3. So, what-is-not cannot be the reason for saying that what-is was, or will be [i.e., what what-is grew out of or will grow into].

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1 January 22,

2 Stage 1 goes something like this: 1. What-is-not cannot be said or thought. 2. If something can t be said or thought, then it cannot be the reason for saying something else. 3. So, what-is-not cannot be the reason for saying that what-is was, or will be [i.e., what what-is grew out of or will grow into]. [by 1,2] 4. What will be is not what is [i.e., what-is-not]. 5. What was is not what is [i.e., what-is-not]. 6. So, neither what will be nor what was can be the reason for saying that what-is was, or will be. [by 3, 4, 5] 7. If something cannot be the reason for saying something, then it cannot be the cause of that thing. 8. So, what-is neither was nor will be. [by 7, 6] Stage 2 goes something like this: 1. A thing either is, or is not. 2. If a thing is, then it can be thought. 3. If a thing is not, then it cannot be thought. 4. If a thing cannot be thought, then it cannot come to be (what is). 5. If a thing cannot be thought, then cannot perish (because it never is what is). So, 6. Nothing can come to be or perish from whatis-not (except what-is-not). 2

3 Stage 3 goes like this: 1. If a thing came to be, then [at some prior time] it is not. 2. But (by the conclusion of Stage 2), nothing can come to be from what-isnot. 3. So, nothing can come to be. 4. Perishing is a form of coming to be. [i.e., the coming to be of the nonbeing of something which now is.] 5. So, [by 3, 4] perishing cannot be (either). Stage 4 goes something like this: 1. What is, is all alike. [i.e., is not different from itself] 2. If what is were more than what is, it would be divisible (into more and less). 3. If one thing is more than another thing, these must be different things. 4. Therefore, what is is not more than what is. [by 1, 3] 5. Therefore, what is is not divisible. [by 2,4] 3

4 Stage 5 goes something like this: 1. If something is not lacking, then it is not incomplete. 2. If something remains the same, and in the same, and lies by itself, and remains fixed, then it is not lacking. 3. What is remains the same, in the same, lies by itself, remains fixed. 4. What is is not lacking. [by 2,3] 5. Therefore, what is is not incomplete [i.e., complete, by 1,4]. The other lines equate remaining the same and being in the same thing, and being by itself, with remaining fixed and without starting or ceasing. Presumably any of these would imply that what is lacks something. Stage 6 goes something like this: 1. Fate determined what is to be whole and changeless. 2. If something is whole and changeless, then nothing else is or will be. 3. What is is whole and changeless. [by 1, 2] 4. Therefore, nothing else other than what is is or will be. [by 2,3] 5. Thinking cannot depend on what is not. 6. Therefore thinking (and the existence of thinking) depends on what is. [by 4, 5] 7. Therefore, what is for thinking is the same on account of which there is thought. [by 4,6] 8. Therefore, what is has been named all things that mortals have posited (including what they claim comes to be and perishes, exists or doesn t, and otherwise changes, even though these things are not possible). [by 4,7] 4

5 The final stage goes something like this: 1. What-is meets uniformly with its limits. 2. Therefore, what is is all inviolable. 3. Therefore, neither what-is-not nor a what-is greater than what is in one way and less than what-is in another are possible. 4. Therefore, what is must be no greater or lesser. 5. Therefore, the limit of what is is ultimate. 6. Therefore what is is complete from all directions. So for Parmenides, what is the nature of what is? 5

6 Plato describes him as wanting to defend Parmenides. So how does he do this? By knocking down arguments for pluralism, such that what is is not many (cf. Parmenides). Zeno offers a number of arguments against pluralism, two of which concern: 1. Density 2. Finite size According to Aristotle, Zeno has four arguments about motion that present difficulties. These are recounted at the outset of Plato s Parmenides. They are all presented in the form of paradoxes. 1. The Dichotomy 2. Achilles and the Tortoise 3. The Arrow 4. The Stadium. 6

7 First Argument against Pluralism If there are many, they must be just as many as they are, neither more nor less. But if they are as many as they are, they must be limited. If there are many things, the things that are are unlimited, since between things that are there are always others, and still others between those. Therefore the things that are are unlimited. (Simplicius, Commentary on Aristotle s Physics ) Second Argument against Pluralism For if it should be added to something else that exists, it would not make it any larger. For if it were of no size and were added, nothing it is added to could increase in size. And so it follows immediately that what is added is nothing. But if the other thing is no smaller when it is subtracted and it is not increased when it is added, clearly the thing added or subtracted is nothing. (Simplicius, Commentary on Aristotle s Physics ) 7

8 The Dichotomy First is the argument that says that there is no motion because that which is moving must reach the midpoint before the end.... It is always necessary to traverse half the distance, but these are infinite, and it is impossible to get through things that are infinite.... (Aristotle, Physics b9 13; Physics a5 6) Achilles and the Tortoise The second <argument> is the one called the Achilles. This is to the effect that the slowest as it runs will never be caught by the quickest. For the pursuer must first reach the point from which the pursued departed, so that the slower must always be some distance in front. This is the same argument as the Dichotomy,but it differs in not dividing the given magnitude in half. (Aristotle, Physics b14 20) 8

9 The Arrow Zeno makes a mistake in reasoning. For if, he says, everything is always at rest when it occupies a space equal to itself, and what is moving is always at a now, the moving arrow is motionless. (Aristotle, Physics b5 7) The third argument is the one just stated, that the arrow is stopped while it is moving. This follows from assuming that time is composed of nows. If this is not conceded, the deduction will not go through. (Aristotle, Physics b30 33) The Stadium The fourth argument is about equal bodies moving in a stadium alongside equal bodies in the opposite direction, the one group moving from the end of the stadium, the other from the middle, at equal speed. He claims in this argument that it follows that half the time is equal to the double. (Aristotle, Physics b33 240a17) 9

10 For our purposes, Anaxagoras is interesting as a follower of Parmenides and Zeno. Many of the fragments from Anaxagoras appear to be paraphrases of Parmenides. E.g.: Even though these things have been dissociated in this way, it is right to recognize that all things are in no way less or more (for it is impossible that they be more than all), but all things are always equal. (Simplicius, Commentary on Aristotle s Physics ) He accepts a plurality of basic entities, and six (!) basic principles: Basic entities: 1. Objects and their parts 2. Basic Ingredients 3. Portions 4. Seeds 5. Mind Principles: 1. There is no coming to be or perishing 2. There are many different types of basic ingredients. 3. There is a portion of everything in everything. 4. Each thing is most plainly those things of which it has the largest portions. 5. There are no smallest portions. 6. Mind is unmixed with other things and has the following functions: 1. It knows all things 2. It rules all things 3. It sets all things in order 4. It causes motion 10

11 Leucippus is the originator of atomic theory, and the teacher of Democritus. Leucippus... did not follow the same route as Parmenides and Xenophanes concerning things that are, but seemingly the opposite one. For while they made the universe one, immovable, ungenerated, and limited, and did not even permit the investigation of what-is-not, he posited the atoms as infinite and ever-moving elements, with an infinite number of shapes, on the grounds that they are no more like this than like that and because he observed that coming-to-be and change are unceasing among the things that are. Further, he posited that what-is is no more than what-is-not, and both are equally causes of things that come to be. His associate, Democritus of Abdera, likewise posited the full and the void as principles, of which he calls the former whatis and the latter what-is-not. For positing the atoms as matter for the things that are, they generate the rest by means of their differences. These are three: rhythm, turning, and touching, that is, shape, position, and arrangement. (Simplicius, Commentary on Aristotle s Physics ) Our sources for their views are mostly Aristotle and commentators on Aristotle. By contrast with Parmenides, Zeno, and the earlier monists, atomic theory posits an indefinite number of eternal, indivisible entities that make up everything else. In one sense, this is a clearly pluralistic view: how many things are there in the universe? Indefinitely many. But in another sense, this view could be considered a kind of monism, since the atoms are all uniform, unchangeable, and imperceptible, and all the same kind of stuff. More confusingly, the atomists contrast atoms with the concept of void, which, if considered a category of being, would make their view either pluralistic, or dualistic. So we have a puzzle: what kind of theory is atomism? It is uncontroversially mechanistic (as opposed to the teleological views of Plato and Aristotle). No thing happens at random but all things as a result of a reason and by necessity. (Aetius ) 11

12 There is more to say about Atomism, and this will tie in nicely with the shift to Aristotle s Physics and Posterior Analytics. Once we finish with Atomism, we will have moved forward in time past the socalled Pre-Socratics to the views of Plato and Aristotle. Most of the rest of the course will be concerned with various interrelated aspects of their views and the development of philosophy that arises as a result of their work. You may have noticed that Aristotle is a major source for our knowledge of the Pre- Socratics, so you will have already read some excerpts from the Physics. Now we will be able to place these in the context of Aristotle s own views. It will be helpful to keep what we ve already learned in mind,. 12

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