One of the easiest examples which describes Plato’s Theory of Forms can be found in mathematics.
Think of the line as a mathematical object, beginning at zero and ending at, say, ten. Zero is an end point, and ten is the point at the opposite end of the line. In between, there are an infinite number of other points, which make up the line. We can name some of these points: one, for example, or two. We can find them on the line quite easily; one will be one-tenth of the way along the line, and two will be one-fifth of the way along. There are also points that have a decimal place, such as 2.5; we can find it a quarter of the way along the line. Indeed, we can locate the position of any point we care to name between zero and ten. We can even find a point with a long decimal place. There are some points with infinitely long decimal parts, such as, 3.33’ (3.3 recurring which means that the decimal part is represented by an infinite row of 3’s: Also the same as 1/3) or pi or the square root of two, but we can still, theoretically, locate them on the line. There are also some points with infinitely long decimal parts that we cannot even name though it is not unreasonable to assume that despite our inability to name them, they are still there.
There are also many points that we could name if only we could be bothered to, such as, a point with a billion decimal places. It would take some time to name one, but once we had written it out, we could be sure that it was on the line and that we could find its exact location. The idea is that we have a world of actually existing and known points, all of which can be located on the line. The line represents the Platonic realm of points. Prior to discovering or naming even the most boring point, we know that it already exists on the line.
The theory of forms, or ideas, marks the basis of Plato’s entire philosophy. The realm of ideas is the place in which generic existence can be found. Take, for example, the concept of a table. We are all familiar with a wide range of different types of tables. But is it possible to define what a table actually is? It is clear that we cannot include at all, as a definition, that a table is an object with four legs because we could quite easily point to tables that have more legs or fewer legs, which would effectively counter the definition of having four legs. Tables exist that have no legs, so to define a table as a thing that has legs or does not have legs is not to define the table at all. All things have legs or do not have legs, so such a definition would be vacuous. Citing the way that a table is used would be unhelpful because tables can be used for a wide range of purposes, and finding a single use to which all tables are put would be impossible.
So what is it about a table that makes it a table? Where, precisely, are we to find the essence of “table-ness”? Plato answers by saying that we know the essence of what a table is because we have access to the eternal realm of forms. We know, via this privileged access, what comprises the essence of a table, so that when we come across a table in the world that we experience, we are able to identify it as a particular table from the realm of all possible tables.
The realm of ideas, then, is a realm of perfection. These days, philosophers contrast particular objects with the notion of universals. A point is an actual position; the line is the universe of points. In the actual world, a particular is something that we can experience — for example, a specific shade of yellow.
When we experience something that is yellow, we know it to be yellow even though we may never have experienced that particular shade of yellow before. How is it possible to know the color of something when we have never experienced that color before? The doctrine of Plato’s forms claims that we bear knowledge of the universal notion of yellowness, and as such, we are able to recognize even those shades with which we have no prior experience.
The philosophy of the Greeks still offers many ideas relevant to the work of contemporary philosophers: the problems with which the Greeks were concerned continue to crop up over and over again in various guises. The notion of substance was a chief concern of the Greeks. It was also a chief concern of the philosophers of the seventeenth century. In later posts we shall look at how the notion of substance was developed or used during these two time periods.

Plato was born in 428 BC and was a prolific writer for some fifty years. The general philosophical position to which Platonism adheres speaks of an eternal realm in which we are able to find true knowledge. In the sensory world, we find a number of particular objects that are open to our investigation by virtue of being in the realm of our direct experience. In the eternal realm of ideas, we find perfect examples of the objects—or forms, as Plato called them—that we access with our senses. For instance, although a perfectly straight line cannot be drawn in the three-dimensional
realm of our experience, it can exist within the mind and, likewise, in Plato’s eternal realm of forms. This formulation was expressed in an attempt to define such concepts as beauty, justice, and largeness. Objects in the sensory world cannot be defined as just or beautiful without qualification because an object is only deemed beautiful via reference to some other object. Consequently, there can never be any true knowledge of beauty in the sensory world — only a true belief in it.
Truly knowing a concept such as beauty or justice required Plato’s theory of recollection. The theory of recollection first appears in the Meno, and it demonstrates Plato’s view that we are unable to acquire knowledge. Rather, knowledge is already present in the mind of each person, and the discovery of new knowledge is only a recollection of knowledge that we have forgotten.
The dialogue in Meno describes a scene in which Socrates shows an uneducated slave boy a square and asks him to draw a second square with an area twice as large as the first. The boy thinks that this is an easy task and proceeds to draw a square in which the sides are extended to twice their original size. Socrates then tells the boy to work out the area of the second square, and the boy realizes that his square is, in fact, four times the area of the original square. Socrates points out to the boy that realizing he is wrong is better than being wrong while believing he is right. The boy goes on to work out the answer to the problem without any assistance from those around him, all of whom already know the answer. This little exercise is supposed to demonstrate the process of the uneducated boy recollecting knowledge that he already had.
According to Plato, not only does the mind bear within it knowledge of mathematics, it bears all the knowledge that can possibly be had.
This may seem like an extreme view, but is worth considering milder versions of Plato’s theory. The mind can be viewed as a kind of container for ideas in much the same way that a computer screen is a container for information to be displayed from the internet. In the case of the computer screen, the color, the resolution and the screen size all provide a framework with regard to what it is that is capable of being displayed, as indeed does the type of browser in use. Lines that have been coded to be twelve inches in length cannot be displayed as such on a ten inch monitor for example. A web page has to be displayed within the capability of the computer screen in question.
When I click on a web link, the page will assemble itself on my screen according to the instruction of the html, php or other code.
My screen is to some degree, just displaying what is already present in my computer and having it organized by the process of accessing some external realm. My screen is quite capable of displaying all possible web pages, even those web pages that have yet to be written. It is equally capable of accessing web pages that are unique to my computer. For example, if I type in some chain of words into a search engine then the page that displays is created according to those words. That page may never have existed before on any computer screen, yet I can access it in the same way that I can access all the other infinite variety of web pages that either exist or potentially exist. My computer screen is capable of displaying them all.
The concept of the infinite leads us toward the notion of some kind of transcendental realm wherein specific individuals can be located. Continuing with the screen metaphor, it would obviously be ludicrous to expect my computer to store in its memory every possible web page that it is capable of displaying. Yet by the fact that my computer can represent all possible web pages on my screen it is in a mild sense at least just remembering a particular configuration when it is displaying a particular page. The computer has always been able to display that page and consequently can be considered to be remembering that web page. The idea is focused more sharply when we consider the idea of performing a search and accessing what may be a uniquely designed page. That page has always existed in the internet (platonic) realm even if it has never been an actual page before.
This example is not directly analogous to the idea of Plato’s theory of recollection. Explanations of concepts that contain the notion of infinity are difficult to express clearly. But by way
of further depth we can think of two numbers each of which are a billion digits long and of the sum of those two digits.
No one has ever thought of these two particular numbers before and so no one has ever done this particular addition.
However, this sum has always existed within the Platonic realm and despite never having come across this particular corner of mathematics our mind is clearly in some sense remembering the sum. The example is clearest within the topic of the eternal realm of mathematics but Plato intended us to view this principle in all areas of knowledge. Everything we ever come to know is already in the mind and thus is being remembered.
Plato’s theory of forms relies upon the notion of existence by virtue of possible existence. If we are capable of having a particular thought, then that thought is already within us even if we haven’t yet had the thought and even if we aren’t yet aware of the thought’s possible existence. For Plato, the forms (or ideas) do exist in a real sense, but they exist in a realm that is accessible only to the mind, not to any of the five senses.
Platonism will be a recurring theme on this website. It will crop up as one side to just about every philosophical argument that occurs.

In the previous post we saw how Democritus proposed an atomic theory of matter. Then along came Aristotle who offered an account that assumed that matter can be cut into ever-decreasing size. However, permanence and change had to be accounted for in any explanation of the universe. To do so, Aristotle explained the universe in terms of form and matter. For Aristotle, matter is a pure thing, which has no characteristics at all other than its ability to exist in some form or another. Matter is a permanently existing thing; yet, it can only exist in some form. The form constitutes the appearance of the matter that our senses receive. Anything that exists has to be understood in terms of both its form and its matter. The matter is always present, and the form of the matter is simply the way it is at any given time.
These brief explanations of the ideas of Democritus and Aristotle show how the problem of permanence and change has been dealt with in the past.
Any metaphysical position still needs to account for these basic features of the universe. Indeed, anyone who wishes to construct a metaphysical system needs to somehow account for all the problems that metaphysicians have encountered in the past, many of which are closely related. In some respects, these problems are more difficult now because contemporary science has contributed so much that the present-day metaphysician must take into account. Modern-day science has the same metaphysical problems in some respects.
Quantum mechanics show us that matter can be seen to have atomic properties (i.e., a smallest possible size) and yet also has wavelike properties. It is a similar metaphysical problem,
albeit couched in different terms and within a different context.

One of the earliest metaphysical problems concerned permanence and change. To the early thinkers, the world contained things that appeared to change; yet, these very same things also possessed a certain endurance and permanence.
These changing and permanent qualities seemed to give the world a sense of inconsistency. If everything changed, then nothing was permanent, and if nothing were permanent, nothing could be studied or understood. But if the world contained a permanent entity, then it could not change or account for any change that took place in the world.
The Greek philosopher Heraclitus argued that everything in the universe changes (everything, that is, but the principle that everything changes). He was the oft-quoted philosopher who claimed that it is impossible to step into the same river twice because by the time one steps into it again, the river has changed; it’s a different river entirely.
This argument was stretched to the limit by Cratylus, who went so far as to claim that one cannot even step into the same river once because by the time the step is taken, the river has changed! Cratylus even refused to engage in conversation because by the time the speaker had finished his sentence, the words, the speaker, and the listener had all changed. He allegedly used to wiggle his finger to acknowledge that he’d heard something. If everything is in a constant state of change, however, then there is no way to make any sense of the world because there is nothing lasting to investigate. Viewing change as a fundamental characteristic of the universe was, therefore, problematic, but the notion that everything remained the same also posed some serious challenges.
Parmenides argued that everything in existence is permanent and unchangeable. Needless to say, anything that is unchangeable is not subject to the impact of happenings.
The only property that unchangeable entities can have is that of existence. The single thing that can be said of the permanent is that it is. Anything that is subject to change, Parmenides argued, goes through the cyclical stages of not existing, existing, and then, not existing again. A student of Parmenides, Zeno of Elea, devised some well-known paradoxes that supposedly demonstrated the contradiction of motion. I shall address this in more detail later.
A kind of resolution was made between the two schools of thought — permanence and changeability — when Democritus proposed the concept of the atomistic universe. Previous arguments had been concerned with whether the matter that makes up the world is infinitely divisible. People wondered if units of matter can be divided in two forever or if there is a smallest possible size — an indivisible unit. Democritus debated in favor of smallest possible units. This allowed him to argue that the world is both permanent and changeable.
The atoms are permanent, Democritus argued, because there is always the same number of atoms in the universe.
The relation between atoms does change, and it is this flux in relation and distribution that accounts for changeability.
Ultimately, however, Democritus chose to side with Parmenides and claim that the world is basically unchanging; the movement of atoms merely explains the change apparent in human perception while, in reality, the universe is fixed.
This is a good example of a metaphysical position offering a solution to a problem, reconciling the apparently contradictory views of permanence and change by introducing atomicity. Having a theory of atoms helped Democritus give an account of the universe that had both permanent and changeable features. Although the atoms were small, fixed objects, the movement between them was a changeable feature.
Democritus adopted a position on one metaphysical feature of the universe—claiming atomicity was correct over infinite divisibility — and then used this position to explain how the world could be permanent and, thus, capable of investigation while still being able to account for the changing features of the world. The reason why this should be thought of as a metaphysical argument is because there was no way for the Greeks to go out and test this idea. It would be two thousand years before man had the technical ability to test whether such an idea was true or false. We would now class an atomic theory as a scientific theory, but when there was no means by which an empirical investigation could be performed, such a theory would have to be considered metaphysical.

The best way to approach an understanding of metaphysics is with the use of an example, so let’s begin by looking at the kind of problem with which the Greeks were concerned. They had what one might call a crude system of beliefs. They attempted to explain the workings of the universe in terms of four fundamental elements: air, fire, earth, and water. Briefly explained, according to the Greeks, the planet Earth was at the center of the universe, and the heavens rotated around Earth. The elements of water and earth found their natural place on the planet Earth and were thought to “fall” to Earth. The elements of air and fire naturally rose to the heavens.
The primary question that the early metaphysicians asked was “are these four elements really the most fundamental things, or does some other thing exist beneath what is apparent and give rise to these four elements?”
The metaphysicians divided into two camps on the issue: those who argued that there could only be one “real” thing (monists) and those who argued that we needed more than one thing to account for
those things in the universe that we knew of (pluralists). The Greeks were asking “what is the true nature of what exists?
Can the things that we observe in the world be explained by one entity that underlies the four entities that we observe, or are the four categories of air, fire, earth, and water ultimately fundamental in themselves?”
Today, we have a more sophisticated scientific view, but we still have similar metaphysical problems. We have discovered that air, fire, earth, and water are all made of the same things (i.e., protons, neutrons, and electrons). Protons and neutrons, it turns out, are made of the same one thing — quarks — so some believe that the universe is made up of quarks and electrons.
Others argue that along with these physical objects, we have to include mental phenomena as objects of the universe. These are all different forms of pluralism. The monists would still argue that, ultimately, there are only physical objects and that one day, they will all be reducible to some fundamental thing and that mental things would be accounted for in this reductionism.
The metaphysician, then, is trying to account for all the current scientific knowledge, but in a broader context. Not only does he deal with science but anything else that may be known or believed about the universe. He can only function in rather vague terms but still seeks some kind of explanation for the most fundamental or general characteristics of the universe, and his work encompasses everything from matter to minds to God or other things that the metaphysical system under development may require.

Many systems have been developed over the last two thousand years, a few of which you might find on this blog. Though the speculations of the metaphysicians hold some interest, by no means is there any general agreement as to which set of speculations should be held up as the one true picture of the universe. Every school of thought within metaphysics can produce what appear to be convincing arguments against other systems of thinking; yet, they still remain unable to produce a completely infallible justification of their own views. And some philosophers have argued that metaphysics is a worthless exercise in and of itself, that due to basic limitations in our abilities as humans, the entire metaphysical enterprise is doomed to failure.

Since the emergence of the German philosopher Immanuel Kant, the emphasis of metaphysical study has been switched from a systematic study of reality to a study of the structure of thinking about reality. Kant tried to show us that the structure of the mind will, in some way, organize the sensory information that the mind receives, thus proving that the way we receive experience is somehow tailored by the structure of our rational minds.
The biggest criticism of all against metaphysics is that any assessment thereof can only be formed within the particular metaphysical construct that is under analysis. Any description of the universe would have to offer an account of the observers within that universe and, consequently, an account of how the observer relates to the universe. The account of the universe, then, would depend on the way the observer views the universe. But the way the universe is would have some relevance to the account of how the observer views it. This leaves every metaphysical system wide open to accusations of circularity. An argument like that cannot be defeated.
However, if we perceive the correct metaphysical system, then the perspective from within that system is the correct one, and the argument of circularity becomes irrelevant.
With all this in mind, we are wise to only suggest ways of thinking rather than offer any degree of certainty that one way of thinking is the correct one. If a metaphysical system is incoherent or inconsistent, then we have a duty to abandon it, but if it is not falsifiable via some empirical method, then it at least stands a chance of being correct. Also, if it manages to offer a wide range of explanation, then it again has a chance of being correct. Furthermore, if it manages to offer a wide range of explanation without being so intrinsically broad that its explanations are vacuous, then all the better for that system. Even if we did ever manage to describe the absolute, fundamental principles at the foundation of the universe, we could probably never be sure that we were describing or establishing the right principles. However, we can explore different metaphysical systems to see if we can discover what it is we should seek in any metaphysical description.

Metaphysical notions are often met with criticism. The same goes for those who engage in the practice of metaphysics. Such criticisms can be addressed or challenged. It is arguable that metaphysics is the foundation for everything and is, thus, the most important subject in any attempt we might make to improve our knowledge of the universe. I will sometimes argue for this point in articles on this blog, but the basic principle is that whatever we can claim to know about anything at all has to be put into some framework or viewed within some context. The framework functions as a backdrop theory for whatever it is that we are claiming or investigating. The denial of such a theory denotes a hard form of skepticism wherein no knowledge of anything is possible apart from the direct
experience of the senses and the tautologies of mathematics.
But even the most die-hard philosophical skeptic is forced to relax his positions when faced with carrying out his everyday activities. Whether he likes it or not, the extreme epistemological skeptic has to have a basic framework of beliefs — if not to do philosophy, then to live.
Some also argue that because metaphysics is neither falsifiable nor verifiable, then any claims made by metaphysics are meaningless. Furthermore, the same arguers will likely tell you that any attempt at describing the whole of reality can be expressed in terms of the concepts used to describe each and every part of reality and would, thus, be insufficient on its own. Nonetheless, we find a range of concepts and principles employed in the physical sciences that are, in fact, metaphysical notions. Energy and gravity are but two of them.

Metaphysics is the most abstract of all the subjects within philosophy. A theory is often said to be metaphysical if, because of its abstract nature and complexity, it appears to be incomprehensible. Metaphysics is derived from the untitled works of Aristotle, which came along after his work entitled Physics. The word physics comes from the Greek word for “concerning nature,” and much of what we discuss under its heading is called “physical science.” The prefix meta means “after.” Accordingly, metaphysics literally means “after science.” It deals with those problems that are left unresolved after the work of the scientist has been completed.
But what does this mean?
It can mean a number of things. Science, in its various branches, only looks at a small part of nature at any one time, but metaphysics attempts to conjure up a holistic description of reality. It could also be said that the aim of metaphysics is to get beyond the world of experience, to try and understand the realm of the suprasensible (if it exists). Another task of metaphysics is to explore the foundations of knowledge in an attempt to establish fundamental—or first—principles, which is similar to the task of examining critically what other disciplines take for granted. Finally, there is metaphysics’ search for the fundamental constituents of the universe (i.e., what actually exists).