Fulvio Di Blasi’s The Invention of Philosophical Rationality: An Introduction to Philosophy by Way of the Presocratics explores the foundational role of Presocratic philosophy in shaping Western thought. Through an interdisciplinary approach that integrates philosophy, science, and theology, Di Blasi argues that early Greek thinkers were not merely precursors to modern science but authentic philosophers who pioneered rational inquiry. He emphasizes the transition from mythology to rationality, as seen in the works of Thales, Heraclitus, and Pythagoras, where logos (reason) and physis (nature) became key concepts in understanding reality. The book critiques contemporary positivism, advocating for a holistic vision that acknowledges the interwoven nature of philosophy and theology. Di Blasi highlights Aristotle and St. Thomas Aquinas as key figures in advancing Presocratic insights, linking early metaphysical inquiries to modern philosophical debates. Written in an accessible style, the book serves as both an introduction to philosophy and a call to rethink the historical significance of early rational thought.
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Anaximander’s Apeiron
The Ionian philosopher who immediately follows Thales, and who was probably his disciple, is Anaximander, who was born in Miletus in 611 BC and presumably died at the age of 64. I have already told you that he is one of my favorite ancient philosophers, and now it is time to explain why. I hope to make this explanation simple and understandable enough because the truth is that Anaximander’s answer on the archè is in many ways the murkiest. Generally, almost all students remember this answer not because they really understand it but because it is mysterious and eccentric both for the concept and for the name chosen to express it. The first principle of all things for Anaximander is in fact the apeiron, which is not the name of a bitter, but a very precise technical concept coined for the occasion.
Those of you who have studied a little Greek will remember that the “a” (alpha) placed before the word indicates deprivation. “A-peiron” therefore indicates “without-peiron“, where “peiron” comes from “peirar” which means limit or border. The apeiron is therefore the limitless or the borderless or the endless. Not in the sense of infinity, pay attention. This would already be a positive predication of the apeiron almost certainly extraneous to Anaximander’s thought. When we think of the apeiron, we must avoid any mental image that we might have of the infinite and focus only on the technical sense of “limitless”.
The reason why Anaximander thought of the apeiron as a first principle is fascinating, and understanding this is an absolutely necessary step for us if we want to continue studying the logic of becoming. It is also a tremendous step forward in understanding philosophy in general. Let’s try to get there slowly, then, trying to calmly visualize, so to speak, the philosophical problem he faced and the concept (apeiron) he produced to answer that problem.
The Boundaries of Knowledge and the Clarity of Thought
Think about when you do not understand something well, when you start studying a book and find yourself very confused, or when you listen to a speaker at a conference and cannot follow his discourse or understand what he is trying to say. How could you mentally visualize this experience? Maybe like a big havoc or a messy room. My favorite image is being lost in an ocean with no support points, risking drowning. Mental confusion is like an undifferentiated chaos in which you cannot find anything certain or mentally clear to hold onto. The confusion begins to cease only when we see an island or raft in which to take refuge: that is, a concept or a clear reference that is familiar to us and that we are able to follow.
This island or raft is like our key to access the book that we did not understand, or the re-entry point in the speaker’s discussion. The cessation of confusion and the emergence of mental clarity are linked precisely to the fact that the raft or the island are not indefinite or undifferentiated. They are something delimited that, as such, we can observe and study. In the chaos of everything, or in the undifferentiated pandemonium, I begin to distinguish something, which is like placing a boundary in a point of the sea or focusing on just one of the objects in disorder in the room. Distinguishing and clarifying is equivalent to putting limits, terms, or boundaries around what was previously lacking them.
This is what we do in general when we know reality and conceptualize it. When we know the lion, when we give it this name, “lion”, it is as if in the undifferentiated whole of nature and the other animals that are in front of us, we put limits or boundaries around this particular element (the lion) distinguishing it from the others and identifying it according to its specificity. The knowledge of the lion occurs when we begin to see clearly what it is with respect to the other things around it: that is, when we isolate its concept or essence from the being of other things, or when we differentiate it (or we remove it from the undifferentiated set) by isolating it and by giving it a specific name. Knowledge is therefore putting boundaries or limits around things: it is circumscribing them within limits. When we fail to set these limits, we are confused and do not understand anything. The analogy with sight can help us because the same happens when we focus on a specific thing from an overall indistinct gaze. It is the focus that, by distracting us from the blurry gaze, makes us see or know a particular thing. Focusing coincides with putting limits or boundaries on things.
Why this premise? Because we know reality precisely by focusing or isolating things in their specificity: lions, trees, sky, earth, water, etc. Whenever we identify something by giving it a name, we put boundaries or limits around it, and for that very reason we know and understand it. Our mind knows and understands according to these limits. If things appear to us without borders or limits, they appear confused or devoid of consistency.
The Need for a Non-Formal Cause of Change
Anaximander has a fundamental intuition in the wake of that same logic that Thales had already highlighted. What does Anaximander see? He sees that if there is a change, for example from child to adult, there are two boundaries or limits at stake: “child” and “adult”. In the undifferentiated whole we have, on the one hand, a boundary that delimits the being or the concept of “child” and, on the other, a boundary that delimits the being or the concept of “adult”. These boundaries cannot change into each other, precisely because they delimit two different things, making them what they are. As long as the boundaries are not broken, so to speak, there can be no change. The change is in a certain way the child who loses the child’s boundaries and takes on those of an adult, but where there is “adult” the “child” boundaries can no longer exist, otherwise the child would still be.
I am not sure whether this picture and its rationale are clear enough. Let us now call “lion”, “child” and “adult” by the technical name of “forms”. Borders are the shapes of things understood as something other than what they are made of: like the shape of the statue compared to marble or the shape of the toy boat compared to the lego cubes of which it is made. The transition from one form to another, like that from “child” to “adult”, implies that the thing that exists before and behind the change—the thing that remains the same throughout the entire process—cannot be either the child or the adult. The marble is not the statue as the lego cubes are not the toy boat.
The substratum of change cannot have the limits of the shapes that are at the far ends—for example, “child” or “adult”—because if it had them there would always be either only the child or only the adult. For there to be change, it is logically necessary that the substratum of change has neither the boundary, or limit, of the child nor that of the adult. The substratum must simply be something that in itself has no boundaries. If in nature everything changes or transforms itself into something else—and this is an evident fact—it means that the first principle underlying every change must be “the without borders” or “the without limits” or “the formless”. It must be real in some way, but devoid of any form. This seems like a paradox because what is real is real as a function of a form that makes it what it is. Talking about a formless reality is almost like trying to give being to “not being”. This paradox, including the terminology “not being”, is something we must bear in mind in order to understand the development of philosophical logic in this early period of philosophy. The first principle of nature’s becoming is for Anaximander “not being (i.e. not child, adult, lion, sea, mountain, stone, marble, etc.)”.
This intuition is absolutely brilliant.
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Music and the Stars
Pythagoras’ idea of seeing and looking for numbers in reality is brilliant because, as I said, if reality moves or becomes according to regularity then it is necessary that the rational principle that controls its movements is intrinsic, that is, is there to actually regulate its regularity. Numbers, which for Pythagoras are the essence of the rational, must exist as such in things: they must be real, in the sense of concretely existing. Indeed, they must be what is truer in reality, in the same way in which Mr. Ferrari’s mind is truer than the Ferrari (compared to the Ferrari) or in which Dante’s mind is truer than the Divine Comedy (compared to the Divine Comedy). In fact, the Ferrari and the Divine Comedy are true, in a certain sense, by derivation from a deeper principle that precedes and underlies them.
Let us try to enter even more into the concreteness with which the Pythagoreans thought of this intuition by considering it through another beautiful image that they gave us. I have already mentioned music as part of the way in which the Pythagoreans viewed numbers in nature. In music, however, there is more than that.
“The Pythagoreans, whom Plato often follows, say that music is harmony of opposites and unification of the many and agreement of the discordant.”
In the eyes of the Pythagoreans, music appears as the very embodiment of number or rationality, just as fire appeared to Heraclitus as the embodiment of the non-being of becoming, and as air in its indeterminacy appeared to Anaximenes as the manifestation of Anaximander’s apeiron. In fact, let us always remember that in the eyes of the ancients some physical realities were not simply physical and, precisely for this reason, they could embody the arche as an operating and effective principle. Music was one of them.
“He [Pythagoras] heard the harmony of the universe, meaning the general harmony of the spheres and of the stars moved by them, which we cannot hear due to the insufficiency of nature.”
For the Pythagoreans, the universe itself constantly produces a certain music, which we can somehow imagine as the tangible aspect of its rational functioning. It is a music produced by the world and by the stars by moving in the harmony of reason: a beautiful music that we cannot hear because we are too used to it. We have always heard it from birth and for this very reason, as happens with constant background noises, we are no longer able to notice its presence.
“they assert that the sound given forth by the circular movement of the stars is a harmony. Since, however, it appears unaccountable that we should not hear this music, they explain this by saying that the sound is in our ears from the very moment of birth and is thus indistinguishable from its contrary silence, since sound and silence are discriminated by mutual contrast. What happens to men, then, is just what happens to coppersmiths, who are so accustomed to the noise of the smithy that it makes no difference to them.”
Likewise, there would be much to say about the stars because for the ancients they ruled everything: they were conceived as something halfway between the divine and the human, and composed of the quintessence and on which the entire universe depended.
“The motion of the heavens is the measure of all movements.”
For Plato, the stars themselves were guided by the soul, as the properly divine element in nature endowed with intelligence and capable of moving itself. Plato transforms these Pythagorean ideas on the harmony of the stars into some of his most evocative images, such as the one which, in the myth of Er, makes the harmony of the universe resound from the song of the sirens and from the three women of time.
“the spirits which were in the meadow…another day’s journey brought them to the place, and there, in the midst of the light, they saw the ends of the chains of heaven let down from above…From these ends is extended the spindle of Necessity, on which all the revolutions turn…Now the whole spindle has the same motion; but, as the whole revolves in one direction, the seven inner circles move slowly in the other…The spindle turns on the knees of Necessity; and on the upper surface of each circle is a siren, who goes round with them, hymning a single tone or note. The eight together form one harmony; and round about, at equal intervals, there is another band, three in number, each sitting upon her throne…Lachesis singing of the past, Clotho of the present, Atropos of the future.”
Plato then makes sight and hearing the channels with which, by divine will, we are able to relate to the cosmos: the first to understand, by observing it, its rationality and the second to listen to this rationality and assimilate its grace and harmony.
“Thus much let me say however: God invented and gave us sight to the end that we might behold the courses of intelligence in the heaven, and apply them to the courses of our own intelligence which are akin to them, the unperturbed to the perturbed; and that we, learning them and partaking of the natural truth of reason, might imitate the absolutely unerring courses of God and regulate our own vagaries. The same may be affirmed of speech and hearing: they have been given by the gods to the same end and for a like reason. For this is the principal end of speech, whereto it most contributes. Moreover, so much of music as is adapted to the sound of the voice and to the sense of hearing is granted to us for the sake of harmony; and harmony, which has motions akin to the revolutions of our souls, is not regarded by the intelligent votary of the Muses as given by them with a view to irrational pleasure, which is deemed to be the purpose of it in our day, but as meant to correct any discord which may have arisen in the courses of the soul, and to be our ally in bringing her into harmony and agreement with herself; and rhythm too was given by them for the same reason, on account of the irregular and graceless ways which prevail among mankind generally, and to help us against them.”
It is no coincidence that the first Greek intellectuals were also, and perhaps above all, astronomers. The sun, the moon and the stars are among the first objects that arouse the astonishment of the intellect in the face of the mystery of the cosmos. Thales (at least according to tradition) predicted an eclipse not because he was a philosopher but because he was assiduously engaged in the study of the solstices, the equinoxes and the dimensions of the Sun and Moon. Anaximander seems to be responsible for the invention of the gnomon, the first sundial, with which to also detect the inclination of the ecliptic. The Pythagoreans, by contrast, seem to have inscribed on the map of the sky the zodiac, which is like a principle of order in the indeterminacy of the sky, and which is what inspired the Platonic Demiurge to model the cosmos. If the music of rationality or number necessarily resounds in the cosmos making it work correctly, it was normal that, for the ancients, the main musicians were the stars.
This remains for us a beautiful poetic image of the theories of the Pythagoreans, but for them it was something more and it should become so again for us too. Let us not forget that every philosophical image contains a concept. For the Pythagoreans, numbers had to be something real because reality moves in a rational way and the principle that causes and allows this movement must be intrinsic to it. Rationality is order and order is number. Music presents itself as the materialization of the rational order of numbers because the melody is just that: it is the coming to life of a precise (rational) order between sounds made up of notes and of clear and precise chords, and of fugues and protrusions towards the indefinite.
Music is even more: it is dynamic existence that adds power to the static character of number as a rational concept. If all reality is order, if order is number, and if number acts effectively in the process of becoming, then all reality resounds with the melody of order, which is music, and is moved by it. For this reason, the number is also soul, and not surprisingly, in Greek cosmology the stars move the sub-lunar world of the Earth: that is, they cause becoming. The stars, therefore, are rational order and music because they are the principle of the world as the cosmos as well as the power of the order that effectively moves it. The numbers of the Pythagoreans therefore express well the need for the efficient causality of becoming, or for the energy of the cosmos.
Now let us try to use ourselves the power of this image, stripping it of those ancient outlines. If all reality moves to the rhythm of rationality—and this should appear obvious from the simple observation that everything becomes according to a regular order that our reason is able to understand and predict—then (music and numbers aside) it must be true that reality is enveloped by a rationality which constitutes its essential and effective foundation.
From this point of view, since our mind needs images to be able to think better, why shouldn’t we use the image of a universe guided by music? If I were to produce a fantasy film to show that the world, in its most intimate aspect, is enveloped, pervaded, and made up of the effective power of reason, the image of a secret (rational) music that resonates within it by moving it would certainly be palatable. Another image could be that of a mysterious aura that envelops all things and in which all things participate by drawing vital energy, but which is secretly visible only in certain circumstances and to those who can observe it. In the film, the chosen ones who can observe it could be a caste of priests or magicians. In the history of human thought, they have been the philosophers. The fact is that, somehow, we should be able to see with our mind’s eye the intrinsic rationality that constitutes the discovery of the world as cosmos, otherwise we would never understand its conceptual significance.
The images are not only poetic, therefore, but reveal the depth and power of the concept. If the Pythagoreans had not offered us that image of the music of the universe we would have had to invent another one to fully understand the logical intuition that the world is the cosmos. In fact, this is another of the logical and necessary aspects of becoming. The rationality that governs change must somehow be part of the change, it must be present and operative in the changing reality. Remember that becoming is not the simple appearance of one thing where there was another before. Before there was the elephant, now there is the man. No, becoming is the moving of a thing, for example of a man, from A (child, here, ignorant) to B (adult, there, educated). This change can occur only as a function of the rational structure of the human substratum and of the things that surround it, which justify, allow, regulate, and operate that change. This rational structure is therefore present to change and is its cause. The adult whale will never come from the lion cub because the rational being of the lion works differently from the rational being of the whale, since it is a sufficient and effective cause of the lion’s being.
It is this rationality that, with the music of the Pythagorean universe or with other images which most excite our imagination, we must be able to see in the logic of the becoming of things. All Presocratic philosophers should also be studied and understood through pictures. Heraclitus’s fire must help us see the dynamic power of becoming in which things cease to be to become others. The air of Anaximenes must help us see the indeterminacy that the becoming of reality implies in the passage from one form to another. The music of the Pythagoreans must now make us understand that becoming is or takes place in the loving and powerful arms of reason.
