Sunday, October 30, 2016

Free will and theodicy

Reading through Origen's On First Principles, I discovered that he used free will as a way of justifying God, to the point where he quite apparently says that all souls are born into different stations in life because of the good or bad they did in previous lives. Aside from the fact that this sounds more like a Hindu doctrine than a Christian one, I was struck by how much it differs from the Augustinian interpretation of grace. Calvin took Augustine to the extreme. For Calvin, there is no reason to justify God in the first place. God foreordains everything according to His good purpose, and if it makes no sense to us, it is only because we are so limited and/or corrupted.

Now being acquainted with these two extremes in Christian thought, I'm tempted to go the moderate route. It seems perfectly reasonable that God would create the world with creatures of various stations, not because of any question of merit, but rather simply because diversity is a good and beautiful thing (contra Origen). On the other hand, it also seems reasonable to think that many of these creatures have free will, and will be judged on the basis of what they do with their limited capacities, in proportion to the extent of those capacities. To suggest, as Calvin seems to do, that we can't use our common sense to understand what is right and wrong for God to do puts us in a pretty bad position when it comes to theology--how do we know that God is not actually a demon?

But the moderate route isn't entirely satisfying. If God isn't truly in control of everything that happens, how can we call Him Lord of all creation? There are many passages of Scripture that seem to attribute to God absolute power over human actions, even the human mind. So Isaiah 63:17--"Why, O Lord, do you make us stray from your ways and harden our heart, so that we do not fear you?" Or Proverbs 16:9--"The human mind plans the way, but the Lord directs the steps." Or Jeremiah 31:33--"I will put my law within them, and I will write it on their hearts." There are plenty of other verses which affirm human responsibility, but these are hard to ignore.

The difficulty in trying to justify God is trying to determine just what kind of universe He should have made. I suppose Calvin saw this more than most of us. It seems impossible to imagine a universe for which God could not receive some reproach. The fact that anything exists at all is a miracle and, at the same time, a condemnation--if I exist, I am doomed to be whatever it is I am and not something else. One could imagine that this horrible tension is the root of all sin. Adam and Eve had a paradise to live in, yet they still found themselves tempted by what it was not.

At the same time, to jettison all sense of justice by which to evaluate God's action is to destroy prayer as it is found in the Bible. There are, of course, the psalms, which make very direct complaints to God, calling on Him to remember His steadfast love and His promises. But the paragons of prayer are Abraham and Moses. Abraham negotiated with God over the destruction of Sodom: "Shall not the Judge of all the earth do what is just?" And Moses interceded for his people on the basis of reason: "Why should the Egytians say, 'It was with evil intent that he brought them out to kill them in the mountains, and to consume them from the face of the earth'?" If these men had been willing merely to accept God's plans, convincing themselves by some theological argument that whatever God did was right, they would never have been heroes of the faith.

I don't see any way out of the tension between what is and what is not. It seems to me the essence of life itself. We desire to reach a point of perfection, where we can finally stop and say, "It is enough." Yet we know that if we stopped completely, that would be an end to life itself. All life is motion and change. A perfect, finished worked of art is lifeless. It is only in the contemplation of that art, in the active appreciation, that we derive any pleasure from it.

Behold the central paradox of Christian theology. Christ did not consider equality with God as something to be grasped, but emptied himself, taking the form of a human being, and become obedient even to the point of death on a cross. He who knew no sin became sin. God took on imperfection in order to attain perfection.

What does this have to do with free will? Only that in Christian thought, free will relates to theodicy, the justification of God. Some will justify God's wrath by reminding us of our responsibility. Others will justify it by asserting God's supremacy. The argument goes back and forth eternally. The disagreement is honest. It is a living response; any resolution to the argument would mean we are no more than a lifeless work of art.

Prayer, more than debate, is a living response. Abraham and Moses argued their case before God. Jesus, and then Stephen the martyr, prayed, "Father, forgive them, for they know not what they do." Ultimately, the resolution of God's wrath is on the cross. Christ died for us while we were still sinners. We are told he even went and proclaimed the good news to the dead (1 Peter 3:19). For the Christian, then, there is limitless hope for the salvation of the world, of every soul. There is no reason to resign ourselves to believing in the eternal damnation of some for the sake of God's eternal purpose (contra Augustine and Calvin). God's eternal purpose is the cross, that impossible event which changes everything.

Jesus told his disciples to take up their own cross. This is the ultimate living response. Instead of justifying God by our theories, we ought to vindicate Him by imitating Him. Whether or not this is a free choice, I still don't know, but it is a choice: to take up our cross daily, to embrace the contradiction in our own lives between our desire to be and our desire to be something else.

Sunday, October 23, 2016

Breath, spirit, will

My wife pointed out to me the other day something profound. The breath, she said, is essentially the border between the conscious will and the unconscious, automatic processes governing the human body. The heart, for example, beats at whatever rate it's supposed to. The stomach gets to work whether you tell it to or not. On the other hand, most things we control consciously do very little automatically. We choose to walk around; it is extremely rare for someone to start walking in their sleep. As for our mental life, well, it is true that we may have both conscious and subconscious thoughts, but how they interact is a complete mystery to me; in my common sense experience of the world, my thoughts are purely conscious.

But the breath is in between. On the one hand, I don't need to consciously think about breathing. When I sleep, my body automatically breathes. Even when I don't sleep, my lungs will automatically work at the pace they need to when the occasion calls for it. Yet I can choose to override these automatic rhythms. I can hold my breath. I can choose to breathe more slowly, or more quickly if I so desire.

This is especially evident in that most human of all activities: speech. To speak, I must take a breath big enough to finish the phrase I have in mind. This act of will is taken to a higher level in song.

In the Bible, "spirit" means "breath" or "wind." As far as I know, this is true in both Hebrew and Greek, both Old and New Testaments.

The Spirit of God, then, might be seen as the will of God coming to life in the physical world. As God prepares to speak, He takes a breath... and the Word that comes out will not fall to the ground without accomplishing its purpose. God is a good speaker, a well-trained singer.

The traditional Christian Trinity is recited as "Father, Son, and Holy Spirit," but one could make the case that "Father, Spirit, Son" is also an appropriate order. The Son is the Word, and the Word comes from the Father through His Spirit, that is, His Breath. Do we not say that the Son was conceived by the Holy Spirit? And if the Son is God Incarnate, that is, the Will of God made into a body, then is not the Spirit of God, so to speak, the boundary between God and His body? But I am stretching the image rather far; I don't mean to invent new theories, only jot down hypotheses.

For us, I think rediscovering the breath as spirit is important for our lives. When we focus on the breath as the center of our being, we reconnect the spiritual with the physical. We reconnect the human will with the human animal.

Sit and concentrate on your breathing. Sit up straight, fix your posture so that you have plenty of room to take in the air. Breathe slowly, so that you can enjoy it. As you breathe, you will notice that the rest of your body responds. Your heart changes its rhythm in response to the breath. You will feel the blood flow through all parts of your body and be made more aware of them. You will come into contact with your body on a physical level which is not habitual. On the other hand, you will also be more spiritually alert. The breath is an act of the will; it is a striving toward truth, toward beauty, toward the good. As you straighten out your back and breathe deeply, you will be reminded that your body is a sanctuary for the divine, a building that reaches upward.

Sunday, October 16, 2016

Florensky on evolutionism -- "What is the differential equation?"

From At the Crossroads of Science and Mysticism, Lecture Four:
Renaissance culture also gave attention to the other principal form of being--time. The examination of the concept of time occurred later, and the fragmentation of being in time was performed later than the fragmentation in space: evolutionism came after mechanism.

Evolutionism does have a healthy seed--gentism, according to which an essence does not unfold in some single moment, and the spiritual meaning of an object is not exhausted by some single state, but exists in the totality of its states. But evolutionism errs when it states that this genesis is made up of infinitely small additions, so small that each separately can be considered not a creative act. ...

For example, let us consider the question of the origin of man. Evolutionism denies that there is a qualitative and fundamental difference between man and animals. But if this process occurs discontinuously, if man is descended from the apes, this theory loses its anti-religious character, since a qualitative change suddenly occurs. And if man was created from the dust of the earth by a special creative act, why not then allow in principle--only in principle--that man was created by a momentary addition of spiritual qualities to the ape?
What I am pretty sure Florensky is saying is that one need not take the creation story in the Bible literally to have a Christian worldview, but on the other hand he does insist on a "discontinuous" development of spiritual qualities. On the one hand, I suppose that science can't now and perhaps never will be able to address the important qualitative differences between man and the apes. For example, there will never be a fossil record of spoken language, so we will never know definitively when or how speech developed. On the other hand, Florensky (writing in 1920, mind you) could be taken as throwing his lot in with what might be called the "intelligent design" crowd. How else to interpret this statement, particularly with its wording about "creative acts"?

There's a very thought-provoking passage on how the differential calculus was absorbed into modern science:
For the immediate consciousness rest is opposite to motion, while the essence of science is the fact that we can study motion only by separating it into states as if of rest, with the result being the differential equation. The latter becomes the universal instrument of mathematics, and then of all science and the whole Renaissance epoch, since, to quote Kant, every science is a science insofar as it incorporates mathematics.
 He goes on:
What is the differential equation? Some sort of process is occurring, and we stop it and break it up into a series of instants and see it as if in sectional view. The differential equation is a general formula suitable for the sectioning and study of any process. With this method we are not concerned with the past, with what occurred earlier in time, with whether these are people or whether they are statues who suddenly started moving again after we had stopped them. Only the present is important for us here, not the past; but for many phenomena it is precisely the past that is important.
Writing in 1920, I suppose Florensky could simply not have known about all the modern developments in differential equations. Now it is commonplace to deal with integro-differential equations which were developed to take into account nonlocal interactions across both time and space. I wonder what he would say if he could have lived to see the era in which most differential equations do not involve continuous functions and Taylor series, but rather wild, mysterious functions and generalizations thereof.

Even today, one might think at first glance that Florensky is basically right in his description of differential equations, in that they are meant to break down a process into infinitesimal moments, each of which may be viewed as "not a creative act" but rather a blind obedience to some universal law. But even creative acts or subjective experiences can be modeled quantitatively. The whole use of optimal control theory to predict social behavior comes from the idea not that human beings follow mechanical laws but rather that they exhibit optimizing behavior, i.e. genuine acts of will. Florensky simply could not have seen this, since its development came only after his death.

Still, Florensky challenges me like no other thinker, perhaps because so few theologians know or write anything about differential equations! It would be naive to assume that mathematical objects appeared in a philosophical vaccuum. I should pay closer attention to how today's concepts are used (or could be used) to shape our world view.

To me, there will always be one fundamental discontinuity that cannot be ignored by any scientific theory, and that is the mere fact of existence. Between existence and non-existence there is no continuum. There can be no "probability" that the universe would come into being. Rather, its existence is pure impenetrable mystery. For me, this is basically the same thing as to say that God spoke the universe into being.

Thursday, October 13, 2016

Florensky on philosophy

"Psychologically, it is natural for people to say that everything is very simple. This is opposite to the sense that begot philosophy--the sense of wonder. To be a philosopher is always to perceive reality as something new, as something that is never boring or stale. The adventure of the spiritual life consists in the fact that everything is renewed, first is one's consciousness and then outside oneself. The one essential thing is to transform all of reality. We must die and forget everything that seemed boring and stale, and when we awaken, all will be renewed for us; it will be beautiful and eternally joyous." -- Pavel Florensky, At the Crossroads of Science and Mysticism
I think this is my new mission statement for life. For context, this is actually part of a critique of modern thought. The quote continues:
"And to some degree this actually happened. The second part of Faust represents spiritual renewal after suffering. Its beginning is depicted in hues reminiscent of the sky, an approximate vision of the primordial creature, in contrast to the task of Renaissance culture--not to wonder at anything." 
 This book is a gem, absolutely necessary for anyone thinking about building a Christian worldview.

Saturday, October 8, 2016

Elon the Zebulunite

After him Elon the Zebulunite judged Israel; and he judged Israel ten years. Then Elon the Zebulunite died, and was buried at Aijalon in the land of Zebulun. (Judges 12:11-12)
There are certain passages of scripture, like this one, which stand out for being so...useless. There is no wisdom, no moral teaching, not even a story. Even Ibzan of Bethlehem and Abdon son of Hillel the Pirathonite, who came before and after Elon, had little tales attached to their name (Ibzan had thirty sons and thirty daughters, who all married people from outside the clan; Abdon "had forty sons and thirty grandsons, who rode on seventy donkeys"). Elon judged ten years; that's it.

That's not to say there isn't a lot to be gleaned from a deep analysis of these two verses. A quick Google search yielded an article delving into the historical Israelite practices surrounding transfer of territory. Of course, even that topic is history mainly for history's sake. If Israel is itself sacred, then understanding its history is of religious value. Perhaps that is one of the main draws of this brief passage. We can imagine an historian dutifully recording Elon's brief appointment as judge, for no other reason than to faithfully reproduce the sequences of events that led Israel from the days of Joshua up to the time of the kings.

Still, what about Elon himself? We will never know anything about him other than his name, his title, and the fact that he bore that title for ten years. I often imagine all the saints meeting in the kingdom of heaven. Many of them will meet Elon and ask him what he did during his life on earth. Perhaps he will respond with many stories. Or maybe he will just smile and say, "I judged Israel ten years."

Following the teaching of Jesus, who said such things as "the last will be first and the first will be last," and, "whoever wishes to be first among you must be your slave," one might say Elon is the greatest of all the judges. There are no stories glorifying him. It is enough for him to have served the nation of Israel, God's people. In this way, maybe a Christian can glean from this brief mention of Elon a model of heroism, after the manner that Christ taught us. But I suppose that's rather reaching. After all, Elon was judge. He was not slave of all; unlike Christ, he did not refuse to be put in a position of power (cf. John 6:15).

Implicit in my questions about this text is the notion that every text of scripture should be edifying, as in 2 Timothy 3:16, "All scripture is inspired by God and is useful for teaching, for reproof, for correction, and for training in righteousness." One has to really reach in order to apply this principle to all scripture. For the Christian, it's not enough that a passage should faithfully record the history of Israel; some application to our lives, as we strive to become more like Christ, is necessary. And anyway, modern historical criticism casts so much doubt on the history recorded in scripture that taking these passages at their word is a leap of faith.

So what do we do with Elon the Zebulunite? What do we do with any of the judges? Even the great ones like Samson can hardly be considered models. But at least a story like that of Samson may or may not have an allegorical interpretation which is edifying. Elon is simply a footnote.

But there he is, eternally etched into the narrative of scripture, refusing to budge. I am tempted to think one simply has to have a sense of humor when approaching the Bible. It did not come together the way anyone would expect if one were imagining God speaking directly to us. Now that it has enjoyed its 2000 year status as canonical, there's no changing it. We can rest assured Elon the Zebulunite will remain there, challenging us to find a spiritual meaning behind his name and his ten years as judge.

I think there is something edifying about this, after all. We need continual reminders that the universe is the way it is because of events that preceded us, that we cannot change, and that defy any sort of theoretical explanation. We live in God's world, not a world which is "designed" according to human standards. Not everything has an immediately obvious purpose. And yet, if it had not been for all of these apparently meaningless events in the exact sequence they happened, I would not exist.

In other words, as much as I might naturally feel that my life would be totally unaffected if Elon the Zebulunite's name did not appear where it does in scripture, in fact it would change everything. Over two thousand years of history would be altered. If a butterfly flapping its wings can cause a hurricane...or however that's supposed to go,,.one can only imagine what it would mean if even a single character, however uninteresting, were removed from the Bible.

The more I read the Bible and reflect, the more I become less concerned with the abstract principles it teaches (though I have not lost sight of them), and the more I am aware of its very presence. Almost the very essence of the Bible's power is that it cannot be changed. Although it may have gone through many revisions to become what it is today, from now on no such revision is even conceivable. (Here I am not talking about translation and interpretation. I am mostly certainly aware that there will always be as many interpretations of scripture as there are human beings on the planet, but I think this can be safely distinguished from the content of the Bible.) That is the kind of presence in our world that can be felt, all the more so when one makes it a habit to read these now unchangeable document.

Paradoxically, this judge without a story has provoked in me more thought than any other, thus becoming the judge I would be least in favor of omitting from any reading of scripture. Of course, I doubt anyone would know who I'm talking about if I casually brought him up in conversation. The presence of scripture can be felt, but its contents remain a secret hidden in plain sight. I suppose that's natural. I don't mean to lament the lack of biblical literacy of our society based on the evidence that no one has ever heard of Elon the Zebulunite. This is simply a meditation, one that cannot possibly resolve all the mysteries surrounding this strange text.

Then again, it would be nice to know that the Christians who, in speaking about scripture practically deify it, actually knew its contents. Maybe then they would speak about it with much less certainty.

Saturday, October 1, 2016

Aristotelian realism

An article I read in Aeon Magazine by James Franklin gives me a good springboard for some of my own thoughts about the philosophy of mathematics. The author (who has a book on the subject) essentially opposes two extreme positions, the one nominalist and the other Platonist. The nominalist seems to say that mathematics doesn't study any real objects; it is merely a language, a series of tautologies that has great instrumental value but has no content on its own. The Platonist says that, on the contrary, mathematical objects exist in their own realm, and that the human mind has access to that realm through contemplation and logical reasoning.

The problem with the first view is that to any mathematician, it seems fairly straightforward to assert that we actually discover something--not just logical relationships between symbols, but actual content. The problem with the second view is that the world of mathematical concepts seems remote; how can we physical beings have access to it?

The alternative is Aristotelian realism, which asserts that mathematical objects inhere in nature. Our minds have access to them initially through observation, then through abstraction and logical reasoning.

This alternative is very attractive for at least two reasons. One reason is that it makes sense of applications far more easily than either Platonism or nominalism. Why should mathematical models be so good at describing real world phenomena? Under the Platonist view, there's not much reason even to wonder about it, since mathematical objects are eternal and inherently separate from the contingent world we live in. Under the nominalist view, the puzzle is why a mere language would be so effective in discovering things about the universe before they are even observed (think about the mathematical development of general relativity). Realism has a simple explanation: we draw mathematical concepts out of the real world, so it's natural that we should use them to explain how it works.

Another reason is that it's satisfying from the point of view of a practicing mathematician. Platonism also has that trait, in that it elevates the objects of mathematical study themselves. But Aristotelian realism allows us to assert that mathematics has real content without divorcing it from common experience. I find this accords well with my own practice of mathematics, both in research and teaching. I always emphasize to my students that common sense should be the starting point for thinking about any mathematical problem. Of course we have to take a long journey out from that starting point, but ultimately each step is grounded in reasoning that any flesh and blood human being can understand.

For me there's a third, more theological reason to appreciate Aristotelian realism. Franklin alludes to theological import himself:
Aristotelian realism stands in a difficult relationship with naturalism, the project of showing that all of the world and human knowledge can be explained in terms of physics, biology and neuroscience. If mathematical properties are realised in the physical world and capable of being perceived, then mathematics can seem no more inexplicable than colour perception, which surely can be explained in naturalist terms. On the other hand, Aristotelians agree with Platonists that the mathematical grasp of necessities is mysterious. What is necessary is true in all possible worlds, but how can perception see into other possible worlds? The scholastics, the Aristotelian Catholic philosophers of the Middle Ages, were so impressed with the mind’s grasp of necessary truths as to conclude that the intellect was immaterial and immortal. If today’s naturalists do not wish to agree with that, there is a challenge for them. ‘Don’t tell me, show me’: build an artificial intelligence system that imitates genuine mathematical insight. There seem to be no promising plans on the drawing board.
This paragraph is delightfully provocative. I suspect many proponents of artifical intelligence believe they are not so far off as Franklin believes, but I can neither confirm nor deny such claims. In any case, artificial intelligence is not what interests me most. Instead, I tend to fixate on this question, "What is necessary is true in all possible worlds, but how can perception see into other possible worlds?"

To me the advantage Aristotelian realism has over Platonism is that it lets us see the eternal, even the sacred, in all things. Whereas the Platonist sees objects in the world as mere shadows on the wall, as it were, the Aristotelian sees them as sources of truth in themselves. For this reason I think Aristotelianism can affirm creation in a way that Platonism can't.

It is common for applied mathematicians to point out that their models are only approximations of reality, and that real life, unlike beautiful mathematical theories, is "messy." And I think that both for the nominalist and the Platonist, there is a sense in which one must choose between the beautiful realm of theory and the messy realm of facts. I reject this dualism by taking the radical position that eternal, necessary truths are inherent in real objects. I do not thereby deny the contingency of the universe; of course it could have been different from the way it is. Yet every object reveals necessary truths; paradoxically, we find the infinite and the eternal in the finite and temporary.

To put it in starkly theological terms, I would compare Platonism to gnosticism and nominalism to idolatry. The one would have discovery be a way of escaping the created order; the other would have discovery be entirely about finite, contingent reality. Instead, I think discovery involves an interlocking of the temporal and the eternal. From real world objects we discover eternal, necessary truths; in return, we can use these eternal truths to understand--and also care for--the world we inhabit.

Indeed, is it not the mystery of whether physical laws are truly necessary that drives so much of theoretical physics? One encounters mathematical relations between objects with fundamental constants which can be measured empirically, and it is natural to wonder whether such constants could actually be deduced from some deeper principle. Or whether the laws of physics themselves are actually corollaries of some more fundamental Law. Could the universe have "come into being" through some means other than what we call the "big bang"? Such questions magnify the interlocking of the eternal and the temporal, the necessary and the contingent. God's glory shines in all things, to such an extent that it is difficult to see where his invisible glory ends and the more visible nature of things begins.

As a corollary, I see mathematics not so much as a way of escaping into abstract truths in a higher realm, nor as a mere tool of the sciences, but rather as a humble servant of empirical investigation. We study mathematics not only to understand what the world is like but also how it must be, and in that sense it gives some of the deepest insight of any science. Yet the inspiration for its progress is not so much a desire to ascend toward heaven as to see the heavenly on earth. Whose heart can be so cold as to resist finding the beauty in Euler's formula? Yet if we never saw such things as oscillations in common experience, I'm sure we never would have seen such a beautiful equation.