A Few Theses

Given the day today, I figured that it was only appropriate to post some theses of my own. So, here are some of the points on which I've been struggling, put out for discussion rather than waiting for better exposition and argument. Some of these are new, some are recaps (and exaggerations) of old posts.

1. Fideism is morally wrong, as it privelages a group over others by arbitrary means, imposing illegitimate human authorities over non-members.
2. Out of four classes of proofs for Christianity, rational, historical, experiential, and moral, there are none which escape fideistic grounding (see earlier posts for criticisms of these proofs).
3. One should not do apologetics until one can sympathize with and argue for the other side (or any other sort of criticism, for that matter).
4. If theology contains and set truths which are important to know, then it is immoral to let theology be done in a democratic or congregationalist fashion.
5. There are no grounds for certainty which can stand up to reasonable criticism, and any claim to certainty can only be bought by ignoring legitimate views.
6. Morality is only meaningful insofar as it results in good for fellow creatures.
7. God is irrelevant in providing direct grounds for morality, as any real morality must appeal to what would be actually good for me anyhow. God may provide grounds for hoping that my good will be attained along with that of others, however.
8. The notion of providence is irrelevant for daily life once it must take care of the actual circumstances of the world.
9. The One, it in its hyperperfection, emanates Mind. In turn, Mind in reaching beyond itself yields Soul, who in its striving produces Nature.

Homomorphisms, Language, and God

Back to mathematical ruminations about the relation between language and reality...

In math, there is something called an isomorphism. The point behinds an isomorphism is this: you take two systems, and show that at some level the only difference is a change in symbols (at least, within the context of a given type of mathematical structure). So, for example, I can take the integers (all positive & negative whole numbers + 0), and I can work with them under everyday, ordinary addition. At the same time, I can take the set of doubled integers (..., -6, -4, -2, 0, 2, 4, ...), again under addition. Now, if I take 1 + 1 = 2 from the normal set of integers, I can map 1 onto 2 and 2 onto 4 to get 2 + 2 = 4 in the set of doubled integers. This is again a true statement. I can, in fact, take any statement about addition in the normal integers, double the numbers, and get a true statement about addition in the doubled integers. The structure of the systems, with regard to addition, is the same.

Another set of relations are called homomorphisms. Before, I could take my doubled integers, halve them, and get equivalent statements about normal integers; the isomorphism works both ways. Homomorphisms which are not also isomorphisms only work one way, and so they preserve important structural elements while losing much as well. Let us take again our normal integers with addition, and then let us take the numbers 0 and 1. Every odd integer we will map to 1, and every even integer we will map to 0. Further, in our new set, 1 + 1 = 0, with other relations staying the same. Essentially, 1 = "odd" and 0 = "even", so a statement like 1 + 0 = 1 could be said to mean "odd" + "even" = "odd". Again, for any true statement in our normal integers, we get a true statement in our even-and-odd system. 3 + 4 = 7 becomes 1 + 0 = 1, and both are fine. Let us call our new system Mod-2.

We can have multiple systems like this. Let us take the numbers 0, 1, and 2, where 1+2 = 2+1 = 0 and 2+2 = 1. This system is Mod-3. The normal integers will map like such: anything which is divisible by 3 becomes 0, anything 1 more than such a number becomes 1, and anything 2 more than such a number becomes 2. Again, true statements in the integers stay true statements in Mod-3.

Let us take Sally, who is a fluent speaker of Mod-2. Sam, on the other hand, speaks Mod-3. Now, Sally makes the casual statement that 1+1=0. Sam is flabbergasted; every kindergartner knows that 1+1=2! Sally can't understand such nonsense; not only is 1+1 clearly 0, 2 is simply gibberish.

Each of these statements is perfectly correct within its own system. Therefore, the two speakers are both right. These statements are truly incorrect inside the other system. There is also more than a chance resemblance between their terms; it is not as if "1" means something completely different within the two systems, although its relations within the systems are different. Therefore, the two speakers are genuinely contradicting each other. Not only are both speakers correct within their own systems, both systems do genuinely reflect the structure of the integers ("reality," as it were), albeit in a pallid fashion. Finally, there are genuinely wrong statements; 0 + 1 = 0 is false in any Mod system, as it cannot possibly be part of a system which mirrors the structure of the integers.

Also, every speaker can only master a finite set, but reality is an infinite one. Therefore, although speakers can master larger and larger sets, they can never hold out on the basis that a given set doesn't fully capture reality; the limited versions are all that they can access. Bigger sets do capture reality's structure better, though (they participate in it more fully?), so there is a point to continuing to search for ways of expressing the world. Also, while if each speaker could be a pure individual, cut adrift from others, she may be able to mistake her own Mod-language to be whole in itself. However, once she must interact with speakers of other Mod-languages, through their differences she realizes that her own Mod-language must relate to something beyond itself.

Finally, does this help to explain the God-world relation? The Mod sets are not the integers; they are different sets with different properties. On the other hand, they are nothing, except insofar as they are finite structures within the integers and borrow terminology from the integers; they have no being over and above that. The integers, also, must contain all of the structures presented in the Mod sets, and so is the "perfect," that is complete, set. With regard to language, the sets only analogously represent the structure of the integers, although they do genuinely do such. The integers themselves are ineffable, in a sense, as no Mod-statement really captures them; though we can still talk about them in another sense, as every Mod-statement refers to them.

Conferences

I went to two conferences last week. The first was at Notre Dame with the SIEPM (Société Internationale pour l'Étude de la Philosophie Médiévale) , on "Philosophy and Theology in the Studia of the Religious Orders and at the Papal Court." Basically, studia were the smaller, religious schools as opposed to the universities. It was very heavy on the history (especially 14th century, where I'm more interested in 13th century though), and so I was lot for a good deal of it. It did rekindle some enthusiasm for a couple days though, which was good; I've been (and currently am) running on pretty much zero motivation, with focus and energy to match.

The second conference was at Marquette, and it was part of the "Aquinas and the Arabs" project. I could follow that one a fair bit more. There was some interesting work done on Aquinas' thought, and particularly on how he borrowed from Arabic sources. Turns out that in his commentary on the Sentences, he pretty much adopts Avicenna's metaphysics, almost down to the terminology; pace Gilson, Aquinas' metaphysic was not a specifically Christian one, although it fit that use nicely. Aquinas' psychology was borrowed first from Avicenna, but he later switched to a more Averroistic one, at least with regard to internal senses.

Père Oliva from the Leonine Commission in Paris (a group working on the critical edition of Aquinas' works) was our guest speaker - a rather soft-spoken, likeable Italian man. He seemed to like what our project is doing, and it sounds like we're going to get a fair bit of money, to run things for a couple decades. So that's pretty cool.

Currently, I'm scrambling to get through secondary sources for my papers. I have one for Aristotle (most likely on the potential intellect, though the logos between sensibles and the senses seems interesting as well), for Plato (assuming my midterm paper did well, I'm analyzing some of Socrates' more pragmatic statements in the Meno), and Medieval Islamic Philosophy (on the epistemology of the rather interesting Persian mystical philosopher Suhrawardi). Unfortunately, I can't focus for the life of me on my studies. Hopefully this will pass before it sinks my grades....