Logic and Harmony

Yesterday, I wrote about the logic of things, partly because people sometimes use logic in that way, and also because I’m sometimes tempted to think that way but resist due to my training. In "Logic in the Wild," I discuss logic as the guardian of coherence, but I leave the definition of coherence open. This is intentional. If readers learn to engage with coherence rather than content, I’ll be proud of them, regardless of their interpretation of coherence.

One thing I’ve learnt while writing the book is that logic is much more than the symbolic game I played for twenty years. Once you start thinking about coherence instead of obsessing over consistency, you can shed new light on old, difficult questions or those dismissed by symbol manipulators. The case I want to present this morning is the way Ancient Greeks talked about harmony. Harmony, for them, was much more than pleasing sound ratios; it was a way of being, for the soul to be balanced, and for the universe to be organised. Literally, there were theories about the harmony of the soul and the harmony of the spheres. Music was just the introduction, exciting a person by making them feel harmony. As with other bodily pleasures, hearing harmonious sounds would inspire the youth to seek harmony within themselves and direct their attention to the universe, the movement of planets, and marvel at the universal harmony. Mathematics developed to treat music was thus constructed alongside mathematics for the motion of planets.

What does this have to do with logic? I realised that harmony for the Greeks is one way of seeking coherence. To find proportions of sounds that are pleasing and correlate them with the proportions of positions and movements of planets in the sky, and to understand this as the same kind of patterns that regulate the soul, is to seek coherence in the universe. It’s not about finding content or truth in things but seeking a coherent whole that makes sense of it all. And that, I submit, is essentially logical thinking. Furthermore, it is logical thinking directed at things, allowing us to talk about the logic of things.

Harmony and Coherence: A Logical Perspective

In "Logic in the Wild," I advocate for the notion that logic serves as the guardian of coherence. This role entails analyzing reasoning structures, patterns of inference, and the interconnectedness of beliefs and theories. To those familiar with logical terminology, coherence relates to validity as cogency does to soundness. Importantly, coherence does not equate to truth. It's possible for scientific or theological theories to be coherent without necessarily uncovering truth. History offers ample examples, from ancient theories of optics and astronomy to modern debates on the existence of God.

Despite its significance, coherence remains an elusive concept, taking on different meanings in various contexts. A thought-provoking question arises: How far can we extend this concept? To explore this, consider the concept of harmony, traditionally associated with music and defined as a pleasing combination of sounds. Yet, its roots extend deep into European scientific thought, influencing astronomical, geometrical, and moral theories long before the development of intricate musical harmonies.

In Ancient Greece, harmony meant not only melodious sounds but also the arrangement of celestial bodies and the balance of the soul. Music provided a sensory gateway to harmony, inspiring deeper intellectual pursuits. This search for balance encompassed the entire universe, individual souls, and everyday life. The notion of the "harmony of the spheres" is a pivotal concept in this historical narrative, depicting the universe as playing a harmonious tune through the movement of celestial bodies. Johannes Kepler, profoundly influenced by this idea, used complex geometries to formulate laws of motion still relevant in classical mechanics. Newton's third law of motion, known as the harmonic law, directly stems from this line of thought.

In a surprising turn of events, while developing a new geometrical approach to astronomy, Kepler inadvertently laid the foundations for what we now know as modern harmony. This leads to a compelling question: Can harmony be seen as an extension or embodiment of the concept of coherence? Is the pursuit of a unified structure, linking the movements of stars and the human soul, essentially a quest in safeguarding coherence?