Ancient Philosophy
For Philolaus numbers are basically the arché of reality.
If you posit number as the principle of all things, then you are talking about introducing measure to a continuum. Nature or whatever you find is actually a continuity. One of the famous phrases of antiquity is that ’nature does not make any jumps’. If a blossom is to flourish it needs all the stages of the year to do so well. And then you can introduce measure to a continuum by introducing number. You have a combination of limit and the unlimited. They are just two constituents of the universe wherever you find it. You need some kind of interplay between these to explain all things in reality. Once you introduce this kind of opposite, you can reduce all other opposites to these. You can now attribute these opposites to either side of limitation or unlimitation. We have lists of couples of opposites which the pythagoreans have been introducing based on this.
How do we bring this to life? This is a metamathematical scheme which is applicable, but they do so very specifically. They explain reality through music and geometry.
If you bring the first 4 numbers you get the pythagorean triangle, and the sum of these is 10.
If you halve the length of the string, you get 1 octave higher. At 2/3 of the string you get the fifth, ie. the jump of one tone to another. ¾ are a fourth.
This is similar to how they determine the harmony of the spheres.
In Heraclitus harmony exists in opposites that try to destroy one another, the pythagorean understanding is a sequence of things brought together in a scale. This is how the universe works without opposition. What you do is to measure a continuum. A scale that is in principle is limited, and you introduce a measure. Once it is there there is no talk of forces that try to destroy each other, it is rather the perfect status of things in which things are as they must. If you lose this measure, you will have a continuity that will go astray. The universe of Heraclitus is a wrong situation in which nothing is guiding the continuity from a normative standpoint. What Heraclitus sees as a virtue the pythagoreans see as a flaw.
In Plato it seems that numbers are not as abstract as the forms. The status of mathematics is propadeutic. You need mathematics in order to come to an understanding of the forms. And so begging the question, what is the status of mathematical objects like squares? Aristotle critiques Plato for not giving a satisfying answer to this.
The point is a basic element, like that of Euclid. Itself it is undefinable, because it lacks magnitude and such. Once you have more points, there can be extension between the points. If you extend this further, you can get a surface, a plain; ie. three points tied together. It still lacks dimension. If you have 4 dots, you can explain all the mathematical geometrical dimensions of the universe. This is why they see 1-4 as the basic numbers you need to construe everything.
Time for Aristotle will be the measurement of movement.
The pythagoreans were the first to argue that the celestial bodies are spherical. Many philosophers, including Plato, Aristotle, and so on, will accept the sphericity of celestial bodies.
The pythagoreans also accepted 10 celestial bodies, the first one was not the earth. Everyone except the pythagoreans thought the earth was in the center. They argued that hestia was in the center, ie. the god of the hearth. The second planet was earth. Then the moon and the sun. And then there is counter-earth. Some kind of duplication of earth in kind of dark matter. It was added to fit with the number 10.
The pythagorean’s discoveries determine the later systems of the sphere very concretely. A lot of people go against their principles, but also take over the principles like musical harmony of the spheres.
The Classical Period
Where we start referring to the normative description of historical evolution.
The first ones we will discuss are the underdogs in the history of philosophy. Their name is pejorative; the sophists. Sophos means wise, so they are the people who know what needs to be done in regard to practical advice. People have an idea and apply it as a scheme to everything and thereby deteriorate the initial inspiration. No one in antiquity uses this name positively. Not just in the fifth century bce. But also in the second century ce; the second sophistic movement where rhetoricians assume the name sophist as a kind of sobriquet.
What are the sophists?
Philosophy comes to exist first as cosmology. The work of explaining nature after nature has been discovered.
In the fifth century, with demographic and social revolutions, a new domain is opened, on which philosophy is going to be applied. Namely human conduct; ethics. In democratic states like Athens, we see that relativistic accounts take possession of minds. It is not all by nature how things are, but there is some convention. One’s own norms can be a standard which are applied to society. They start to recognise that societies and its organisation can differ from place to place, with opposing basic claims against each other. The whole discussion which sophistry flourishes on is the debate between Physis and Nomos.
You shouldn’t underestimate this discovery. Athens has not yet rose in the history of philosophy before this. Before this it was only Anxagoras in Pericles’ court. Now the athenian mentality will take first place in that they thought about how to organise society. The underlying idea is the maleability of human society. All of the Greek cities generally are making a lot of new colonies, and with time they start to reflect on their own organisation. Logos now opens a new working domain. Before it was limited to science and cosmology, now it comes to involve human society also. This does not come out of nothing. In Athens, in 624 bce, you have Dracon. He abolished the punishment from one clan to another, the family structure in the operation of justice, and claimed that the state had the monopoly on violence. No more vendettas or blood vengeance. Before Clisthenes in Greece there were lots of tribal consitutions all over the province of Athens which held local sway. They were then subidivided into districts and so on so that every tribe had equal access to everything, and the power was concentrated into the city of Athens. From now on the state representatives were chosen by the deans. It was no longer important what family you belonged to, only where you locally reside. This meant that the division of state authority is left over to districts, because this is how your council and assembly are composed. You would have 10 districts with like 50 representatives, so an assembly of 500, and you would be eligible depending on where you live.
Clisthenes himself belong to aristocracy, and before him was Solon who redivided the land. Clisthenes is important in that he argued that Athens state priority cannot be maintained without decision-making including the general free-people populace. Of course in classical athens, the aristocratic party remained very powerful and was most often elected. But the fact that they were aristocrats was no longer any reason to be a ruler in and of itself. There were still forces that denied the validity of democracy all together, like at the end of the pelopenesian war.
In Athenian democracy, if you want to weigh in the decision process you need to be heard. So a school of rhetoricians come into being. All of the sophists are in fact not athenians. They came to athens because they found a lot of money to be made from their teaching. Athens attracted people from abroad to teach them rhetoric. One of the first was Gorgias of Leontini. It’s a very small city in Sicily
He wrote a text in praise of Helena. ie. the woman who occasioned the Trojan war by being abducted. If you have Logos you can make people do whatever you like. In the rest of the fragment he compares Logos with the administration of drugs, as medicine, or as something that you can get addicted to. When I talk to you and convince you as rhetorician I am actually administering drugs and take control of the other person’s mind. For Gorgias this is a virtue. He thinks being able to convince people is the best power in the world. For Gorgias this seems to have also been a kind of play-thing. He has a philosophical treatise called on Nature in which he argues nature is non-being. If there is anything we learnt from the presocratics it was the necessity of excluding non-being. But Gorgias tries to maintain that this is the truth. He argues that if something is it cannot be expressed, and so nature must be non-being. If I talk to you and you misunderstand me this is a structure of the universe.
Speech is actually entirely bodily for Gorgias, but it is something entirely invisible. Once you say there is immaterial reality then non-being gets a status.
With the rise of rhetoric as a means of getting political influence, convention decides it all becomes quite apparent. Then you have new domains where the view of things will be entirely conventional. We find this in Euripides for example. He was heavily influenced by the sophists. He has one of his characters say that ’by convention we believe in gods.’ He doesn’t deny gods, but rather say that we translate what we find as important into gods. We divinise god and grain into Demeter as the one who looks after crops. We value wine for its constant health.
Hippias of Elis argues that everything is by nature. There are two platonic dialogues with Hippias, minor and major. Plato uses him to be mocked. Even Hippias when he argues everything is by nature if playing the game of convincing people. He is involved with this system of conventional conviction, of making people accept what I am saying. This leads to Plato’s reproach that this is just a skill, and has nothing to do with truth. Plato argues that we need acess to truth, not just majority = truth. They immorally detach rhetoric for any claim to truth. What you see is that the problem of truth get onto the table in Plato. He thinks we need a real criterion of truth. In the case of the sophists however we have texts like dissoi logoi, twofold discourses, in which opposite discourses are provided on the same subject. The sophists teach their subject to argue on either side.
Protagoras of Abdera.
He is much of a philosopher. There is more philosophy to be found in him. We don’t know too much about him. Same city as democritus. His main position is expressed in the following:
”the human is the measure of all things: of the things that are, that/how they are, of the things that are not, that/how they are not.”
In latin this is often shortend as homo mensura.
That/how is hoos, I can tell you that something is or how something is, and they’re the same in Greek. Depending on how we interpret the phrase it gets a lot more radical. If you translate how, it is quite lame. If it is that, it is an existential measure, which is quite radical. It is likely that he played with this ambiguity intentionally.
If I think something is cold, then it is cold.
Depending on who I am, I am going to interpret the world differently, but every interpretation here is true.
If it is the second interpretation, then it is that whatever someone sees as existing, it does exist. It doesn’t exist if you deny its existence, I am the source of truth. The one who perceives is the one that makes a truth claim.This goes together with a kind of agnosticism. For so long as we haven’t perceived something, we cannot say it exists or does not exist. This will be Platos’ remark on Protagoras, because he reduces all truth to sense-perception.
”About the gods I can know nothing, neither whether they exist or not, nor how they look like. For there are many obstacles that prevent us from knowing: the lack of clarity and the brevity of life.”
Existence is linked to perceptibility. If something is perceivable then it can exist, or can be known as such.
Any subject can be treated from different angles.
What Protagoras is doing in a theoretical way that is well-founded is justifying his activity as a sophist. He is almost giving a theoretical framework in which sophistry can make sense. He is given much interest and place in Plato’s dialogues. He is taken more seriously.
A meter for example is nothing but convention. All systems of measurement are by conventions and this is part of what Protagoras is working on. Even when it comes to meters and miles, Protagoras would say that there is a fundamental difference of perspective there. It is the force of the majority that wins.
Plato argues that Protagoras is like Heraclitus because we are a principle that make things in flux. Because everyone interprets things differently there is no stable structure to the things themselves. Platos ideas and intelligible objects however are unchangable which is why they are so good.
There seems to also be difficulty in universalising this claim of Protagoras. In Theaitetos, Plato argues that this cannot be universalised. If I say that this is the case, and everyone says it is not, how can we say which is right? If we universalise relativism we have a universal claim. Plato is actually using a kind of sophistic argument against the sophists. Truth is all over the place, but my viewpoint is the only true one. So it looks contradictory.