Nature and Mathematics

Considering our discussion in class today, I've found myself mulling over a few different thoughts, all of which come from a primary consideration: the difference between Aristotle's conception of nature and a mathematical (contemporary) one. For example, a set of coordinates describes the location of an object based on a grid that we imagine spans the earth. New York City is roughly 40°N by 74°W, but there is not some ontological reality that is this coordinate set. The reality is New York City, the coordinates describe it as it relates to other things on earth. Another example is our concept of velocity: I might move from my chair to the door and think "hmm, I didn't move very quickly." But if I apply a mathematical perspective, I might say "in my movement from my chair to the door I sustained an average velocity of .3 meters per second." On the surface, it looks like all that math is doing is helping us to be more accurate in describing the world.

Here's my primary inquiry. Obviously the tool called math can't apply to things like "that-for-the-sake-of-which," ethical claims, and so forth. But it seems that concerning those things to which it can apply, it necessarily applies with greater accuracy than any alternative system.
Might we assert that any time we are able to make a claim about something using a mathematical system (in locomotion, for example), a similar claim that does not utilize this system is always inferior?

Infinity Qua Infinity

Aristotle makes this assertion: "For as it is, they have no need of the infinite (for they do not use it), but they need only that something finite can be as great as they want" (III.7.207b.30). Let's first look at Zeno's paradox with the walking to the door example. (It's important to use the word to here because with the word through you would simply walk through the doorway, hence making the paradox absurd and useless). Zeno's paradox seems troublesome to Aristotle because it does not depict the way in which reality actually operates; however, the concept that Zeno was describing is actually a simple, common occurrence in mathematical physics, (especially as described by calculus). What Zeno is describing is called an infinite series. Each successive move towards the door actually represents a distinct function that is mapped out by the infinite series. The series winds up looking something like this:

S1: 1/2....................................................................0.5
S2: (1/2)+(1/4)=(3/4).............................................0.75
S3: (1/2)+(1/4)+(1/8)=(7/8)...................................0.875
S4: (1/2)+(1/4)+(1/8)+(1/16)=(15/16)...................0.9375

And so on and so forth continuing on until infinity. As long as you keep on going another half of the distance, you will find that the total distance traveled gets closer and closer to the whole (1). If one were to use only "something finite that can be as great as one wants," they would certainly have some sort of silly answer, in this case an example would be 1/128. It is only through adding up every step of the infinite series that we see that the true value can be asserted to be 1, despite the fact that the numbers will never truly show it to be as such if you look at any one individual answer.

I strove with this example only to show the importance of the concept of infinity qua infinity. I made the example as simple as possible while still showing the nature of what is actually going on. Hopefully this explanation of Zeno's Paradox will either help your understanding of the nature of infinite series, or raise some interest as to the nature of Aristotle's "potential" infinity in relation/contrast to a mathematically relevant infinity.

Artistotle & Chance

I really do love how Aristotle handles chance and fortune. I'd echo and agree with Dr. Davis' comment that Aristotle manages to encsonce these terms into his existing framework without having to make any serious changes. I say all of this because I'm about to get pedantic.

If chance and fortunate are differentiated by a capacity to "make choices" (a rock versus a human), I have to wonder about situations where choice making beings (like said humans) temporarily lose the ability to make choices. It seems like a situation where you are being forced to do something against your will requires an explanation of its own. The weirdness can possibly be unpacked in this analogy/question:

If a man puts a gun in your hand and forces you to play Russian Roulette, is your subsequent death by chance, misfortune, or nature?

Physics III and Motion

     What I got from the first part of book III is how Aristotle describes motion and how it is infinite, and when it is combines with change we get nature as the outcome. It is also described as being 2-dimensional because there is no motion above or over things. If two things are of a certain kind, that is one that is capable of being moved and the other being capable of moving, these two things will act upon one another and allow one another to be acted upon.
    Using a building as an example, the things used for a building are both considered the buildable as buildable. This is equivalent to the process of building. When there is a house, the buildable is no longer buildable. It is the building being built, then the process of of building has to be the kind of actuality required. So then in this case building is a kind of motion.
     Part two seems to discuss more of the existence and what motion actually is. Even though it is thought to be indefinite, it doesn't exist as a potentiality or an acutality. This is concluded because of the reasons that it is incapable of having a certain size or going through a change of size. He keeps repeating the point that motion can only exist when it acts on both the "mover" and the "moved". When it acts, "this" or "such" will then be the cause of change.
     In part three he seems to continue on the subject of the composition of motion. Saying that motion is completed by 2 sides; a thing that is capable of causing motion, and it has to act on something that is capable of being moved. He starts talking about how there is a dialiectical difficulty because he says that "patiency" and "agency" are the two parts of motion and upon completion there is an 'action' and 'passion'. Then a conflict comes about, which is how can two things that exist as different things, be considered to react as one. Like even though in some perspective the travel from Road A to Road B is the same as Road B to Road A. In some aspect this must be true, but in actuality the paths are taken by deliberating two different ways.
      How can there be two separate components of motion, but they are acted upon as one. Or in other words, how can two things represent the same thing, but in actuality be different. At least that is how I interpreted everything. Putting my thoughts to paper was a lot tougher than I thought it would be.

Chance in Happiness

In Chapter 2, books 4-6 of the Physics, Aristotle extensively explores fortune and chance as causes. In at least one manner, fortune is an incidental cause stemming from a made choice. Chance, however, is broader and can occur without choice (197b). In the Nichomachean Ethics, Aristotle discusses chance as it relates to human happiness.  He consents to some things being caused by chance, but insists that the happy person will bear the misfortune calmly (Nichomachean Ethics- 1100b 30). However, how does the person attempting to achieve happiness, not yet there, bear chance? Presumably, there are a number of demonstrable things that help a human achieve happiness. Some of these could are of fortune; for instance, you chose to attend a college and happened upon a good education. However, think of the incidents related to chance that affect happiness. When you were a child, as Aristotle states, you could not choose (197b 9). Aristotle stresses that it is necessary to instill virtues (a component of happiness) into the youth, sometimes against their will (NE). But what if you are not immediately instilled with the virtues? Is in not by chance then (for you have no choice according to Aristotle) that you have been handicapped towards happiness?

Post Reading and Discussing Physics Book I- Mackenzie Foster

     After class today, I began to think about forms, materials, and potencies in regards to social responsibility. While I realize we cannot instill potencies in others (e.g., we cannot make it possible for a man to birth a child), we can focus our attention to the what potencies do exist in others. Aristotle's continual reference to the educated and uneducated (Sachs p.36 187a, p.37 line 188b, p.40 190a, p.41 190a20, etc.) makes it clear that all human beings (as long as they are healthy, still have mental capabilities, etc.) can be an educated human being because what one needs to educated is 1) to be a human being (which is the underlying thing/material/potency) and 2) to be uneducated, so a change occurs (which is a contrary/form/activity). The consequences of realizing this are that no one can make an argument that teens living in poverty are incapable of graduating high school, that homeless people are inherently incompetent, that the elderly are impotent in the face of learning new things, and so forth. They all have the material to be worked on. If we take this all to be true, how do we actualize this potency?

-Mackenzie

Hello and welcome to the Aristotle class blog. One post will be posted after each class (i.e. M and W before midnight). Post about what still confuses you, about the application of a promising idea, about a connection between sections or ideas, ask a question or propose a topic for further discussion. Try to keep posts under 200 words and comments under 60 (roughly speaking). [This post so far was 59 words, FYI.]

Oh and cite the books with line numbers when possible, i.e. Physics 185b10. The line numbers for Physics are embedded in the text. It is unfortunate, but that's just the way it is. The other texts have them in the margins.