a whole but seeking the universal in these ethical matters, and fixed thought for the first time on definitions; Plato accepted his teaching, but held that the problem applied not to sensible things but to entities of another kind—for this reason, that the common definition could not be a definition of any sensible thing, as they were always changing. Things of this other sort, then, he called Ideas, and sensible things, he said, were all named after these, and in virtue of a relation of these; for the many existed by participation in the Ideas that have the same name as they.3

Aristotle goes on in his Physics, Nichomachean Ethics, and Metaphysics, to critically examine Plato’s theory of Forms. Some scholars have found twenty five or more arguments against the Platonic theory in Aristotle’s works. Here, we will only focus on a few of the more important ones.

The first one, is famously known as the “third man argument.” He develops this argument in his Metaphysics and Sophistic Refutations. In this argument, Aristotle states that in order to explain the similarity between a man (1) and a second man (2) we must posit a third ideal man or form of a man, a third man. But then we must explain the similarity between the first two men and the form of a man with another, “higher” form of a man. The situation becomes an endless regression of positing further higher forms and the original instance of the first man or thing is never explained. Because the forms are not only patterns of sensible things, but of Forms themselves, nothing gets resolved.

In book two, chapter two of his Physics, Aristotle argues against the existence of separated Forms based on the mathematical properties inherent in physical objects. Here, Aristotle makes the point that physical bodies contain surfaces and volumes, lines, and points, and these are all mathematical properties. Aristotle makes the common-sense observation that material objects have mathematical properties and uses this fact to mount an interesting critique of Plato’s Forms. Remember, for Plato, forms are separate from matter. Forms exist in an ideal transcendent realm away from the realm of becoming and change. According to Plato, there are not any Forms in material objects. Aristotle finds this situation incredibly hard to believe. Plato’s theory of the Forms says that among the Forms are mathematical objects such as the form of equality, the form of a triangle, the form of a triad, and so forth. Aristotle reasons that mathematical objects can not be separated from material objects because material objects have mathematical properties. He concludes that if mathematical objects (a sample of Forms) could not be separated from material objects (physical things), then forms can not be separated from matter. Physical things have mathematical order to them.

In his Nicomachean Ethics, Aristotle makes an important ethical objection. He points out that Plato’s Form of the Good is only an ideal to to be contemplated. It does not have effective power itself. The Form of the Good is an ideal that can not effect change or transmit potency. If, on the other hand, particulars have no form in them and are only matter, what then inclines the particular towards orderliness, beauty and to its good? What is there in matter, material beings, that gives them their natural impetus and direction towards the good, if Forms are transcendent and not immanent in matter?

All these questions and objections, point to the biggest problem that Aristotle believes is at the center of Plato’s theory. It is the problem that the Forms are separated from matter and sensible things. Aristotle correctly represents Plato as having placed the ultimate causes of things (the Forms) in a transcendent world and thus separated from the things they are supposed to be the causes of. Aristotle’s great concern was to discover the cause of a thing or the cause of a property of something. He thought that by studying individual things, one could rationally discern the basic causes and principles of all Being. To understand why something is the case, we must first examine its cause.

In book one, chapter nine of his Metaphysics, Aristotle describes what he thinks is the biggest problem with Plato’s view of reality:

Above all one might discuss the question what on earth the Forms contribute to sensible things, either to those that are eternal or to those that come into being and cease to be. For they cause neither movement nor any change in them. But again they help in no wise either towards the knowledge of the other things (for they are not even the substance of these, else they would have been in them), or towards their being, if they are not in the particulars which share in them; though if they were, they might be thought to be causes, as white causes whiteness in a white object by entering into its composition …

But, further, all other things cannot come from the Forms in any of the usual senses of “from.” And to say that they are patterns and the other things share in them is to use empty words and poetical metaphors …

Again, it would seem impossible that the substance and that of which it is the substance should exist apart; how therefore, could the Ideas, being the substances of things exist apart? In the Phaedo the case is stated in this way—that the Forms are causes both of being and becoming; yet when the Forms exist, still the things that share in them do not come into being, unless there is something to originate movement.4

Aristotle points out that, by definition, Forms do not change because they exist in an unchangeable realm of being without becoming. The result is that Forms have no potency or ability to effect change. The separation between being and becoming, Form and matter, is very significant indeed. Platonic Forms have no way to account for the change, motion, coming into being and ceasing to be that one experiences every day.

As we have seen, Aristotle does not reject the idea of essence or Form entirely. In the next post, we will explore the most important elements of Aristotle’s metaphysics and his solution to the Platonic separation of Form and matter.

1It may not be entirely correct, but for our purposes, we’ll use “forms,” “universals,” and “essences” synonymously. The term “idea” is also used to describe the Platonic Form.

2Cratylus was a follower of Heraclitus but pushed the teaching of his master even further, for he said that one could not step into the same river even once!

3Aristotle, Metaphysics, 987a-b, tr. W. D. Ross, in Basic Works of Aristotle, ed. Richard McKeon (New York: Random House, 1941).

4Ibid., 991a-b.

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.