How can I relate Aristotle and Plato

If I wanted to write a treatise on the pre-Socratics, I would now have to deal with the so-called pluralists and atomists such as Anaxagoras, Empedocles, Leukippus and Democritus in this blog post. But I do not want to give an outline of the philosophy of the pre-Socratics here. That has happened often enough elsewhere, and certainly after a much more thorough study of the literature of the past millennia than I can show. I am essentially interested in the thoughts of the pre-Socratics, in which one can discover the harbingers of the way of thinking of modern physics, mathematics and logic.

There are no doubt the three basic ideas that were expressed so appropriately and so early in intellectual history by the school of Miletus, the Pythagoreans and Xenophanes: In nature there is such a thing as a causal connection, the regularities in the Nature can be formulated in the language of mathematics, and knowledge can be attained by “searching for the better”. However, there cannot be any ultimate knowledge.

The first tentative steps of the pre-Socratics in the direction of basic concepts such as "movement" are also remarkable. The long history of the clarification of this term over the millennia clearly shows the effort it makes to gradually move from the darkness of the first considerations to a clear idea with which one can argue reliably.

If I now pursue the development of the “logo” in the history of philosophy, I will be even more selective. I will focus on the highlights, the works in which significant progress has been made. Of course, one often only recognizes this by looking back from the current situation. Developments in logic, mathematics and physics will be in the foreground that have become significant for the current state of the art in terms of methodology and the formation of terms.

So if one begins to look at the development in the period after the pre-Socratics, one must first come to speak of the three greats of Greek philosophy: Socrates (-469 to -399), Plato (-428 to -348) and Aristotle (- 384 to -322). As mentioned in the first blog post, Socrates introduced a new topic into philosophy: ethics. But not only this new topic created a new era in philosophy. In the meantime it had arrived in Athens, the capital of the Greeks; Anaxagoras from Kleizomenai (ionia) had moved to Athens in -462 and had made the thoughts of the Milesians and other pre-Socratics known there.

Where more people can come together, there is a greater likelihood that people with the same interests will meet and exchange ideas. In addition to teacher-student relationships, communities can now also emerge in which discussions can take place on an equal footing. The dialectic came into fashion. Zeno of Elea had already been her great friend, and Aristotle later even praised him as its inventor (Mansfeld & Primavesi, 2011, pp. 361, no.4). Attic democracy flourished, it was an early type of democracy in which the "state people" ruled, the state people consisting of the full male citizens of the city of Athens who had reached the age of 30. These full citizens could also turn to things that were not directly necessary for daily life; There were enough slaves, women or newcomers for such work. In political meetings and in court in particular, eloquence and the art of dialectic were required, i.e. finding the right reasons for opinions and spreading those that could be applauded by the audience. Sophists taught against money to master this art, even to be able to skilfully involve the opponent in a contradiction in discussions.

We know a lot about Socrates from Diogenes Laertius (Laertius, 2015, pp. 67-90), in particular he is said to have said: “He knows nothing, except that he does not know anything” (DL 83). And “the good may not be small, but it starts with the small” (DL 83). But we don't know any of his writings. However, Plato puts a lot in his mouth in his works. These works always represent dialogues that Socrates conducts with various interlocutors and in which the aim is always to clarify a concept or a question.


After the death of Socrates, Plato stayed in his apprenticeship and traveling years with a follower of the philosophy of Parmenides, traveled “to Cyrene to the mathematician Theodoros and from there to Italy to the Pythagoreans Philolaos and Eurytos; thence to Egypt to the prophets ”(Laertius, 2015, p. 141). He collected a wide variety of impressions and combined them to form a grandiose, mythical building of ideas that is still powerful today and continues to inspire many people.

He must have been a great storyteller. In his works he described in the form of a dialogue the effort to find concepts and answers to the question of right action or a good life. It is controversial who was the first to choose this literary form. “One hears that Zeno, the Eleate, was the first to write dialogues, but Aristotle mentions Alexamos from Styra as such [...]. On the other hand, I think that Plato has secured his claim to first place through his strict treatment and training [...]. The dialogue is “a question and answer elaboration of a philosophical or political topic”, but the dialectic “is the art of conversation through which we prove something to be void or correct based on the question and answer procedure of the speakers” (all quotations: (Laertius, 2015, p. 159)).

Regarding the works of Plato, Diogenes Laertius says: “The field of physics belongs to Timaeus, into the logic of the Politics, Kratylos, Parmenides and Sophistes“(Laertius, 2015, p. 160).

If he, as in the Timaeus When the pre-Socratic ideas about the cosmos came up, he did so in mythical form or linked to Pythagoras and saw the world made up of geometric shapes. At that time, logic was primarily understood to mean working on concepts, i.e. the uncovering of the relationships between related concepts, e.g. their classification as superordinate or subordinate concepts. Such a division of terms, called "Dihairesis", was expected to have a clearer definition. However, one already saw that a definition often required definitions of the defining pieces, which could lead to an infinite regress.

Aristotle grew up using this method in the academy. Thus the concepts were at the center of his logic, which he was soon to develop. So this became a so-called conceptual logic. Modern logic, on the other hand, is propositional logic. In the next blog post, I'll work out the difference in detail.

For a demonstration, Plato mainly used induction, that is, the inference from the particular to the general, "which through some true cases appropriately reveals the same truth for other cases", as Laertius says (Laertius, 2015, p. 161) . For a long time this conclusion was considered to be “appropriate”, only David Hume emphasized that this conclusion is not mandatory, that is, not always “appropriate”. There is no place for this conclusion in modern logic.

But the central theme of Plato was the human soul and how it can be expressed in language, ethics, art and politics. He decorates existing myths, redesigns them or invents completely new stories (see Wikipedia: Platonic Myth).

The Platonic Academy

None of this gives much for the development of the “logo”. In this context, it is interesting that he also greatly encouraged training in the analytical subjects, probably motivated by the impression that Pythagorean mathematicians made on him. Because he was not only a great storyteller, but also a good organizer and designer. So he founded a school to teach philosophy and science to young people. For this he bought, presumably in -387, a piece of land near a grove, which was called Akademeia because it had been dedicated to the hero Akademos. In addition to metaphysics, ethics, dialectics and the theory of the soul, physics and especially mathematics were studied there, which soon became part of the basic training of every student of a philosopher. The academy remained, with interruptions, for many centuries; it was only closed around 530.

The Platonic Academy became the model: since Augustine (354 to 430) and Martianus Capella, a Roman encyclopaedist from the 5th or 6th century, a canon of seven subjects had become standard for the schools of late antiquity. This was divided into a trivium (grammar, rhetoric and dialectics or logic) and a quadrivium (arithmetic, geometry, astronomy, music theory). These subjects were called the seven liberal arts because they were “worthy of a free man,” and a man was “free” when he was free from the necessity of a livelihood.

In the Middle Ages, this study of the liberal arts was regarded as preparation for academic studies in theology, law and medicine. In the universities, the liberal arts were soon taught within the framework of a separate faculty, the artist faculty (Facultas Artium). The "Liberal Arts", which we know from the USA, e.g. as "undergraduate studies" and which are nowadays sometimes also being introduced in Germany, for example, try to continue this tradition. However, the dialectic is more in the foreground here than any of the mathematical disciplines.


With Aristotle, a pupil of Plato, the strict training in the Platonic Academy fell on particularly fertile ground. Born into an educated and well-to-do family in Stageira (Chaldidike) in -384, he was sent to Plato's Academy in Athens in -367 at the age of 17. The mathematician Eudoxos of Knidos (approx. -395 to approx. -350) played an important role there at that time.

On the one hand, Aristotle loved to confront and discuss with people who thought differently. On the other hand, he showed - as in the case of people who do not leave a mark on a mathematical education - a tendency to work systematically and to collect the doctrines of earlier philosophers such as Pythagoras or Democritus (Schupp, I 256).

Aristotle became such a great systematic, attentive to the methodical in a line of thought and vigilant for connections. He was the first of its kind, and with it he was also supposed to establish a completely new kind of philosophy, which is no longer a poiesis, a "production" of doctrines in a poetic manner. Instead, analysis and method are in the foreground, justifications are required and conclusiveness is checked.

It is probably plausible that you feel the urge to do this when you have a large body of doctrines in your mind's eye and at some point ask yourself why the respective philosophers can represent their views so firmly. But you also have to live in a stimulating environment and, above all, have the talent for such a new beginning. So Aristotle soon went his own way in the academy. According to Diogenes Laertius, Plato is said to have said: “Aristotle has knocked out against me as young foals do against their own mother” (Laertius, 2015, p. 225).

In the list of Aristotle's writings, Laertius lists 146 titles and speaks of a total of 445 270 lines. According to him, the work on logic is "sharply identified as a tool for all sub-areas." These writings were later summarized in a collection of six books with the title "Organon" (Greek ὄργανον = tool).

The organon

The titles of the six books in the Organon Collection are:

1. The categories
2. About the interpretation (peri hermeneias),
3. The doctrine of logical conclusion (analytika protera, first analysis),
4. the doctrine of proof (analytika hystera, second analysis),
5. the topic and
6. the sophistic refutations

Books 3, 4 and 5 are particularly significant for the development of logical thinking, i.e. the doctrines of logical conclusion and proof as well as the topic. So this is where the so-called Aristotelian logic is developed. So this is the fruit of a time when dialectics held a high place in society. Discussions about more fundamental questions such as that of a good life or a “reasonable” morality soon became more a matter of the power of arguments than of authoritarian stance, and in the end it was inevitable that one would think directly about which forms of argumentation would be used have such power that they are incontestable, that is, must be accepted by everyone who understands.

The new era of philosophy, with its emphasis on dialectics, has in no way allowed the idea of ​​the logos to take a back seat or hindered its spread. On the contrary, dialectic was precisely the area in which this idea could prove to be a particularly useful and valuable tool for thinking. The idea was concretized in Aristotelian logic, which was to become a template for a science that plays an important role today in the context of artificial intelligence. In the next blog post I will go into the Aristotelian logic explicitly.

Aristotle and the System of Sciences

Aristotle's talent for analytical thinking and systematic work, as well as his passion for collecting the doctrines of earlier philosophers, also showed other fruits. He sets up a system of all sciences known at the time. He divides the sciences into practical like ethics, into poietic (manufacturing) sciences like medicine or handicraft and finally into theoretical sciences. In the latter, he differentiates between mathematics, natural science and "first philosophy", to which he included theology, ontology and logic. The theology at that time essentially consisted of a study of the unchangeable “divine” stars.

This division of Aristotle is, so to speak, the first “cash drop” of knowledge of a time and subsumes everything that creates knowledge under science. Presumably he also counted the theoretical sciences mathematics and natural research under philosophy, even if not "first".

About 500 years later, Diogenes von Laertius wrote:

As far as the parts of philosophy are concerned, a distinction is made between three: physics, ethics and dialectics. " (Laertius, 2015, p. 10),

where dialectic also stands for the doctrine of the principles of thought, i.e. for logic and, more generally, for epistemology. So ethics had immigrated to philosophy and mathematics was eliminated. A thinker like Pythagoras, who did mathematics but also represented a certain worldview with religious fervor, could no longer exist. Important mathematicians of antiquity, such as Euclid of Alexandria or Archimedes of Syracuse, do not appear in the work of Diogenes Laertius on the life and opinions of famous philosophers - with the exception of Eudoxus of Knidos, who was for a time a member of Plato's academy.

But physics was also to emigrate from philosophy, albeit not until about 2,000 years later, when Galileo Galilei overcame the Aristotelian theory of motion. By demonstrating how to describe regularities in nature in the language of mathematics, he discovered a "new science". Natural research became modern physics. We will deal extensively with the consequences of this discovery.

Finally, at the end of the 19th century, logic also emigrated from philosophy in the form of mathematical logic. It is now a branch of mathematics and computer science. Nowadays one can even observe how epistemology is becoming an area of ​​cognitive science that not only deals with our ability to think, but also with all conscious and unconscious processes in our brain, such as perceiving, learning or remembering.

Cosmology, the subject of the pre-Socratics and the first subject of philosophy in general, is today a field of modern physics. A history of cosmology from the pre-Socratics to Hawking would be highly interesting: The “question of the whole” arose in mythical thinking and is still present in this form in all religions, and the pre-Socratics were already beginning to look for physical reasons for their ideas. But only for about 100 years has there been a physical cosmology in which the logos strictly rules. This cosmology is a reconstruction of the history of the universe with consistent consideration of physical theories. You could only tell convincingly about the development of the cosmos after understanding the phenomena of nature on the basis of reliable theories. Because this knowledge provided the necessary guidelines for a history of the universe that no longer wants to be a mythical but a logical one.

Josef Honerkamp was professor for theoretical physics for more than 30 years, first at the University of Bonn, then for many years at the University of Freiburg. He has worked in the fields of quantum field theory, statistical mechanics and stochastic dynamic systems and is the author of several text and non-fiction books. After his retirement in 2006, he would like to devote more time to interdisciplinary discussions. He is particularly interested in the respective self-image of a science, its methods as well as its basic starting points and questions and can report on the views a physicist comes to in view of the development of his subject. Overall, he sees himself today as a physicist and "really freelance writer". newsletter

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