It is often very early on or just prior to delving into philosophy that a person either asks where to begin with philosophy, or a friend or someone close recommends that they begin reading philosophy at a certain era or place.
Some people will shout from the rooftops to start with their favorite philosophers such as René Descartes, John Locke, or Marcus Aurelius, and perhaps you’ve already heard a few of these names without even knowing what it is these three men wrote about. However, each one of these men is in some way or another planted within the soil of western philosophy that is the ancient Greeks.
Even now, despite being separated from the end of the classical age of Greece by 2300 years, the golden age of Athens by some 2400 odd years, the archaic age by 2500 years, and almost 2800 years since the end of the Homeric age, our thoughts are still being shaped by the ancient Greeks today in ways you wouldn’t immediately recognize at first glance. Revisiting the three men mentioned prior, Descartes, Locke, and Aurelius, all three of these men have their thoughts deeply seated within Greek philosophy.
Starting with René Descartes, where would his philosophy be if it were not for the works of the ancient Greek skeptics such as Xenophanes, Gorgias, and Pyrrho?
Where would John Locke’s political works find themselves without the influence and groundwork of Aristotle, Plato, or Socrates?
Going back to Marcus Aurelius, which with a modern eye would be viewed as an ancient philosopher in his own right, where would his works have found themselves without first having learned from Antisthenes, Diogenes, and Zeno?
Looking at philosophy this way, it is clear to see that almost every major western philosopher, and to a broader extent almost all modern philosophers are influenced by the Greeks deeply and profoundly. Knowing that every subject first begins with its simplest components, it is easy to see why someone should not start with modern philosophers and their specialized subjects.
Yet how did we get this point, what made ancient Greece so influential? What was it that made them so special? Why did philosophy see such an explosion in the Aegean Sea? These questions would bring someone to many crucial answers, but the gist of them all is this. Many warring city states with many rivaling thinkers documented their ideas and started schools which would be passed down to the Romans who would later expand into and conquere Greece. The Romans then took into their laws ancient Greek ethics as their basis. The Romans took into their religions ancient Greek cultic and theological views. The Romans even took into their art and poetry ancient Greek styles and stories. From here ancient Greek ideas flourished and were distributed across the entire Roman Empire and into almost all modern thought today.
You are a product of the times you live in, son of modernity. The times you live in have the Roman Empire to thank for their influences, son of Rome. And the Romans had the ancient Greeks to thank for their influences, son of Greece. Look not to the modern world for your beginnings, but go back first to their beginnings to look for your answers. If you are to understand the men who write now and their influences, you must look at who influenced them in very life altering ways, and those men are the Greeks.
So to the original question, where does one start with ancient Greek philosophy? Is it Homer? Is it Hesiod? Is it perhaps Anaxagoras? There are so many ancient Greek philosophers, who do you begin with?
In general you may divide ancient Greek philosophers into two groups, the pre-Socratics, and the Socratics, the turning point of which was Socrates himself.
One may start wherever they like with the pre-Socratic philosophers if they wish to see behind the curtains of the most ancient world, but if one wishes to understand modern thought, it would be wise to visit the big three ancient Greek philosophers of the Socratic school, Socrates, Plato, and Aristotle. Socrates himself refused to write down his own words, and as such was mostly written into the works of his greatest student, Plato. Aristotle influenced more than just the modern western world, especially touching the hearts of middle eastern thinkers more than any other Socratic philosopher, but he himself was the student of Plato.
So if one is to start philosophy, where should one begin? Start by opening the dialogues of Plato and be prepared to be brought back to the thoughts and worldview of this ancient student of Socrates.
I would start with Heraclitus. Only fragments left, all of them brilliant.
I don't mean to sound silly, but one should start with Homer. Not explicitly philosophy, but foundational.