Dr. MontyHall (or, How I came to stop worrying and love the irrationality)

I swear that the Monty Hall problem proves that there is a deep logical inconsistency in the universe. The problem goes as such: A contestant is on a game show, and can pick from one of three doors. Two doors have a goat behind them, and one has a car. The contestant picks a door, and one of the doors which contains a goat (and is not the door which he picked) is opened. He can then either stay with his door, or switch to the other non-revealed door. Which is he better off doing? For an example, there are doors A, B, and C, and Contestant Qof (Roman and Greek letters are so restrictive in mathematics). Qof picks door A. Door C is revealed to have a goat. Should Qof stick with A, or switch to B? It seems that with one door down, Qof has a 50/50 chance, right? You'd LIKE to think that. Turns out that reality has a surprise for us (and by reality, I mean mathematics). Here's how it really works. Qof has a 1/3 chance of getting things right with his/her (we really need a neutral, but personal, 3rd personal pronoun) choice of A. Now, once C has been opened, Qof could stay with that 1/3 chance of A. Alternatively, you could say that Qof had 2/3 a chance of missing with picking A. Given this and the fact that C has been shown to be a goat, B must be the prize, and there is a 2/3 chance that by switching to B Qof will be riding home in style. It seems like there is something fishy here. What about the earlier argument? Why doesn't that work, as switching doors could be considered to be equivalent to picking one of two doors? Alternatively, it seems as though one could end up with two different probablities for the same door, depending on whether one starts with it and stays with it, or picks another door and then switches to it. However, after running a few million trials on a computer program (quite literally), it turns out that the solution is that switching doors doubles one's chances of winning. This brings one down to an ultimatum: Either accept the mathematical explanation of the Monty Hall problem, or face the fact that reality is inconsistent at its core. Given the obviousness of this choice, I think that maybe I should invest more of my time in Continental philosophy.

Subjectivity vs. Objectivity

Another Kierkegaardian idea (considering that I'm in a class where I'm reading umpteen works by him) is that truth is subjective. This has raised some interesting thoughts in my mind. The first reaction to this is repulsion, linking it together with standard postmodern theories of relative truth. However, this would be far from Kierkegaard's own view; after reading his biography, I think he might have a lot of trouble with people who freely quote his sentences in Religious Epistemology essays in postmodern, Wittgensteinian ways (not that I have any particular beefs with any authors I read in Philosophy of Religion...). He did hold to objective truth; he was not trying to undermine this. Rather, what he was saying was that having a bunch of objective facts really doesn't mean a whole lot. Truth must become personal and internalized.

Why is it that the idea of truth as a subjective thing (in a non-relative way) rather than objective seems to be a problem? I do not propose to say "truth is entirely subjective" here, or really any other position, so much as bring some things out for thought. When I looked inside myself, I realized it is because objectivity seems to be more certain, while subjectivity lends itself to "its true for you but not for me" - even if not meant in a relativistic way, there is still a sense that people can arrive at completely different truths with no way to check to see who is right. Maybe, though, if we have faith in the methods of arriving at truth, this is not as much of a problem. In order to communicate truth objectively, I give facts, I give arguments. I give the "what" of truth. In order to communicate truth subjectively, I must rather tell someone the "how" of truth: how they can find it for themselves. I point to the path, not the destination. If this "how" is trustworthy, than do I need to worry as much that the "what" will be so radically different?

What really spurred these thoughts on (though I had been thinking about them before) was a conversation at lunch today about the inerrancy of the Bible. The following is not meant to disparage inerrancy - I am an inerrantist (though still trying to figure out what that means) - or even to deny that it has importance. Sometimes, however, this doctrine seems to be considered to be almost as important as the gospel message itself, and I wonder where the line should be drawn for "necessary ingredients of faith," "important but not necessary," and "debatable but let's get on with more important things." For example, why is it that people consider strict inerrancy, down to the last details, so important? It seems to be that it is because if there is any error, how can one know what is true and what is false? However, why is this important? It seems that it is only important if one assumes that one must come to Scripture and understand it primarily through human reason and scientific methods. Ironically enough, those who hold this view strongly say they do because they want to follow God instead of man, and yet it seems they are the ones who exalt man's understanding the most. On the other hand, if the primary way of understanding Scripture is through the work of the Holy Spirit, the discrepencies in some facts do not matter as much: the Holy Spirit can still guide us into the Truth if we let it. Again, it's the objective vs. subjective thing: objective, reasoned interpretation of Scripture, and subjective, Spirit-led interpretation of Scripture. The latter is less open to external scrutiny then the former (even if the Spirit leads in the church as a whole rather than in the individual, this is the case though on a larger level), but if it is reliable, then what is the problem?

Again, this is not to say that the Bible is not inerrant or that we shouldn't be concerned about correct doctrine. It is perfectly coherent to speak of letting the Holy Spirit guide us into the truth while maintaining inerrancy. These thoughts are more concerned with why we believe what we believe, and how we pursue truth rather than the truths themselves.

Kierkegaard on Teaching

"That if real success is to attend the effort to bring a man to a definite position, one must first of all take pains to find him where he is and begin there. This is the secret of the art of helping others.... In order to help another effectively I must understand more than he - yet first of all surely I must understand what he understands. If I do not know that, my greater understanding will be of no help to him. If, however, I am disposed to plume myself on my greater understanding, it is because I am vain or proud, so that at bottom, instead of benefiting him, I want to be admired. But all true effort to help begins with self-humiliation: the helper must first humble himself under him he would help, and therewith must understand that to help does not mean to be ambitious but to be patient, that to help means to endure for the time being the imputation that one is in the wrong and does not understand what the other understands.... For to be a teacher does not mean simply to affirm that such a thing is so, or to deliver a lecture, &c. No, to be a teacher in the right sense is to be a learner. Instruction begins when you, the teacher, learn from the learner, put yourself in his place so that you may understand what he understands and in the way he understands it, in case you have not understood it before. Or if you have understood it before, you allow him to subject you to an examination so that he may be sure you know your part." - Kierkegaard, The Point of View for My Work as an Author I came across this quote in some of my reading, and I found it rather interesting. Any thoughts?

The Anderson Chicago Theorems

So I'm at Trinity right now, and I had an observation to make while driving through Gary. No matter when I drive through there, whether it be morning or night, weekend or weekday, it seems like there is always more traffic going into Chicago then out of it. I came to some startling conclusions when mathematically analyzing the data. Here are my results, maybe I'll write up a paper for some prestigious math journal or something. Lemma 1: The population of Chicago is expanding. Proof: Let C be the population of Chicago, X be the rate at which people are leaving, and Y the rate at which people are coming in. Then, C' = (approx.) Y - X. As noted, Y > X, so therefore C' is postive. QED. Axiom 1: The birth rate and death rate for Chicago are neglible compared to C'. Justification: This can always be controlled if necessary to make the results of this theorem work better, either by limiting Mafia activity or providing defective birth control. Lemma 2: C" is zero or positive. Proof: Suppose that C" were negative. But then traffic at Gary would get better over time. This appears to be a logical contradiction, so therefore C" is zero or postive. (Alternatively, outbound traffic could be getting worse, but in my vast experience of 1 and a half years this does not appear to be the case). QED. Axiom 2: C will not have an inflection point, or is linear. Justification: Because that makes my theory more interesting. Lemma 3: C is monotonically increasing and not approaching an equilibrium point. Proof: See Lemmas 1, 2, and Axioms 1,2. QED. Lemma 4: Chicago will either a) engulf the whole earth, or b) the earth will blow apart due to the weight of too many people. Proof: Let (W - C) be the population of the world oustside of Chicago. As C' is positive, (W - C)' is negative unless the birth rate/death rate ratio for (W - C) is large enough. If it is, there are an awful lot of people being born on the rest of the planet, so it stands to reason that the planet will explode because of it (though as in Axiom 1 this ratio can be controlled, so we can prevent this case). Otherwise, C will eventually include all of (W - C) and so Chicago will hold the entire population of the world. QED. Theorem 1: Chicago will reach critical mass and either attain sentience or nuclear fission. Proof: As the population of Chicago is increasing (to the point of including the entire world's population), and the size of Chicago is apparently not increasing as quickly, eventually there will be a high enough level of population density that either Chicago will start acting as a giant brain with an AI of its own (see Serial Experiments: Lain for an example on a global scale), or will act as a giant plutonium atom and start a nuclear reaction, whichever would make a better sci fi film. QED. Theorem 2: There will eventually be hordes of undead outside of Chicago. Proof: As proven by axiom 2, there cannot be an equilibrium point in C, so even after (W - C) is 0 C' will still be postive. This will make (W - C) negative, and the only way this could be is if there are mindless zombies entering Chicago through Gary. This entails that there will be said zombies in the population of (W - C). QED. I realize that this research will be startling to some, and perhaps even mildly controversial, but the math proves that this must be the case. Such grisly results for the future of humanity should be prepared for at once. One possible plan of action is to start watching as many sci-fi and horror films as possible in order to be ready for whatever Chicago and the world may throw at us.

Reason and Creativity

It seems that so often, reason (and its handmaid logic) and creativity are paired off as opposites. They control different spheres. Reason is the realm of the scientist; creativity of the artist. However, many times scientists and philosophers of science state that creativity is an integral part of the field. As a mathematician, I can attest that a merely logical mathematician won't get terribly far; creativity is absolutely necessary to be a good at math, particularly higher mathematics. Am I saying that mathematics is fundamentally irrational, or at least not a rational subject? By all means no. This confusion is part of the whole misunderstanding of creativity and reason being opposites. The most rational person has both; creativity is not against reason, but shows the most promising routes for it. Sometimes, one has to take a leap with reason, whether because there are multiple open routes ahead or none. Logic is the guide along the known path, creativity the woodsman looking for a new trail or to see which trail is best. Reason is the overall process of making it through the woods. Creativity therefore can be considered a part of a full concept of reason at times, depending on how it is used.

Gödel's incompleteness theorem (my senior paper topic) may say something about this. According to J.R. Lucas (at http://users.ox.ac.uk/~jrlucas/Godel/implgoed.html), the theorem shows that in general, the concept of truth outruns the concept of provability. This, however, is not to mark the end of reason; merely the end of strictly formalized, single-method reason. For example, 1st order logic (logic that allows one to look at every simple object as a group, but not at all propositions or functions of the simple objects at once; see http://en.wikipedia.org/wiki/First_order_logic for a better, more detailed explanation) is complete; one can prove every true statement expressible in the system starting with the standard axioms. However, it is not decidable (one cannot apply a test to see if a statement is true or false).

The implications of being complete but non-decidable are this: one can show that any true statement is true (just start with the axioms and start cranking out theorems until you get to the right one). However, there is no methodical way of telling that a given statement is false; one can tell that certain statements are false, but there is no single method (however complex) which works for all false statements. However, this is a problem for formalizability, not reason. A person could conceivably come up with an unlimited number of ways of showing propositions to be false; this is where creativity comes in. All of these ways are rational, there just is no single method of judgement. Thus, neither modernism with its criterion of methodology nor postmodernism with its avoidance of reason have it entirely correct.

As Lucas puts it,

Reason is creative and original. It goes beyond antecedently established canons of right reasoning. And it can do so in a personal way, so that one man's original insight may differ from another's without either being wrong. Just as different men, using different codings, may pick out different Gödelian formulae, each of them true, so in other disciplines too, different thinkers may develop the subject in their own individual ways without any of them being necessarily wrong. We have been too long in thrall to a monolithic view of reason, supposing that it must yield just one right answer valid for all men in all places and at all times. And then we have felt that reason's uniform light obliterated all personal idiosyncrasy and individuality, and that real fulfilment was to be found in feeling and sensibility rather than rationality and common sense, and that the life of reason was a poor thing, cold and lacking all romance. But it is a false antithesis resting on a false view of reason. Reason not only can be original, but original in very variegated ways, well capable of accommodating the variety of individual genius.

Which I agree with in that the same truth may be expressed in multiple ways, or that truth can be complex and multi-faceted, though not (of course) in that there could be multiple truths or that truth is subjective.

On a side note, I've been playing some strategy games of late (most notably Go, along with Shogi (Japanese chess, which allows one to put captured pieces back into play on ones own side) and Xiang Qi (Chinese chess, which tends to be quicker and more aggresive than Western chess)). They're forcing me to think ahead and be patient rather than trigger-happy (which is a good thing that I sorely need). I found a rather interesting chess variant here: http://www.chessvariants.org/shogivariants.dir/taikyoku_english.html with a "playable" version here: http://taikyokushogi.hp.infoseek.co.jp/taikyoku.html. I have no idea how one would even start playing that....

Major News (or, rather, New Major)

Yeah, so I did it again. Haven't even gotten to seminary yet and I'm planning on changing majors. Only have four more times to go, right? Due to interests in languages, history, the middle east, and a curiosity on how the old testament fits with the new, I had originally signed up for the Old Testament/Semitic Languages program at Trinity. However, I also want to do more work with philosophy afterwards, and I have been finding that I enjoy big-picture theology that involves putting stuff together from various sources rather than detailed exegetical work. In addition, I have over a semester's worth of entrance deficiencies to take care of as of now. So, the plan is that I will switch to either the Christian Thought major (which requires an emphasis and a cognate field, where I would have an emphasis in philosophy of religion and biblical/systematic theology as my cognate field), or to the Philosophy of Religion major with some extra Systematic Theology courses on the side (It's only 32 hours, and I'll need to spend 2 years there due to when courses are offered as well as having time to do a thesis and fieldwork). This way, I'll be better prepared for Ph.D. work, I'll probably be more interested in the subject, and I'll have no entrance deficiencies. So far, my first semester classes will be: Theology I: Intro to Theology Introduction to Theological Research Methods Philosophers of Religious Significance: Kierkegaard Seminar on Current Issues: Metaphysics of World Religions Seminar on Current Issues: Sovereignty and Salvation in Wesleyan-Arminian Theology And now for something completely different: a proof of free will. Assume that I have free will. Case 1) I have free will. Q.E.D. Case 2) I do not have free will. Thus, I could not have chosen to believe otherwise and I had no choice in giving this argument either. Q.E.D.

Contemplating New Seeds of Contemplation

I've been reading New Seeds of Contemplation by Thomas Merton. I had picked it up out of curiosity; I've been reading some stuff on Indian philosophy for a course with Dr. Corduan, and I was interested in seeing how some of the things that one sees in East Asian mysticism play out in a Christian setting (I'm not sure to what extent Merton has borrowed from Eastern sources. I know that he has been interested in Christian-Buddhist dialogue and has done some stuff with Eastern meditation practices, but I think this book stems more from the Western tradition of St. John of the Cross, whom I haven't read). I had been expecting to find a book that was full of fluff and/or semi-pantheism. While Merton does at times delve into flowery pietistic prose, and there are a couple passages that raise eyebrows, I think that overall he does a better job than expected at giving a genuinely theistic expression of contemplation based on Christian values. I don't think he focuses nearly enough on Christ and the trinitarian nature of God for me to say that his work is the best example of Christian thought on the subject. However, he generally does keep a distinction between God and human beings (except for one paragraph, where he says that God is identical with a person's true self, but this seems at odds with other stuff that he says and so I'm giving him the benefit of the doubt and assuming that he picked a bad way of phrasing his thought).

His connection between the typically East Asian idea that we need to go beyond what we think of as our self in order to find the true self and the Christian idea of sin I think is particularly interesting. At first, I thought this was rather new-agey and rolled my eyes, but he gives a plausible explanation that our false selves are who we try to be when we seek to put ourselves in God's place and live for ourselves, while our true identity is in God. This reminds me of Revelation 2:17 ("...and I will give him a white stone, and a new name written on the stone which no one knows but he who receives it.") along with other verses about our new life and new identity in Christ (although, unfortunately, Merton does not mention much about Christ's part in forming the new identity). So, in the end it is more like a reformulation of a traditional view of sin. He also stresses the role of God in the contemplator's life; one doesn't choose to contemplate God, God calls him. I appreciate this focus on the work of God, although again I don't think he gives enough attention to the Holy Spirit's role. The goal of contemplation is to see things as God does and to will as he does; that is, to see everything God made is good, especially as it does what he meant it to do (though our desires can be evil - he is not advocating antinomianism), and that we should live our lives loving God. This love and will of God are not merely feelings (Merton emphasizes in his preface that contemplation is not about calm and pleasant feelings), but do actually result in practical results in how we live with others. In addition, he makes the point that God is, fundamentally, a "Who", not a "What". This point in particular separates Merton from pantheistic ideas of "Brahman", the impersonal absolute, as well as from trends in theology and philosophy to "deanthropomorphize" God and make him into merely a "ground of being", or identifying him with the possibility of eternal love, or some similar abstract concept (I'm still trying to figure out what Kierkegaard meant by saying "God does not exist, he is eternal.")

In the end, I think what has made what I have read interesting to me is that it almost seems to be a "translation" of ideas (and being the language geek that I am, taking something from one language, whether of sounds or concepts, and putting it into another interests me). He takes Christian ideas, which many times in Western Christianity are formulated in almost legal concepts, and translates them into his scheme of the contemplative life. It is more than mysticism with a Christian veneer, though as I have mentioned I don't think it goes far enough. It has helped me to look at things from a different angle, though I wouldn't say that I've had any profound insights. I think that the best and most orthodox example of Christian mysticism, though, would be in the Eastern Orthodox concept of Theosis (or Divinification). I'll probably blog about that in a couple days.

Hello, World!

I'll post something up here in the next day or two, this is just to set the blog up now.