The Aesthetics of Mathematics

I've been trying to think of what it is that makes math seem beautiful (for those who disagree with this, it really is a fundamental truth on par with the law of non-contradiction. Just ask any pure math student). After all, I recoil from the thought of a deterministic universe, one which could be completely described with math. And I don't really see why the fact that mathematical laws govern things is all that spectacular - I'm sure that some mathematical figure could describe just about anything, even random chaos. The way in which math fits together really is a giant tautology.

This morning, though, it hit me. Mathematics is the hope of a fundamental peace in the universe, that beneath the dizzying complexity, there is a clean-fitting unity. Math is music, a vast harmony which subsumes the discordance and disorder of the concrete. Math is a gaze at the infinite through the finite, and the presence of stately structures of the whole within every individual. It is the recognition that there can be a skillful composition underlying the chaos, and that even from the simple things of life magnificent melodies can be produced.

Would this give some meaning to math being the thoughts of God?

The Meaning of Life

After looking at this cartoon, my whole life has been changed. I now have the answers to all of life's most perplexing questions.

Disagreement with Arabic Grammar

When do terms get stretched beyond an acceptable range?

Take the word "agreement," as it tends to be used in grammar (subject/verb, noun/adjective). One would think that it would be rather straightforward. So when my Arabic book tells me that adjectives always agree with their nouns, this is no big deal, right?

So, sometimes this agreement is what is called "strict agreement;" as I would be used to calling it, this is real agreement. The adjective is the same case, gender, and number as the noun. However, the case endings also denote definiteness, and sometimes the adjective agrees with the noun in this, and sometimes not. Not a huge deal.

But wait - now we have "deferred agreement." This means that sometimes, we just decide to treat things as if they were feminine singular (used with groups of inanimate objects). In Qu'ranic Arabic, there is a further exception to this, since feminine plural things that form their plural in a particular way can have strict agreement with their adjectives.

And then there is "chiastic concord." When dealing with numbers 3-10 (a friend reminded me that Hebrew is the same way), one takes the opposite gender from the singular of the noun in order for the two to "agree."

And all of this isn't getting into the fact that the verb does not always agree with its subject in number if the subject follows the verb.

Supervenience and Levels of Reality

In ethics and the philosophy of mind, there is a notion called supervenience. Basically, this is a way to try to get around the problem in the last post: if something is entirely determined by something else, how does it exist? The epiphenomenalist in philosophy of mind would say that there are mental events, but these events a) are completely and regularly correlated to physical events, and b) have no causal power of their own. So, if physical state P1 gives rise to mental state M1, and P2 to M2, then if P1 causes P2, M2 will follow M1. However, M1 does not cause M2, and in some versions P1 and P2 do not cause their respective mental states; in any case, though, the existence of P1 would guarantee the existence of M1.

I'm not the biggest fan of this application to mind (indeed, in a moment I will try to reverse it), but I think that there is a logical structure here which would be helpful. In order to bring it out, let me call attention to Scotus' notion of accidental and essential causes. If A, B, and C, are in a chain of accidental causes, then A causes B and B causes C, but B's causing C is independent of A. So, a grandfather might beget a father, and the father a son, and the father's begetting of the son can take place even if the grandfather were dead.

Essential causation, however, is transitive. If I hit a ball with a bat, we can both say that I hit the ball and also that the bat hit the ball while I swung the bat. Also, due to this feature, all the members of an essential chain of causation are simultaneous.

This appears then to be a good way of parsing out the notion of hierarchical levels of reality, within submitting on to an other. Let us take causal classes C(n), where for every member x,y in C(n) for a given n, x and y can causally interact (they have accidental causation). Further, for x in C(n) and y in C(n+1), x can be a member of an essential chain of causation with y (we could expand this to y from C(m) where m > n), though the two do not interact in the typical fashion. This would seem to explain the supervenience relation: we have two types of causation which hierarchically relate to each other. Unlike supervenience, mental events would interact with each other if they are in the same causal category, but as that appears to be the most unattractive part of epiphenomenalism, I don't see the problem.

Finally, we could say that if x from C(n), y from C(m), and z from C(o) (where o < m < n) are in a causal chain, then it is an essential chain in which it could be said that y causes z and that x causes z. This is not in supervenience theories, but it seems inescapable if supervenience were to apply to multiple levels of reality.

So, we could say that God is in C(0) by himself. Everything that occurs in any other layer of causation is due to God, and so we can say that God is more real than creation. There is a fundamental difference between God's causative actions and ours. However, I do not see that this must entail that God's actions completely determine ours; I'm still working on what both the affirmation and negation of this would entail. We could place agents on C(1), and finally non-volitional aspects of creation of C(2) (of course, this could be modified as need be; maybe animals do not qualify as agents, but still have a level of causative reality higher than plants). Therefore, it could be said that God causes everything. It could also be said that minds cause everything (where "mind" refers to God and the non-divine agents). It, finally, could also be said that there is causation in the physical world.

Determinism and Ontology

Can something exist which is not either a) an irreducible component of the explanation of how things are in terms of causation, or b) an abstract object (or, possibly only a)? What I mean is this: if A and B jointly cause C, and are both necessary and sufficient for C's existence and everything that it does, does C exist? More specifically, let us assume (perhaps problematically) that if F and G necessarily/sufficiently cause H which necessarily/sufficiently causes I, then I can be explained without reference to H. So, why talk about H, except as a shorthand, a practical tool for accounting for a particular aggregate of the effects of F and G?

Where am I going with this is the following: if determinism is true, do we exist? If for every action X which I perform, X occurs due to a set of necessary and sufficient conditions which do not need to include me, then could actually be considered a being?

If I am not a being at all, let alone an agent, let alone a moral agent, could I be held responsible for my actions? Would it be just for God to simply create pain states for their own sake in hell? I think that I could make some sense of our being in heaven: we don't exist per se, but God loves our particular aggregates, and so God's action toward us differentiates us even though we would have no intrinsic existence. So, I could be a universalistic/annihilationistic determinist. However, punishing an aggregate just makes no sense to me.

The Importance of Criticism

I've been wrestling for some time now, over issues like the church (which I've been blogging about) and about various political and ethical issues, especially related to the presence of systematic sin. I reject the individualistic notion that I can be holy simply by focusing on my own actions; my actions affect others, and my deliberations are important in that process. So, when I consider that some system is corrupt, what is the best course of action?

The knee-jerk response is to say that we ought to replace the system. If capitalism is bad, then let us try socialism. If democracy is bad, maybe we should be more authoritarian. If this were the case, then the best action would be to overthrow the current system (in line with moral standards). The other possible response is to say, perhaps democracy is bad, but it's not as bad as everything else, so we should stop complaining and deal with it. Why criticize if we cannot also be constructive?

The reason why is that all human systems are corrupt. So, on the one hand, democracy as run by us will always be corrupt; there will always be large blocs of voters who vote accord to mob opinion with no understanding of the issues (we academics, of course, would never do such a thing; we merely happen to have converged onto similar ideas through our enlightened intellects). But, what do we do? Any other system that we put in its place will be similarly corrupt. Maybe some systems are in the end worse than others, but simply changing the problem does not fix it.

So, if the current system is in error, but so are other possible replacements, should we simply let things be and ignore the problem? This seems to me to be the response of the person asking for a constructive response. There isn't any single response to give. What can be given, though, is the criticism of the system in which we live; we can point out the flaws, and struggle to deal with them and bring about justice in a small way. We can raise red flags and keep people from becoming complacent. In short, we can press the point that our citizenship is not in our present lives by keeping things from becoming too settled, either in the present system or in ideal changes.

Questions of Retribution

Can there be just retributive punishment in any situation? Or is all punishment corrective? Is it ever justified to simply harm someone with no remedial possibilites, even ones which they will not accept?

If we do not freely choose our actions, could there be any just retribution? How could it be just for us to suffer harm for something we were compelled to do by another, no matter how much our phenomenology suggests otherwise?

Could there be just retributive punishment in which neither the punishee nor the punisher gains? God would not need anything which the punishment of the unjust would provide, so what would retribution for its own sake avail?

Could there be justice without an eye toward a given result in which someone at least benefits? Is there some abstract honor or justice of which God needs to keep track, even if this is one with God's nature? What does justice mean without reference to concrete states of affairs and the results for persons of one sort or another?

Procrastination

I figure that I'll post an update here, since I'm getting tired of studying and I haven't said much about what's been going on here recently. I'm currently working on language proficiency, as I am in no classes and have been told by my adviser that I don't need to do any more work on my thesis until after comps. So, I took up Greek (again) for fun, and when I finished the grammar for that, I started on Arabic; there may be some opportunities for me to do work in Arab-Christian interactions during the middle ages, which is the closest I will be able to get to combining medieval philosophy with other religions within a single program in the Chicago area. Latin and Greek suddenly seem easy, and I can't quite pinpoint the reason (though the unvoweled texts and the strange vocabulary certainly don't help).

As far as doctoral programs go, I'm basically sitting and waiting. I've been turned down at Northwestern, haven't heard back at Notre Dame, and have been waitlisted at Marquette. I've also realized that I really can't make the commute to Notre Dame (all the trains seem to be more interested in coming to Chicago early in the morning; odd thing, that), which basically means that I'm left hoping that I'm high up on the list at Marquette (I know I'm in the top 12 applicants, so I have a fighting chance, but I may not know anything definite until April). It seems to be a crazy year for applicants; almost twice as many applied to Marquette than the average, and I got a letter from Northwestern back in January saying that they had so many applications that they could only even look at the top few.

In addition, I'm currently waiting for my old car to be picked up for a charity. It's been sad; this was my first car, after all, almost like a sort of pet. It even miraculously started up for me for the first time in 3 weeks this morning, as if it were giving me a last drive to say goodbye.... Ah, Shadow, who will I get lost with now?

Ok, that's enough procrastinating. Back to filling my head with language information which I'll forget tomorrow, or if I'm really good, in 5 mintues.

Update: After going downstairs to check my mail, I found that I have yet another reason to cross ND off my list. Actually, two reasons, one for each program to which I had applied. Maybe I should start looking for a second masters program....

Invididual vs. Corporate Ethics

I just got back from a trip down to South Carolina for a graduation at Parris Island. My younger brother James is now officially a Marine. I must say that I have mixed feelings about this. On the one hand, before joining he was making money just to spend it on computer games, which he would spend most of his free time playing. Now, he's putting aside his own desires and freedom for what he sees to be the greater good, and has willingly put himself through three months of hell in order to do this. On the other hand, if I have not been fully persuaded of pacifism, I'm at least getting pretty close to it; I would only count WWII as a legitimate war within US history, and I'm not even sure that we entered it for just reasons (I'm sure that we often did not do just acts during it). Even besides this, there was an aura of patriotism at the base which without exaggeration came close to religious. I'm all for my ability to speak my voice in public, but to say that the flag is watching over me wherever I go? To cultivate feelings of, more or less, ultimate concern for my nation?

What is best to do in such a circumstance? What happens when the growth of virtue in an individual (or in individuals) conflicts with the overall good of society and the spread of peace, especially when any other likely choice from the individual would likely have continued the old habits? Tied to this is the epistemological problem: am I ever sure enough of my position to denounce that of another, when the position in question would lead to at least some moral improvement?

After this comes the relation between the roles of intellectual and of prophet. As an intellectual, I consider the cases concerning the way in which our faith should work in our lives, in our churches, in our nations, more than the average person. I have the practice and the leisure time to do so. I can spend more time pondering the ways in which the worldviews of many are formed by contingent historical factors taken to be immutable moral laws. It would seem from this that I have the responsibility to share these thoughts with the community, since I have the provisions to partake in intellectual exercise. However, in academia I am cut off from the life of the average person. My daily life simply is not that of the common member of the church, and my solutions are indicative of my own preoccupations rather than the concerns of Joe Steelmiller. It is similar to the problem in economic politics, where the poor know their concerns, but not how to fix them, while the rich would have a better idea of how to fix them but don't have the same concerns (indeed, they have interests which lie in the direction of not listening to the poor).

So, what does one do when one sees a truth, but too dimly to be quite sure of it? What does one do when the proclamation of this truth will hurt many? How does one proclaim the message in a way in which it would be heard (after all, telling my mother and brother that the American church is often idolatrously patriotic, or at least ties its own end far too much to that of the nation would be an exercise in futility), or should one really care about this?

Consequences and Morality

I've been thinking about ethics lately, on the relation between the ought-ness of moral statements and the consequences of actions. So, I have a thought experiment here in three stages, and I'm interested in hearing people's opinions on the matter.

First, let us imagine a world in which action F is right and action G is wrong. Maybe we can say that God willed that we do F and nilled G, or maybe it's just there. At any rate, let's say that there are two agents, X and Y, where X does F and Y does G. Now, both X and Y approach these actions with the same attitudes (they both intend to do right, and if these actions are willed to be done by God, then they both intend to fulfill God's will), and there will be no different consequences either in this life or the next for either X or Y. Is it still meaningful to say that F was right, and G wrong?

For the second stage, let's say that X does F, and Y G; God will condemn Y to Hell (or annihilate Y; take your pick) while X gains an eternal reward. However, actions F and G result in the same consequences here in this life (again, assuming that X and Y approach them with the same attitude and all). Can we really say that F is a right action? I guess this is asking whether God would be just in condemning Y for doing G, even though no temporal effects would have distinguished G from F.

Finally, let's say that F and G do differ in consequences, where G produces some good while F does not. In this case, would it be meaningful to say that F is right and G is wrong? If not-F would produce good, would it be meaningful simply to mandate F and anathametize not-F? How about if not-F were as neutral/bad as F? Let us say that this good that G and not-F produces comes from the character of the action (and similarly, the lack of good from F), rather than from accidental circumstances.

On Cars

Currently reading:
Hareíos Potêr kaì hē toû philosóphou líthos
   by J. K. Rowling (tr. Andrew Wilson)
Cattus Petasatus
   by Doctore Seuss (tr. Jennifer & Terence Tunberg)

This week has been . . . interesting. On the lighter note, I now have the reading material listed above (Cattus Petasatus was the book behind the quote a couple of posts ago). The kids' foreign language section at Borders is actually an interesting place to go for Latin books.

In other news, it seems like this was the week for car troubles (I seem to be learning similar lessons about potholes, Scott). This Wednesday, I was driving my wife's car to school and tutoring. As luck would have it, everything went swimmingly until I got back to the apartment complex - and hit a pothole coming in. Dead on, hidden within the slush and shadows, even at 5-10 miles an hour I got a flat. Needless to say, Joy was not happy. We do now have experience in changing tires, however.

For most of the trip in her car, though, I was impressed by all of its modern conveniences, even in the midst of the snowstorm and 9 inches that we got. Conveniences such as heat, or windshield wiper blades that clear off the windshield in front of your eyes, or directional turn signals that work so that you don't have to look for cops every time you turn and make manual signals in icy cold weather, or an engine that doesn't decide to be picky about starting. Of course, this all brings up the question of why I was driving Joy's car, now, doesn't it?

I am sorry to say that, on Monday the 4th, Shadow Snail-Mail went to sleep and never woke up. Never quite as quick as a fax, ol' Snail-Mail kept chugging along until his last days. There are currently signs of electrical activity, but the engine is done gone for, and any possible repairs would most likely cost a grand or two to extend his misery for a couple more months. RIP, Snail-Mail.

So, later this week my new car should be coming in. We went with a Hyundai Accent, minus any bells and whistles. For that reason, I get to learn to drive a stickshift. I'll probably post something about how that's coming along in a week or so....

Christian A-Gnosticism

Before I say anything, I perhaps should clarify the title. I don't mean to continue the project of deconstructionists such as Derrida or Caputo; rather, I am concerned with how Christianity can avoid becoming a form of gnosticism. Basically, gnosticism as well as considerable strains in Asian religions (Buddhism, and much of Hinduism) consider ignorance to be our main problem, and so to fix our problem we need a piece of knowledge. Now, how can Christianity avoid this pitfall?

The first thing I'll most likely hear is that Christianity posits sin as our chief problem, and faith in the work of Jesus Christ as the solution. However, this faith has a cognitive content, which brings back the problem. One can talk about "faith in a person" rather than "faith in a proposition" as much as one wants, but as far as I can tell certain propositional content is necessary in order to have the proper faith in the person of Jesus Christ. Maybe we could even go a step further, and claim that there exists a set of propositions such that acceptance of any one of these would constitute the cognitive sine qua non of faith, without requiring that all those with faith share the acceptance of any single proposition. At any rate, knowledge is essential to salvation on this view. What, then, are the alternatives? I'll explore a few that have come to mind; I don't think that there can be an exhaustive list. In a way, this is simply another perspective on many of the issues which I've raised previously.

(1) Calvinism. Or any form of divine determinism, if one prefers. I've already stated my opinions on this view, but it does break through the problem of gnosticism; I think that in many cases this is implicitly in view when people accept Calvinism. There may appear to be knowledge which we need in order to be saved, but in reality, one's salvation is really based solely on God's (arbitrary?) unconditional election. The attaining of knowledge may be a means which God uses, or it may be some ruse (I really can't get away from the picture of a divine puppet show, and maybe even a divine puppet conducting the show, no matter how many people try to explain why determinism doesn't lead to this result). At any rate, determinism gets away from the problem, but I don't think that I can accept the cost.

(2) Broad Inclusivism/Pluralism. On this view, we can accept that there is a salvation, and we need to attain to this salvation, but a specific piece of knowledge is not necessary for the attainment. Or, perhaps, some knowledge is necessary, but it is something accessible to all. We can talk about the degree to which on acts on one's own, and the degree to which God helps one (just because the word "works" is involved does not imply semi-Pelgianism; that only follows if one reduces everything to a monergistic framework for any given action). The difference between inclusivism and pluralism is metaphysical, but I would think that phenomenologically the two could end up similarly; differences would accrue from specific accounts, not from the difference between the two categories. Because the knowledge would be accessible to all (perhaps as a recognition of the good?), I don't know that I would qualify this as a gnosticism. At any rate, it doesn't cause the difficulties which I see which other gnosticisms. One must say that there is something which is in principle available to all; if everyone actually sins, moral perfection is not actually available. Similarly, if knowledge of God is lacking in some large segment of society, I don't care what your exegesis of Romans 1 declares, they do not have access to knowledge of God.

(3) Universalism. If everyone is saved, then we don't have to worry about the problems with the two above views. We aren't saved simply by a random, amoral divine command to pick out a select few, we don't have to worry about any possible charges of pelagianism, and we have less to worry about concerning the denial of core Christian truths. It's certainly tempting. However, it seems that some people simply wouldn't be able to enjoy heaven; I don't even know what it would mean for these people to attain salvation if everyone would be there by default. Maybe we'd also have to have a purgatory of some sort or another which would prepare people? As I've heard it put in relation to Bonaventure's view of justification, spiritual fitness is like physical fitness. We could be forgiven for being couch potatoes, but that forgiveness wouldn't immediately change our bodies; we would need to get on that treadmill and diet. Similarly, we can be forgiven spiritually, and so have the debt we owe to God satisfied, but there needs to be a process of sanctification. Otherwise, we end up with the problem that either a) God could have made everyone perfect instantly, either at the Garden of Eden itself, or at a moment of faith for each of us (it would makes Christian claims actually convincing, if nothing else), or b) Heaven would really be a repeat of this world, with perhaps more sanctified people putting up with the continuing sinners. Can I opt for annihilationism, please? Perhaps, though, (3) could be combined with (1); this may make (1) more palatable, and (3) more understandable. I'm not sure.

There are many other alternatives within each of these categories, and many ways of drawing out the implications within each. One book which I've been picking up from time to time, The Beauty of the Infinite, appears to grapple with this issue as well: as opposed to most strands of postmodern thought, which claim that there is an irreconcilable difference at the core of reality which leads to an ontology of primal violence, the chief analogate of being is God as Triune, in whom difference is seen to be a difference of peace and harmony. For this reason, our distance from God and from each other, rather than a necessary cause of alienation, is the distance which allows us to see each other and rejoice. This infinitude is beautiful, and beauty is infinite, and so (skipping over vast sections of the book's argument) we can persuade each other through rhetoric in hope of an underlying peace uniting us. In terms of that which concerns me, there is a way of convincing everyone of whatever is necessary for salvation without shoving a (possibly unpalatable) truth down their throats.

So, why am I concerned with this issue? Because I never seem to see things as being quite as certain as those around me, because I see that faith in most people seems to come more through tunnel vision than anything else. As much as people denounce "blind faith," it seems impossible to get beyond a "myopic faith" at best. I want to know what it means to have faith, but the only way that I can know that I have a hope is if there is no "scandal of particularity," if I don't absolutely need to have some one bit of information in order to be saved. I can't simply have faith that God will guide me to whatever I need to know, because most people aren't so guided, unless some option like (2) or (3) above is correct. So, why should I actually accept the gospel as good news, rather than the destroyer of peace, trust, and happiness through its insistence on the narrow path? I guess I could perhaps accept a narrow path which at least everyone could find; what I can't accept is a narrow path which is only given to a few elites (even if they are elite through their own weakness, or through random chance). If everyone is a sinner, then we all may need to be put right and cannot enter heaven otherwise; however, it would seem to be a structural defect and not a moral one, and so in many cases worthy of annihilation at worst rather than hell (a position toward which I am inclined), and worthy of annihiliation only after all other possibilities have failed.

Tied in to this is the extent to which we can trust Scripture. I hold, as I have noted before, that even is Scripture is fallible, there is still significant evidence that the gospels intended to be eyewitness accounts of Jesus' life, and even if inaccurate are not likely to get something wrong like the resurrection. So, there is a grounding for the Christian life no matter what view we take of Scripture, as long as we can accept this. However, if Scripture teaches exclusivism, and philosophically I cannot maintain the view, what do I do? I'm not sure I agree with Scriptural arguments for inerrancy (not to mention that an errant text could still declare its own inerrancy), and there seems to be nothing outside of the text and the tradition which would suggest the concept (not to mention I'm not even sure of what it means). But, my own reasoning could be faulty, and I need something which can stand against it and correct it if need be. However, this can only be done by yielding it up to some authority, for which I need my reason to substantiate the authority of this authority, and so on and so forth.

Put in another way, there is no such thing as simply having faith in God. Faith in God is also first and foremost a faith in humans, unless we can escape this gnosticism in some fashion. I have to trust human beings when they relate the gospel, I have to trust them when they tell me what the Bible says, I have to trust them when they tell that the Bible is (or the preaching of it is) the Word of God. And all of this is already assuming that the testimonies of Christians are more trustworthy than anyone else; a rather tall claim indeed. I don't really find too many people that I'm willing to stake my eternal salvation on. Not that I'm any different; I shudder to think that people will actually one day listen to me and heed what I have to say. The point is, as finite beings in a confusing world, no human being would be trustworthy for such matters even if sin weren't an issue. So, how is God not cruel when he leaves our salvation in the hands of such incompetent, lazy, stupid, selfish messengers (yes, myself included), and quite honestly seems to do nothing to make the message palatable? The only way out that I can see is to assume that either (1) God really is doing all the work behind the scenes, (2) this message is one vehicle among others which can work for our salvation (maybe it is more a proclamation of God's glory than a necessary piece of knowledge), or (3) we're all saved anyhow. None of these seem quite acceptable to me.

Ok, enough rambling for now. Time for comments!