An original version of this was written on 23 January 2010 but subsequently some alterations were made and some paragraphs added—just added, without any attempt to unify the whole.
The greatest obstacle to understanding Plato (and ourselves for that matter) is the supposition, assumption, or expectation that he has a ‘system’, and although he is careful to disguise it, it is possible to work it out. The task of philosophy, thus understood, is to extricate from the written works, supplemented by tradition and earlier interpreters, the intricacies of the system—its principles, its structure, and its logic.
We owe this presumptuous and mistaken view to a whole host of commentators, starting with Plotinus and the NeoPlatonists and ending with Hegel and the (highly divergent) Hegelians.
It is perhaps noteworthy that none of these seem to have been very interested in ‘music’ or to have thought that ‘music’ could help our understanding of Plato (and ourselves). Most modern commentators are the same.
And yet it may turn out that ‘music’ exhibits as clearly as possible the structure that ‘philosophy’ and human knowledge may have.
In the first place, ‘music’ has two aspects, or may be understood in two different ways. It may be considered as something that is heard, that is, it may be considered ‘sensibly’, as coming to us through the sense of hearing. But it may also be considered arithmetically, that is, ‘intelligibly’, or intellectually. Thus, a great deal of human knowledge is of this type—the conversion of sensibles into intelligibles.
It may be asked—somewhat petulantly—but what is ‘music’? Is it sound or numbers? The answer is yes.
The term ‘music’ is put in inverted commas to indicate the fact that it is not an unequivocal term. If we are careful, every time we use the term, we, as speakers, and our hearers, if any, must understand the double nature of what we are saying.
The other, second place consideration is simply the fact that in neither sense of ‘music’ are we dealing with a system. Music, whether heard or thought, is never a complete and closed system. We can, for whatever immediate purpose, treat it AS IF it were one, or we can make it one simply by fiat and definition. Or we can reduce to a minimum those stubborn irrational elements that prevent it from being a system; but although reason may persuade necessity it is only a persuasion. The necessity remains. [cf. the Pythagorean Comma.]
It is only possible to speak of the irrational elements or the necessities because they are defined—or at least, identified or isolated—by the rational elements. Thus, the octave or the ratio of 1:2 may be sub-divided; we assume that it is rational, sensibly, because its first and last tones sound the same, and, intelligibly, the two numbers—the first two natural numbers, so called—are probably the most basic unit of intelligibility. The various divisions of the octave are not ‘a system’ but a whole range of ‘systems’—without any way of making one dominant over all the others, or of claiming that one is better or more natural than the others. [Incidentally, the ratio 1:2 cannot be sub divided, but the difference between the ratios 1:1 and 1:2 may be; and the ‘gap’ between 1 and 2 cannot be subdivided either except by the invention of new numbers, by creating ultimately a continuum. See below.]
The end terms of the octave act as boundary conditions within which the intellect may inquire, create, or just play. Ultimately, it would be good if, by the adoption of certain boundary conditions, we could pass beyond them, that is, transcend them or overthrow them. This seems to be the passage from the third to the fourth and highest section of the Divided Line.
The end terms of human understanding seem to be the human intellect and the world we live in, the sensible world, but we are born into the middle of this ‘octave’, and, in a certain sense, we both know them and do not know them. We know they are ‘there’ but not in any precise way. But just as in music, we can only make the octave if we know one of its end tones, and can make many octaves as we vary that fundamental or base note, so in human thought generally we need a base note—if we define the human intellect in a certain way, then our knowledge (its octave) will be of a certain corresponding kind. And if we define it in some other way, then it will be of another kind. Alternatively, ignoring the intellect as such, we can define the world in a certain way—making it our ‘base note’—and then define the intellect in a way that corresponds to it. Plato did this by creating the Ideas or Forms.
It makes no sense to ask which is right, any more than it would be to ask if a diatonic or pentatonic scale were more correct.
‘Music’ is, therefore, the clearest paradigm for all human understanding—but it is not a fixed entity. It is capable of assuming (seemingly) an unlimited number of forms. All that is required of us is that we are very clear of what exactly we are doing, and what exactly we are not doing. That is why, in all true education, what we are learning can never be separated from how we are learning it.
That philosophy is the highest music—an assertion given on excellent authority—is the case because philosophy does for human nature and the whole cosmos what ‘music’ does for a part of them.
The additional reason for the appropriateness of music as a paradigm is that it endures, it lasts through time, or it is a process, as our sensible world is. Panta rei. The problem is to make change intelligible—the old issue of the permanent in the changing. Geometry gives us a static continuous cosmos, while arithmetic gives us a static contiguous cosmos. Astronomy provides a dynamic continuous cosmos, and harmonics (or ‘music’) a dynamic contiguous cosmos.
In music (as heard), the structure or meaning of the piece (song or symphony) is not contained in the last tone or even the last few tones; if we cannot carry in our souls the whole piece then the meaning will always elude us. The meaning is in the totality but that is confirmed by the last tone, and it consists in the structure of the whole and the dynamics by which the wholeness is both exhibited and confirmed.
The other interesting aspect of ‘music’ is that it may be created by humans. That is, once the ‘music’—in either sense—has been heard or numbered, it may be re-created. Furthermore, its ‘parts’ may be separated out and then recombined in a new way; and, following the pattern, new ‘parts’ may be invented or created. This is the counterpart of what Plato means when he defines the soul as that which moves itself.