No, I don’t intend on being terribly philosophical in this post; rather will discuss a philosopher and one (or two) of his philosophies.
I heard the term Aristotelian Square today for the first time. So I Googled it (what else?) and gained no additional understanding into what it means. I know what it IS, but not what it MEANS. From what I could gather from my detailed, 10 minute perusal through a couple of sites about it, it’s a way to deduce. Not even a way to deduce. It’s a diagram graphing the way we think or logic our way through things.
I’d never heard of such a thing before (but I didn't go to graduate school, so there). Isn’t thinking just…thinking? Some people are better at it than others – and by that I don’t mean to say that anyone is dumber than anyone else (although I sure do know a lot of dumb people!), just that people have different ways of approaching problems. There are creative thinkers, logical thinkers and idiots. Everyone looks at the same thing different ways and comes up with different ways of arriving at a solution – perhaps even a different solution.
From what I gather, this is a mathematical (logical) way of describing problems. Things are either all the way one way or not, or some of the way one way or the other. Another name for this is “The Square of Opposition.” It looks like this:
I know. It doesn’t make any sense to me either. And the more I read about it and tried to figure it out, the more I thought, “Well, but what’s the point?” I mean, do we really need someone to tell us this? Isn’t thinking just … thinking? It is what it is. Do we need to think about thinking now?
So I Googled, “Aristotelian Square what’s the point” and found a lesson plan from someone at (I think, but don’t ask me to think how I think about it) the University of Kentucky, “Venn Diagrams and the Modern Square of Opposition.” Ah, this is something I understand. I love me a good Venn diagram. I bet you do too, you just don’t know it. It’s a simple way to diagram complex ideas without a lot of words. Take, for example, this (stolen from thisisindexed.com):
From the UKY lesson plan:
These are standardized drawings that help us visualize and represent categorical propositions, and later, with modifications, categorical syllogisms. There is no real reason for them to be the way they are, rather than the little doodles you are probably already making to visualize what's going on in categorical propositions, except to standardize them so they are recognizable to anybody. (at least anybody who knows the conventions.)The text should be pretty self-explanatory here. Just remember:Þ The basic diagram for a proposition is two interlocked circles, side by side.Þ The left circle represents the S class. Label it with a letter that suits the particular term you are diagramming.Þ The right circle represents the P class. Label it with a different letter.
Venn Diagrams for Boolean Propositions:
The difference between the Boolean diagrams and Aristotelian or traditional diagrams, which you'll learn soon, lies in the way you draw universal statements. Boole figured that universal statements made no assumptions about the existence of the objects being talked about. In the modern interpretation, "All unicorns are animals with one horn" means "if you do encounter a unicorn it will have one horn." or "There are no unicorns that are not also one horned animals." So the diagrams for these simply indicate where individuals named would be found if there are any, and where they aren't in any case.
Here – try one on your own. Here’s a picture I took this morning of a treat I found in my break room. The large label says “Bacon Covered Chocolate.” The smaller label says, “Chocolate Covered Oreos.” You could easily draw a Venn diagram describing my level of excitement at the prospect of bacon-covered chocolate vs. the disappointment of discovering it was only an Oreo.
On another note – I did a little more reading on Aristotle and his two main predecessors Socrates and Plato. Socrates was eventually executed for thinking too much. Rather, for making other people think too much. They didn’t like it. They probably didn’t like to be made to feel dumb, which wasn’t Socrates’s point at all – he just wanted people to think and reason for themselves. Plato, one of Socrates’s students, continued his tradition adding some other layers to his belief system – and I couldn’t really find one of Plato’s that I could get behind. I’m glad I wasn’t around when he was in charge.
Aristotle seemed to be a bit more reasonable and friendly. (He was also Alexander the Great’s tutor/mentor.) One of the new theories he developed was called The Theory of Potentiality which says, in part:
Potentiality means that within everything, people included, there exists a natural evolution toward fulfilling its own potential, in essence becoming its own Form. A movement in nature and in humans from imperfection to perfection, or as close as anything can get to perfection. This is a hardwired component in all things that is an involuntary process, according to Aristotle. The universe is in a constant progression of being and becoming, from the Big Bang to the inevitable Big Chill on a cosmic scale to the cycle of birth and death in the human condition.
Aristotle speaks of causes in the process from potentiality to actuality and identifies four:
- The material cause means that an external force is creating or initiating the new thing.
- The efficient cause is the process of creation.
- The formal cause is that certain something in its natural state.
- The final cause is what it can become when it fulfills its potential.
And his ethical philosophy is that happiness is the ultimate goal of humankind. I like that quite a bit as well.
For Aristotle, true happiness can only come from leading a virtuous life. He believed in a happy medium in all things. Moderation was a major virtue. It kept one free from vice and free to work toward one's potentiality. In this goal-oriented age, people may mistake this for ambition and getting ahead in the material world. Aristotle was referring to an innate forward motion of potentiality that unconsciously drove all things in the universe, people included. So, we are constantly “potentializing,” whether we know it or not. This is the path and the goal of the person living the truly virtuous and happy life.
Aristotle places a high premium on friendship as well. True friendships are to be cultivated and treasured. Your true friend is almost like your doppelganger, your spiritual double. A true friend is there “to hold, as 'twere, the mirror up to nature; to show virtue her own feature, scorn her own image, and the very age and body of the time his form and pressure.” In other words, Aristotle advocates a virtuous buddy system.
Go live up to your potential today (don’t limit yourself).
Be happy (but not at the expense of others).
Be a good friend.
Sounds like another good Venn diagram! Meanwhile, here's some more food for thought, diagram-aly speaking: