Life at Marquette

I've been in my grad program at Marquette for about a month now, so I figured that a post on how my life is going would be in order. I have three classes: Plato, Aristotle, and Medieval Islamic Philosophy. The Plato and Aristotle profs tend to banter back and forth between classes. Medieval Islamic Philosophy is interesting, though there is a ton of dense reading for the course; we're basically reading through major works of several thinkers of the Classical Rationalist period in Islamic philosophy. We started with a paraphrase of Plotinus (the so-called "Theology of Aristotle") and another Neo-Platonist paraphrase which came in the Latin West as the Liber De Causis. From there, we've been through al-Kindi (who was in charge of an early translation circle and very keen on showing the unity of Greek thought and how it fits with Islam) and al-Farabi (called "The Second Teacher" after Aristotle, at least once Farabi's work was discovered).

I'm also in a couple of reading groups, for Latin and Arabic. The same prof (Dr. Richard Taylor) heads up both, as well as the Islamic Philosophy class. So, the Arabic reading group usually takes on texts which we are already reading in class. The Latin reading group is working on a text from Aquinas which ties into the Aquinas and the Arabs project, on which I'll be doing some work as a student participant. It looks like I came to the right place for cross-cultural medieval philosophy.

Getting away from school concerns, we recently (as in, a month ago) got ourselves a cat: a rather slender Russian Blue by the name of Starshine. She's taken a bit to get used to me, but now she's an attention hog. Last weekend we introduced her to Tiger, our rabbit. Much to Starshine's consternation, Tiger has taken up cat-chasing as a new hobby.

Intellectual War

How can we be truly cooperative in intellectual matters, without asserting ourselves to the detriment of another?

I find within myself a drive toward competitiveness, a need for a foil, which rather frustrates me. After all, to declaim someone as clearly wrong is to declare oneself as dead certain about something. But, I have yet to come across anyone whose certainty on an issue I can truly respect and emulate. On the contrary, the extent to which someone is certain (with the possible exception of certain moral issues), I generally see them as culpably and reprehensibly close-minded and ignorant of basic truths which are plainly obvious to me (and see, I have already inserted my despised foil!).

Part of this seems to come out of a desire to be above the rest of humanity. People everywhere, at all times, seem to fall into this one pit, and I must be the one who does not. How realistic is this, though? Is it even possible in theory to avoid making the same mistake which those better than I have made? But, how can I purposefully run and jump into a pit I see gaping before me?

Is the answer to simply accept that perspectives can only meet in battle? To acknowledge from the start that I will clash, I will wrong and be shown wrong no matter what I do, and that I must overlook my foibles in order to progress?

It seems that cooperation needs to assume the sort of firm foundation which I cannot accept. One must know enough to have stability, to have an unshakable faith in something (despite any evidence to the contrary), in order to meet the Other calmly and in peace. Is this because most cooperation is really an assimilation of the Other?

And skepticism is similarly resting on the firm foundation that what one doesn't know either doesn't matter, or is so certainly unknowable that it doesn't matter whether it matters.

One has to take these matters seriously, and not merely play at them. One must pour oneself out; I must pour myself out, into some scheme which I choose, even though it will fail. I must grow my thought as if it were a new hand, in order to chop it off.

I am finite, and in my finitude I am ignorant, noxiously so. But dash it all, stopping isn't really an option either.

Galois Theory and Languages

So, I've been thinking about mathematical metaphors for philosophy again, and this time Galois theory has come up. But first, the philosophical problem: when I speak in different languages, am I saying the same thing? Is there actually an English statement that corresponds to a French one? Are there propositions embedded in human sentences? If the mathematical analogy which I propose works, than there exists a complex yet satisfying answer to the problem.

Abstract algebra is about mathematical convenience. Mathematicians were tired of proving a theorem in numbers, then in geometry, then in permutations, and so on, when the theorem in question is practically the same thing in each case. So, they abstracted out the common features of the systems which were actually what ground the systems, and gave names to the sets of features. Two systems in particular are "groups" and "fields" (for those interested, the set of integers under addition is a group, and the set of rational numbers under addition and multiplication is a field). Galois theory states that there are relations between groups and fields such that you can match them up.

Now, groups and fields are not reducible to each other. One could perhaps say that groups are building blocks for fields, but there are interactions within fields which are not directly reducible to their group properties. So they are different, and one is not saying the same thing about groups as one is about fields. However, there is a direct connection between them as Galois theory points out, such that the structure of individual groups is the "same" (in a precise mathematical sense) as that of individual fields. So they are saying the same things as well. Further, the interplay of difference and similarity is what Galois Theory uses to establish its unique points: for example, that there is no general equation for solving fifth-degree polynomials or higher.

To bring this to play with languages: English and Japanese are just saying the same things; they have different webs of meaning, and this is important. But that doesn't mean that there are no structural isomorphisms at all. In addition, bringing the two together doesn't merely increase our understanding of our native tongue, but actually produces new thoughts.