Discussion Question 7

Read:  Aristotle, Physics IV (7-8), Epicurean fragments on physics, Selection of fragments from Zeno

Many of Zeno’s arguments rely on the infinite divisibility of matter and magnitudes, i.e. the claim that no matter how many divisions I make of some distance, there are always further divisions into more parts (e.g. fragments 6,7,8 in the pdf I gave you). What is the Epicurean response to these sorts of arguments in fragment 9A? Why must we not only say that we cannot cut an atom into infinitely many parts, but that we also cannot consider traversel to infinity? Do you find the arguments and view compelling?

9 thoughts on “Discussion Question 7

  1. The Epicurean view refutes Zeno’s claims that all matter is infinitely divisible with the simple claim that if the body of an object is finite then so should its matter be. It also addresses transversal towards infinity, quickly denouncing it as a paradox, and stating that something infinite could not reach greater levels of infinity and that something finite transversing towards infinity is, by its own definition, no longer finite. Though it would seem natural that everything in this Universe is made of some kind of divisible matter when taken to the logical, philosophical viewpoint, it becomes clear that that is impossible, the Epicurean response making that even more obvious.

  2. I do not find Epicurean arguments very compelling, because he doesn’t provide any evidence to support his initial claim, which he uses to build the rest of his arguments. His initial statement of course being there is no lower limit, to which he then uses to define that there is, therefore no way for things to be split infinitivally. He does this throughout his argument, such as when he says if you plot things forever they would eventually seemingly disappear. Furthermore, his claim that those things split would also have their own infinite is correct, however he seems to be phrasing the claim, as though that would be impossible.

    Finally, if one considers the math it would work out logically. Consider the number line, one can select any two points and you’d have an infinite number of points between them, similarly if you selected any two points inside the selected points you’d again get an initial number of points. Therefore, it would workout mathematically that one would be capable of cutting something into just as many infinite pieces.

  3. In response to Zeno’s paradox that an atom could, hypothetically, continually divide forever, into an infinite number of smaller pieces, the Epicureans denied the possibility of such an occurrence being able to exist. Their reasoning was this: should an atom—the initial ‘smallest’ building block of a whole—continually divide, it would eventually cease to exist, the pieces becoming so small, they could no longer be considered as the building blocks of an atom, but rather adhere to their own boundaries. Essentially, what the Epicureans decided was that it is impossible that a finite object could be a sum of infinite parts, because if an object is made up of infinite parts (i.e., forever expanding and dividing and so forth), the object itself would not, by definition, be finite—meaning that it would have to be infinite. This creates a paradox, because as we know, objects are not infinite, they are finite, and thus, the Epicurean response is that in dividing a finite object, at some point we must reach a finite end of division.

    On a surface level, the Epicurean argument isn’t particularly compelling, due to a lack of qualifiers or evidence—however, when we look at math, Zeno’s idea that an infinite number of parts must result in an infinite whole, can be disproven. The knowledge we have now does allow us to better support the Epicurean argument, but at the time, without said evidence, it can be said that the argument isn’t exactly well-supported, nor compelling.

  4. The Epicurean response to claims of infinite divisibility would be one that rejects it. In 9A, several ideas are laid out, one major one being that there is not infinity for the finite. The reasoning give for this says that this is because one cannot grind the existing into non existence. We cannot cut an atom into infinitely many parts because there is limits as to its size and physical space.

    Since the claim was made there cannot be an infinite division, the Epicurean stance says that traversal is not possible if one is to have the stance that there is infinite parts to a finite body. In 9A it is stated that traversal for this idea of inifinity isn’t possible, but neither is the opposite. This is because it appears to have that traversal ability but not the distinction of parts that is necessary, making it appear to be neither. I don’t find the Epicurean arguments very compelling. At first they do seem to make sense, and the points can be followed as you read the argument. However, I think these arguments lack a lot of information on the concept of infinity and they ways in which it has been used in major fields, especially math and computer science.

  5. The Epicurean view denies that the finite body is made up of infinite “bits” or parts and that these parts can be cut into smaller and smaller parts or “bits” to become infinitely smaller. The topic of traversal is argued to be impossible. If something contains a infinite number of parts with no limit to size, it cannot be added up to any object of infinite size. We cannot divide objects into infinite parts or “bits” so therefore we also cannot have traversal to infinity. I find the argument not one hundred percent compelling because of mathematical proof, but at first glance I would perceive the argument to be compelling.

  6. The Epicureans response to Zeno’s paradoxes is that we cannot divide an atom into an infinitely amount of parts because the atom itself would cease to exist and therefore the parts themselves wouldn’t constitute an atom and rather that each individual piece of the atom would constitute it’s own parameters. What I understood from the reading is that by cutting an atom, the atom itself ceases to exist and it is the inherent inability to slice the atom that defines the purpose and makeup of the atom and what the thing is that contains the atom. Basically, there has to be an unalterable starting point or else everything would cease to exist.
    In terms of traversing to infinity, we cannot traverse to infinity because the only way to satisfy Zeno’s paradox is to assume that the sum of the infinity is a finite number and that number is divisible. We cannot traverse something that has no beginning or end because that inherently wouldn’t be traversing, in order to traverse you have to be able to cross or move along something and that means in order for Zeno’s paradox to be correct, one must assume that infinity is a finite number that has been divided infinitely.

    I find Epicurean’s arguments compelling because, quite frankly, they use fewer assumptions than Zeno’s paradoxes.

  7. Epicureans claims that it is impossible for one finite thing to have an infinite number of bits. No matter how many times we divide an object, the bits must still be of some size however small the size is.Thus, if we put the infinite many of bits, each still of some size, back together into the original object, then the object must also be of an infinite size, which contradicts with the condition given. Therefore, be it some visible distance or some invisible atom (which still has a certain size, or else it cannot pile up to form bigger objects), they all cannot be divided into infinite many parts. Since we cannot divide things into infinite many parts, we also cannot have traversal to infinity.

    The arguments are not compelling if we consider Math. For example, 1/x will in fact to to 0 as x approaches infinity, which means when an object is cut into infinite many bits, the size of the bits will in fact be zero. Similarly, it is also possible for an equation in the form of 0•∞ to reach some real number when we take the limit (thanks to L’Hôpital’s Rule), meaning theoretically we can pile up those infinite many bits of zero size back into the original object of finite size. In short, infinity functions in a very different way from real numbers, and the arguments have unfortunately failed to observe some special subtlety of it.

  8. As for the argument of divisibility of the atom, the reason for that we cannot cut an atom in to infinite parts is that parts could not provide the exact quantity measured for this atom. Everyone has different judgments on the size of the point itself. Furthermore, if we assume that there are X(it could be an “infinite number”) parts in the atom, we just the know the number of parts, neither the mass nor the volume in the three dimensional space, which indicates a very quantitive impression for reality. We could regard that the amount of parts seem to extend the atom itself on an infinite line, however, it has no help for us to determine the length of a line, which is another form of the atom. We choose volume, mass of length as a “logical posterior instead of the composition of points or segments” (from Zeno’s Paradoxes) because they enable us to make comparison of measurement between different objects, offering a unified standard. And even there are infinite parts of atoms, what about the unit to quantity of one small part? Obviously it could be infinitely small, approaching to zero. According to this theory, when one part of atom is considered as zero, the sum of zero could be zero. Thus, the atom does not exist in this idealized model, which will be contracted to the fact that infinite parts could form a whole atom.

    So we must figure out the relationship for the number of atoms, known as the external measurement of individual, and the number of “parts” divided inside the atom. Also, the argument is based on whether the infinity is countable. Firstly the definition we give to an atom is really clear and it is inside our cognition as “knowledge”, so we could count the number of atoms by employing the tool of scanning tunnel telescopes, observing the micro world. On the flip side , as the number in mathematics is defined being infinite, we can not apply the countable infinity of parts on the atoms. The point or part also has difference with units, because at first we do not know exactly about the properties of the part, instead we know that the part is divided by a certain number of a whole individual. Thus, it does not own any measurement of the part.

  9. The Epicurean view denies that 1) any whole may be composed of infinite parts, and that 2) these parts may be infinitely small in size. It is argued that traversal, i.e., moving from part to part in a sequential manner, would not be possible if there were infinitely many parts with no lower limit to size, and that an infinite number of parts could not possibly be added up to make an object of finite size. Moreover, a body has a “distinguishable” extremity, and thus while one might imagine infinity as one approaches this extremity, in actual fact an end must be reached. Accordingly, an atom cannot be cut into infinitely many parts since it must have a finite size, even though this may not be seen with our eyes. The impossibility of traversal to infinity follows from the idea that parts may be so small as to be indistinguishable from one another. If one cannot distinguish parts, then one cannot move from part to part.

    The arguments given by the Epicureans are not particularly substantial and as such are not very compelling, so it would appear on the surface that Zeno’s paradoxes might hold. However, we have mathematical evidence (unavailable to the ancients) that disproves Zeno’s basic assumption that if you add infinitely many numbers, the result must be infinity. Contrary to this belief, it was shown in the late nineteenth century by Cantor that there exist numbers that are larger than any finite numbers, but that are not absolutely infinite. These so-called transfinite numbers permit the infinite addition to be reduced to the limit of a sequence, and allow us to compute the *finite* amount of time it takes Achilles to catch up with the tortoise.

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