The library of the modern world is much vaster than that of Alexandria. The number of texts dedicated to different epochs and their remarkable authors is overwhelming. Despite this fact, we can read treatises on the history of science or philosophy written by notable specialists such as Karl Popper, Geoffrey Kirk, and Geoffrey Ernest Richard Lloyd without ever finding out why Thales asserted that the world is animate and full of gods, or how he maintained the axiom of the immortality of the soul, defining divinity as “that which has neither beginning nor end.” Usually, the interpretations proposed by contemporary historians do not explain any of the fragments of the Presocratics that contain such statements.
In some cases, when the author under discussion places particular emphasis on metaphysical-religious statements, they are eliminated without comment. This is how Popper dealt with Pythagoras and he undoubtedly would have done the same with shamans like Epimenides or Empedocles. Eventually, if he had discussed their fragments, he would have completely avoided all of their statements related to subjects considered—according to his own paradigm—“unscientific” or “irrational.”
Such an attitude is exemplified by the marginalization of any source that is not in line with the paradigm of modern experimental science—a paradigm that was inspired by the same Enlightenment rationalism that generated the French Revolution. Anything that seems to be “science” is emphasized and applauded as rational, while everything related to the religious or the metaphysical is silenced or presented as “irrational.”
The major problem here lies in the application of one’s own intellectual categories to the “actors” of history under study, without making the effort to understand the specific mental categories of their world. Thus, if Popper, Kirk, and Lloyd see rudiments of “science” everywhere (sometimes even where they do not exist), then it is due to a hidden premise that influences their interpretative approach: the category of reason they operate with is not similar to the rationality of the ancient Greeks.
For such modern thinkers, scientific reason excludes religion and metaphysics. In the case of the ancients, however, the reference to the “unseen world” and the spiritual beings that inhabited it—God, gods, daimons, the souls of heroes and ancestors—was fully rational. To consider the “unseen world” as more important than what is seen, due to the influences it exerted on our world, was not an irrational attitude. The main thing that distorted such a vision was the numerous superstitions that parasitized authentic religious ideas. However, to deny the latter in the name of the former is as wrong as denying all religious ideas in the name of reason. Moreover, a world conceived in the terms of today’s materialist vision would have been inconceivable for Greeks or Latins. For them, not only was the entire social fabric structured around religious beliefs, as brilliantly demonstrated by the scholar Fustel de Coulanges in La Cité Antique (1864), but even elements of geometry had metaphysical meanings, as shown by Aram Frenkian in his study The Postulate in Euclid and in Modern Times (1940). That mathematics and religion intertwined harmoniously is evident in the example of Thales’ ox, recorded in ancient sources about the Presocratic thinkers.
Thales’ ox
In the first book of his important work Lives and Opinions of Eminent Philosophers, Diogenes Laertius recounts the following about the sage Thales:
Pamphila states that, having learnt geometry from the Egyptians, he was the first to inscribe a right-angled triangle in a circle, whereupon he sacrificed an ox.
For historians and philosophers of science, the inscribing of a right-angled triangle in a circle is an event of significant importance. However, the association of such a “scientific” discovery with a religious sacrifice is something that certainly astonishes any modern historiographer. Classical Greek culture also records other similar accounts.
A tale recorded by the same Diogenes Laertius notes that, after Pythagoras discovered the famous theorem bearing his name, he offered rich sacrifices to the gods:
We are told by Apollodorus the calculator that he offered a sacrifice of oxen on finding that in a right-angled triangle the square on the hypotenuse is equal to the squares on the sides containing the right angle. And there is an epigram running as follows:
What time Pythagoras that famed figure found,
For which the noble offering he brought.
From all of this, our textbooks only retain Pythagoras’s theorem, and in no case the ritual sacrifice through which he honored the gods who guided him to such a discovery. Whether it is Thales or Pythagoras, the cited fragment presents a curious association to the modern reader. Kirk mentions it in his anthology of ancient texts related to the Pre Socratics without commenting on the connection between geometry and religious sacrifice. Among ancient authors, Cicero is the one who will take up again, in On the Nature of the Gods. He considers the account regarding Pythagoras to be false, but without rejecting the underlying religious attitude:
It is true there is a story that Pythagoras used to sacrifice an ox to the Muses when he had made a new discovery in geometry! But I don’t believe it, since Pythagoras refused even to sacrifice a victim to Apollo of Delos, for fear of sprinkling the altar with blood.
Aligning with the “hermeneutics of suspicion” practiced by Cicero, erudite professor Ivor Thoms questions the animal sacrifice associated by Thales with inscribing a right-angled triangle in a circle:
The reference to the sacrifice of an ox is suspiciously like the better-attested story that Pythagoras sacrificed oxen when he discovered a certain theorem.
Although he had initially stated that the writer Pamphila—invoked as a source by Diogenes Laertius—“may have been right in ascribing to Thales the discovery that the angle in a semicircle is a right angle,” he rejects, without any explanation, the second part of the narrative, that in which Thales is presented as offering a sacrifice to the gods in gratitude for his discovery.
No matter how much we explore studies dedicated to ancient mathematics or the history of Greek philosophy, we have not found any explanation, however brief, of this association between mathematical discoveries attributed to Thales or Pythagoras and the religious sacrifices they dedicated to their gods. There are very few historians of philosophy, like the brilliant French researcher Pierre Vesperini from the Centre national de la recherche scientifique, who have shown that, in fact, the god of the Greek philosophers was Apollo (or, I will add, possibly Plato’s Demiurge). Even fewer are those who understand why Thales and Pythagoras made sacrifices after a geometric discovery: because its meanings were related to a form of “inspired” intuitive knowledge that was the result of God’s Wisdom, and not human wisdom. Unfortunately, such “details” are completely incomprehensible to many modern scholars.
Faced with a mathematical discovery that they consider of utmost importance, most historians of ancient science and mathematics are embarrassed by the association of these contributions with specific elements of archaic religiosity. No modern thinker expresses this astonishment more clearly than the one considered both a pioneer of the scientific revolution and an innovative philosopher who decisively contributed to the downfall of traditional philosophical thought: René Descartes.
The ignorant Descartes
Writing about the mathematics of the early Greek philosophers, which made him wonder whether “they had recognized a kind of mathematics quite different from the vulgar one of our own age,” Descartes promptly expresses his disdain for their discoveries, arguing that “their mad exultation and sacrifices for trivial discoveries clearly show how primitive they must have been.” Commenting on this passage, professor Jean-Luc Marion points out that when Descartes speaks of “insanae exsultationes et sacrificia pro levibus inventis,” he undoubtedly refers to the animal sacrifices offered by Thales, Pythagoras, or Eratosthenes.
Demonstrating both his sovereign disdain for antiquity and a complete misunderstanding of a world that was alien to him, Descartes considers the pre-Socratic thinkers to be rudimentary and uneducated (Latin rudes)—an assessment that we can consider paradigmatic for most modern thinkers, be they historians or philosophers. However, beyond the obtuseness of certain interpreters, I discern an essential underlying issue.
As I have already stated, the concept of ‘reason’ employed by the authors mentioned, led by René Descartes, does not coincide with the ‘reason’ of the ancient Greek thinkers. For most positivist historians today, reason necessarily excludes any reference to metaphysics and religious matters. In their opinion, this belongs to the irrational territory of the superstitions, so it must be placed outside the sphere of the concept of reason that they employ. This is why, as noted by the esteemed professor John Henry of the University of Edinburgh, investigations into the origins of modern science often exclude any reference to religion, mysticism, magic, or other domains in the same category. However, the only issue lies in the completely secular view projected onto the past, which has always been religious.
Although for Descartes, Popper, or Kirk, associating a mathematical discovery cannot be linked to a religious sacrifice, for Thales and Pythagoras, doing so is entirely rational. Their conception of knowledge and its nature is completely different from today’s scientific one. For the former, any form of inspiration, divination, or intuition must be carefully excluded from the realm of knowledge. For the ancient authors, this was inconceivable. This is why they can assert that everything is full of gods or that the soul is immortal: their own religious belief provides valid content for their rational reflection. Just as the Christian faith represented both the framework and the method of philosophical reflection for Saints Augustine, Albert the Great, and Thomas Aquinas, Greek thinkers attempted to understand the world within the context of their own beliefs and traditions.
The category of reason in ancient Greece is much broader than that of post-Enlightenment thinkers. Popper, Kirk, and many others are mistaken when they speak of the “science” of classical Greece and its achievements because they ignore the difference between what the ancients considered “rational” and what moderns conceive as “rational.” Without being incapable of certain discoveries, observations, and experiments, the pre-Socratic thinkers belong to a completely different world than the modern one. Their moral values and intellectual priorities are vastly different from those of today’s historians. Without thoroughly embracing this premise, the historiography of classical Greek thought will never succeed in sketching the true profile of ancient philosophers. Fortunately, there are thinkers who have managed to steer historiographical research in a much more objective direction. Francis McDonald Cornford, André-Jean Festugière, Louis Gernet, Karl Albert, Ioan Petru Culianu, and Giovanni Reale are some of those who can lead us along unexpected paths. The question remains: was there Greek science?
For now, I will only answer thus: if by “science” we understand metaphysical/religious certainties akin to those held by shamans or contemplative sages, then yes, there was “science.” But if by “science” we understand only observation, verifiability, experimentation, etc., then no, such a thing did not exist in antiquity. By this I do not mean that the Egyptians, Greeks, and others like them were not able to observe and draw certain conclusions. It’s just that such actions were peripheral and accidental, not essential. The inconsistency of the transient, visible world, and of “material” things, was never considered by the great Greek and Latin thinkers as the domain of a rigorous knowledge that could be called “science.” If for Aristotle “science” necessarily involved “theory” (i.e., the contemplation of eternal truths), his perspective represents the most important synthesis for which the “world beyond” was not treated as a mere illusion or “projection” of rudimentary intellects at the dawn of knowledge.
