26

Aristotle's solution was largely accepted until the end of 19th century when Cantor and Dedekind formalized the notion of continuum in terms of set theory. Under their interpretation time is in fact composed of indivisible nows, just like a line is composed of points, and any other magnitude is composed of indivisible elements as well. It does not mean that ...


12

Nothing directly attributed to Thales that has come down to us, but Aristotle does mention four views in his books: The earth rests on water. (De Caelo) Water is the archê of all things. (Metaphysics) The magnet has a soul. (De Anima) All things are full of gods. (De Anima) Aristotle inteprets this in several ways: Archê is Aristotle’s word: it means ...


11

Both of the answers are correct to point out that the dialogues are fictitious. It is extremely unlikely any section of any length is a transcript of an actual conversation between Socrates and anyone. This, however, should not surprise us because the idea of making dialogue in a written work a transcript is a modern concept. No one would have done so until ...


7

Welcome, Delforge Heraclitus and constant change - a vexed question THE thought of Heraclitus of Ephesus is still often summarized as " All things are flowing ", panta rhei; by which it is inferred that everything is in constant change. This summary goes back ultimately to Plato, who at Cratylus, 402a, wrote as follows: " Heraclitus says ...


6

Assuming that there are no extant works of Thales or Thales of Miletus (c. 620 BCE – c. 546 BCE), numerous sources, starting from his contemporaries accredited him with sicentific discoveries (geometry) and a "naturalistic" approach, based on rejection of godly intervention in the explanation of natural phenomena.


6

As far as I know Plato's dialogues are fictitious. E.g., Parmenides died at about 460 BCE in the South of Italy, while Socrates was born at 470 BCE in Athens. Hence the meeting of Parmenides with a young Socrates, teaching Plato's theory of forms, cannot be historical. Even when the dialogues are fictitious, some of the interlocutors in Plato's dialogues ...


6

Plato and Pythagoras There is evidence that the Platonic Academy was modelled on Pythagoras's school in Sicily : The Academy (probably modeled after Pythagoras's school in Sicily) was established as a quasi-religious association (or thiasos), a "brotherhood dedicated to the muses" and charac- terized by reciprocity, equality, and friendship (...


5

If I was teaching this I'd give a brief description of the major pre-Socratic cosmologists: essentially the Milisian Monists - Thales and the world as water, Anaximander and the world as indeterminate (apeiron); and Parmenides as the World as One. And then follow through with some extracts on Lucretious On the nature of things to link up with the early-...


5

We have a good number of fragments that are attributed to Parmenides himself. Specifically regarding the void, Parmenides asserts that you cannot separate what is from what is, because doing so implies a something that is not. Since what is not is not, it can't be used as a property of difference. Thus, there can't be any difference in the world, which ...


4

In the longer version Russell says this, inter alia, about Thales: According to Aristotle, he thought that water is the original substance, out of which all others are formed;... The statement that everything is made of water is to be regarded as a scientific hypothesis, and by no means a foolish one. Twenty years ago, the received view was that everything ...


4

The aphorism "πάντα ρει" (everything flows) which is attributed to Heraclitus τὰ ὄντα ἰέναι τε πάντα καὶ μένειν οὐδέν "All entities move and nothing remains still"// Plato's Cratylus is related to the nature of the world and not specifically to "time" . The river is a metaphor and it means that "change" differentiates the being of things constantly. (...


4

For a very easily understandable discussion of the Pre-Socratics, I would check out the first dozen-or-so episodes of the History of Philosophy podcast, or refer your students to them. Each episode has a list of further readings that would also be useful in putting together a lecture.


4

Aristotle does seem to reason about time with a mathematical model (geometrical magnitude) different from the one usually used today (real number). This is not at odds with modern mathematics as much as with the way time is modeled in modern physics. The real numbers (and measure theory) lead to paradoxes of their own such as Banach-Tarski (not directly ...


4

Everything that Anaxagoras wrote survived until well after Plato's time. The so-called "fragments" of the Pre-Socratic philosophers are fragmentary only to us. They were transmitted to us by authors who had access to the originals, who lived up to hundreds of years after Plato. Nearly all the fragments of Anaxagoras were transmitted to us through ...


3

From Parmenides's On Nature: Come now, I will tell thee - and do thou hearken to my saying and carry it away - the only two ways of search that can be thought of. The first, namely, that It is, and that it is impossible for anything not to be, is the way of. conviction, for truth is its companion.. The other, namely, that It is not, and that ...


3

The following is actually the content of a question asked here; but which has a bearing on the question above: Zeno is well-known as the storyteller of Achilles and the Tortoise and how the tortoise never catches Achilles; which is against our experience; the question of how to square these two notions generally falls to the theory of infinite series; and ...


3

There's a good entry on SEP about Pre-Socratic Philosophy,where Cosmology is also mentioned. you might want to take a look over there. http://plato.stanford.edu/entries/presocratics/ Presocratic Philosophy The Presocratics were 6th and 5th century BCE Greek thinkers who introduced a new way of inquiring into the world and the place of human ...


3

Protagoras's famous statement that "man is the measure of all things" has been variously related to relativism, Perspectivism, subjectivism, phenomenalism, anti-realism and skepticism. But not, as far as I know, to anything like the Turing Test (which is, to my mind, just a piece of common sense, hardly philosophical). Here is Plato's Socrates, ...


3

Presocratics in Greece Socrates is a false marker for the start of philosophy even in Greece. To begin, if he wrote anything, nothing has come down to us and it is possible (as tradition has it) that he wrote nothing. What little we know of Socrates' ideas and arguments has to be gleaned from Xenophon's Memorabilia of Socrates and the Platonic dialogues. ...


3

First, Define Philosophy I would argue, contra some of the answers above, that what we call philosophy is, perhaps arbitrarily, a specific historical tradition usually traced to Thales and the Pythagoreans, who probably originated the word. It requires, at a minimum, writing and geometry or some elements of axiomized math. It isn't simply that we cannot ...


3

Leonardo Tarán discusses in detail lines 42-49 in Fragment VIII (pages 150-160). Here are some comments on those pages. He claims "The ancients were already divided about the interpretation to be given to the comparison of Being with a ball or sphere." (page 150). He initially concerns himself "with the arguments that have been adduced to assert that the ...


3

Very few fragments extant. The source is Aristotle, De Caelo, II, 13: [295b10-296a21] there are some, Anaximander, for instance, among the ancients, who say that the earth keeps its place because of its indifference. Motion upward and downward and sideways were all, they thought, equally inappropriate to that which is set at the centre and indifferently ...


2

Chesterton offers one alternate reading of Oedipus Rex. In his book The Soul of Wit, Chesterton compares Oedipus to Macbeth, saying that Oedipus is the supreme pagan Tragedy because of its focus on fate, whereas Macbeth is the supreme Christian Tragedy because of its focus on free-will and sin. This theme of fate is the point of Oedipus Rex for Chesterton, ...


2

See in SEP the entry on Ancient Atomism : ancient atomists theorized that the two fundamental and oppositely characterized constituents of the natural world are indivisible bodies—atoms—and void. The latter is described simply as nothing, or the negation of body. Atoms are by their nature intrinsically unchangeable; they can only move about in the void and ...


2

Its a great question; I hadn't come across this particular one before by Democritus; I had understood that the documentary evidence for his thinking is thin. It appears part of a whole host of questions about analysing and understanding the behaviour of the very small, along the lines of Zeno. Democritus is an atomist; and against infinite divisiblity; so ...


2

The answer to this mystery is in the modern mathematical idea of a boundary. The key point is that points on the the boundary of a set need not belong to the set. In this case, the plane cuts the cone into an upper half and the lower half. It doesn't matter which way the cone's oriented, so you can get any picture you like in your mind. The intersection of ...


2

The most clear way for me to resolve this famous-seemingly-deep-hard paradox lies in the modern infinite calculus which can be clearly expressed using Leibnitz dx symbol. So in summary, Zeno "describes" the displacement of a straight line trajectory as: 0 + 0 + 0 + ..(infinitely many).. + 0 = 0, while the honest thus sensible way to "describe&...


2

There is a difference between a point and an indivisible. I guess the important thing is to consider the distinction. The easy way out here is to consider a point as an object without magnitude and indivisible as an object with magnitude. If we assert that a line is made out of points, that will mean that a string of infinitely many zeros will add up to a ...


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