by Henry Piper (all rights reserved)
What Do We Mean by “2+3=5”?
Let us first agree that it is true that 2+3=5, and let’s be clear that when we use these five terms, “2,” “+,” “3,” “=” and “5,” we are not referring to the symbols as here written or the words that identify those symbols; rather, we are referring to the things themselves. Clearly these symbols and words are purely artificial and conventional: they have been invented by human beings in the past and we now accept them and use them in communication among ourselves by agreement only and not because they are innately “true” or “real” in any way. The very fact that different people with different languages at different times and places can and have and do use very different words and symbols reminds us of how artificial these mere signs are. A “sign,” such as a symbol or a word, is a sign for or symbol of something else: there’s no reality in the sign itself. The sign refers to something that is not now or cannot be present here and now or cannot appear to the senses at all. Some signs represent things that can be seen but are not here now, such as a road sign that pictures a bump that is up ahead: the sign pictures and resembles a bump, but it is of course not itself a bump but a sign that merely represents the bump itself.
The mathematical signs we’re using here, however, represent things that cannot be seen at all, at least not by the senses. Admittedly, we can see two apples, but when we see the two apples we’re seeing apples and not the number two. What does the number two look like? It doesn’t look like anything: remember it’s not the symbol we’re talking about here, but the thing itself, and that thing is in fact a purely mental thing, “the idea of quantity ‘two’” we might say, which can be thought by the mind but cannot be seen by the eyes, for only physical things can be observed by the senses. So the number two itself is merely an idea, an idea of a quantity of something, of anything, even of something that doesn’t physically exist. Thus we know what you mean when you say “two little green men from Mars” and that two green men is one fewer than three green men, even though little green men from Mars do not exist! So the numbers, as ideas, are entirely independent of the physical world: again, they can be thought but they cannot be seen.
Signs and Symbols v. Ideas
The same goes for the plus and equal signs: they are symbols for mental operations of putting things together and of the equivalence of two ideal quantities, respectively; but you cannot see addition or equality. Again, you can see two apples being gathered together with three other apples to make five apples, but again you are only looking at apples. This is how we typically learn to add, isn’t it? Our teacher puts out two apples and asks us to count them, which we have previously learned to do by memorizing the words and signs for the numbers (through watching Sesame Street perhaps). This learning how to count is a matter of memorizing the invented, artificial and conventional signs and symbols so we can communicate with others who use the same language and symbols. So we count the two apples, then we count the three other apples the teacher places next to them, and then the teacher pushes them together (as represented by the plus symbol) and asks how many are 2+3? Then we go back and count the five apples to conclude that 2 apples plus 3 apples equals five apples.
As kids, we need the help of the visual aid provided by the apples because we have not yet learned to use our minds: we can’t yet do arithmetic (in our heads), so we have first to count the apples (which we see on the table). But before too long, when the teacher asks, “if two little green men join three other little green men, how many little green men would there be?”, we can answer “five” without having to see the little green men! How can we do this, given that little green men don’t exist? We can know this because the truth of 2+3=5 is not in the apples, and it obviously can’t be in the little green men; rather it is, it exists, not in time and space but in our minds—not physically in, rather the mental power of our minds is able to mentally perceive the truth of 2+3=5 even though that mental truth is not a physical thing and thus cannot be in any physical place. It is an idea, not a physical thing, so it can’t be seen but it can be thought, since obviously we do think it. If two widgets are added to three widgets, how many will there be? Do we know that there will be five by counting widgets?—no we do not, we cannot, because there’s no such thing as a widget! Yet we still can do the math, because the mathematical truth is not in any physical thing, it is not in any time or place, it is purely mental and exists not in the physical world but in the mental world alone.
Doing Math “In Our Heads”
When the teacher asks us, how many are 17 plus 25, is there anyone with a reasonable elementary education who cannot quickly come up with 42? We could get the answer by gathering together a whole bunch of apples, but that would be laborious and awkward, it would take awhile and with that many apples rolling around we might easily miscount them and get the wrong answer. But who needs to count apples when in a brief second we can get the answer by doing it in our heads? The fact that we can do that at all attests to the fact that such mathematical truths are purely mental and do not depend at all on physical reality. Do I have to have apples to know how many I would have if I add 17 and 25?—of course not! Thus clearly the truth of 17+25=42 is independent of the physical world! Note finally that everyone else who considers this problem of 17+15—if they concentrate sufficiently—will get exactly the same answer, which establishes that the reality of “17+15=32” is not some physical thing that we can see but something purely mental that anyone, anytime and anywhere can grasp with the power of the mind alone?
Today and Tomorrow
Here’s a question: will the sun rise tomorrow? What is the most accurate answer to this question? It is not “yes, definitely”—why not? It is very likely―based on past experience as well as on our knowledge of the rotation of the earth and its revolution around the sun, which has evidently been happening for some 5 billion years―that the sun will rise tomorrow; however, in the meantime, it is possible, though not very likely, that events could occur overnight to prevent tomorrow’s sunrise, thus it is not logically necessary that the sun rise. If the sun blows up overnight, or if an asteroid collides with the earth stopping its rotation, the sun will not rise tomorrow. So although tomorrow’s sunrise is a very good bet, it is not absolutely certain, and the most accurate answer to the question of whether it will rise tomorrow is thus “very likely” or “probably” or “almost certainly.” The best scientific prediction of astronomers suggests that there is good reason to believe that the sun will continue to rise for another 4 or 5 billion years, more or less; but that is only a prediction, though a scientifically reliable one, and in any event such scientific prediction also informs us that at some time in the future the sun will definitely not rise in the morning (once the sun expands into a red giant and burns the earth to a crisp).
Now here’s another question: will 2+3=5 be true tomorrow? I suggest that the answer to this question is yes, absolutely definitely—it cannot not be true! How can I know this about tomorrow, when tomorrow hasn’t happened, when I can’t even be absolutely sure the sun will rise? The answer is that 2+3=5, unlike the rising of the sun, is not a physical event that happens in time and space. It does not happen that 2+3=5, it just is, it has always been and always will be. How do I know this? This is where we begin to do philosophy. Ask yourself: can you sincerely fail to see that 2+3=5 involves a fundamentally different kind of reality than “the sun rises”? The rising sun happens, it is a physical event that happens (or not) at some time and in some place, it is a merely possible event. But when is 2+3=5?—always and ever! Where is 2+3=5—everywhere, or nowhere. 2+3=5 is not something you look at with your eyes, it’s not something your teacher hands over to you or that your teacher could hide from you, in other words it is a necessary truth! The sunrise is a mere possibility, if a very likely possibility, whereas 2+3=5 is a logical necessity.
Now consider the Pythagorean Theorem: did Pythagoras invent it? No!—Pythagoras did not invent it, it’s not an artificial creation; rather, he discovered it, dis-covered—that is, it was there all along, as if “covered,” but no one had noticed it before he came along. But it was still true and would have been true, necessarily, even if he had not discovered it and will always be true even if all intelligent life in the universe dies out leaving no one ever to know it again. Even then it still will be! And this is all still more remarkable when you consider that the Pythagorean Theorem concerns triangles, which are perfectly flat, plane figures, because nothing in the physical world can be perfectly flat since space itself is curved, meaning that perfect, flat triangles do not and cannot physically exist, any more that the idea of quantity “two” physically exists! But triangles do exist, most assuredly, but not to be seen; rather, they exist mentally, or ideally, that is, we can think them even if we can never see them.
The Physical v. the Mental
In the distinction between these two questions, one about the sunrise and the other about a math problem, we observe the distinction between the physical world and the mental. In the physical world, everything is constantly changing, every instant. Thus although it may appear or feel as though the chair you’re sitting in is stable and the same chair you were sitting in a minute ago or even yesterday, in fact that is only approximately true. In fact, the chair is changing every instant. If it is wooden, it’s rotting away right now, as you read this, even if it appears not to be, if metal it is rusting away right now even if your eyes are not strong enough to see it. Physics tells us in fact that all the objects in the (physical) world are buzzing energy systems with particles whizzing around at dizzying speeds in a mind-boggling synthesis of order and chaos. You know of course that the chair was made quite recently and that before it was made it was not, and you know also that in the not-too-distant future it will be scrapped and burned or crushed such that it will no longer be.
The point is that all physical things are constantly changing, constantly variable, in a constant state of coming-to-be and passing-away: every physical thing is in such a constant process, even if it does not appear so, of becoming something else, constantly moving from one condition to another, from oblivion in the past and heading right back to oblivion again in the future—“from dust to dust”. There is nothing in the physical world that is invariable; everything in the physical world is constantly changing. But compare mathematical and geometrical truths: they are invariable, as we have seen! Will 2 and 3 add up to 5 tomorrow?—yes! Will the ratio of the circumference of a circle to its diameter equal the irrational number “π”?—yes! These truths are invariable, they do not depend on physical events, they are true utterly independent of the physical world!
Back to the Question―How do we Know: Plato’s Epistemology (Theory of Knowledge)
Now we are ready to consider the original question, “how do we know that 2+3=5?” We often say “seeing is believing,” which effectively asserts that to know something for sure you must see it with your own eyes. Indeed, as we go about life day by day, it is the physical world that most demands our attention. For kids learning math, as we noted above, it is through counting physical objects that they observe with their senses that they discover and learn to use their minds. But where is this knowledge, really, where does it come from? The German philosopher Immanuel Kant famously says, “knowledge begins with experience, but it does not depend on experience” (for more see the chapters on Hume and on Kant’s response to Hume). The “experience” he refers to is empirical experience, that is, experience of the physical world we get through the senses—sensible experience, as opposed to mental. So Kant means that, as for children, it is our encounter with the physical world that begins our quest for and discovery of knowledge; however, the knowledge of things like 2+3=5 does not itself depend upon or derive from the physical world, rather knowledge in the truest sense is not empirical but a priori (the opposite of empirical), that is knowledge known “prior to” or is independent of physical experience. Such knowledge, strictly speaking, is a function of the mind alone, and utterly independent of empirical—physical, sensible—experience. In other words, the knowledge perceived by the mind, but it is our encounter with the physical world through the senses that first motivates us to think about it.
This reflects (and extends) the view of the ancient Greek philosopher Plato (429-347 B.C.), for whose thought the distinction between the physical and mental worlds we’ve been talking about was the foundation. For Plato, in order to know a thing, that thing must truly be, that is, it must not change: it must be what it is, rather than becoming something else. This means, effectively, that nothing in the physical world, according to Plato, can really be known, because, as we have seen, everything in the physical world is variable, all physical things are in fact changing every instant and thus constantly becoming something else! That is why we can’t know for certain what will happen in the physical world tomorrow, why we can’t even know with certainty that the sun will rise. Thus for Plato, nothing physical can be known at all since, for him, to know means to know with certainty. You and I use the term “to know” much more loosely than Plato does, obviously: “I just know it’s going to rain tomorrow,” we might say; but of course this is obviously not “real” knowledge. In fact, as any physical scientist would acknowledge, all knowledge of the physical world (which is what scientists concern themselves with) is merely approximate, although it can be very accurate or reliable (such as in predicting that the sun will rise tomorrow); but scientific (that is, physical) knowledge is fallible, that is, it is never perfect or absolutely certain and thus, on Plato’s terms, it does not really qualify as “knowledge” at all.
Being and Becoming
But there are things we can know with perfect certainty, as we have seen, such as mathematical truths: we can know that they are true today, were true yesterday and will be true tomorrow. We can truly know such things, according to Plato, because these things truly are—they are what they are, invariable, unchanging, eternal. These things belong to what Plato refers to as the realm of Being, whereas physical objects belong rather to the realm of becoming, for reasons which should now be clear—every physical thing is at every instant changing and becoming something else, becoming different.
The question now is, how can we know eternal, unchanging things, since we human beings seem ourselves to live in the physical, changing world. We are not eternal or immortal, we are subject to the changes of time, we live in space and time, we are not gods; so how can we possibly come to know eternal, unchanging things? First of all, let’s recall that we do in fact seem clearly to know things that are truly in being, things like mathematical truths, which are invariable and eternal; indeed, though we seem only to live in the present and cannot know the future, nonetheless we can know that tomorrow 2 plus 3 will equal 5! What can we infer from this rather perplexing, indeed perhaps astonishing, state of affairs? According to Plato, this can only mean that we human beings, who can and do know eternal things, clearly must be partly eternal ourselves! If we were purely physical beings, totally changing every instant along with everything else in the physical world, we would never get any inkling of anything not changing; we would be forever living “in the moment,” probably not even able to anticipate the future or remember the past. We would be like plants and animals, without a sense of personal identity, without knowledge of our own mortality, without the ability to make free decisions and to shape our own lives. But we are not like this, at least not completely. Our bodies are of course purely physical and changing, and we need nutrition like plants and are governed by instincts (at least in part) like animals, but we are not merely animals, for we can also think: we have the ability to contemplate purely mental things, to “see” (with our “mind’s eye”) eternal truths like 2+3=5 and the Pythagorean Theorem. In short, we can and do constantly feel the pull of instinct, like animals, but, unlike animals, we can choose to resist it; moreover, we can contemplate and “see” (with our minds) things that seem to be entirely independent of the physical world.
The “Immortal Soul,” or Mind
So, according to Plato, this can mean only one thing: we humans must not be merely bodies; rather, we must also have what he calls “a soul” which, like the eternal truths of math, is eternal and immortal. In modern terms, we might better use the term “mind” rather than soul, for what Plato is referring to is precisely the thinking part of us, the part of us that can “see” things such as mathematical truths that are not limited by the physical reality of constant change. Indeed, if we did not have a “soul” or mind how could we possibly know things that are eternal and unchanging? In other words, although our bodies obviously are bound by the rules of physical becoming, our souls or minds must rather reside in the realm of unchanging Being.
Plato’s Theory of “Recollection”
In his philosophical dialogue entitled Meno, Plato sets forth this theory of knowledge. To know something, says Plato, is in fact simply “to recollect” an eternal truth through the immortal soul. The soul can do this because it is unchanging, just like truth itself: in other words, since the soul is part of the realm of Being, it is mentally “in touch with,” so to speak, the eternal truths of Being. The soul, being immortal, eternal, unchanging, is “in being” just like the truths themselves; it must be, for if it weren’t, it would never be able to mentally perceive such things as “2+3=5.” Human souls (or minds) are not bound by time and space any more than are the truths of Being themselves; immortal souls and eternal truths dwell together in the realm of Being, they are “of a kind.”
By contrast, the human body, like all physical objects, resides in the realm of becoming. When we are young children we are subject completely to bodily urges and instincts, we can’t think of the future thus we cannot be responsible for ourselves, we are continually grasping for instant, physical gratification. This is so because we have not, obviously, learned to think. This is what education is all about: we learn step by step, starting with counting apples with our eyes and fingers, that we have minds, so that gradually we become able to do math in our heads. As we learn more, thinking enables us to become responsible for ourselves, to make judgments and free choices about our future, to resist the instinctual desire for immediate pleasure where it is not good for us or where delayed gratification would serve us better. And we learn to look out for others, to live in society, to sacrifice some of our immediate needs for the greater good of our families and communities. All of this we become able to do by learning to think.
Important Note: “Recollection” is Not About Things we’ve Seen in “Past Lives”
As we have seen, thinking, according to Plato, is entirely separate from our bodily becoming, since thinking is a function of Being. Plato sometimes describes human life as involving a soul “falling into” a body; the soul is immortal and never changes, whereas the body changes and dies eventually, leaving the soul free to find another body, and so on forever. This “reincarnation” idea leads to a common misunderstanding of the real meaning of Plato’s theory of Recollection. It might seem that Recollection is about our soul “remembering” things it has seen and learned in “past lives”; indeed, in Meno Plato himself makes reference to this idea, perhaps seeming even to endorse it himself. However, as a logical matter, it is clear that, strictly speaking, Recollection can not reasonably be about “past lives,” for this would imply that our knowledge is something that we “picked up,” through our senses, in the past. This cannot be, because, as we have clearly seen, knowledge for Plato is about eternal, unchanging truths that do not happen in the past or future or ever and cannot be seen because they are not in the physical realm of becoming; rather they just are, in Being, that is, they are eternal, beyond space and time. Knowledge cannot be had through the senses, because the senses only perceive physical things, which cannot be known in Plato’s sense of the word because they are always changing, they never are what they are but are always rather becoming something else, in space and time. This should all be clear to us by now, but it is vital to keep in mind how easy this misinterpretation concerning “past lives” might be, because if we think of “Recollection” that way we miss the entire point of Plato’s whole philosophy of Being and becoming. In sum, the theory of Recollection is not about “past lives,” because that would imply that the knowledge happened in a past time, which violates the very logic of Plato’s point!
It’s not clear why Plato even mentions the reincarnation idea. Perhaps he’s trying to explain his theory of knowledge to relatively unsophisticated listeners who might find the “past life” notion to be easier to digest than the abstract philosophical theory of the eternal, unchanging Ideas of Being. Or, at the time he wrote Meno, Plato himself might not fully have developed his mature account of Being and becoming, a revolutionary development in the history of philosophy that breaks radically with most of previous philosophy, which had been very much preoccupied with explaining the physical world and its constant changes. And, throughout his writings, Plato frequently employs stories and myths to make his complex, abstract and sometimes startling ideas more palatable to his readers, who were themselves steeped in the highly mythical culture of ancient Greece. In any event, in Plato’s later masterpiece The Republic, the distinction between Being and becoming assumes full and mature form.
The Allegory of the Cave
In The Republic, Plato contrives a mythical story about a cave as a metaphor for this distinction. In the cave people are bound by chains, unable to move their heads, and thus see only the cave wall before them on which is reflected shadows of objects cast by a fire behind them. To them, the shadows and images on the wall are all that exist, since that’s all they ever see. The cave represents the physical world of becoming, and the shadows on the walls our sensations of physical things. Since this is all the cave dwellers see, they are like children, who have no awareness of their minds or their ability to think. “Reality” is for them limited to the changing, physical images of the realm of becoming. They can only “see” what is visible to the senses, but because they have not yet discovered their minds and learned to master their faculty of reasoned and responsible thought, they are incapable of thinking or understanding the things of Being, which are not visible (to the senses) but are rather strictly intelligible (to the mind) .
When they are freed from their chains, they turn to see the physical objects that have been casting the shadows, and they are a small step closer then to genuine “reality,” though they are still in the cave, still in the realm of physical becoming, thus in fact nothing they see is truly real because nothing in the realm of becoming (“in the cave”) truly is; but we might say that the physical objects are “less unreal” than the images and shadows on the walls. Plato says that only our faculty of “imagination” (the faculty not of creativity, by the way, but simply of sensory “imaging”) is at work when we are looking at the images on the cave walls, whereas when we encounter the “less unreal” physical objects themselves, we are capable of engaging the faculties of “belief and opinion.” Still, however, no knowledge is possible here because we are still bound to the realm of becoming.
When the former prisoners venture out of the cave into the light, however, they have entered the realm of Being. At first they are blinded by the light and their first instinct is to go back into the cave, which is familiar and safe. Indeed it seems that they “know” what happens in the cave, whereas in the dazzling light they can’t at first see anything. In Meno, Plato uses an uneducated slave boy to demonstrate his theory of Recollection. Confronted by a tricky math problem, the slave boy comes up with a quick answer which “feels” right and obvious to him, but Socrates (who takes Plato’s place in the dialogue) points out to the slave boy that he is mistaken, leaving the slave boy in an uncomfortable and disorienting perplexity. In other words, the slave boy is like a man who has just stepped out of the cave (where he thought he knew everything but in fact had no real knowledge at all) into the light and finds all his previous “knowledge” to be worthless. But gradually, he is able to adapt to the light, which represents his learning, to use his mind to see real knowledge. This is what the slave boy does in Meno, where he overcomes his initial perplexity to be able to see for himself, using his own power of thought, the answer to the geometry problem. The point is that one must first become aware of one’s own ignorance and delusion, like the cave dwellers and the slave boy, in order to discover and use the mind to gain real knowledge. The demonstration is effective, moreover, because the slave boy could not have been remembering this lesson from school since he never went to school, so his mental perception of the truth can only have come from within himself and been present already in his “soul.”
Platonic Ideas (or Forms): The Ideas if Beauty and Justice
So the space outside the cave represents the realm of eternal, unchanging Being, the realm of true reality as well as of the soul or mind. Thus far we have considered only mathematical truths as belonging to this realm because we can fairly readily and intuitively grasp how 2+3=5 and the Pythagorean Theorem, for example, will be true tomorrow and forever, arguably, and thus are, by extension, outside of time and space; and yet we can still “see” them (with “the eye of the mind,” so to speak, thus establishing the plausibility of our possession of an eternal soul). But for Plato, beyond the truths of math and geometry there are things even “more real” than those, which he refers to as Ideas or Forms (two terms meaning the same thing) such as the Idea of Justice and the Idea of Beauty. At first it may seem highly dubious that justice, and even less so beauty, could be eternal, unchanging things. Is “justice” a “real thing” at all—has anyone ever seen true justice?; and isn’t it true and obvious that “beauty is in the eye of the beholder”—in other words, that beauty is precisely not an eternal, unchanging thing, universally true for everyone, but rather a thing different for different people at different times and for different cultures? That is true, however, only of the “many beautiful things”—i.e. physical things—that people might find beautiful, but Plato isn’t talking about that; rather, he is talking about the “one” (eternal, unchanging) Idea of Beauty—“beauty itself.” [Republic 507b] Thus “beauty is in the eye of the beholder” (and thus purely subjective) only with respect to the “many” physical things of the material world; but the Idea of Beauty is an unchanging, mental perception that all of us understand alike: in other words, I can disagree with you about what physical things we find beautiful, but I still understand what you mean (conceptually, mentally) when you call something “beautiful.”
And let’s consider justice. Of course there is no “perfect justice” in the (physical) world—no one has ever “seen” it; but does this make the term “justice” meaningless? If it were, we wouldn’t be able to use the word at all, would we? We may not be able to see it, but should that be surprising since it is precisely the point of Plato’s theory that the eternal truths of Being cannot be seen (by the physical senses, that is)? The point is that we have some firm sense of the meaning of justice even though we can’t see it, because, presumably, we can think about it. And consider, does anyone doubt that, as you look around the world, there are things we can all agree are unjust? We see injustice all around us, don’t we? Well, we must ask ourselves, by what standard do we recognize injustice, if not by the standard of justice itself? In other words, we may never be able to see justice in this (physical) world, but we must have some (mental) knowledge of it, otherwise we would never be able to recognize its opposite or even think and talk about it.
So, to repeat, when we say “beauty is in the eye of the beholder” we are claiming that beauty is purely subjective and not universal, that beauty changes rather than stays the same, and this assuredly is assuredly true of the physical world; but this is limited to the “beauty” beheld by our sensible eye, the eyes of the visible world, not the intelligible. So arguably this not only does not serve to refute Plato, rather if anything it supports his position, since Plato would be the first to point out that physical beauty, like all things physical, is incessantly becoming and not in Being and so physical beauty is subjective and different for everyone, so when you are talking about physical things it is correct to say “beauty is in the eye of the beholder”; however, that is precisely not what Plato is talking about when he discusses the Idea of Beauty, which for him is an eternal, unchangeable, non-material thing. Thus when you say “beauty is in the eye of the beholder” you are speaking of the beauty of the cave, so to speak, and not real beauty, which is an Idea to be “seen” by the mind or soul only; and that Beauty is the same for everyone, always, because as much as we may disagree about the “beauty” of things physical, we all know what we mean when we use the word “beauty,” which attests to its ideal quality.
In sum, the statement “beauty is in the eye of the beholder,” which seems to be refutation of Plato, in fact supports his theory once we understand the distinction he is making between the changing, physical world of becoming and the unchanging, ideal (and truly “real”) world of Being. We don’t get this at first because we are so inclined to be bound by “cave thinking” and to assume that “seeing is believing,” when in fact, according to Plato, the senses are agents not of knowledge but of deception and illusion, showing us not what truly is real and true but only what seems or appears to be real and true. And consider, is it not precisely true that that is exactly what our physical eyes do—show us how things appear (and not how they are)? The eyes do not give us the “physical” things themselves; they merely (at best) transmit reflections of light that bounce off the physical objects through our eyes and into the brain.
So, asks Plato, as in the case of justice and injustice, how would we be able to say that a beautiful thing is beautiful were there not some idea of Beauty itself, the Form or Idea of Beauty? Yet evidently a single beautiful thing is merely an image or pale reflection of true Beauty. To understand how this might be so, consider the various and variable ways we use the term “beauty” in the context of the physical world: 1) different things are beautiful to different people (this again is the meaning of “beauty is in the eye of the beholder”); 2) beauty fades—the rose withers, the beautiful young person gets old and wrinkled (because all physical things are becoming and are not in Being); 3) the beauty of different kinds of things is utterly different—how can we compare the beauty of a rose to that of a person, though to our eyes they are both “beautiful”; 4) beauty is totally different to the different senses, thus the “beauty” of the rose is incomparable to the “beauty “ of a musical melody; 5) even purely intellectual things can be beautiful—a beautiful argument or a beautiful compliment or joke, a person with a “beautiful soul;” and the distinction between intellectual and sensual beauty is greater even than the difference between a beautiful sight and a beautiful sound. Yet, and here is the point, notwithstanding all these different physical manifestations of beauty, we still use the one term “beautiful” in these many ways and we know innately—in our soul, as it were (and this for Plato is precisely where and how we do and can know anything)—what we and others mean when we say that something is “beautiful.” So yes, physical beauty is variable, always becoming different, even to the same person, thus physical beauty is a function of “the eye of the beholder”; however, the Idea of Beauty, just like the Idea of Justice, is an eternal, unchanging entity resident in the realm of Being.
The Idea of the Good
For Plato, the ultimate truth of Being—the ultimate Form or Idea―is the Idea of the Good, which accounts for the origin of all reality as well as being the source of the truth and perception of all reality. Thus, to continue the story of the cave, Plato posits, as a metaphor for the Idea of the Good, the light of the sun. Consider that the physical sun’s energy makes life on earth possible (just as, indeed, the primordial solar energy of nuclear fusion, from the Big Bang, constitutes the origin of the physical universe itself); moreover, the light of the sun makes it possible for us to perceive, by the sense of sight, the physical world. In other words, as the sun makes physical life on earth possible, and the primordial solar explosion of the Big Bang created the physical universe, so, for Plato, the Idea of the Good is the source of all metaphysical reality, that of the Forms and Ideas and mathematical truths; and as the visible light of the sun enables sensible perception, so the intelligible illumination of the Idea of the Good is the source of all knowing. Moreover, though this goes beyond Plato’s own philosophy, we might well liken the Idea of the Good to monotheistic conceptions of God, since such God is both the creator of all that is as well as the source of all truth (note, coincidentally, that we only need to omit an “o” to get “God” from “Good.”!)
Thus this sun metaphor represents the two sides of Plato’s philosophy—metaphysics (the theory of reality, of what is and why what is is the way it is), and epistemology (the theory of knowledge, how we know what we know about what is). These theories are interrelated and interdependent because our way of perceiving or knowing a thing is a function of the kind of thing we are seeking to know or perceive. Thus as we have seen, we can know a thing in Being because it is real, it never changes, it is necessarily what it is eternally, whereas we can only have a “belief or opinion” about physical objects, for example, because they are ceaselessly changing and contingent, or a sensible “image” of an image because it’s only an image or shadow of something physical.
Indeed, as Plato concludes his discussion of the Cave, he has Socrates remark, “Education isn’t what some people declare it to be, namely, putting knowledge into souls that lack it, like putting sight into blind eyes.” No, says Plato, “the power to learn is present in everyone’s soul,” so “education… isn’t the craft of putting sight into the soul,” because “Education takes for granted that sight is already there, but that it isn’t turned the right way, or looking where it ought to look, and it tries to redirect it appropriately.” In other words, consistent with Plato’s theory of Recollection, he asserts that the soul already has access to the knowledge of eternal reality, so it is not the function of education “to put it” there; rather, the problem is that the soul starts out facing the wrong direction, namely, into the shadows and images on the cave wall (like the slave boy in the Meno), and it is the task of education to turn the soul around to recognize and see the light of truth emanating from the Idea of the Good. It is fitting, moreover, that Socrates accomplishes the task of education through conversation, such as that with the slave boy: the root of the word “conversation” is the same as that of “conversion,” and means, literally, “to turn around with”—“con” means “with,” “verso” is Latin for “turn”—and it is in conversation with Socrates that the slave boy turns around, with Socrates, from the cave to the light of the Good, just as a religious conversion entails the turning from sin to God; indeed, education is precisely such a conversion, but an intellectual or philosophical one rather than religious.
Conclusion
By now we should be familiar with the notion that things may not be as they seem. It is the physical senses, after all, that give us what seems, or appears; they do not give us what is. When we reflect upon it, we can see that the limitations of the senses, in fact, are commonplace. Thus eyewitnesses to crimes and accidents are notorious for how inaccurate their memories can be, for example. And consider a kind of phenomenon that is even more commonplace. Hold your hand in front of your face and look at it. How big is it, according to what your eyes alone inform you? Now look beyond your outstretched hand at a distant tree: according to your immediate physical vision, isn’t your hand much larger than the tree? Of course you “know” that it only appears so, that “in reality” the tree is much larger than your hand, but let’s be honest and clear: it is not your eyes that tell you that, but your mind, indeed the information provided by your eyes indicates that your hand is much larger—there it is, big as life! But you say, again, I “know” the tree is larger, but again that “knowledge” is a function of your mind’s ability to interpret and correct the “optical illusions” to which your eyes are constantly subject.
So our senses give us appearance only, they are incapable of conveying reality. It is thus that Plato is known as a metaphysical idealist since, though he does not go so far as to assert the non-existence of the physical world, as such, he does assert that the reality of the constant changing of physical things makes perfect knowledge of them, strictly speaking, utterly impossible. Moreover, Plato asserts that there is a domain of genuine, unchanging, eternal reality, namely the realm of Being, by virtue of which the eternal soul is able to encounter the eternal Ideas.
For practical purposes, of course, we can all readily agree that our senses are very useful to us in navigating the physical world; but we can see, now, with Plato, that without the mind and its access to the ideal realm we could arguably do no more than, at best, survive physically and reproduce, like animals; there could be no rational thought, no perception of mathematical truth, no free determination of our future, no human “progress.” Yet clearly we are capable of a kind of existence impossible for all other living things that we know of, and we can reasonably infer that without minds, or “souls,” no such human endeavor is even conceivable.
Epilogue: The Cave We Live In
When Socrates first sets forth his story about the cave in Republic Book VII, his friend Glaucon remarks, “It’s a strange image you’re describing, and strange prisoners,” to which Socrates responds, “They’re like us. Do you suppose, first of all, that these prisoners see anything of themselves and one another besides the shadows that the fire casts on the wall in front of them?” Plato’s cave is an allegory intended, clearly, to represent his views of reality and knowledge, metaphysics and epistemology; thus, when Socrates says that the prisoners in the cave are “like us,” he means that we are all “in the cave” to the extent that we are not aware of our souls or minds, and are living, rather, as if the sensible appearances of the physical world were all that exists. Moreover, as long as the prisoners are bound and unable to move their heads they are unaware that they even have minds and are even capable of thinking for themselves.
Though Plato did not intend it, we today might build on Plato’s intended meaning for the cave as a way to extend its contemporary relevance and to gain some insight about our own lives. Specifically, I suggest that we might see in the cave an image of our contemporary political, economic and social condition, in the context especially of electronic media like video games, smartphones, text messaging and the advertising and information-gathering activities of social media that are so lucrative for the owners of these technologies. Thus, consider what a world of images we live in today, indeed, a world of “myth,” arguably, where our “truth” is largely a function of the oracular pronouncements of talk-radio, cable news, blog pundits and “influencers,” a world in which we are so immersed in advertising images that hardly can any significant purchase be made without the express or implied direction, of which we may remain largely if not entirely unaware, of an advertising message, frequently one targeted to us on the basis of our social media activity or other internet profiling technique.
Let us recall that advertising operates most effectively not on a conscious, but on a subconscious, level. Occasionally, but rarely, one might encounter an advertisement that appeals to our intelligence—an advertisement, in other words, that offers us actual information designed to assist us in making a rational decision about whether to purchase a particular product. Even in such a case, of course, no advertisement is going to give us the whole story or both sides of the story, because an advertisement has only one purpose, and that is to cause us to buy the advertised product, and the advertiser is thus going to tell us what’s good about its product, not what’s bad. But most advertisements in fact have very little to do with information at all but are designed instead to play on certain instinctual responses, to push our emotional buttons, so to speak, to make us want things we in fact do not really want, certainly do not need, may not be able to afford and that might actually do us harm! Given the intrinsic reasons why we might in fact not want to buy what an advertisement is selling (and if we already did want to buy it, why would all that advertising be necessary?), it clearly behooves the advertiser that we think as little as possible about the purchase, for clearly the more we think about it the less likely we are to buy.
So advertisers do not want us to think; they want us, we might say, “ín the cave,” that is, not using our rational minds but simply staring at the images on the screen and responding as if what we see on the screen is real; they want us bound to their world of images, in other words, and, like zombies, unaware of our own powers of thought and free will. Advertisers employ highly sophisticated psychological research to design their messages for maximum subconscious and emotional appeal, and advertising is targeted increasingly at children, who have not yet developed their reasoning abilities and are thus peculiarly vulnerable to and defenseless against such manipulations. Thus children, and all of us to the extent that we operate unconscious of the manipulative images that surround us, frequently without our even being aware of it, are like those prisoners bound in the cave and staring at the images on the cave well (that is, at our video screens), as if that were all that is. Indeed, the more we stare at our screens, immersed in the “virtual reality” of electronic media, the less attuned we will be to the reality of the world around us, including the fact that we have the power, if we choose to exercise it, to think for ourselves, and to think rationally, rather than simply to react automatically when an advertising image pushes an emotional button that makes us feel that “we cannot live” without a certain product, or feel a deep fear that we will not be whole somehow, or successful, or loved, without it.
We might note, finally, that fear, especially, is a deeply powerful motivator. On a fairly trivial note, consider a deodorant advertisement that plays on our anxieties about how we smell: if an advertiser can plant an “emotional seed” in us to make us fear that our smell is repellant to others, we are likely to find ourselves taking off the drugstore shelf that product that promises to take that fear away so that we can find love. And on a more serious note, perhaps, consider the use of fear in political advertising. It seems clear that by far the biggest part of a political advertising budget goes to negative ads, more and more as time goes on; this is because, rather than try to give us positive reasons about a candidate, it is presumably a much more easy, powerful and effective way to influence our voting behavior to make us fear that “the other candidate” will take away, or fail to give us, something we need or want. This is an obvious case of how a quick ad can make us react, instinctually and without serious thought, to try to protect us against the object of such a fear.
In short, increasingly today we find ourselves surrounded by and immersed in images, and these images are by no means natural sights but are rather artificial, carefully controlled, planned campaigns, heavily invested with the latest psychological research, designed to make us feel, act and believe the way the advertisers want us to feel, act and believe. The more we immerse ourselves in, and come to depend upon, our video screens, the more we become subjects of those who pull the media strings and the less we are able to be masters of ourselves; and the billions of dollars that are spent on advertising attest clearly to the fact that the effort to control us is extremely effective, since if it didn’t pay for itself then it clearly wouldn’t exist. Again, Plato’s point about the cave is a fairly simple, philosophical one; but we today arguably find ourselves in a whole new kind of cave, an artificial cave awash in images and shadows whose purpose is carefully designed not only to control us now, but to render us less and less capable of ever seeing our way out of this domain of images and reflections, or even wanting to see our way out of it, or even knowing that there is a way out.
But there is a way, or at least we can make a start: turn it off! Look at faces rather than Facebook, have friends who might actually be friends, have live conversations rather than messages, look at the world, discover your minds, read your own books, think your own thoughts, dream your own dreams. As things now stand, such simple incidents and pleasures of human existence are being crafted for us, and not in order to make us free or fulfilled, but in order to make us dumb and to keep us in chains.
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