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.